# Chapter 11 – Fibre Optics – Applied Physics

## Fibre Optics

#### 11.1 Introduction

Optical fibre is a long, thin transparent dielectric material made up of glass or plastic, which carries electromagnetic waves of optical frequencies [visible to infrared] from one end of the fibre to the other by means of multiple total internal reflections. Thus, optical fibres work as wave guides in optical communication systems. An optical fibre consists of an inner cylindrical material made up of glass or plastic called core. The core is surrounded by a cylindrical shell of glass or plastic called the cladding. The refractive index of core (n1) is slightly larger than the refractive index of cladding (n2), [i.e., n1 > n2]. Typical refractive index values are n1 = 1.48 and n2 = 1.46. The core diameter is ≈ 50 μm and the thickness of cladding is ≈ 1 or 2 wavelengths of light propagate through the fibre. The cladding is enclosed in a polyurethane jacket as shown in Fig. 11.1. This layer protects the fibre from the surrounding atmosphere. Many fibres are grouped to form a cable. A cable may contain one to several hundred such fibres.

#### 11.2 Principle of optical fibre, acceptance angle and acceptance cone

Principle: Once light rays enter into core, they propagate by means of multiple total internal reflections at the core-cladding interface, so that the rays travel from one end of the optical fibre to the other. The phenomenon of total internal reflection in a straight optical fibre is explained in the following way. Let the refractive index of the core is n1 and that of the cladding is n2 such that n1 > n2. As shown in Fig. 11.2, a ray of light AO is incident at ‘O’ on the end face of core; let this ray makes an angle of incidence θ0 with the axis of the fibre. This ray is refracted into the core and passes along OB, the angle of refraction in the core is, say θ1. The ray OB is incident on the core-cladding interface with an angle of incidence, 90°-θ1. Suppose this angle of incidence is equal to the critical angle [θc = 90° − θ1] in core at the core-cladding interface, then the angle of refraction in cladding is 90°, so that the ray (BC) passes along the interface between core and cladding. If the angle of incidence for a ray at the end face is less than θ0, then the angle of refraction is less than θ1 and angle of incidence at the core-cladding interface is lager than critical angle, so the ray suffers total internal reflection at the core-cladding interface. If the angle of incidence for a ray at the end face is larger than θ0, then the angle of refraction is larger than θ1 and the angle of incidence at the core-cladding interface is less than critical angle so that the ray will be refracted into the cladding and get lost in it due to absorption.

Figure 11.1 Optical fibre Figure 11.2 Light propagation in an optical fibre So, all those rays which enter the core at an angle of incidence less than θ0 will have refracting angles less than θ1. As a result, their angles of incidence at the interface between core and cladding will be more than critical angle. As a consequence, they will be totally refl ected in core and travel by multiple total internal reflections.

Acceptance angle and acceptance cone: As shown in Fig. 11.2, if the ray AO is rotated around the fibre axis keeping the angle of incidence θ0 constant, it results in a conical surface. As such, only those rays which are within this cone suffer total internal reflections so that they confine to the core for propagation. If a ray falls at the end face of the optical fibre at an angle greater than θ0 or out of the cone, that ray does not undergo total internal reflection at the core-cladding interface, it enters into cladding material and gets lost in the cladding material. Thus, for light rays to propagate through the optical fibre by total internal reflection, they must be incident on the fibre core within the angle θ0. This angle is known as acceptance angle. Acceptance angle is defined as the maximum angle of incidence at the end face of an optical fibre for which the ray can be propagated in the optical fibre. This angle is also called acceptance cone half-angle.

A cone obtained by rotating a ray at the end face of an optical fibre, around the fibre axis with acceptance angle is known as acceptance cone. Expression for acceptance angle is obtained by applying Snell's law at points B and 0°.

Snell's law at ‘B’ is: Snell's law at ‘O’ Substitute Equation 11.1 in Equation 11.2 As the fibre is in air.

So, the refractive index n0 = 1

The Equation (11.3) becomes: This is the equation for acceptance angle.

#### 11.3 Numerical aperture (NA)

Numerical aperture represents the light-gathering capacity of an optical fibre. Light-gathering capacity is proportional to the acceptance angle, θ0. So, numerical aperture can be represented by the sine of acceptance angle of the fibre i.e., sin θ0.

Expression for numerical aperture (NA): Expression for numerical aperture can be obtained by applying Snell's law at ‘O’ and at ‘B’ in Fig. 11.2. Let n1, n2 and n0 be the refractive indices of core, cladding and the surrounding medium (air), respectively. Applying Snell's law at the point of entry of the ray [i.e., at ‘O’],

We have: At point ‘B’ on the core-cladding interface, the angle of incidence = 90° − θ1. Applying Snell's law at ‘B’, we have:

n1 sin (90° − θ1) = n2 sin 90° Substituting Equation (11.6) in (11.5), we have: If the surrounding medium of the fibre is air, then n0 = 1. According to the definition for numerical aperture (NA), Let the fractional change in the refractive index (∆) be the ratio between the difference in refractive indices of core and cladding to the refractive index of core.  Equation (11.10) can be written as: Substituting Equation (11.10) in (11.11), we have: Numerical aperture can be increased by increasing ‘∆’ and thus enchances the light-gathering capacity of the fibre. We cannot increase ∆ to a very large value because it leads to intermodal dispersion, which causes signal distortion.

