Thermal writing of photonic devices in glass and polymers by femtosecond lasers
Femtosecond laser microprocessing is a direct, maskless technique capable of inducing a permanent refractive index increase buried beneath the surface of transparent glasses and polymers, enabling photonic circuit fabrication in 3D geometries. We describe how the repetition rate influences the heat accumulation between laser pulses, which determines the regime of modification and the resulting morphological change in glasses in polymers. In most silicate and phosphate glasses, higher repetition rates are shown to be beneficial for driving increased heat accumulation, leading to rapid fabrication of low-loss optical waveguides. In pure silica which has low absorption due to its high bandgap, heat accumulation effects are reduced and higher fluences provided by the second harmonic visible wavelength from Yb-based femtosecond lasers are required to form highly confining optical waveguides. In polymers, femtosecond laser waveguide writing generally leads to depressed refractive index changes and a time decaying behavior.
Femtosecond laser microprocessing offers the possibility to tailor the refractive index in the bulk of many transparent materials, including glasses and polymers. Due the nonlinear laser–material interaction, the modification is confined to a micrometer-sized region within the focal volume and can be written along three-dimensional pathways, unlike traditional photolithographic techniques. Chapter 10 describes the fundamentals of the interaction of focused femtosecond laser pulses with transparent materials and gives an overview of the many novel integrated devices fabricated by this technology. In this chapter, we focus on the key exposure variables which influence the resulting morphological changes when femtosecond laser pulses are focused in the bulk of transparent dielectrics. By carefully tuning the laser exposure conditions, these bulk modifications can result in a smooth refractive index contrast yielding optical waveguides, the building blocks for more complex photonic circuits such as passive optical splitters (Eaton et al., 2009) and active lasers (Della Valle et al., 2009) for use in fiber-to-the-home telecommunications, optofluidic fluorescence sensors (Osellame et al., 2007) and temperature/strain (Zhang, 2007) and refractive index sensors (Crespi et al., 2010). We classify the laser–material interaction regime according to the laser repetition rate, since it controls the relative strength of thermal diffusion and heat accumulation. In glasses, high repetition rates are crucial for improving fabrication speeds, increasing refractive index contrast, lowering propagation losses and enabling wide processing windows with waveguide size and mode size easily tuned by the laser dwell time. In polymers, high repetition rates instead are shown to be detrimental to forming high-quality waveguides.
In Section 11.2, we describe the exposure variables of importance in optical waveguide writing. In Section 11.3, we describe waveguide writing in fused silica, borosilicate, phosphate and exotic glasses at both low and high repetition rates. In Section 11.4, we review the current literature on waveguide formation in polymers. We provide a summary of the chapter in Section 11.5 and give insight into future research directions in Section 11.6.
Peak intensities on the order of 10 TW/cm2 can be readily produced by focused femtosecond laser pulses from today’s commercial laser systems. Such intensities result in strong nonlinear absorption, allowing for localized energy deposition in the bulk of dielectrics. After several picoseconds, the laser-excited electrons transfer their energy to the lattice, leading to a permanent material modification. While a complete physical model of the laser–material interaction has thus far eluded researchers, the process can be simplified by subdivision into three main steps: the initial generation of a free electron plasma followed by energy relaxation and modification of the material. In Chapter 10, an excellent overview of the excitation processes are given. Here we further discuss the relaxation and modification processes, in terms of both single pulse and cumulative pulse interactions at high repetition rates. In this section, we focus our attention on glasses since most progress has been made in this important class of dielectrics. Further insight into the role of the numerous exposures parameters on the modification of polymeric materials is given in Section 11.4.
It is well accepted that nonlinear photo-ionization and avalanche ionization from absorbed femtosecond laser pulses are responsible for the creation of a free electron plasma. However, once the electrons have transferred their energy to the lattice, the physical mechanisms for material modification are not fully understood. Of the hundreds of published articles citing the pioneering work by Davis et al. (1996), the observed morphological changes can be generally classified into three types of structural changes: a smooth refractive index change (Miura et al., 1997), a form birefringent refractive index modification (Hnatovsky et al., 2005a; Shimotsuma et al., 2003; Sudrie et al., 1999) and microexplosions leading to empty voids. The regime of modification and resulting morphological change depend on many exposure parameters (energy, pulse duration, repetition rate, wavelength, polarization, focal length, scan speed and others) but also material properties (band-gap, thermal conductivity and others). However, in pure fused silica which is the most commonly processed material for waveguide writing, these three different morphologies can be observed by simply changing the incident laser energy (Itoh et al., 2006).
An isotropic regime of modification is useful for optical waveguides, where smooth and uniform refractive index modification is required for low propagation loss. At low pulse energies just above the modification threshold (~ 100 nJ for 0.6-NA focusing of 800-nm, 100-fs pulses), a smooth refractive index modification has been observed in fused silica (Itoh et al., 2006), which is attributed to densification from rapid quenching of the melted glass in the focal volume (Chan et al., 2001). In fused silica, the density (refractive index) increases when glass is rapidly cooled from a higher temperature (Bruckner, 1970). Micro-Raman spectroscopy has confirmed an increase in the concentration of 3 and 4 member rings in the silica structure in the laser-exposed region, indicating a densification of the glass (Chan et al., 2001). Shock waves generated by focused femtosecond laser pulses giving rise to stress have been shown to play a role in causing densification under certain conditions (Sakakura et al., 2008).
It has been argued that laser-induced color centers may be responsible for the laser-induced refractive index change through a Kramers-Kronig mechanism (a change in absorption leads to a change in refractive index) (Hirao and Miura, 1998). Although induced color centers have been observed in glasses exposed to femtosecond laser radiation (Chan et al., 2003b; Streltsov and Borrelli, 2002), to date only a weak link between color center formation and the induced refractive index change has been demonstrated in the literature. Waveguides formed in fused silica with an infrared femtosecond laser (Saliminia et al., 2005) were found to exhibit photo-induced absorption peaks at 213 and 260 nm corresponding to SiE’ (positively charged oxygen vacancies) and non-bridging oxygen hole centers (NBOHC) defects, respectively. However, both color centers were completely erased after annealing at 400°C, although waveguide behavior was still observed up to 900°C. Therefore, it is unlikely that color centers played a significant role in the refractive index change (Saliminia et al., 2005). Other research found that the thermal stability of color centers produced in borosilicate and fused silica glasses by femtosecond laser irradiation is not consistent with that of the induced refractive index change (Streltsov and Borrelli, 2002).
Recently, Withford’s group has shown for Yb-doped phosphate glasses used in waveguide lasers, femtosecond laser-induced color centers contribute approximately 15% to the observed refractive index increase (Dekker et al., 2010). Using integrated waveguide Bragg gratings, the authors were able to accurately study the photobleaching and thermal annealing of the induced color centers. The color centers were stable for temperatures below 70°C, which is below the operating point during lasing. However, the green luminescence generated by the Yb ions results in a photobleaching of the color centers during laser operation, resulting in reduced lifetime which must be corrected by pre-aging techniques.
Although a complete understanding of the femtosecond laser material interaction in forming optical waveguides has presently eluded researchers, it is evident that densification and color centers play a role. However, their contributions will vary depending on the glass composition and the femtosecond laser exposure conditions, further adding to the complexities in modeling femtosecond laser waveguide writing. In glasses with structures that are more complex than fused silica, further contributions must be considered. For example, in multicomponent crown glass, the authors concluded that the ring-shaped refractive index profile during femtosecond laser irradiation was the result of ion exchange between network formers and network modifiers (Kanehira et al., 2008).
For higher pulse energies (~150–500 nJ for 0.6-NA focusing of 800-nm, 100-fs pulses), birefringent refractive index changes have been observed in the bulk of fused silica glass (Itoh et al., 2006), as first reported by Sudrie et al. (1999). Kazansaky et al. argued that the birefringence was due to periodic nanostructures that were caused by interference of the laser field and the induced electron plasma wave (Shimotsuma et al., 2003). In similarly exposed fused silica samples, Taylor’s group observed periodic layers of alternating refractive index with sub-wavelength period that were clearly visualized after etching the laser-written tracks with HF acid (Fig. 11.1a and 11.1b). The orientation of the nanogratings was perpendicular to the writing laser polarization in all cases. The period of the nanostructures was found to be approximately λ/2n, regardless of scan speed, which implies a self-replicating formation mechanism (Hnatovsky et al., 2006). However, new research suggests a slight variation of the nanograting period with exposure parameters (Ramirez et al., 2010). Taylor’s group proposed that inho-mogeneous dielectric breakdown results in the formation of a nanoplasma resulting in the growth and self-organization of nanoplanes (Hnatovsky et al., 2006). The model was found to accurately predict the experimentally measured nanograting period, but further development is needed to explain why nanostructures have not been observed in borosilicate glasses, and why they only form in a small window of pulse energy and pulse duration in fused silica (Hnatovsky et al., 2006). Preferential HF etching of laser-written tracks was observed when the nanogratings were parallel to the writing direction (polarization perpendicular to scan direction) allowing the HF acid to diffuse more easily in the track, as shown in Fig. 11.1c. This effect can be exploited to fabricate buried microchannels for microfluidic applications (Osellame et al., 2011).
11.1 Scanned electron microscope image of nanogratings formed at 65-μm depth (sample cleaved and polished at writing depth) with polarization parallel (a) and perpendicular (b) to the scan direction. Overhead view (c) of etched microchannels demonstrating polarization selective etching with parallel (top), 45° (middle) and perpendicular (bottom) linear polarizations (Hnatovsky et al., 2006).
