Physics
Total Internal Reflection in Optical Fibre
Total internal reflection in optical fiber occurs when light traveling within the core of the fiber strikes the boundary with the cladding at an angle greater than the critical angle. This causes the light to be completely reflected back into the core, allowing it to propagate along the fiber with minimal loss. This phenomenon is essential for the transmission of light signals in optical communication systems.
Written by Perlego with AI-assistance
Related key terms
1 of 5
12 Key excerpts on "Total Internal Reflection in Optical Fibre"
eBook - PDFOptical Fiber Communications
Principles and Applications
- T. L. Singal(Author)
- 2017(Publication Date)
- Cambridge University Press(Publisher)
The light rays (optical signals) are launched into the cylindrical fiber which can be automatically guided over long distance by an optical phenomenon known as total internal reflection. 2.2.1 Total Internal Reflection Definition of total internal reflection. When a ray (or beam) of light travels from a medium with a higher refractive index (such as fiber core) to another medium with a lower refractive index (such Facts to Know 46 Optical Fiber Communications as fiber cladding) and it happens to strike (incident) the core–cladding intersection at more than the known critical angle of incidence (at which the angle of refraction is 90°), then total light will be reflected back to the medium of incidence (i.e., the fiber core). This particular phenomenon is known as Total Internal Reflection. Reiterating that when an incident light ray strikes the intersection of two different materials (or same materials but having different index of refraction) at an incidence angle which is exactly equal to the critical angle of incidence, then the angle of refraction in the second medium is exactly 90° (in other words, the refracted ray travels along the line of intersection of two materials). This implies that when the angle of refraction in the second medium happens to be 90° or more, the light ray is not allowed to penetrate it (provided the second medium is relatively less dense). The refracted ray, in fact, is reflected in the same material. In such circumstances we say that the phenomenon of total internal reflection has taken place at the intersection of two mediums with the resulting angle of reflection being exactly equal to the angle of incidence. Note : The whole concept of optical fiber communications is based on the fundamental principle of total internal reflection. Fig. 2.6 illustrates the source end of a fiber cable and a light ray propagating into and then down the fiber length, depicting the basic principle of total internal reflection.
eBook - PDF- Sam Beddar, Luc Beaulieu(Authors)
- 2018(Publication Date)
- CRC Press(Publisher)
Basic principles and theory 38 Scintillation dosimetry 3.2 BASIC PRINCIPLES OF OPTICAL FIBER 3.2.1 PRINCIPLE OF LIGHT TRANSMISSION IN OPTICAL FIBER As a dielectric waveguide, an optical fiber can transmit light signals from a light source to a light-measuring device at a long distance using total internal reflection. Under the condition of total internal reflection, light can be reflected at a dielectric interface region between two transparent media that have different refractive indices, without any reflectors. Here, the ray of light must be incident on a boundary from the medium with a high refractive index to another with a low refractive index. If a ray of light transmits with a certain incidence angle ( θ 1 ) that is less than the critical angle ( θ c ) from medium 1 with a high refractive index ( n 1 ) to medium 2 with a low refractive index ( n 2 ), a portion of light will be reflected back to medium 1 with a reflection angle ( θ 1 ), and another portion of light will be refracted into medium 2 with a refraction angle ( θ 2 ), as shown in Figure 3.1a. The relationship between the refractive index and the angle of light is expressed by Snell’s law [1,2]: n n 1 2 sin sin θ θ 1 2 nobreakspace = (3.1) Here, the refractive index ( n ) is the ratio of the velocity of light in a vacuum ( c ) to its velocity in a specific medium ( v ) and is given by the following relation: n c v = (3.2) From Equation 3.2, the velocity of light slows down according to the increase of the refractive index of the medium that the light is traveling in, and Equation 3.1 can be changed using Equation 3.2 as follows: sin sin nobreakspacenobreakspacenobreakspace θ θ 2 1 = = n n V V 1 2 2 1 (3.3) When the incidence angle ( θ 1 ) is increased to the critical angle ( θ c ), the refractive angle ( θ 2 ) reaches 90 ° , as shown in Figure 3.1b and thereby, a ray of light travels along the interface region between two contacted media.