Condition for light propagation in the fibre: If θi is the angle of incidence of an incident ray at the end of optical fibre, then the ray will propagate if θi < θ0

(or) sin θi < sin θ0 (or) sin θi < NA is the condition for propagation of light within the fibre.

#### 11.4 Step index fibres and graded index fibres—transmission of signals in them

Based on the variation of refractive index of core, optical fibres are divided into: (1) step index and (2) graded index fibres. Again based on the mode of propagation, all these fibres are divided into: (1) single mode and multimode fibres. In all optical fibres, the refractive index of cladding material is uniform. Now, we will see the construction, refractive index of core and cladding with radial distance of fibre, ray propagation and applications of the above optical fibres.

(1) Step index fibre: The refractive index is uniform throughout the core of this fibre. As we go radially in this fibre, the refractive index undergoes a step change at the core-cladding interface. Based on the mode of propagation of light rays, step index fibres are of two types: (a) single mode step index fibres and (b) multimode step index fibres. Mode means, the number of paths available for light propagation in a fibre. We describe the diff erent types of fibres below.

(a) Single mode step index fibre: The core diameter of this fibre is about 8 to 10 μm and outer diameter of cladding is 60 to 70 μm. There is only one path for ray propagation, so, it is called single mode fibre. The cross sectional view, refractive index profile and ray propagation are shown in Fig. 11.3. In this fibre, the transmission of light is by successive total internal reflections. i.e., it is a reflective type fibre. Nearly 80% of the fibres manufactured today in the world are single mode fibres. So, they are extensively used. Lasers are used as light source in these fibres. These fibres are mainly used in submarine cable system.

Figure 11.3 Single mode step index fibre: (a) Cross sectional view and refractive index profile; (b) Ray propagation (b) Multimode step index fibre: The construction of multimode step index fibre is similar to single mode step index fibre except that its core and cladding diameters are much larger to have many paths for light propagation. The core diameter of this fibre varies from 50 to 200 μm and the outer diameter of cladding varies from 100 to 250 μm. The cross-sectional view, refractive index profile and ray propagation are shown in Fig. 11.4. Light propagation in this fibre is by multiple total internal reflections. i.e., it is a reflective type fibre. It is used in data links which have lower bandwidth requirements.

(c) Transmission of signal in step index fibre: Generally, the signal is transmitted through the fibre in digital form i.e., in the form of 1's and 0's. The propagation of pulses through multimode fibre is shown in Fig. 11.4(b). The pulse which travels along path 1 (straight) will reach first at the other end of fibre. Next, the pulse that travels along path 2 (zig-zag) reaches the other end with some time delay. Lastly, the pulse that travels along path 3 reaches the other end. Hence, the pulsed signal received at the other end is broadened. This is known as intermodal dispersion. This imposes limitation on the separation between pulses and reduces the transmission rate and capacity. To overcome this problem, graded index fibres are used.

Figure 11.4 Multimode step index fibre: (a) Cross sectional view and refractive index profile; (b) Ray propagation (2) Graded index fibre: In this fibre, the refractive index decreases continuously from centre radially to the surface of the core. The refractive index is maximum at the centre and minimum at the surface of core. This fibre can be single mode or multimode fibre. The cross-sectional view, refractive index profile and ray propagation of multimode graded index fibre are shown in Fig. 11.5(a). The diameter of core varies from 50 to 200 μm and outer diameter of cladding varies from 100 to 250 μm.

The refractive index profile is circularly symmetric. As refractive index changes continuously radially in core, the light rays suffer continuous refraction in core. The propagation of light rays is not due to total internal reflection but by refraction as shown in Fig. 11.5(b). In graded index fibre, light rays travel at different speeds in different parts of the fibre. Near the surface of core, the refractive index is lower, so rays near the outer surface travel faster than the rays travel at the centre. Because of this, all the rays arrive at the receiving end of the fibre approximately at the same time. This fibre is costly. Either laser or LED is used as light source. Its typical applications is in the telephone trunk between central offices.

Figure 11.5 Multimode graded index fibre: (a) Cross sectional view and refractive index profile; (b) Ray propagation Transmission of signal in graded index fibre: In multimode graded index fibre, large number of paths are available for light ray propagation. To discuss about intermodal dispersion, we consider ray path 1 along the axis of fibre as shown in Fig. 11.5(b) and another ray path 2. Along the axis of fibre, the refractive index of core is maximum, so the speed of ray along path 1 is less. Path 2 is sinusoidal and it is longer; along this path refractive index varies. The ray mostly travels in low refractive index region, so the ray 2 moves slightly faster. Hence, the pulses of signals that travel along path 1 and path 2 reach other end of fibre simultaneously. Thus, the problem of intermodal dispersion can be reduced to a large extent using graded index fibres.