At high pulse energies (>500 nJ for 0.6-NA focusing of 800-nm, 100-fs pulses) giving peak intensities greater than ~ 1014 W/cm2, pressures greater than Young’s modulus are generated in the focal volume, creating a shock wave after the electrons have transferred their energy to the ions (~ 10 ps) (Itoh et al., 2006). The shock wave leaves behind a less dense or hollow core (void), depending on the laser and material properties (Juodkazis et al, 2006). By conservation of mass, this core is surrounded by a shell of higher refractive index. Such voids may be exploited for 3D memory storage (Glezer et al., 1996) or photonic bandgap materials (Juodkazis et al., 2002), but are not suitable for optical waveguides.
The above interpretations for the structural changes induced by focused femtosecond lasers were based on single pulse interactions, but can likely be extended to the explain modification from multiple pulses within the same laser spot, assuming the repetition rate is low enough that thermal diffusion has carried the heat away from the focus before the next pulse arrives (Itoh et al, 2006). In this situation, the ensuing pulses may add to the overall modification, but still act independently of one another.
For high repetition rates (>100 kHz), the time between laser pulses is less than the time for heat to diffuse away, resulting in an accumulation of heat in the focal volume. If the pulse energy is sufficient, the glass near the focus is melted and as more laser pulses are absorbed, this melted volume increases in size until the laser is removed, at which point the melt rapidly cools into a structure with altered refractive index. For a scanned waveguide structure, the size of the melted volume can be controlled by the effective number of pulses in the laser spot size, N = 2w0R/v, where 2w0 is the spot size diameter (1/e2), R is the repetition rate and v is the scan speed.
Figure 11.2 shows optical microscope images of borosilicate glass modified by static laser exposure of 450-nJ pulse energy with varied repetition rate and number of pulses. Spherical laser modified zones were observed for all static exposures tested, and arise from the three-dimensional symmetry of heat diffusion from a small laser absorption volume of ~ 2-μm diameter. These refractive index structures are the result of localized melting within a cumulative heating zone that is built up over many laser pulses, which then cools rapidly to resolidify after the laser exposure. Evidence of cumulative heating is noted at repetition rates above 200 kHz, where the diameter of the modified volume significantly exceeds the ~ 2-μm laser spot size. Within each row (constant repetition rate) in Fig. 11.2, one notes a modest increase in the diameter of the heat-affected zone despite a four order-of-magnitude increase in exposure. More dramatic is the ~ 10-fold increase in modified zone radius as noted when the repetition rate is increased from 0.1 to 1 MHz in each column. Since the total laser exposure is identical within any column, 200-kHz repetition rate defines the onset for cumulative heating effects above which thermal diffusion controls the properties of optical circuits formed by the femtosecond laser. One also notes that the size of the modification zone grows more quickly with the number of pulses when in the cumulative heat regime.
11.2 Optical microscope images showing heat-affected zones created in borosilicate glass with 450-nJ pulse energy from a 1045-nm femtosecond laser. Total pulse (top) and fluence accumulation (bottom) is shown for each column and the laser repetition rate is indicated for each row. The laser direction is normal to page and the approximate laser spot size is shown by the black circle.
Linear optical effects such as dispersion, diffraction, aberration and nonlinear effects such as self-focusing, plasma defocusing and energy depletion influence the propagation of focused femtosecond laser pulses in dielectrics, thereby altering the energy distribution at the focus and the resulting refractive index modification.
Incident femtosecond laser pulses are focused with an external lens to achieve a small micrometer-sized focal spot and drive nonlinear absorption. Neglecting spherical aberration and nonlinear effects, the spatial intensity profile of a femtosecond laser beam can be well represented by the paraxial wave equation and Gaussian optics. The diffraction-limited minimum waist radius w0 (1/2 the spot size) for a collimated Gaussian beam focused in a dielectric is given by:
where M2 is the Gaussian beam propagation factor (beam quality) (Johnston, 1998), NA is the numerical aperture of the focusing objective and λ is the free space wavelength. The Rayleigh range z0 (1/2 the depth of focus) inside a transparent material of refractive index n is given by:
Chromatic and spherical aberration cause a deviation in the intensity distribution near the focus so that Eq. [11.1] and Eq. [11.2] are no longer valid approximations. Chromatic aberration as the result of dispersion in the lens is corrected by employing chromatic aberration-corrected microscope objectives for the wavelength spectrum of interest. For lenses made with easily formed spherical shapes, light rays which are parallel to the optic axis but at different distances from the optic axis fail to converge to the same point, resulting in spherical aberration. This issue can be addressed by using multiple lenses such as those found in microscope objectives or employing an aspheric focusing lens. In waveguide writing where light is focused inside glass, the index mismatch at the air–glass interface introduces additional spherical aberration. As a result, there is a strong depth dependence for femtosecond laser-written buried structures (Eaton et al., 2008b; Hnatovsky et al., 2005b; Marcinkevicius et al., 2003). This depth dependence is more pronounced for higher NA objectives (Schaffer et al., 2001), except in the case of oil-immersion lenses (Osellame et al., 2006) or dry objectives with collars that enable spherical aberration correction at different focusing depths (Hnatovsky et al., 2005b).
Dispersion from mirror reflection and transmission through materials can broaden the pulse width (Osellame et al., 2005) which can reduce the peak intensity and alter the energy dissipation at the focus. For a typical Yb-based amplified femtosecond laser with 1-μm wavelength and 10-nm bandwidth, the dispersion in glass is −50 ps/km/nm and the pulse duration increase per length is 5 fs/cm. Since these sources have pulse durations >200 fs, the dispersion is negligible for most laser micromachining beam delivery systems which have less than 1 cm of transmission through glass. It is only for short pulse <40-fs oscillators with large bandwidths that dispersion becomes an issue. In this case, pre-compensation of the dispersion through the microscope objective is required to obtain the shortest pulse at the focus (Osellame et al., 2005).
The spatially varying intensity of a Gaussian laser beam can create a spatially varying refractive index in dielectrics. Because the nonlinear refractive index n2 is positive in most materials, the refractive index is higher at the center of the beam compared to the wings. This variation in refractive index acts as a positive lens and focuses the beam inside a dielectric with a strength dependent on the peak power. If the peak power of the femtosecond laser pulses exceeds the critical power for self-focusing (Schaffer et al., 2001):
the collapse of the pulse to a focal point is predicted. However, as the beam self-focuses, the increased intensity is sufficient to nonlinearly ionize the material to produce a free electron plasma, which acts as a diverging lens that counters the Kerr lens self-focusing. A balance between self-focusing and plasma defocusing leads to filamentary propagation, which results in axially elongated refractive index structures, which are undesirable for transversely written waveguide structures described in the next section. Self-focusing can be suppressed in waveguide fabrication by tightly focusing the laser beam with a microscope objective to reach the intensity for optical breakdown without exceeding the critical power for self-focusing.
In fused silica, n0 = 1.45 and n2 = 3.5 × 1020 m2/W (Sudrie et al., 2002) so that for λ = 800 nm, the critical power is ~ 1.8 MW. From Eq. [11.3], the critical power is proportional to the square of the laser wavelength, therefore, lower critical powers result when working with the second and third harmonic frequencies of femtosecond lasers. Also, the critical power is inversely related to the nonlinear (and linear) refractive index, presenting a challenge in forming waveguides in nonlinear materials such as heavy metal oxide (n0 ~ 2, n2 ~ 10−18 m2/W; Siegel et al., 2005), chalcogenide glasses (n0 ~ 2.5, n2 ~ 10−17 m2/W; Ta’eed et al., 2007) and polymers (n0 ~ 1.5, n2 ~ 10−18 m2/W).
The standard configurations for laser writing of optical waveguides are shown in Fig. 11.3. In longitudinal writing, the sample is scanned parallel, either towards or away from the incident laser. In this configuration, the resulting waveguide structures have cylindrical symmetry, owing to the transverse symmetry in the Gaussian intensity profile of the laser beam. The main disadvantage of the longitudinal writing geometry is that the waveguide length is limited by the working distance of the lens, which for a typical focusing objective with NA = 0.4, is approximately 5 mm. To overcome this issue, researchers have employed looser focusing lenses (NA = 0.2) (Yamada et al., 2001), requiring higher laser power to reach the intensity required for optical breakdown. At such peak powers (~ 1 MW), the optical Kerr effect results in self-focusing, producing filaments which yield refractive index change structures elongated in the axial direction by up to several hundred microns (Yamada et al., 2001). Despite the long length of the filaments, fabrication speeds are still relatively slow at ~1 μm/s to build up enough refractive index increase to efficiently guide light (Yamada et al., 2001).
11.3 Longitudinal and transverse writing geometries for femtosecond laser waveguide fabrication in the bulk of transparent materials. In transverse (longitudinal) writing, the sample is scanned transversely (parallel) with respect to the incident femtosecond laser (Gattass and Mazur, 2008).
In the transverse writing scheme of Fig. 11.3, the sample is scanned orthogonally relative to the incoming laser. The working distance no longer restricts the waveguide length and structures may be formed over a depth range of several millimeters, which is sufficient flexibility for many applications to provide 3D optical circuits. The disadvantage of the transverse geometry is that the waveguide cross-section is asymmetric due to the ratio between depth of focus and spot size 2z0/2w0 = n/NA, where n is the refractive index and NA is the numerical aperture. For waveguides formed in glasses with n = 1.5 with typical NA of 0.25–0.85, the focal volume asymmetry n/NA varies from 6.0 to 1.8. This asymmetry results in elliptical waveguide cross-sections with elliptical guided modes, which couple poorly to optical fibers. Methods for overcoming this waveguide asymmetry are discussed below.
The properties of femtosecond laser-written waveguides in bulk glass depend strongly on laser exposure conditions such as scan speed, average power and numerical aperture. These parameters influence the total laser dosage, or net fluence, NF:
where w0 is the waist radius, R is the repetition rate, Fp is the per-pulse fluence (pulse energy per area) and v is the scan speed. Related to the dwell time (tdwell = 2w0 / v) the effective number of pulses per spot size diameter (2w0) during scanning is given by N = 2w0 R / v. Refractive index modification in femtosecond laser waveguide writing occurs above a bulk modification threshold intensity, typically ~ 1013 W/cm2 in dielectrics (Schaffer et al., 2001). Above this threshold, increasing net fluence via decreased scan speed or increased fluence often leads to increased refractive index, and at sufficiently high net fluence, damaged and irregular modification tracks.