eBook - PDF- Jerry D. Gibson(Author)
- 2018(Publication Date)
- CRC Press(Publisher)
Beyond the critical angle, there is total internal reflection. cladding n 2 n 1 core 2a 50 µ m reflected ray incident ray reflected incident n 1 n 2 n 1 n 2 refracted ray decaying θ 1 θ 1 θ 2 n 2 n 1 θ 1 θ c θ 2 90 ° n 2 n 1 n 1 sin θ 1 n 2 sin θ 2 = Optical Fibers and Lightwave Propagation 45 -3 reflection occurs (internal to the denser medium in which the light originated), and the escape of the light into the less dense medium has been thwarted. There is more to the process of total internal reflection at a planar boundary than merely reflection from the interface. Although the light does not leak into the less dense medium and thereby get trans-mitted outward, it does seep across the interface and propagate, but only parallel to that interface surface [Diament, 1990]. In the direction normal to the interface, there is no propagation on the less dense side of the surface but the strength of the light that appears there decays exponentially. The spatial rate of decay increases with the angle of incidence, beyond the critical angle at which total internal reflection begins. If the decay is sufficiently strong, the light that seeps across is effectively constrained to a thin layer beyond the interface and propagates along it, while the light left behind is reflected back into the denser region with its original strength. The reflection coefficient is 100%. There is undiminished optical power flow along the reflected ray in the denser medium, but only storage of optical energy in the light that seeps across the interface into the less dense region. Much the same process occurs along the curved, cylindrical interface between the core and cladding of the optical fiber. When the light strikes this interface at a sufficiently high grazing angle, total internal reflection occurs, keeping the optical power propagating at an angle within the core and along the axial direction in the cladding.
eBook - PDF- Barry Elliott, Mike Gilmore(Authors)
- 2001(Publication Date)
- Newnes(Publisher)
If a light ray X originates within the base material it will be refracted or bent at the interface. The direction in which the light is refracted is dependent upon the indices of the two materials. If n 1 is greater than n 2 , then the ray X is refracted away from the normal whereas if n 1 is less than n 2 , then the light is refracted towards the normal. Refraction is governed by equation (2.3): s s i i n n r i = n n 2 1 (2.3) When applying this equation to optical fiber then the case of n 1 greater than n 2 should be investigated. Light is refracted away from the normal. As the angle of incidence ( i ) increases so does the angle of refraction ( r ). Figure 2.3(b) shows this effect. However, the angle of refraction cannot exceed 90°, for which sin r is unity. At this point the process of refraction undergoes an important change. Light is no longer refracted out of the base medium but instead it is reflected back into the base medium itself. The angle of incidence at which this effect takes place is known as the critical angle, denoted by c , expressed in equation (2.4): sin c = n n 2 1 (2.4) For all angles of incidence greater than the critical angle the light will be reflected back into the base medium due to this effect, which is called total internal reflection. The two key features of total internal reflection are that: • The angle of incidence = the angle of reflection. • There is no loss of radiated power at the reflection. This, put more simply, means that there is no loss of light at the interface and that, in theory at least, total internal reflection could take place indefinitely. Figure 2.3 (c) shows the effect and the relevant equations. Before passing on to optical fiber and its basic theory it is useful to discuss a further type of reflection, Fresnel reflection. Fresnel reflection takes place where refraction is involved, i.e. where light travels across the interface between two materials having different refractive indices.
eBook - PDF- David Bailey, Edwin Wright(Authors)
- 2003(Publication Date)
- Newnes(Publisher)
This is illustrated in Figure 3.6. Refracted Refracted 9c = Critical angle 9 j = Angle of incidence 9p = Angle of reflection Reflected Figure 3.6 Illustration of critical angle The critical angle (9c) is given by: (N ^ (9c) = arc sin —^ 48 Practical Fiber Optics where total internal reflection occurs, the angle of incidence equals the angle of reflection. 3.1.6 External reflection When a light ray is traveling in a medium and strikes an interface with a denser medium at greater than the critical angle, the same effect occurs as internal reflection but to a lesser degree. This is referred to as external reflection. Total external reflection only occurs when the angle of incidence equals 90^. 3.1.7 Construction of an optical fiber An optical fiber consists of a tube of glass constructed of a number of layers of glass, which when looked at in profile, appear to have a number of concentric rings. Each layer (or ring) of glass has a different refractive index. From the previous discussion, it can be seen that to send light down the center of these concentric glass tubes, it is a requirement that total internal reflection occurs. This will duct the light through the fiber. To achieve total internal reflection the outer glass rings require a lower refractive index than the inner glass tube in which the light is traveling. Figure 3.7 illustrates the construction of a typical optical fiber. The cladding diameter and sheath diameter illustrated in this figure, are accepted as standard for most fibers used world-wide, with the core diameter and refractive indices varying depending on the type of fiber (discussed in the following sections).