#### 11.5 Differences between step index fibres and graded index fibres

Step Index Fibre Graded Index Fibre
1. The refractive index of the core is uniform and step or abrupt change in refractive index takes place at the interface of core and cladding in step index fibres. 1. The refractive index of core is non-uniform, the refractive index of core decreases parabolically from the axis of the fibre to its surface.
2. The light rays propagate in zig-zag manner inside the core. The rays travel in the fibre as meridional rays and they cross the fibre axis for every reflection. 2. The light rays propagate in the form of skew rays or helical rays. They will not cross the fibre axis.
3. Signal distortion is more in case of high-angle rays in multimode step index fibre. In single mode step index fibre, there is no distortion. 3. Signal distortion is very low even though the rays travel with different speeds inside the fibre.
4. The bandwidth is about 50 MHz km for multimode step index fibre whereas it is more than 1000 MHz Km in case of single mode step index fibre. 4. The bandwidth of the fibre lies in between 200 MHz Km to 600 MHz Km even though theoretically it has an infinite bandwidth.
5. Attenuation of light rays is more in multimode step index fibres but for single mode step index fibres, it is very less. 5. Attenuation of light rays is less in graded index fibres.
6. NA of multimode step index fibre is more whereas in single mode step index fibres, it is very less. 6. NA of graded index fibres is less.

#### 11.6 Differences between single mode fibres and multimode fibres

Single Mode Fibres Multimode Fibres
1. In single mode fibres there is only one path for ray propagation. 1. In multimode fibres, large number of paths are available for light ray propagation.
2. Single mode step index fibres have less core diameter (<10 μm) and the difference between the refractive indices of core and cladding is very small. 2. Multimode step index fibres have larger core diameter (50 to 200 μm) and the difference between the refractive indices of core and cladding is large.
3. In single mode fibres, there is no dispersion. 3. There is signal distortion and dispersion takes place in multimode fibres.
4. Signal transmission capacity is less but the single mode fibres are suitable for long distance communication. 4. Signal transmission capacity is more in multimode fibres. Because of large dispersion and attenuation, they are less suitable for long distance transmission.
5. Launching of light into single mode fibres is difficult. 5. Launching of light into multi mode fibres is easy.
6. Fabrication cost is very high. 6. Fabrication cost is less.
7. The V-number of a fibre is less than 2.405 for single mode fibre. n1, r are the refractive index and radius of core respectively, λ = wavelength of light that propagates through the fibre. 7. The V-number of a multimode fibre is greater than 2.405.

#### 11.7 Attenuation in optical fibres

A very important parameter of an optical fibre is the attenuation of light signal in the fibre. Attenuation decreases light transmittance. Usually, the power of light at the output end of optical fibre is less than the power launched at the input end, then the signal is said to be attenuated. The signal attenuation is defined as the ratio of the input optical power (Pi) into the fibre to the power of light coming out at the output end (P0). The attenuation coefficient is given as: The causes of attenuation are numerous, some of them are waveguide structure, material compositions, material dispersion, material scattering, microbending losses, mode coupling radiation losses, etc. The attenuation is the function of wavelength and material. Optical communication wavelengths are 0.8, 1.3 and 1.55 μm. The attenuation is mainly due to: (i) absorption and (ii) scattering.

(i) Absorption losses: In glass fibres, three different absorptions take place. They are ultraviolet absorption, infrared absorption and ion resonance absorption. Ion resonance absorption losses in pure fused silica are shown in Fig.11.6.

Absorption of uv radiation around 0.14 μm results in the ionization of valence electrons. Absorption of IR photons by atoms within the glass molecules causes heating. This gives absorption peak at 8 μm, also minor peaks at 3.2, 3.8 and 4.4 μm. The OH ions of water trapped during manufacturing causes absorption at 0.95, 1.25 and 1.39 μm as shown in Fig. 11.6. The presence of other impurities such as iron, copper and chromium also causes absorption. All these absorptions results in absorption loss in the fibre.

(ii) Scattering losses: The molten glass, when drawn into a very thin fibre under proper tension causes sub-microscopic variation in the density of glass in the fibre takes place. The dopants added to glass to vary the refractive index also leads to inhomogenities in the fibre. The microscopic variation of density and inhomogenities acts as reflecting and refracting facets, these scatter a small portion of light passing through the glass. Thus, the scattering losses. If the size of density-fluctuating regions is of the order of λ/10 or less then they act as point source scattering centre. This kind of scattering is known as Rayleigh scattering. The scattering losses is proportional to 1/λ4. On this basis, the scattering losses at a wavelength of 1.3 μm is about 0.3 dB/Km whereas at a wavelength of 0.7 μm it is about 5 dB/Km. The Rayleigh scattering losses for silica is shown in Fig. 11.7.