At low repetition rates, the time between pulses is long enough so that thermal diffusion has carried the heat away from the focus before the next pulse arrives. The threshold repetition rate for heat accumulation depends on several factors including the glass properties (heat capacity, thermal diffusivity, absorption), the laser pulse energy, the focusing NA and the scanning speed, which will be discussed in further detail in the next section. In the low repetition rate waveguide writing regime, the ensuing pulses may add to the overall modification, but still act independently of one another. Most results in the field of femtosecond laser microfabrication have been carried out at low repetition rates, and usually at 1 kHz, due to the common availability of 800-nm regeneratively amplified Ti:Sapphire femtosecond lasers at this repetition rate. One limitation of waveguide writing in the single-pulse interaction regime is that waveguide cross-sections take on a shape similar to the asymmetric focal volume since the depth of focus is larger than the transverse spot size. The resulting waveguides written with the transverse writing scheme, where the sample is translated transversely relative to the incident laser, are elliptical-like, giving modes that couple poorly to optical fiber. Several methods have been proposed to produce a more symmetric focal volume including astigmatic focusing with a cylindrical lens telescope (Osellame et al., 2003), slit reshaping (Ams et al., 2005; Cheng et al., 2003), multiscan writing (Nasu et al., 2005) and two-dimensional deformable mirrors (Thomson et al., 2008).
Although pure fused silica is the most common glass for photonic applications due to its high transmission, excellent temperature resistance and compatibility with biomaterials, silicate and phosphate glasses offer similar characteristics at a reduced cost. Further, silicate and phosphates may be doped with active ions for amplification or lasing applications.
The most common silicate glasses are boro-aluminosilicate glasses, which in addition to silica (SiO2) contain significant concentrations of boron trioxide (B2O3), aluminum oxide (Al2O3) and sodium oxide (Na2O). Waveguides have been successfully fabricated by low repetition rate femtosecond lasers in several borosilicates including Schott Duran (Ehrt et al., 2004), Corning 7890 (Streltsov and Borrelli, 2002) and Corning 1737 (Low et al., 2005). In Corning EAGLE2000, a common glass used primarily in displays owing to its low density, Zhang et al. explored a wide range of processing conditions with a 1-kHz Ti:Sapphire femtosecond laser. By tuning the compressor alignment, pulse durations of 50 fs–2 ps were studied, revealing promising windows for waveguide writing at both 100 fs and 1 ps (Zhang et al., 2007), disproving the widely held belief that sub-200 fs pulses were needed to form optical waveguides in glass. The most important consequence of this work was a serendipitous discovery from scanning the sample at 0.5 mm/s so that successive pulses only partially overlapped, resulting in a periodic refractive index modulation along the waveguide. The partially overlapped refractive index voxels resulted in segmented waveguides that showed strong and narrowband Bragg reflection while maintaining high optical confinement and low-loss waveguiding at 1550-nm wavelength. For more discussion of waveguide Bragg gratings and related sensing and lasing devices, the reader is referred to Chapter 10.
In Schott BK7, the most common borosilicate glass used in commercial optics, initial reports of waveguide writing with 1-kHz Ti:Sapphire lasers suggested that only negative refractive index modification was possible (Bhardwaj et al., 2005; Ehrt et al., 2004; Mermillod-Blondin et al., 2006). However, it was later shown that by using temporally shaped pulses of ~ 1 ps duration, positive index changes are indeed possible in BK7. It was also recently demonstrated that optical waveguides may be formed at low repetition rates in BK7 using a slit beam reshaping technique (Dharmadhikari et al., 2011). Waveguides may be more easily formed in BK7 without correction techniques by applying higher repetition rates, with demonstrations of low-loss (~ 0.2 dB/cm) waveguides at both 2 MHz (Eaton et al., 2008a) and 11 MHz (Allsop et al., 2010).
Good quality optical waveguides have been demonstrated in phosphate glass, which is easily doped with Er and Yb ions for active waveguide applications. Using the astigmatic writing method with a cylindrical lens telescope, waveguides with low damping loss (0.25 dB/cm) at 1550-nm wavelength were written at 20 μm/s with a 1-kHz, 150-fs Ti:Sapphire laser with a 0.3-NA microscope objective and 5-μJ pulse energy (Osellame et al., 2003). This work is significant since it was the first time a beam-shaping method was applied to correct for the asymmetric intensity distribution in the transverse waveguide writing. The slit shaping method was later applied by Withford and coworkers to produce symmetric waveguides (Fig. 11.4) with similar propagation loss in the same active glass (Ams et al., 2005).
11.4 Microscope images of waveguides fabricated in phosphate glass (a) without and (b) with a 500 μm slit (Ams et al., 2005).
Many groups have applied the femtosecond laser-writing method to pure fused silica glass, but few have shown good quality waveguides with operation at both visible and near-infrared wavelengths, for use in biophotonics and telecom devices, respectively. The best result in fused silica to date was obtained with a multiscan writing procedure to form waveguides with nearly square cross-sections (7.4 μm × 8.2 μm) with a refractive index change of 4 × 10−3. suitable for low-loss coupling to single mode fiber (SMF) (Nasu et al., 2005). The refractive index profile obtained by refracted near field (RNF) profilometry for a waveguide written in Ge-doped silica glass for planar lightwave circuits (PLCs) is shown in Fig. 11.5. The waveguides written in PLC glass were nearly identical to the waveguides written in pure silica. A 775-nm, 150-fs Ti:Sapphire laser with 1-kHz was applied in the transverse writing geometry with a 0.4-NA objective, 182-nJ pulse energy and 10-μm/s writing speed. The waveguides were fabricated with 20 scans separated transversely by 0.4 μm. A propagation loss of 0.12 dB/cm at 1550 nm was reported, which is the lowest reported in the field, and is attributed to the gentle refractive index modification enabled by the novel low-fluence, multiscan fabrication method.
11.5 Refractive index profile of a waveguide written in Ge-doped silica PLC glass by multiple scans (Nasu et al., 2005).
The effect of writing speed on waveguide properties was evidenced in a study in pure silica with a 120-fs 1-kHz Ti:Sapphire laser (Will et al., 2002). With 3-μJ energy pulses focused 0.5 mm below the sample surface with a 0.25-NA lens, the initially single mode waveguide at 1 mm/s scan speed (Fig. 11.6a) showed higher confinement at a decreased scan speed of 0.5 mm/s (Fig. 11.6b). As the scan speed was further reduced, increasing the net fluence, the waveguide became multimode as the effective index was further increased with the V-number exceeding 2.4, the single-mode cut-off value (Agrawal, 1997).
11.6 Influence of the writing speed on waveguide properties at a wavelength of 514 nm. Only the highest-order guided modes are shown for a writing speed of (a) 1 mm/s, (b) 0.5 mm/s, (c) 80 μm/s and (d) 25 μm/s (Will et al., 2002).
The effect of writing laser polarization on waveguide transmission properties was studied using a 1-kHz, 120-fs Ti:Sapphire laser with a 0.5-mm slit placed before the 0.46-NA focusing objective (Little et al., 2008) to obtain symmetric waveguide cross-sections. With 3-μJ pulse energy measured after the slit and 25-μm/s writing speed, a refractive index change of 2.3 × 10−3 was measured for circular polarization, which was about twice as high as that obtained with linear polarizations. This enhancement was attributed to the higher photo-ionization rate for circular polarization compared to linear polarization in the range of intensities studied (42–50 TW/cm2). It is probable that nanogratings also influence the transmission properties of femtosecond laser-written waveguides in fused silica. For more details on nanogratings and their application to post-etching of buried microchannels, the reader is referred to a review by Taylor et al. (2008).
Waveguides were written in a highly nonlinear heavy-metal oxide (HMO) glass with a 1-kHz, 800-nm, 100-fs Ti:Sapphire laser (Siegel et al., 2005). HMO glasses are attractive due to their high optical nonlinearity (n2 ≈ 10−18 m2/W), but this presents significant challenges in femtosecond laser writing because of strong self-focusing, resulting in a delocalized spatial distribution of the laser energy which is difficult to control. By focusing 1.8-μJ femtosecond laser pulses with a 0.42-NA objective and scanning the sample transversely at 60 μm/s, elongated damage structures of 65-μm vertical length were observed when the sample was viewed from the end facets. These elongated structures were the result of filamentation when self-focusing balances against plasma defocusing. The waveguiding regions were found to be adjacent to the filament-induced damage zone, with propagation losses below 0.7 dB/cm demonstrated at 633-nm wavelength. The regions of refractive index increase adjacent to the filament were attributed to compressive stress induced outside the laser-damaged zone, similar to observations during waveguide writing in crystalline materials.
The recent development of high repetition rate, high power femtosecond lasers opens new avenues for manipulating thermal relaxation effects that control the properties of optical waveguides formed when ultrashort laser pulses are focused inside glasses. At low to moderate repetition rates (1–100 kHz), an increase in laser pulse energy leads to formation of larger modification structures as thermal diffusion extends the laser-heated region far outside the focal volume. As repetition rate increases, the time between laser pulses becomes shorter than the time for the absorbed laser radiation to diffuse out of the focal volume and heat builds up in the focal volume. Schaffer et al. (2003) first reported heat accumulation in the bulk of glass using a 25-MHz femtosecond laser oscillator. With increased dwell time, a dramatic increase in the size of laser-modified structures was observed compared to structures formed with single-pulse interactions, where no variation in modification size with dwell time was observed. The combination of high repetition rate and heat accumulation offers fast writing speeds and cylindrically symmetric waveguides together with benefits of annealing and decreased thermal cycling that are associated with low propagation and coupling loss to standard optical fiber.