eBook - PDF- Ray Tricker(Author)
- 2002(Publication Date)
- Newnes(Publisher)
46 Optoelectronics and Fiber Optic Technology 2.5 Critical angle If a situation is reached when the angle of refraction is 90 degrees, there is only a residual refracted ray grazing along the boundary between the two media, and most of the light is internally reflected. The angle of incidence for an angle of refraction of 90 degrees is called the critical angle. When the angle of incidence is greater than the critical angle, the ray is totally internally reflected, as it is clearly impossible for any light to escape from inside the glass. The critical angle for a ray of light emerging from glass into air is approximately 42 degrees. This is the principle on which all optical fibers work, since the light pulses passing along such a fiber have a high angle of incidence on the walls of the fiber, and so are unable to escape from it. Note: The high refractive index of diamond gives it a very low critical angle (24 degrees). This means that light is reflected internally many times before it can escape from a well-cut diamond, and can then come out in any direction. This is why diamonds sparkle. By encasing the glass tubes inside a cladding whose refractive index is only slightly lower than the refractive index of the glass (see Figure 2.10), the critical angle- and hence any dispersion loss (see section 2.14) - is reduced. This, therefore, is the basic principle behind the use of optical fibers and optoelectronics, and is covered by the following three rules: 1 When light propagates, in a glass of refractive index n, it moves by a factor of n more slowly than in free space. Figure 2.10 Critical angle for a tube encased in cladding with only a slightly lower refractive index than the critical angle Theory 47 2 If light emerging from a glass with a high refractive index is incident on a material with a lower refractive index, it changes direction provided it strikes the interface at a steep angle. If the angle of incidence is shallower than the critical angle, TIR occurs.
eBook - PDFColor Imaging
Fundamentals and Applications
- Erik Reinhard, Erum Arif Khan, Ahmet Oguz Akyuz, Garrett Johnson(Authors)
- 2008(Publication Date)
- A K Peters/CRC Press(Publisher)
For angles of incidence larger than θ c , the wave will not refract but will only reflect. This phenomenon is called total reflection , or sometimes total internal reflection , and is illustrated in Figure 2.18. It can be demonstrated by punching a hole in a plastic bottle and draining water through it. By aligning a laser with the opening in the bottle and adding a drop of milk (to make the laser beam visible), total internal reflection such as that seen in Figure 2.19 can be ob-tained. The light stays within the water stream through multiple reflections. The transmittance of light through strands of fiber, known as fiberoptics, works on the same principle (Figure 2.20) . While Snell’s law predicts the angles of reflection and transmission, it does not give insight into the amplitude of the reflected and refracted fields, E and B , respectively. To evaluate these amplitudes, we first need to look at the boundary conditions related to the interface between the two media, which are most easily evaluated by means of Maxwell’s equations in integral form. The components of D and B normal to the boundary are assessed first, followed by the tangential components of these fields. 6 n -n θ i θ t s (t) s (r) s (i) Medium 1 Medium 2 x z z=0 θ c θ r θ r θ i s (i) s (r) θ < θ i c θ > θ i c : Reflection + Refraction : Total Reflection Figure 2.18. Geometry associated with total reflection. 6 As D = ε E , the analysis is equivalent. 2.5. Reflection and Refraction 53 Figure 2.19. A stream of water exits a plastic bottle. Coming from the right, a laser beam enters the bottle and exits through the same hole as the water. Multiple reflections inside the stream of water are visible, essentially keeping the light trapped inside the stream. Figure 2.20. Fiberoptic strands transmitting light with very little loss of energy due to total internal reflection inside the strands.