Figure 11.6 Ion resonance absorption loss effects in fused silica glass fibres Figure 11.7 Rayleigh scattering losses in silica fibres (iii) Bending Losses: In a bent fibre, there is loss in power of the transmitted signal called bending losses. Einstein explained the bending losses. According to Einstein's theory of relativity, the part of the ray that enters into cladding will travel faster. The energy associated with this part of the ray is lost. This loss can be represented by absorption coefficient (α) where C is constant

R = radius of curvature of fibre bend and r = radius of the fibre. The bends with radius of curvature is of magnitude of the fibre radius gives rises to heavy losses.

(iv) Microbending and wave guide losses: A large number of small bends present in the fibre causes large attenuation in the signal transmission. This is known as microbending loss. Usually, microbends are formed when an unsheathed fibre is wound in tension on a drum during manufacture. These bends will be more if the surface of drum is non-uniform.

During manufacturing, if proper care is not taken, then a continuous small variation in the fibre diameter or circularity is formed. This gives scattering loss, known as waveguide losses.

#### 11.8 Optical fibres in communication

Fibre optics essentially deals with the communication [including voice signals, video signals or digital data] by transmission of light through optical fibres. Optical fibre communication system essentially consists of three parts: (a) transmitter (b) optical fibre and (c) receiver (Fig. 11.8). The transmitter includes modulator, encoder, light source, drive circuits and couplers. The light source can be a light emitting diode [LED] or a semiconductor laser diode. Basically, a fibre optic system simply converts an electrical signal [corresponds to analogue information such as voice] to binary data by an encoder and this binary data comes out as a stream of electrical pulses and these electrical pulses are converted into pulses of optical power by modulating the light emitted by the light source. That means the laser drive circuit directly modulates the intensity of the semiconductor laser light with the encoded digital signal. This digital optical signal is launched into the optical fibre cable. The transmitter also has couplers to couple the transmitted light signals with the fibre. Fibres might require connectors to increase the length of the fibre medium. To transmit signals to long distances, repeaters are used after certain lengths in the optical fibre.

Figure 11.8 Block diagram represents optical fibre communication system As the signal propagates in the fibre, it is subjected to attenuation and delay distortion. Attenuation is the loss of optical power due to absorption and scattering of photons. Even the leakage of light due to fibre bends adds to the attenuation effect. Delay distortion is because of spreading of pulses with time. The pulse spreading is mainly due to the variation in velocity of various spectral components of the pulse during its propagation in the fibre. When the attenuation and pulse spreading reaches beyond a limiting stage, then it may not be possible to retrieve the information from the light signal. Just at this threshold stage, a repeater is needed in the transmission path.

An optical repeater consists of a receiver and a transmitter arranged adjacently. The receiver section converts the optical signal into corresponding electrical signal, further this electrical signal is amplified and recast in the original form by means of an electrical regenerator i.e., reshape the signal and this signal is sent into an optical transmitter section, where the electrical signal is again converted back to optical signal and fed into an optical fibre.

Finally, at the end of optical fibre the signal is fed to the receiver. The receiver contains light detector. This can be either an Avalanche Photo Diode [APD] or a Positive Intrinsic Negative [PIN] diode. In the photodetector, the signal is converted in to pulses of electrical current, which is then fed to the decoder, which converts the sequence of binary data stream into an analogue signal as that fed at the transmitting end.

#### 11.9 Advantages of optical fibres in communication

The following are the advantages of optical fibres in communication:

1. Extremely wide band: The rate at which information can be transmitted is directly related to signal frequency. Light has very high frequency in the range of 1014 to 1015 Hz, as compared to radio frequencies ~ 106 Hz and microwave frequencies 108–1010 Hz. So, light can transmit information at a higher rate than systems that operate at radio frequencies or microwave frequencies.
2. Smaller diameter and light weight: Optical fibres are light-weight, smaller diameter and flexible; so, they can be handled more easily than copper cables.
3. Lack of cross-talk between parallel fibres: In copper cable communication circuits, signals often stray from one circuit to another, resulting in other calls being heard in the background.

This cross talk is negligible in optical fibres even when many fibres are cabled together.

4. Longer life-span: The life-span of optical fibres is expected to be 20–30 years as compared to copper cables, which have a life-span of 12–15 years.
5. Temperature resistant: In contrast to copper cables, they have high tolerance to temperature extremes.
6. Easy maintenance: Optical cables are more reliable and easy to maintain than copper cables.
7. Much safer than copper cables: This is because only light and not electricity is being conducted.
8. Potential of delivering signals at low cost, because fibres are made up of silica, which is available in abandance in nature.
9. They possess low transmission loss and noise-free transmission is obtained as compared to copper cables. Since the transmission loss in optical fibres is as low as 0.2 dB/Km.
10. Ruggedness and flexibility: Optical fibre cables are flexible, compact and extremely rugged.