Following the early work by Schaffer et al. (2003), further insight into heat accumulation effects was provided by Eaton et al. (2008b). Using a finite difference thermal diffusion model, the temperature in the focal volume was calculated as a function of pulse number (dwell time) for repetition rates of 0.1, 0.5 and 1 MHz in Corning EAGLE2000 borosilicate glass. Typical writing conditions of 200 nJ of absorbed energy, 0.55-NA focusing and a melting point of 985°C were assumed. As shown in Fig. 11.7, at 100-kHz repetition rate, the temperature relaxes to below the softening point before the next pulse arrives, resulting in minimal heat accumulation and significant temperature cycling during waveguide writing. At 0.5 and 1 MHz repetition rates, heat accumulation is strongly evident, leading to a larger melted volume which increases with pulse number and repetition rate. Decreased thermal cycling with increased repetition rate is anticipated to lead to smoother waveguides with less propagation loss and birefringent stress.
11.7 Model of glass temperature versus exposure at repetition rates of 100 kHz, 500 kHz and 1 MHz, at a radial position of 3 μm from the center of the focal volume. The absorbed energy of 200 nJ was identical at each repetition rate.
To unravel the contributions of thermal diffusion and heat accumulation to the resulting waveguide morphology, a variable repetition rate (0.1–5 MHz) 300-fs, 1045-nm Yb-doped fiber laser was applied to waveguide writing in Corning EAGLE2000 borosilicate glass (Eaton et al., 2008b) with a 0.55-NA focusing lens. Structures were formed at 150 μm below the surface unless specified otherwise. The onset for heat accumulation was determined by comparing waveguide diameters produced by scanned exposures with that of single-pulse exposures, where the only contribution is from thermal diffusion. The threshold was defined as the minimum pulse energy to increase the waveguide diameter 2-fold over the diameter produced by diffusion in a single-pulse interaction. Single-pulse diffusion diameters were found to vary from 2 to 6 μm for pulse energies of 0.1 to 1 μJ (Eaton et al., 2008b).
The threshold pulse energy for driving heat accumulation is shown in Fig. 11.8 as a function of repetition rate (200 kHz–2 MHz) and for scan speeds of 2, 10 and 40 mm/s. The single pulse modification threshold was 50 nJ (2.5 J/cm2) and invariant with repetition rate. In contrast, the energy threshold for heat accumulation decreased sharply from 900 nJ at 200 kHz to 80 nJ at 2 MHz and was only weakly dependent on scan speed. In this 200 kHz–2 MHz range of repetition rates, the thermal diffusion scale length decreases from 1.6 to 0.5 μm, where D is the thermal diffusivity and R is the repetition rate. This decrease in the characteristic thermal diffusion length indicates that the effective laser heating volume decreases dramatically with increasing repetition rate, thereby reducing the threshold pulse energy for heat accumulation. For R > 1 MHz, the thermal diffusion scale length of 0.7 μm falls inside the laser waist radius of w0 = 0.8 μm, resulting in an asymptotic limit of the heat accumulation threshold energy to a minimum value of 80 nJ at 2-MHz repetition rate in Fig. 11.8. Beyond 2 MHz, the available laser pulse energy was below this value, preventing the observation of heat accumulation effects in EAGLE2000 glass. Similarly, when the laser was operated at the lowest 100-kHz repetition rate, the 2-μJ maximum pulse energy available was insufficient to drive heat accumulation effects beyond a larger thermal diffusion diameter of 8 μm.
11.8 Experimental values of threshold pulse energy for driving heat accumulation in borosilicate glass as a function of laser repetition rate for scan speeds of 2, 10 and 40 mm/s and 0.55-NA focusing (Eaton et al., 2008b).
In the same study, a new laser processing window was discovered for producing low-loss waveguides across the large 200 kHz–2 MHz range of repetition rates (Eaton et al., 2008b). By holding the average power constant and delivering the same net fluence exposure at each repetition rate, strong thermal diffusion from high energy pulses at 200-kHz repetition rate balanced the strong heat accumulation with low pulse energy delivered at high repetition rates to produce waveguides with similar diameter and strong guiding at 1550-nm wavelength. Figure 11.9 shows cross-sectional refractive index profiles measured by RNF for waveguides written with 200-mW average power at repetition rates of 0.2–2 MHz and 25-mm/s scan speed. This average power was found to give the lowest insertion loss (IL) at each repetition rate as described later. The core of the waveguides shown in Fig. 11.9 is attributed to the high temperature spikes induced within the laser spot size by each laser pulse, while the outer lower-contrast cladding is formed by a more slowly evolving near-Gaussian temperature distribution, with the overall size determined by the maximum diameter where the temperature exceeds the melting point. Because of the variable temperature across the modified zones, the cooling rates are highly non-uniform, and therefore are expected to lead to a non-uniform distribution of the final glass density (Chan et al., 2003a).
11.9 Cross-sectional refractive index profiles of waveguides written with 200-mW average power, 25-mm/s scan speed and repetition rates of 0.2, 0.5, 1, 1.5 and 2 MHz (Eaton et al., 2008b).
The small, dark spot at the bottom of the index profiles in Fig. 11.9 is attributed to the focus plane location since its depth was constant with varying exposure conditions. The images show that most of the laser energy was deposited upstream of the focus. At 200-kHz repetition rate, the waveguides showed a vertically elongated central core guiding region with peak Δn = 0.005. The waveguide is elliptical due to thermal diffusion from a laser heating volume extended vertically at this high pulse energy of 1 μJ and also from minimal cumulative heating between laser pulses. At 500 kHz, owing to increased heat accumulation, a more circular guiding region was found with a maximum Δn = 0.006 in the guiding region. A small region of increased refractive index is also observed below the main guiding region. At 1-MHz repetition rate, this region below the core has increased in size and magnitude to a peak Δn = 0.007. This region is now responsible for guiding of 1550-nm light but the mode also extends into the weaker central core to yield two transverse modes when formed with a higher average power exposure (> 250 mW). At 1.5 MHz, the guiding region has clearly transitioned below the central core to form a strong guiding region with peak Δn = 0.008. At 2-MHz repetition rate, a similar profile is observed but beyond this repetition rate, the pulse energy dropped below the heat accumulation threshold of 90 nJ (Fig. 11.8) and formed weakly guiding structures. The highly nonlinear laser interactions lead to vertical shifts of waveguide position and differing waveguide profiles that must be monitored and accounted for during fabrication with varying exposure conditions and focal depths in the glass.
Figure 11.10 aids in visualizing waveguide properties as a function of average power and scan speed, shown for 1.5-MHz repetition rate. Insertion loss is classified by circles, squares and triangles representing low (< 3 dB), medium (3–6 dB) and high (>6 dB) IL, respectively, for the 2.5-cm long waveguides. Waveguides exhibiting multiple transverse modes (diamonds) and typically damaged morphology, written with the highest net fluence are found at the top-left. Conversely, the bottom-right corner indicates underexposed waveguides where the index change was too low to efficiently guide 1550-nm light. At 1.5-MHz repetition rate, the lowest IL of ~ 1.2 dB for fiber–waveguide–fiber coupling was observed over a large 10–25 mm/s range of scan speeds, but in a narrow 200 mW ± 10 mW average power range (encircled data in Fig. 11.10).
Similar analysis was carried out for waveguides formed with 0.2, 0.5, 1 and 2-MHz repetition rates and in all cases, revealed a similar processing window of 200 mW and 10–25 mm/s for the lowest IL. The minimum IL and MFD at each repetition rate are presented in Fig. 11.11. This constant 200-mW average power exposure window appears consistent with the optimum 250-mW power for generating low-loss waveguides in phosphate glass at repetition rates of 505–885 kHz with a similar femtosecond laser (Osellame et al., 2006). The decreasing IL with increasing repetition rate in Fig. 11.11 is associated with increasingly stronger heat accumulation that results in higher refractive change and smaller MFD for best coupling to optical fibers at 1.5 MHz. The increased IL and MFD from 1.5 to 2 MHz is attributed to inadequate laser pulse energy (100 nJ) at 2 MHz for driving sufficient laser heating above the ~ 90 nJ threshold for heat accumulation shown in Fig. 11.8. Beyond 2-MHz repetition rate, only narrow ~2 μm diameter waveguides were formed that were barely guiding and showed no evidence of heat accumulation.
11.11 IL and MFD versus repetition rate for waveguides formed with 200-mW average power and 15-mm/s scan speed (Eaton et al., 2008b).
The refractive index profiles of waveguides written with 0.55-NA lens, 200-mW power, 150-μm depth, 1.5-MHz repetition rate and scan speeds of 5, 15 and 30 mm/s are shown in Fig. 11.12. Due to the decreased net fluence, the cladding and guiding region diameters and also the peak refractive index change decrease with increasing scan speed. As shown in Fig. 11.11, a scan speed of 15 mm/s provided the lowest insertion loss of 1.2 dB at 1550-nm wavelength with ~10-μm MFD allowing efficient coupling to single-mode fiber. The highest exposure at 5-mm/s scan speed led to high loss (Fig. 11.10), while 30-mm/s speed resulted in weakly confined modes of ~15-μm MFD, coupling poorly to fiber. At the maximum scan speed of 100 mm/s, the MFD increased to ~20 μm.
11.12 Refractive near-field measurements of cross-sectional refractive index profiles for waveguides written with 0.55-NA lens, 200-mW power, 150-μm depth, 1.5-MHz repetition rate and scan speeds of 5, 15 and 30 mm/s.The writing laser was incident from the top (Eaton et al., 2008b).