eBook - PDF- J.P Goure, I Verrier(Authors)
- 2016(Publication Date)
- CRC Press(Publisher)
(This can be verified by calculating the Poynting vector in the second medium: its average is zero). There is no light actually transmitted into the second medium. The light is said to be totally internally reflected . For all angles of incidence greater than this critical angle , total internal reflection will occur. This critical angle occurs for the angle of incidence at which the transmitted ray is refracted along the surface of the interface (the case illustrated by ray 2). Setting the transmission angle equal to 90 8 , the critical angle y ca corresponding to y 2 , is found from the relationship: sin y ca ¼ n 0 = n ð 1 : 5 Þ To understand the behaviour of light rays at the interface, let us talk in terms of wave propagation. The incident ray is associated with an electromagnetic wave of three vector components ( E 0 , H 0 , k 0 ). k 0 is the propagation vector in the medium of refractive index n 0 and the lines of force corresponding to k 0 are represented by the ray fj k 0 j ¼ 2 p n 0 = l ¼ o = v 0 g . E 0 and H 0 are the electric and magnetic vectors in the same medium. Figure 1.3. Illustration of total internal reflection for ray 3 (ray 1 is transmitted). 4 Optical fibre and propagation In the general case, the propagation vector k 0 (or the incident ray) is not necessarily in a direction perpendicular to the interface plane. This ray is said to be at oblique incidence. So the electrical field vector E 0 is not always in the plane including the propagation vector k 0 and the direction perpendicular to the interface, named the incidence plane ( x, z ) and represented on Figure 1.2. To see the behaviour of electrical field E 0 at the air-glass interface, E 0 has to be decomposed into two parts; one component in the incidence plane ( x, z ) which will be noted E P and one component perpendicular to the incidence plane ( x, y ) noted E N .
- Pascal Richet(Author)
- 2021(Publication Date)
- Wiley-American Ceramic Society(Publisher)
Figure 4 .(a) Total internal reflection, single/multi/and GI fiber designs, (b) electromagnetic modes, and (c) schematic designs of photonic crystal fiber and MOF.Figure 4Source: Reprinted with permission from [5 ].2.2.1 Conventional Core–Clad Optical Fibers
As noted above, in the ray‐optic view, optical fibers guide light via total internal reflection whereby the light is confined in the high‐index core, which is surrounded by a lower‐refractive index cladding. Under this condition, i.e. light incident from a high‐index region into a lower‐index region, Snell's law for light refraction is violated when the angle of incidence exceeds a critical angle (given by sin−1 (nclad /ncore ), where nclad is the refractive index of the clad and ncore is the refractive index of the core, and reflection, instead of refraction, occurs (Figure 4 a). The index difference between core and clad need not be large and actually is one of the design parameters that define the behavior of the resultant waveguide.For simple descriptions, the ray‐optic picture generally suffices. For more sophisticated designs, however, light is more correctly described as a wave, and the aforementioned ray‐optic construction is replaced with a wave‐optic formalism in which electromagnetic modes are confined and allowed to propagate within a higher refractive index core coaxially surrounded by a lower‐refractive index cladding. In the wave‐optic perspective, the transverse components of the light waves constructively and destructively interfere across the core, influenced by the cladding, yielding stable propagating fiber modes. Some of the light power inevitably extends into the cladding: this component is called the evanescent field. The exact distribution of these modes depends on the core size, refractive index contrast between core and clad (defined by the numerical aperture, NA = [ncore 2 − nclad 2 ]1/2 ), the wavelength of light, and the cross‐sectional geometry of the core; i.e. whether rectangular, circular, elliptical, etc. Thorough reviews of conventional core/clad optical fiber designs are given in [5 , 11
eBook - PDF- William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
Special minute optical filters inserted at the end of the fiber bundle have the capacity to image the interior of organs located tens of microns below the surface without cutting the surface—an area known as nonintrusive diagnostics. This is particularly useful for determining the extent of cancers in the stomach and bowel. In another type of application, optical fibers are commonly used to carry signals for telephone conversations and internet communications. Extensive optical fiber cables have been placed on the ocean floor and underground to enable optical communications. Optical fiber communication systems offer several advantages over electrical (copper)-based systems, particularly for long distances. The fibers can be made so transparent that light can travel many kilometers before it becomes dim enough to require amplification—much superior to copper conductors. This property of optical fibers is called low loss. Lasers emit light with characteristics that allow far more conversations in one fiber than are possible with electric signals on a single conductor. This property of optical fibers is called high bandwidth. Optical signals in one fiber do not produce undesirable effects in other adjacent fibers. This property of optical fibers is called reduced crosstalk. We shall explore the unique characteristics of laser radiation in a later chapter. Corner Reflectors and Diamonds Corner reflectors (The Law of Reflection) are perfectly efficient when the conditions for total internal reflection are satisfied. With common materials, it is easy to obtain a critical angle that is less than 45°. One use of these perfect mirrors is in binoculars, as shown in Figure 1.18. Another use is in periscopes found in submarines. 22 Chapter 1 | The Nature of Light This OpenStax book is available for free at http://cnx.org/content/col12067/1.4 Figure 1.18 These binoculars employ corner reflectors (prisms) with total internal reflection to get light to the observer’s eyes.