#### 11.10 Fibre optic sensing applications

Fibre optic sensors are used to monitor displacement, liquid level, flow, temperature and pressure, chemical composition etc. Optic fibre sensors can be devided into two types, they are:

(a) Intrinsic sensors/active sensors and (b) extrinsic sensors/passive sensors.

The Active sensors: In active sensors, the quantity to be measured acts directly on the fibre and modifies the radiation passing down the fibre.

The various active sensors are:

(i) Intensity modulated sensors: These are based on the change in refractive index, temperature, absorption, etc

(ii) Phase-modulated sensors: These involve the interference between the signal and reference in the interferometer. This leads to a shift in the interference fringes by the variable.

(iii) Polarization-modulated sensors: In this, a change in polarization state of the guided signal by the variable takes place.

(iv) Wavelength-modulated sensors: In this, the spectral dependent variation of absorption and emission by the variable takes place.

The passive sensors: In passive sensors, the modulation takes place outside the fibre. The fibre acts merely as a convenient transmission channel for light. The passive sensors has a sensor head and the sensed optical signal is transmitted to a remote point for signal processing. The table below gives the physical parameter to be measured using passive sensor and the modulation effects in the fibre.

Physical Quantity to be Measured Modulation Effects in the Fibres
1. Temperature Thermoluminescence
2. Pressure Piezo optic effect
3. Density Triboluminiscence
4. Mechanical force Stress birefringence
5. Electric field Electro optic effect
6. Magnetic field Magneto optic effect
7. Electric current Electro luminescene

Now, we study some sensors in detail.

#### (a) Displacement sensors

Intensity modulation of the transmitted light beam is utilized in this sensor. Figure 11.9 shows the displacement sensor.

Light from the source passes through one optical fibre and incident on the target. The reflected light reaches the detector through another optical fibre. Light reflected from the target and collected by the detector is a function of the distance between the fibre ends and the target. Hence, the position or displacement of the target may be registered at the optical detector. Further, the sensitivity of this sensor may be improved by placing the axis of the feed and return fibre at an angle to one another and to the target.

Figure 11.9 Displacement sensor Figure 11.10 Fluid level detector #### (b) Liquid level sensor

Figure 11.10 shows the operation of a simple optical fluid level switch. If the level of liquid is below the optical dipstick, due to total internal reflection, light from the source reaches the detector. If the level of liquid is above the camfered end of the dipstick, then the light is transmitted into the fluid and the detector ceases to get light.

#### (c) Temperature and pressure sensor

When a single optical fibre is subjected to temperature or pressure variations, then its length and refractive index changes. This causes change in phase of light at the end of fibre. The change in phase of light is proportional to magnitude of the change in temperature or pressure. The phase changes can be measured by an interferometer method shown in Fig. 11.11.

Here, the light from a laser source is split into two beams of approximately equal amplitude by a 50% beam splitter. One beam is passed through sensing fibre, which is subjected to temperature or pressure variations and the other beam through reference fibre, which is not subjected to any changes and is used for comparison. Light from these two fibres is superimposed using another beam splitter. Interference of these two waves gives fringes. The intensity of the fringe depends on the phase relation between the two waves. If the waves are in phase, then the intensity is maximum; this happens when the sensing fibre is not disturbed. The intensity is minimum if the waves are out of phase due to λ/2 change in length of sensing fibre. The intensity of interference fringes can be measured with a photodetector and temperature or pressure changes can be measured.

Figure 11.11 Measurement of phase changes by interferometer method #### (d) Chemical sensors

Here, the sensing element is a modified fibre, and this sensing element senses the concentration of a chemical in terms of the phase change of the light wave. For example, in hydrogen sensor, palladium wire is fixed to the sensor. Hydrogen absorption changes the dimensions of the wire. This change produces strain in the optical fibre. This strain in the fibre changes the path length of light in the fibre. So, the concentration of hydrogen is proportional to the change in path length of light.

#### 11.11 Applications of optical fibres in medical field

Optical fibre medical instruments may contain bundles of optical fibres. An optical fibre instrument used to see the internal parts of human body is endoscope. The endoscope facilitates the physicians to see the internal parts of body without performing surgery. The main part in endoscope is fibrescope. Based on application, the endoscopes are classified into:

1. Gastroscope is used to examine the stomach. A gastroscope can be fitted with various parts to photograph tumours and ulcers. Laser-used gastroscope is used to remove objects that have been swallowed. Gastroscope can also guide a laser, used to destroy tumours.
2. Bronchoscope is used to see upper passages of lungs.
3. Orthoscope is used to see the small spaces within joints.
4. Couldoscope is used to test female pelvic organs.
5. Peritoneoscope is used to test the abdominal cavity, lower parts of liver and gall bladder.

Also in ophthalmology, laser guided by the fibres is used to reattach the detached retina and to correct the defects in the vision.

The fabrication of fibrescope is used in endoscope. Fibrescope is shown in Fig. 11.12 below.