The refractive index profile for the optimum waveguide at 15-mm/s scan speed (1.2-dB insertion loss, ~ 0.3-dB/cm propagation loss) was used to confirm the accuracy of the RNF measurements, as shown in Fig. 11.13. The RNF data were imported into a numerical mode solving routine (Lumerical MODE Solutions 2.0) and the resulting mode profile shows excellent agreement with the experimentally measured mode profile, confirming the accuracy of the RNF measurements. The arrow indicates the relative position of mode and waveguide cross-section.
11.13 Waveguide fabricated with 1.5-MHz repetition rate, 200-mW power, 0.55-NA lens, 150-mm depth and 15-mm/s scan speed: crosssectional refractive index profile (left), simulated mode profile (middle) and measured mode profile (right). A gray arrow indicates position of mode relative to waveguide cross-section (Eaton et al., 2008b).
To take advantage of femtosecond laser writing of waveguides in all three dimensions, one must carefully address the problem of spherical aberration at the air-glass interface, which varies dramatically with the focusing depth. The effect of spherical aberration is reduced with oil-immersion lenses (Osellame et al., 2006), objectives with collars for variable depth correction (Hnatovsky et al., 2005b) and asymmetric focusing with slit reshaping (Ferrer et al., 2007). It well known that spherical aberration is less pronounced with lower NA focusing (Schaffer et al., 2001). Further, one can take advantage of strong heat accumulation effects to drive spherically symmetric heat flow which compensates for an axially elongated focal volume. A combination of heat accumulation effect and low numerical aperture of the focusing optic (NA < 0.55) was shown to enable depth-independent, low-loss waveguides (Eaton et al., 2008b).
For the cumulative heating regime of 0.55-NA focusing applied above (200 mW, 1.5 MHz, 15 mm/s), waveguides with similar low loss and mode size could only be obtained in a narrow depth range of d = 50–200 μm (Eaton et al., 2008b). Figure 11.14 shows the MFD of these waveguides to increase 60% from 10 μm at 50-μm depth to 16 μm at 300-μm depth, spherical aberration precluding a deeper waveguide writing range. Much deeper waveguide writing was possible with the 0.25-NA lens, but 5-fold lower peak intensity at the maximum available laser power (400 mW) yielded only small diameter waveguides and weak refractive index change. A better balance was found with the 0.4 NA lens, providing only a small increase in MFD from ~11.0 to 13.5 μm as the depth was increased from d = 50 to 520 μm. The measured propagation loss of ~ 0.35 dB/cm was nearly independent of focal depth. The ability to write waveguides to depths of 520 μm is a substantial improvement over the maximum depth of ~ 200 μm reported by other groups employing MHz repetition rate femtosecond lasers with higher NA focusing objectives (Osellame et al., 2005).
11.14 Mode field diameter versus focusing depth for waveguides formed with 1.5-MHz repetition rate, 15-mm/s scan speed with 0.55 NA (230 mW) and 0.4 NA (200 mW) (Eaton et al., 2008b).
Thermal annealing experiments were performed on the above borosilicate waveguides to test their thermal stability (Eaton et al., 2008b). Waveguides were written at 230-mW power, 1.5-MHz repetition rate, 0.4-NA, 150-μm depth and 8–20-mm/s scan speed. After waveguide characterization, the EAGLE2000 sample was baked for 1 h in a tube furnace in repeated heating and testing cycles of increased temperature in 100°C steps. A peak temperature of 800°C was tested that exceeds the annealing point of 722°C, the temperature at which stresses are relieved after several minutes, but remains below the softening point of 985°C at which the glass deforms under its own weight. For reference, the strain point of 666°C is the temperature below which glass can be rapidly cooled without introducing stresses.
Figure 11.15 shows the mode profile (top) and overhead morphology (bottom) of the waveguide written with intermediate 15-mm/s scan speed for increasing annealing temperature. There is little change in the mode size and waveguide morphology at temperatures up to 500°C. At 600°C, the mode diameter increased ~ 10% and there is less contrast in the cladding. At 700°C, the mode diameter increased ~ 40% compared with the unheated sample (25°C), and the cladding is barely visible. At the last heating step of 800°C, the mode was undetectable due to high losses and the cladding has completely disappeared.
11.15 1550-nm mode profile (top) and overhead microscope (bottom) image at different annealing temperatures for waveguide fabricated in EAGLE2000 with 230-mW power, 1.5-MHz repetition rate, 0.4-NA, 150-μm depth and 15-mm/s scan speed.
It was found that above 500°C, the MFD for all waveguides tested increased with temperature (Eaton et al., 2008b), with the degree of degradation being smallest for the waveguides written with the lowest speed or highest net fluence. Glass has a frozen-in structure that depends on the cooling rate which corresponds to a fictive temperature of the equilibrium melt (Bruckner, 1970). Waveguides fabricated with the highest net fluence are expected to cool fastest from the highest temperatures, creating modification structures with the highest fictive temperatures. Therefore, waveguides written at the highest exposure required annealing at higher temperatures to undo the thermal history of the laser-modified glass and restore its properties to that of the unmodified bulk. Further, the disappearance of the cladding before the central core in Fig. 11.15 is attributed to a lower fictive temperature in the outer cladding due to lower temperatures and slower cooling rates (Eaton et al., 2008b).
By comparison, waveguides written in EAGLE2000 borosilicate glass with 1-kHz repetition rate were less stable than the present 1.5 MHz results, undergoing an 80% increase in MFD after annealing at 500°C, and resulting in undetectable guiding at 1550 nm after annealing at 750°C (Zhang et al., 2007). The higher temperature stability of waveguides written with 1.5-MHz repetition rate is attributed to the higher fictive temperatures driven by the cumulative heating regime.
As demonstrated by Shah et al. (2005), the fundamental 1045-nm wavelength led to weak refractive index contrast and irregular morphology in high repetition rate waveguide writing in pure fused silica. However, processing with the second harmonic wavelength of 522-nm wavelength enabled relatively low loss (1 dB/cm) waveguides and moderately high refractive index change (Δn = 0.01). The benefits of thermal diffusion acting with heat buildup to form circular waveguide cross-sections were not observed in fused silica as reported in lower bandgap silicate glasses (Eaton et al., 2008b; Schaffer et al., 2003). The lack of cumulative heating in fused silica was previously attributed to less absorption in high bandgap fused silica (Shah et al., 2005) and later confirmed experimentally with a 2-fold lower absorption in fused silica measured compared to borosilicate glass for the same laser fluence (Eaton et al., 2011). Also, the working point temperature of fused silica is about 1.5-fold higher than that of borosilicate glasses making it more difficult to melt fused silica and drive heat accumulation. As demonstrated by Osellame et al. (2005) with a tightly focused 26-MHz repetition rate femtosecond laser, heat accumulation is possible in fused silica with a combination of higher repetition rate and fluence. However, unlike other glasses (Eaton et al., 2005, 2008b; Minoshima et al., 2001; Osellame et al., 2006; Schaffer et al., 2003) where low propagation loss waveguides were reported, the structures defined by heat accumulation in fused silica were non-uniform and unable to guide light (Osellame et al., 2005). By exploring repetition rates from 0.25 to 2 MHz, a more comprehensive study of waveguide optimization with the second harmonic wavelength was recently performed in fused silica (Eaton et al., 2011) compared to the initial study (Shah et al., 2005).
A repetition rate of 1 MHz yielded the absolute minimum IL of 1.0 dB (sample length 2.5 cm) with 0.55-NA focusing. Cross-sectional profiles taken by optical microscopy and RNF for the optimum waveguide written at 1 MHz, 175 nJ and 0.2 mm/s are shown in Fig. 11.16a and 11.16b, respectively. The modified structures for 0.55-NA focusing were vertically elongated significantly beyond the 2.2-μm depth of focus by self-focusing and plasma defocusing because the peak power was equal to the 0.8-MW critical power. Good qualitative agreement between the microscope and RNF images was found as shown in Fig. 11.16, with the RNF profile showing a guiding region with peak Δn = 0.016 formed below an irregular damaged region.
To improve the symmetry of the guiding structures in fused silica, a high 1.25-NA oil-immersion lens was applied in the same study (Eaton et al., 2011) to enable increased laser absorption from higher peak intensity and a more symmetric focal volume. With tighter focusing by the 1.25-NA lens, the best IL of 1.2 dB (L = 1.25 cm) was obtained for 500-kHz repetition rate, 0.2-mm/s speed and 133-nJ energy, with the corresponding microscope and RNF images shown in Fig. 11.16c and 11.16d, respectively. Weaker waveguides were produced at 1-MHz repetition rate, limited by the maximum on-target energy of 100 nJ. Compared to 0.55-NA, the waveguide formed by 1.25-NA focusing was significantly less elongated, which was attributed to a more symmetric focal volume, and reduced self-focusing (0.6-MW peak power). The peak Δn = 0.022 represented the highest refractive index increase ever reported for a femtosecond laser-written waveguide in fused silica.
The mode profiles at 1550 nm for the optimum waveguides written by 0.55- and 1.25-NA focusing are shown in Fig. 11.17b and 11.17c, respectively, along with the mode for SMF in Fig. 11.17a with 10.5-μm MFD. The waveguide mode produced by 0.55-NA focusing (MFD = 9.7 μm × 11.9 μm) becomes significantly smaller and more symmetric (MFD = 7.1 μm × 7.4 μm) with 1.25-NA focusing, defining the smallest reported mode to date for a laser-written waveguide in fused silica with simulations predicting that small R = 15 mm bends are now feasible (Eaton et al., 2011), opening the door for much higher density integrated optical circuits.