eBook - PDFFiber Lasers
Basics, Technology, and Applications
- Liang Dong, Bryce Samson(Authors)
- 2016(Publication Date)
- CRC Press(Publisher)
For single-mode opti- cal fibers, the core refractive index n co is only slightly higher than the cladding refractive index n cl . A useful parameter is the numerical aperture (NA), which is closely related to the acceptance angle θ a of the acceptance cone illustrated in Figure 2.2. ( ) = - = θ n n n NA sin co 2 cl 2 0 a (2.1) n 0 is the refractive index of the medium outside the fiber and is usually 1 for air. Light guidance in an optical fiber can be easily understood by visualizing total internal reflection as illustrated in Figure 2.2. Ray 1, within the acceptance cone (dashed line), first enters the core and then reflects off the core and cladding boundary at an incident angle θ larger than the critical angle for total internal reflection. Ray 1 experiences total internal reflection with no loss at each reflection and is, therefore, trapped in the core. Ray 2 outside the acceptance cone (dotted line) experiences loss at each reflec- tion at the core–cladding boundary due to the power carried by the refracted beam into the cladding. Its power is continuously radiated away from the core at each reflection. Another very useful fiber parameter is normalized frequency V defined at vacuum wavelength λ with corresponding vacuum wave number k as = ρ = π λ ρ V k NA 2 NA (2.2) 10 Fiber Lasers: Basics, Technology, and Applications The normalized frequency V takes account of both the dimensional and refractive index scalability of an optical waveguide and describes the modal properties of any optical fiber at a given V value. Its significance will be better appreciated when we find waveguide solutions later on in this chapter. If many rays share the same forward propagation constant β, they would travel together in phase as a guided mode while maintaining the same transverse field distribution along the fiber.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 3 Basic Concepts in Optics 1. Refractive index Refraction of light at the interface between two media The refractive index or index of refraction of a substance is a measure of the speed of light in that substance. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium. The velocity at which light travels in vacuum is a physical constant, and the fastest speed at which energy or information can be transferred. However, light travels slower through any given material, or medium, that is not vacuum. A simplified, mathematical description of refractive index is as follows: n = velocity of light in a vacuum / velocity of light in medium Hence, the refractive index of water is 1.33, meaning that light travels 1.33 times as fast in a vacuum than it does in water. ________________________ WORLD TECHNOLOGIES ________________________ As light exits a medium, such as air, water or glass, it may also change its propagation direction in proportion to the refractive index. By measuring the angle of incidence and angle of refraction of the light beam, the refractive index n can be determined. Refractive index of materials varies with the frequency of radiated light. This results in a slightly different refractive index for each color. The cited values of refractive indexes, such as 1.33 for water, are taken for yellow light of a sodium source which has the wavelength of 589.3 nanometers. Definitions The refractive index, n , of a medium is defined as the ratio of the speed, c , of a wave phenomenon such as light or sound in a reference medium to the phase speed, v p , of the wave in the medium in question: It is most commonly used in the context of light with vacuum as a reference medium, although historically other reference media (e.g. air at a standardized pressure and temperature) have been common.
Index pages curate the most relevant extracts from our library of academic textbooks. They’ve been created using an in-house natural language model (NLM), each adding context and meaning to key research topics.