Figure 11.12 Flexible fibrescope The fibrescope is also useful in industry. It could be used to examine welds, nozzles and combustion chambers inside the aircraft engines. These are not easily accessible for observation otherwise.

#### Formulae

1. 2. 3. #### Solved Problems

1. The refractive indices of core and cladding materials of a step index fibre are 1.48 and 1.45, respectively. Calculate: (i) numerical aperture, (ii) acceptance angle, and (iii) the critical angle at the core-cladding interface and (iv) fractional refractive indices change.

(Set-1–May 2006)

Sol: Let the refractive index of core, n1 = 1.48

and the refractive index of cladding, n2 = 1.45

1. Numerical aperture(NA) 2. Let θ0 be the acceptance angle 3. 4. The fractional refractive indices change, 2. Calculate the angle of acceptance of a given optical fibre, if the refractive indices of the core and cladding are 1.563 and 1.498, respectively.

(Set-3–Sept. 2008), (Set-1–May 2004)

Sol: Refractive index of core, n1 = 1.563

Refractive index of cladding, n2 = 1.498

Numerical aperture, Acceptance angle, 3. Calculate the fractional index change for a given optical fibre if the refractive indices of the core and cladding are 1.563 and 1.498, respectively.

(Set-1–Sept. 2007), (Set-4–May 2004)

Sol: Refractive index of the core, n1 = 1.563

Refractive index of cladding, n2 = 1.498

The fractional refractive indices change, 4. An optical fibre has a core material of refractive index 1.55 and cladding material of refractive index 1.50. The light is launched into it in air. Calculate its numerical aperture.

(Set-4–May 2006), (Set-2–May 2004)

Sol: Refractive index of core, n1 = 1.55

Refractive index of cladding, n2 = 1.50

Numerical aperture, 5. The numerical aparture of an optical fibre is 0.39. If the difference in the refractive indices of the material of its core and the cladding is 0.05, calculate the refractive index of material of the core.

(Set-1–May 2008), (Set-3–May 2004)

Sol: Numerical aperture, NA = 0.39

The difference in refractive indices Refractive index of the core, n1 = ?

From Equation (1)  Substituting Equation (2) in (3), we get:

3.042 = n2 + 0.05 + n2 = 2n2 + 0.05

n2 = 1.496 n1 = n2 + 0.05 = 1.493 + 0.05 = 1.546.

6. An optical fibre has a core material of refractive index 1.55 and cladding material of refractive index 1.50. The light is launched into it in air. Calculate its numerical aperture.

(Set-4–May 2006), (Set-1–June 2005)

Sol: Refractive index of core, n1 = 1.55

Refractive index of cladding, n2 = 1.50

Numerical aperture, 7. Calculate the numerical aperature and acceptance angle for an optical fibre with core and cladding refractive indices being 1.48 and 1.45, respectively.

(Set-4–May 2007), (Set-4–June 2005)

Sol: Refractive index of core, n1 = 1.48

Refractive index of cladding, n2 = 1.45

Numerical aperture, NA = ?

acceptance angle, θ0 = ? 8. Calculate the refractive indices of core and cladding of an optical fibre with a numerical aperture of 0.33 and their fractional difference of refractive indices being 0.02.

(Set-2–May 2006)

Sol: Refractive index of core, n1 = ?

Refractive index of cladding, n2 = ?

Numerical aperture, NA = 0.33

Fractional difference of refractive index, ∆ = 0.02 9. An optical fibre has a numerical aperture of 0.20 and a cladding refractive index of 1.59. Find the acceptance angle for the fibre in water which has a refractive index of 1.33.

(Set-3–May 2006), (Set-1, Set-2, Set-4–Sept. 2006), (Set-2–May 2007), (Set-2–Sept. 2007)

Sol: Numerical aperture of the fibre, NA = 0.20

Refractive index of cladding, n2 = 1.59

Refractive index of water, n0 = 1.33

Acceptance angle of fibre in water, θ0 = ?  10. A fibre has the core and cladding refractive indices 1.45 and 1.44 respectively. Find the relative refractive index difference.

(Set-4–Sept. 2007)

Sol: Refractive index of core (n1) = 1.45

Refractive index of cladding (n2) = 1.44

Relative refractive index difference (∆) 11. The refractive index of core of step index fibre is 1.50 and the fractional change in refractive index is 4 %. Estimate: (i) refractive index of cladding, (ii) numerical aperture, (iii) acceptance angle in air and (iv) the critical angle at the core-cladding interface.

Sol: (i) The refractive index of the core, n1 = 1.50

The fractional change in refractive index, where n2 = refractive index of cladding (ii) Numerical aperture, (iii) Acceptance angle, (iv) Critical angle,  12. The refractive indices of core and cladding of a step index optical fibre are 1.563 and 1.498, respectively. Calculate: (i) numerical aperture and (ii) angle of acceptance in air.