It is not immediately evident why processing with the green wavelength offers much better quality waveguides than the fundamental wavelength in pure silica glass. It was previously thought the benefit of the green wavelength was due to an enhanced absorption from a lower order nonlinear process, thus providing stronger index contrast waveguides (Shah et al., 2005). However, a similar 40% absorption for 522- and 1045-nm wavelengths for the same laser fluence was found in a recent study (Eaton et al., 2011). Schaffer et al. (2001) have shown that multiphoton ionization plays a smaller role in large bandgap materials like fused silica. Instead, avalanche ionization dominates, and since this process is relatively independent of wavelength, the second harmonic wavelength does not offer an advantage in terms of increased absorption. Instead, the benefit of the green wavelength may be due to its higher on-target fluence (Eaton et al., 2011). After accounting for the 50% conversion efficiency of the SHG process and the 4-fold smaller focal area, a 2-fold higher maximum fluence is possible with 522-nm wavelength. In previous studies, the maximum fluence was required to fabricate the optimum waveguide structures at 522-nm wavelength. It is expected that if higher power lasers were available providing fluences at the fundamental wavelength similar to the optimal value at green wavelength, stronger guiding structures could be formed. This is supported by the recent demonstration by Pospiech et al. (2009) of waveguides with 1.2-dB/cm loss in fused silica using a 1-MHz repetition rate femtosecond laser with more energetic pulses (500 nJ) at the 1030-nm fundamental wavelength. However, the reported waveguides showed more irregular morphology compared to the structures demonstrated here with the green wavelength. It is likely that other factors which have yet to be identified may contribute to the green wavelength’s advantage in femtosecond laser waveguide formation in fused silica.
High-quality waveguides were written in an exotic bismuth borate glass (Nippon BZH7) with a 150-fs, 250-kHz regeneratively amplified Ti:Sapphire laser (Yang et al., 2008a). At this moderate 250-kHz repetition rate, the regime of waveguide fabrication is likely the result of both thermal diffusion and heat accumulation. Bismuth borate has similar nonlinear properties as the HMO glass described in the section titled ‘Exotic glasses’ and is therefore a good candidate for nonlinear optics applications but because of its low critical power, presents a challenge for writing symmetric waveguide structures. To overcome the problem of an axially elongated distribution of laser energy at the focus, the slit reshaping method was applied. With 200-nJ pulses focused with a 0.55-NA objective and with a writing speed of 200 μm/s, a symmetric waveguide cross-section was produced with a slit width of 380 μm, as shown in Fig. 11.18. The symmetric aspect ratio was found to be preserved up to focal depths of about 100 μm but beyond this value, spherical aberration due to the large refractive index of the glass (n = 2) led to an increase in the aspect ratio. When probed with 1550-nm light, the waveguide exhibited a circular mode with MFD of 11 μm, well-matched to SMF. Using the Fabry–Perot method, a propagation loss of 0.2 dB/cm was measured, which is the lowest loss achieved in a high index glass waveguide fabricated by femtosecond laser writing.
11.18 Cross-sectional microscope image of buried waveguides for different slit widths and depths (Yang et al., 2008a).
In addition to pulse energy, scan speed, and focusing, several other exposure parameters have been found to influence the resulting properties of femtosecond laser-written waveguides. These factors include pulse duration (Fukuda et al., 2004; Zhang et al., 2007), polarization (Eaton et al., 2008b; Little et al., 2008), direction (Yang et al., 2008b) and wavelength (Eaton et al., 2011).
Buried structures formed in fused silica with moderate fluence show no evidence of heat accumulation even as the repetition rate is raised from 1 kHz (Little et al., 2008) to 1 MHz (Eaton et al., 2008b) and the waveguide properties were found to be strongly dependent on the incident writing polarization. In contrast, no detectable difference in insertion loss or mode size was found when waveguides were formed with different polarizations in borosilicate glass within the heat accumulation regime at MHz repetition rates (Eaton et al., 2008b). In addition, the waveguide properties in borosilicate glass were invariant to pulse duration when varied 300-700 fs, which is in contrast to results in fused silica, where pulse duration was observed to strongly affect waveguide mode size and loss (Little et al., 2008). The sensitivity to pulse duration and polarization in fused silica is associated with form birefringence arising from nanogratings formed within the laser-modified volume (Hnatovsky et al., 2005a). In borosilicate glass, nanogratings have not been observed (Hnatovsky et al., 2006), and such polarization and pulse duration dependence may possibly be erased by the strong thermal annealing (Hnatovsky et al., 2006) within the heat accumulation regime.
Due to energy depletion, self-focusing and plasma defocusing, pulse duration influences the spatial distribution of the energy density in the focal volume (Rayner et al., 2005). At 1-kHz repetition rate, where heat accumulation is not present, the dependence of waveguide properties on pulse duration in lithium niobate (Burghoff et al., 2007) and fused silica glass (Zhang et al., 2006) was attributed to nonlinear pulse propagation. However, in the heat accumulation regime, nearly spherically symmetric thermal diffusion washes out the elliptical distribution of energy in the focal volume to yield waveguides with cross-sections that are relatively circular. Therefore, one would expect pulse duration, despite its effect on the energy distribution at the focus, to play a lesser role on the properties of waveguides fabricated in the heat accumulation regime.
Kazansky et al. recently discovered the quill effect (Yang et al., 2008b), in which laser material modification is influenced by the writing direction, even in amorphous glass with a symmetric laser intensity distribution. The researchers conclusively showed that the cause of the directional writing dependence is due to a pulse front tilt in the ultrafast laser beam (Yang et al., 2008b). Although any material should show a direction dependence due to a pulse front tilt, the effect was found to be almost negligible when processing borosilicate glass within the heat accumulation regime as evidenced by a directional coupler formed by arms written in opposite direction but showing a remarkably high peak coupling ratio of 99% (Eaton et al., 2009).
As described in Section 11.3.2 wavelength is an important variable when processing high bandgap materials such as pure fused silica. Due to its large bandgap and low melting point, the increased fluence and enhanced multiphoton absorption provided by the second harmonic wavelength enabled stronger index contrast and lower loss waveguides in this material (Shah et al., 2005). An infrared wavelength of 1.5 μm was applied to fused silica (Saliminia et al., 2005), revealing a very wide energy processing window of 1–23 μJ in forming smooth waveguides compared to 0.5–2.0 μJ at 800-nm wavelength. Such a large processing window is desirable, but the added complexity of using an optical parametric amplifier has dissuaded researchers from adopting this approach for waveguide device fabrication.
Lab-on-a-chip (LoC) devices aim at miniaturizing and integrating standard laboratory processes on a single substrate for reduced cost and improved sensitivity (Whitesides, 2006). Traditionally, LoC device containing microfluidic channel networks have been fabricated with photolithographic techniques, which involve multi-step fabrication procedures requiring clean room environments. Femtosecond laser processing is a promising tool for fabricating surface microfluidic channels and buried optical waveguides, two important building blocks for LoCs. Although glasses such as fused silica have been proposed as substrates for LoC platforms fabricated by femtosecond lasers (Martinez-Vazquez et al., 2007), thermoplastic polymers such as poly(methyl methacrylate) (PMMA) are potentially more attractive substrates since they offer similar optical transparency and biochemical compatibility but with significantly reduced costs.
Watanabe and coworkers demonstrated waveguides in PMMA using a low 1-kHz Ti:Sapphire laser amplifier (Sowa et al., 2006; Watanabe et al., 2006). They observed using microscopy the modification evolve from a negative refractive index change in the first 10 min after writing to a permanent and uniform positive refractive index with Δn ~ 10−4 twenty minutes after the initial exposure (Fig. 11.19). To achieve the uniform and symmetric modification, a slit reshaping method was applied with a pulse energy of 185 nJ, NA of 0.55 and scan speed of 0.2 mm/s (Sowa et al., 2006).
11.19 Time-lapse transmission images of the waveguide cross-section. The optical images of the exit surface of the waveguide cross-section when illuminated with a halogen lamp (Watanabe et al., 2006).
Scully’s group also reported a positive refractive index contrast of Δn ~ 10−3 using a similar 1-kHz femtosecond laser, but with a looser focusing condition provided by a 75-mm focal length singlet lens (Baum et al., 2007). However, light was not launched into the structure to demonstrate waveguiding.
Of the many exposure parameters required to optimize the laser–material interaction, the repetition rate plays the most important role in defining the regime of modification (Eaton et al., 2008b). The benefits of processing within this heat accumulation regime has been demonstrated in fused silica and borosilicate glasses, as described in Section 11.3.2.
The first report of waveguide writing in PMMA within the cumulative heating regime of modification was with a 25-MHz stretched cavity oscillator providing 30-fs, 20-nJ pulses (Zoubir et al., 2004). Buried structures were formed using the longitudinal writing configuration using a 0.25-NA microscope objective, giving rise to a tubular refractive index morphology with annular waveguide modes (Fig. 11.20).
11.20 (a) Microsocope image of waveguide cross-section. (b) Guided modes at 633-nm wavelength (Zoubir et al., 2004).
In our work, we exploit a variable repetition rate femtosecond laser to explore the vast intermediate range of conditions between the single pulse interaction regime at 1 kHz and the heat accumulation regime at high repetition rates (> 1 MHz). Using the 0.55-NA aspheric lens, optimal guiding structures at 100-kHz repetition rate were obtained with 20-mm/s scan speed using 1.2-μJ pulse energy, producing two vertically offset zones of depressed refractive index (Fig. 11.21), attributed to self-focusing and refocusing effects since the peak power was significantly above the critical power. These two zones were able to confine the 633-nm mode in between them, similar to the effect of using two separate scans to confine light between two zones of negative index change in crystals (Burghoff et al., 2006). Propagation losses of 3 dB/cm were measured at the red wavelength, suitably low for sensing applications.
At 500 kHz, only a single annular zone was present (Fig. 11.22) which we attribute to diminished self-focusing from the 2-fold lower energy (600 nJ). Optimum guiding characteristics were obtained with 15-mm/s scan speed, although propagation losses were significantly higher and measured to be 6 dB/cm at 633-nm wavelength. As shown in Fig. 11.22, guiding only occurred around the outer ring of the modification, similar to the annular modes reported at 25-MHz oscillator (Zoubir et al., 2004).