Sol: Refractive index of core (n1) = 1.563

Refractive index of cladding (n2) = 1.498

1. Numerical aperture (NA) = ? 2. Acceptance angle (θ0) = ? #### Multiple Choice Questions

1. The light sources used in fibre optic communication are. ( )
1. LEDs
2. semiconductor lasers
3. phototransistors
4. both a and b
2. Acceptance angle is defined as the _____ angle of incidence at the endface of an optical fibre, for which the ray can be propagated in the optical fibre is. ( )
1. maximum
2. minimum
3. Either a or b
4. none of the above
3. The core diameter of single mode step index fibre is about: ( )
1. 60 to 70 μm
2. 8 to 10 μm
3. 100 to 250 μm
4. 50 to 200 μm
4. In multimode graded index fibre, light rays travel _____ in different parts of the fibre. ( )
1. at different speeds
2. with same speed
3. both a and b
4. none of the above
5. In optical communication system, the light detector is: ( )
1. Avalanche Photo Diode (APD)
2. Positive Intrinsic Negative (PIN) diode
3. phototransistor
4. Either a or b
6. Optical fibres guides light waves by: ( )
1. interference of waves
2. diffraction of waves
3. polarization of waves
4. by total internal reflection of waves
7. In an optical fibre, if n1 and n2 are the refractive indices of core and cladding, the condition for light propagation through fibre is: ( )
1. n1 = n2
2. n1 > n2
3. n1 < n2
4. none of the above
8. Loss of intensity of light in optical fibre is due to: ( )
1. absorption
2. scattering
3. reflection
4. both a and b
9. If n1 and n2 are the refractive indices of core and cladding, then numerical aperture (NA) of the fibre is: ( )
1. n12n22
2. n22n12
3. 4. 10. By increasing the refractive index of core material, the number of modes of propagation in an optical fibre _____. ( )
1. increases
2. decreases
3. remains same
4. none of the above
11. The life span of optical fibres is expected to be: ( )
1. 40 to 50 years
3. 20 to 30 years
4. less than 10 years
12. Fibre optic sensors are used to monitor: ( )
1. displacement and flow
2. temperature
3. pressure
4. all the above
13. Total internal reflection takes place when the angle of incidence is _____ the critical angle. ( )
1. greater than
2. less than
3. equal to
4. both a and b
14. Numerical aperture represents _____ capacity of a optical fibre. ( )
1. light gathering
2. light dissipation
3. heat dissipation
4. magnetic lines gathering
15. In optical fibres, mode means _____ available for light rays to propagate in the fibre. ( )
1. the number of paths
2. the number of fibre in optical fibre cable
3. the change in refractive index
4. none of the above
16. In multimode step index fibres, the core diameter is _____. ( )
1. 8 to 10 μm
2. 10 to 30 μm
3. 50 to 200 μm
4. 100 to 250 μm
17. In multimode graded index fibre, the core refractive index profile is _____. ( )
1. circularly symmetric
2. non-linear
3. step index
4. none of the above
18. The widely used optical fibre in the world is: ( )
1. multimode step index fibre
3. single mode step index
4. none of the above
19. The acceptance angle is maximum if the critical angle is _____. ( )
1. minimum
2. maximum
3. both a & b
4. none
20. In multimode optical fibre, the core diameter is _____ in single mode fibre. ( )
1. lesser than
2. larger than
3. equal to
4. none
21. Optical fibres are made up with _____ materials. ( )
1. semiconductors
2. metals
3. conductors
4. dielectrics
22. In a reflective type optical fibre, the light rays pass from one end of the fibre to the other end by means of _____. ( )
1. multiple total internal reflections
2. refraction
3. diffraction
4. polarization
23. If the angle of incidence for a ray at the end face of an optical fibre is larger than acceptance angle, then the ray _____. ( )
1. will not propagate in the fibre
2. will propagate in the fibre
3. both a & b
4. none of the above
24. All the light rays which enter at a time into the multimode graded index fibre may arrive at _____. ( )
1. different times at the other end of the fibre
2. same time at the other end of the fibre
3. both a & b
4. none of the above
25. Delay distortion of light pulses in optical fibre is because of: ( )
1. spreading of pulses with time
2. spreading of pulses with wavelength
3. spreading of pulses with refractive index
4. none of the above
26. Optical fibres carry very large information compared to copper cables because of: ( )
1. large thickness of fibre
2. extremely wide bandwidth
3. extremely less band width
4. none

 1. d 2. a 3. b 4. a 5. d 6. d 7. b 8. d 9. c 10. a 11. c 12. d 13. a 14. a 15. a 16. c 17. a 18. c 19. a 20. b 21. d 22. a 23. a 24. b 25. a 26. b

#### Review Questions

1. Explain the advantages of optical fibres in communication.

(Set-3–May 2004)

2. Explain the terms numerical aperture and acceptance angle.

(Set-4–May 2006), (Set-1–June 2005), (Set-2–May 2004)