There are several mechanisms that may occur during femtosecond laser irradiation of PMMA which can influence the resulting refractive index morphology. These include degradation by unzipping or chain scission, crosslinking, and alteration of the absorption spectra through defects or impurities. In a previous study on phase gratings formed in PMMA by loosely focused 1-kHz repetition rate femtosecond laser pulses, the effects of laser-induced absorption changes, end groups and crosslinking were found to contribute a positive index change, although their contribution of Δn~10−4 was below the claimed refractive index increase of Δn~10−3(Baum et al., 2007). A time dependence of the refractive index change was observed and attributed to the outward diffusion of photoinduced monomer MMA, which is soluble in PMMA (Liu et al., 2010).
At higher repetition rates (100–500 kHz in this work), the interaction regime is observed to lead to a more violent laser–polymer interaction, resulting in an ablative-type mechanism such as thermal unzipping, leading to damaged structures lacking a positive refractive index increase at their cores. Unzipping is a thermal degradation mechanism, resulting in a breakdown of macromolecular chains into smaller monomer fragments, and therefore a decrease in density and refractive index. In this regime, therefore, we expect that the refractive index increase observed around the irradiated regions is due to material densification caused by the compressive stresses generated in the expansion of the irradiated volume. The waveguides fabricated in this regime are therefore more stable than those created at 1 kHz since they are related to material damages that are less prone to time decay.
In view of the results presented above on femtosecond laser waveguide writing in polymers, we can conclude that this class of materials is much less amenable to this microfabrication technique with respect to glasses. The disadvantages are low or negative refractive index change, high damping losses, and time instability. Although optical waveguides in PMMA may be suitable for certain sensing applications where propagation losses may not be a relevant issue, efficient light excitation and collection in LoCs would benefit from a more efficient device.
In glasses, femtosecond-laser writing now offers propagation losses as low as 0.2 dB/cm, but this is still substantially higher than the 1 dB/m loss typical with PLC technology relying on photolithographic techniques. The maximum refractive index contrast induced is Δn = 0.01–0.02 using high repetition rate femtosecond lasers, which is suitable for coupling to SMF, but still limits waveguide bends to a radius of 15–40 mm. Higher index contrast would lead to smaller mode sizes for tighter bends allowing for increased density of functions on a photonic chip. However, laser writing in out-ofplane architectures, exploiting the 3D volume of bulk glass, remains the most highly promising opportunity for dense optical integration enabled by femtosecond lasers.
In polymers, single mode waveguiding has been demonstrated in PMMA, an important substrate for biophotonic LoC devices. However, the propagation losses are relatively high at 4 dB/cm, with low positive index change demonstrated at 1 kHz repetition rate, and depressed refractive index changes at 100 kHz to 25 MHz repetition rates. Despite the non-ideal waveguide properties demonstrated by femtosecond laser microfabrication in polymers thus far, they are a promising alternative to glasses for commercial applications owing to their low cost, biochemical compatibility, mechanical flexibility and lack of brittleness.
The rapid development of optimized recipes for femtosecond laser fabrication of waveguides enables high-quality passive and active devices in a variety of transparent materials in both 2D and 3D geometries. However, to further exploit the third spatial dimension, future work must address the issue of asymmetric refractive index profiles to enable out of plane evanescent coupled mode devices. The goal of writing a cylindrical waveguide with a symmetric, uniform and high refractive index contrast has still eluded researchers.
Higher resolution translation stages may result in more uniform structures for reduced propagation losses. However, the relatively high waveguide propagation loss of femtosecond laser-written waveguides is mainly attributed to the non-uniform refractive index modification resulting in scattering loss. By exploring a wider range of exposure parameters aided by the recent commercial development of higher power (> 20 W), shorter pulse duration, high repetition rate femtosecond lasers, more extreme temperatures giving increased heat diffusion and accumulation with faster cooling rates may be driven, yielding greater material densification over larger volumes, possibly with smoother refractive index profiles. Further development of real-time monitoring systems to study spectral emissions and infer glass temperatures may in the future be used to control laser exposure to avoid cracks, stress and other defects that lead to scattering loss. In the last few years, laser polarization, pulse duration, multiple scan lines and titled pulse fronts have been shown to play an important role in waveguide writing. The effect of other exposure parameters such as spatial beam profile, temporal pulse shape, bursts of pulses and external heat or stress treatment during writing, have yet to be studied and may offer improvement in waveguide losses and higher refractive index contrast.
In polymers, future work must be devoted to addressing the problem of high propagation losses and low or negative refractive index contrast shown to date. Post-thermal treatment has shown promise for improving waveguide properties and may be needed to produce high-quality waveguides in polymers for biophotonic applications.
The commercial success of the femtosecond laser waveguide writing in dielectrics in the context of displacing existing photolithographic technology is contingent upon addressing the remaining roadblocks of moderate refractive index contrast and waveguide losses described above. The femtosecond laser-writing technique is maskless, simple and flexible, making it ideal for rapid prototyping, refractive index trimming of existing optical circuits and sensor fabrication. With recent discoveries of easily tailored and predicted waveguide shapes enabled by cumulative heating and thermal diffusion, along with Bragg grating waveguide functionality in three-dimensional architectures, femtosecond laser fabrication now shows tremendous potential in fabricating tomorrow’s integrated photonic circuits.
For an introductory overview of femtosecond laser waveguide writing, the reader is referred to the first review paper in the field by Itoh et al. (2006) entitled ‘Ultrafast processes for bulk modification of transparent materials’. This paper provides an excellent overview of the fundamentals and gives an insightful classification of the regimes of femtosecond laser modification in fused silica glass based on the pulse energy (smooth isotropic refractive index change at low energy, nanogratings at moderate energy and voids at high energy).
In the high-impact Nature Photonics journal, Gattass and Mazur gave an excellent review of the field, where they emphasize the fundamentals in the femtosecond laser–material interaction (Gattass and Mazur, 2008). Della Valle et al. (2009) followed with an excellent review of photonic devices for telecommunications applications with the paper entitled ‘Micromachining of photonic devices by femtosecond laser pulses’. This was followed by a review by Ams et al. (2009) entitled ‘Ultrafast laser written active devices’ discussing primarily active devices, including Bragg grating devices in bulk and fiber.
To date, there have been three books published relating to femtosecond laser fabrication of waveguides. The first book edited by Misawa and Juodkazis (2006), 3D laser microfabrication: Principles and applications, includes several chapters relevant to the field, including Chapter 2 by Gamaly et al. on the fundamentals of the femtosecond laser interaction in the bulk of a transparent material and Chapter 8 by Kazansky on the formation of nanogratings in glass. A second book edited by Sugioka et al. (2010), entitled Laser precision microfabrication, features a chapter by Sugioka and Nolte, providing an excellent introduction to the field. The recent book entitled Femtosecond laser micromachining: Photonic and microfluidic devices in transparent materials edited by Osellame et al. (2012) features 17 chapters, all relevant to the field.
Since the field’s inception, the most relevant journals have traditionally been Optics Letters, Optics Express, Journal of the Optical Society of America B and Applied Optics. published by the Optical Society of America. Other important journals include Applied Physics Letters and Journal of Applied Physics by the American Institute of Physics, and Photonics Technology Letters, Journal of Lightwave Technology and Journal of Selected Topics in Quantum Electronics by the IEEE. With the recent trend towards real-world integrated devices with applications in interdisciplinary fields such as sensing, quantum optics and biophotonics, a growing percentage of recent publications have appeared in high-impact journals such as Nature Photonics, Advanced Materials, Physical Review Letters and Lab on a Chip. A simple way to find new advances in the field is by tracking papers that cite the original publication by Davis et al. (1996) and the review by Gattass et al. (Gattass and Mazur, 2008) using ISI Web of Science, Google Scholar or Scopus databases.
Allsop, T., Dubov, M., Mezentsev, V., Bennion, I. Inscription and characterization of waveguides written into borosilicate glass by a high-repetition-rate femtosecond laser at 800 nm. Applied Optics. 2010; 49:1938–1950.
Ams, M., Marshall, G.D., Spence, D.J., Withford, M.J. Slit beam shaping method for femtosecond laser direct-write fabrication of symmetric waveguides in bulk glasses. Optics Express. 2005; 13:5676–5681.
Baum, A., Scully, P.J., Basanta, M., Paul Thomas, C.L., Fielden, P.R., Goddard, N.J., Perrie, W., Chalker, P.R. Photochemistry of refractive index structures in poly(methyl methacrylate) by femtosecond laser irradiation. Optics Letters. 2007; 32:190–192.
Bhardwaj, V.R., Simova, E., Corkum, P.B., Rayner, D.M., Hnatovsky, C., Taylor, R.S., Schreder, B., Kluge, M., Zimmer, J. Femtosecond laser-induced refractive index modification in multicomponent glasses. Journal of Applied Physics. 97, 2005. [083102-1–083102-9].
Chan, J.W., Huser, T.R., Risbud, S.H., Krol, D.M. Modification of the fused silica glass network associated with waveguide fabrication using femtosecond laser pulses. Applied Physics A. 2003; A76:367–372.
Cheng, Y., Sugioka, K., Midorikawa, K., Masuda, M., Toyoda, K., Kawachi, M., Shihoyama, K. Control of the cross-sectional shape of a hollow microchannel embedded in photostructurable glass by use of a femtosecond laser. Optics Letters. 2003; 28:55–57.
Crespi, A., Gu, Y., Ngamsom, B., Hoekstra, H.J.W.M., Dongre, C., Pollnau, M., Ramponi, R., Van Den Vlekkert, H.H., Watts, P., Cerullo, G., Osellame, R. Three-dimensional Mach-Zehnder interferometer in a microfluidic chip for spatially-resolved label-free detection. Lab on Chip. 2010; 10:1167–1173.