3. Define acceptance angle and numerical aperture. Obtain an expression for numerical aperture of an optical fibre.

(Set-4–May 2007), (Set-1–May 2006), (Set-4–June 2005)

4. What are the advantages of an optical fibre communication system over the conventional ones?

(Set-4–Sept. 2007), (Set-4–Nov. 2003)

5. Describe the basic elements of a fibre optics communication system with a block diagram.

(Set-4–Nov. 2003)

6. Write a note on the applications of optical fibres.

(Set-1–Sept. 2007), (Set-4–May 2004)

7. Explain how the optical fibres are classified.

(Set-3–Sept. 2008), (Set-1–May 2004)

8. Describe the construction of a typical optical fibre and give the dimensions of the various parts.

(Set-4–May 2007), (Set-1–May 2006), (Set-4–June 2005)

9. With the help of a suitable diagram, explain the principle, construction and working of an optical fibre as a waveguide.

(Set-4–May 2006), (Set-1–June 2005), (Set-2–May 2004)

10. Explain the principle of an optical fibre.

(Set-3–Sept. 2008),(Set-1–May 2004)

11. Derive expressions for the numerical aperture and the fractional change of an optical fibre.

(Set-1–Sept. 2007), (Set-3, Set-4–May 2004)

12. Describe the graded index optical fibres and explain the transmission of signal through it.

(Set-3–Sept. 2007)

13. Derive an expression for the numerical aperture of an optical fibre.

(Set-1–May 2008), (Set-3–Sept. 2006)

14. Explain the advantages of optical communication system.

(Set-1–May 2008)

15. Derive the expressions for (i) acceptance angle and (ii) numerical aperture of an optical fibre.

(Set-2–May 2008), (Set-4-Sept. 2008), (Set-3–Sept. 2006)

16. Describe different types of fibres by giving the refractive index profiles and propagation details.

(Set-2–May 2008), (Set-4-Sept. 2008)

17. What are important features of optical fibres?

(Set-3–May 2008)

18. Describe the communication process using optical fibres.

(Set-3–May 2008)

19. Write the uses of fibre optics in different fields.

(Set-3–May 2008)

20. Distinguish between light propagation in (i) step index optical fibre and graded index optical fibre.

(Set-4–May 2008), (Set-2–May 2006)

21. Write a note on fibre optic medical endoscopy.

(Set-4–May 2008)

22. Define the relative refractive index difference of an optical fibre. Show how it is related to numerical aperture.

(Set-1, Set-3–May 2007)

23. Draw the block diagram of an optical fibre communication system and explain the function of each block.

(Set-1, Set-3–May 2007)

24. Discuss the various advantages of communication with optical fibres over the conventional coaxial cables.

(Set-2–May 2006)

25. Explain the principle behind the functioning of an optical fibre.

(Set-2–Sept. 2007), (Set-2–May 2007), (Set-1, Set-4–Sept. 2006), (Set-3–May 2006)

26. Derive an expression for acceptance angle for an optical fibre. How it is related to numerical aperture?

(Set-2–Sept. 2007), (Set-2–May 2007), (Set-1, Set-4–Sept. 2006), (Set-3–May 2006)

27. What is meant by an acceptance angle and numerical aperture; obtain mathematical expressions for acceptance angle and numerical aperture.

(Set-2–Sept. 2006)

28. What is the principle of optical fibre communication? Explain.

(Set-3–Sept. 2006)

29. Explain the basic principle of an optical fibre.

(Set-3–Sept. 2007), (Set-1–Sept. 2008)

30. What are different losses in optical fibres? Write brief notes on each.

(Set-3–Sept. 2007)

31. Explain the difference between a step index fibre and graded index fibre.

(Set-4–Sept. 2007)

32. Write the applications of fibre optics in medicine and industry.

(Set-1–Sept. 2008)

33. Describe the structure of an optical fibre.

(Set-1–Sept. 2008)

34. Describe the step index fibre and explain the transmission of signal through it.
35. Write short notes on acceptance angle in a fibre.
36. Explain the propagation of light waves through an optical fibre.
37. Draw the block diagram of fibre optic communication system and explain the function of each element in the system.
38. Describe the structure of different types of optical fibres with ray paths.
39. Explain the terms: numerical aperture and acceptance angle of a fibre. Derive expressions for them.
40. Explain the transmission of signal in step index and graded index fibres.
41. Describe optical fibres in communication system.
42. What is the principle of optical fibre? Describe various types of optical fibres.
43. Distinguish between step index and graded index fibres with the help of refractive index profile.
44. What is mode in optical fibre? Distinguish between single mode and multimode step index fibres.
45. Describe the various fibre optic sensor applications.
46. Explain the advantages of optical fibre communications.
47. Write briefly on step and graded index optical fibres and numerical aperture of optical fibres.
48. Write briefly on numerical aperture of optical fibre, step and graded index optical fibres.
49. Write short notes on acceptance angle in optical fibres.
50. Write short notes on refractive index profiles of step-graded index fibres.