Dekker, P., Ams, M., Marshall, G.D., Little, D.J., Withford, M.J. Annealing dynamics of waveguide Bragg gratings: Evidence of femtosecond laser induced colour centres. Optics Express. 2010; 18:3274–3283.
Dharmadhikari, J.A., Dharmadhikari, A.K., Bhatnagar, A., Mallik, A., Singh, P.C., Dhaman, R.K., Chalapathi, K., Mathur, D. Writing low-loss waveguides in borosilicate (BK7) glass with a low-repetition-rate femtosecond laser. Optics Communications. 2011; 284:630–634.
Eaton, S.M., Chen, W., Zhang, H., Iyer, R., Ng, M.L., Ho, S., Li, J., Aitchison, J.S., Herman, P.R. Spectral loss characterization of femtosecond laser written waveguides in glass with application to demultiplexing of 1300 and 1550 nm wavelengths. IEEE Journal of Lightwave Technology. 2009; 27:1079–1085.
Eaton, S.M., Ng, M.L., Bonse, J., Mermillod-Blondin, A., Zhang, H., Rosenfeld, A., Herman, P.R. Low-loss waveguides fabricated in BK7 glass by high repetition rate femtosecond fiber laser. Applied Optics. 2008; 47:2098–2102.
Eaton, S.M., Ng, M.L., Osellame, R., Herman, P.R. High refractive index contrast in fused silica waveguides by tightly focused, high-repetition rate femtosecond laser. Journal of Non-Crystalline Solids. 2011; 357:2387–2391.
Eaton, S.M., Zhang, H., Herman, P.R., Yoshino, F., Shah, L., Bovatsek, J., Arai, A.Y. Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate. Optics Express. 2005; 13:4708–4716.
Eaton, S.M., Zhang, H., Ng, M.L., Li, J., Chen, W.-J., Ho, S., Herman, P.R. Transition from thermal diffusion to heat accumulation in high repetition rate femtosecond laser writing of buried optical waveguides. Optics Express. 2008; 16:9443–9458.
Ferrer, A., Diez-Blanco, V., Ruiz, A., Siegel, J., Solis, J. Deep subsurface optical waveguides produced by direct writing with femtosecond laser pulses in fused silica and phosphate glass. Applied Surface Science. 2007; 254:1121–1125.
Fukuda, T., Ishikawa, S., Fujii, T., Sakuma, K., Hosoya, H. Improvement on asymmetry of low-loss waveguides written in pure silica glass by femtosecond laser pulses. Proceedings of SPIE. 2004; 5279:21–28.
Hnatovsky, C., Taylor, R.S., Rajeev, P.P., Simova, E., Bhardwaj, V.R., Rayner, D.M., Corkum, P.B. Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica. Applied Physics Letters. 2005; 87:014104.
Hnatovsky, C., Taylor, R.S., Simova, E., Bhardwaj, V.R., Rayner, D.M., Corkum, P.B. High-resolution study of photoinduced modification in fused silica produced by a tightly focused femtosecond laser beam in the presence of aberrations. Journal of Applied Physics. 2005; 98:013517.
Hnatovsky, C., Taylor, R.S., Simova, E., Rajeev, P.P., Rayner, D.M., Bhardwaj, V.R., Corkum, P.B. Fabrication of microchannels in glass using focused femtosecond laser radiation and selective chemical etching. Applied Physics A. 2006; 84:47–61.
Juodkazis, S., Matsuo, S., Misawa, H., Mizeikis, V., Marcinkevicius, A., Sun, H.B., Tokuda, Y., Takahashi, M., Yoko, T., Nishii, J. Application of femtosecond laser pulses for microfabrication of transparent media. Applied Surface Science. 2002; 197–198:705–709.
Juodkazis, S., Nishimura, K., Tanaka, S., Misawa, H., Gamaly, E.G., Luther-Davies, B., Hallo, L., Nicolai, P., Tikhonchuk, V.T. Laser-induced microexplosion confined in the bulk of a sapphire crystal: Evidence of multimegabar pressures. Physical Review Letters. 2006; 96:166101.
Little, D.J., Ams, M., Dekker, P., Marshall, G.D., Dawes, J.M., Withford, M.J. Femtosecond laser modification of fused silica: The effect of writing polarization on Si-O ring structure. Optics Express. 2008; 16:20029–20037.
Liu, D., Kuang, Z., Perrie, W., Scully, P., Baum, A., Edwardson, S., Fearon, E., Dearden, G., Watkins, K. High-speed uniform parallel 3D refractive index micro-structuring of poly(methyl methacrylate) for volume phase gratings. Applied Physics B. 2010; 101:817–823.
Low, D.K.Y., Xie, H., Xiong, Z., Lim, G.C. Femtosecond laser direct writing of embedded optical waveguides in aluminosilicate glass. Applied Physics A: Materials Science and Processing. 2005; 81:1633–1638.
Mermillod-Blondin, A., Burakov, I.M., Stoian, R., Rosenfeld, A., Audouard, E., Bulgakova, N., Hertel, I.V. Direct observation of femtosecond laser induced modifications in the bulk of fused silica by phase contrast microscopy. Journal of Laser Micro/Nanoengineering. 2006; 1:155–160.
Minoshima, K., Kowalevicz, A.M., Hartl, I., Ippen, E.P., Fujimoto, J.G. Photonic device fabrication in glass by use of nonlinear materials processing with a femtosecond laser oscillator. Optics Letters. 2001; 26:1516–1518.
Osellame, R., Chiodo, N., Della Valle, G., Cerullo, G., Ramponi, R., Laporta, P., Killi, A., Morgner, U., Svelto, O. Waveguide lasers in the C-band fabricated by laser inscription with a compact femtosecond oscillator. IEEE Journal of Selected Topics in Quantum Electronics. 2006; 12:277–285.
Osellame, R., Chiodo, N., Maselli, V., Yin, A., Zavelani-Rossi, M., Cerullo, G., Laporta, P., Aiello, L., De Nicola, S., Ferraro, P., Finizio, A., Pierattini, G. Optical properties of waveguides written by a 26 MHz stretched cavity Ti:sapphire femtosecond oscillator. Optics Express. 2005; 13:612–620.
Osellame, R., Maselli, V., Vazquez, R.M., Ramponi, R., Cerullo, G. Integration of optical waveguides and microfluidic channels both fabricated by femtosecond laser irradiation. Applied Physics Letters. 2007; 90:231118–231123.
Osellame, R., Taccheo, S., Marangoni, M., Ramponi, R., Laporta, P., Polli, D., De Silvestri, S., Cerullo, G. Femtosecond writing of active optical waveguides with astig-matically shaped beams. Journal of the Optical Society of America B. 2003; 20:1559–1567.
Pospiech, M., Emons, M., Steinmann, A., Palmer, G., Osellame, R., Bellini, N., Cerullo, G., Morgner, U. Double waveguide couplers produced by simultaneous femtosecond writing. Optics Express. 2009; 17:3555–3563.
Ramirez, L.P.R., Heinrich, M., Richter, S., Dreisow, F., Keil, R., Korovin, A.V., Peschel, U., Nolte, S., Tunnermann, A. Tuning the structural properties of femtosecond-laser-induced nanogratings. Applied Physics A: Materials Science and Processing. 2010; 100:1–6.
Sakakura, M., Shimizu, M., Shimotsuma, Y., Miura, K., Hirao, K. Temperature distribution and modification mechanism inside glass with heat accumulation during 250 kHz irradiation of femtosecond laser pulses. Applied Physics Letters. 2008; 93:231112–231114.
Schaffer, C.B., Brodeur, A., Mazur, E. Laser-induced breakdown and damage in bulk transparent materials induced by tightly focused femtosecond laser pulses. Measurement Science and Technology. 2001; 12:1784–1794.
Siegel, J., Fernandez-Navarro, J.M., Garcia-Navarro, A., Diez-Blanco, V., Sanz, O., Solis, J., Vega, F., Armengol, J. Waveguide structures in heavy metal oxide glass written with femtosecond laser pulses above the critical self-focusing threshold. Applied Physics Letters. 2005; 86:121109.
Sudrie, L., Couairon, A., Franco, M., Lamouroux, B., Prade, B., Tzortzakis, S., Mysyrowicz, A. Femtosecond laser-induced damage and filamentary propagation in fused silica. Physics Review Letters. 2002; 89:186601.
Ta’eed, V., Baker, N.J., Fu, L., Finsterbusch, K., Lamont, M.R.E., Moss, D.J., Nguyen, H.C., Eggleton, B.J., Choi, D.-Y., Madden, S., Luther-Davies, B. Ultrafast all-optical chalcogenide glass photonic circuits. Optics Express. 2007; 15:9205–9221.
Thomson, R.R., Bockelt, A.S., Ramsay, E., Beecher, S., Greenaway, A.H., Kar, A.K., Reid, D.T. Shaping ultrafast laser inscribed optical waveguides using a deformable mirror. Optics Express. 2008; 16:12786–12793.
Watanabe, W., Sowa, A.S., Tamaki, T., Itoh, K., Nishii, J. Three-dimensional waveguides fabricated in poly(methyl methacrylate) by a femtosecond laser. Japanese Journal of Applied Physics. 2006; 45:L765–L767.
Yamada, K., Watanabe, W., Toma, T., Itoh, K., Nishii, J. In situ observation of photoinduced refractive-index changes in filaments formed in glasses by femtosecond laser pulses. Optics Letters. 2001; 26:19–21.
Yang, W., Corbari, C., Kazansky, P.G., Sakaguchi, K., Carvalho, I.C. Low loss photonic components in high index bismuth borate glass by femtosecond laser direct writing. Optics Express. 2008; 16:16215–16226.