Unit-03: Properties of Light https://sites.google.com/a/faculty.muet.edu.pk/abdullatif Department of Telecommunication, MUET UET Jamshoro 1
Refractive index Department of Telecommunication, MUET UET Jamshoro 2
Refractive index The refractive index is the ratio of the speed of light in a vacuum, c, to the speed of light in the medium, v. Since the speed of light in a medium is always less than it is in a vacuum, the refractive index is always greater than one. In air, the value is very close to 1. Department of Telecommunication, MUET UET Jamshoro 3
Refractive index In a homogeneous medium, that is, one in which the refractive index is constant, light travels in a straight line. Only when the light meets a variation or a discontinuity in the refractive index, the light rays will be bent from their initial direction. The light travelling into an optically denser medium (with higher refractive index) would be bent toward the normal, while light entering an optically rarer medium would be bent away from the normal. Department of Telecommunication, MUET UET Jamshoro 4
Refractive index The refractive index varies with the wavelength of light. Department of Telecommunication, MUET UET Jamshoro 5
Refractive indices Department of Telecommunication, MUET UET Jamshoro 6
Optical Fiber Department of Telecommunication, MUET UET Jamshoro 7
Optical Fiber Fiber optics (optical fibers) are long, thin strands of very pure glass about the diameter of a human hair. They are arranged in bundles called optical cables. It has the following parts: Core (n 1 ) - is a cylindrical rod of dielectric material. Light propagates mainly along the core of the fiber. Diameter of core is 8 µm in single mode and 50 µm for multimode fiber. Cladding (n 2 )- Outer optical material surrounding the core that reflects the light back into the core. The index of refraction of the cladding material is less than that of the core material (n 2 < n 1 ). Diameter of cladding is 125 µm Department of Telecommunication, MUET UET Jamshoro 8
Optical Fiber The cladding performs the following functions: Reduces loss of light from the core into the surrounding air Reduces scattering loss at the surface of the core Protects the fiber from absorbing surface contaminants Adds mechanical strength Buffer coating - For extra protection, the cladding is enclosed in an additional layer called the coating or buffer. It is a layer of material used to protect an optical fiber from physical damage and moisture. Diameter of buffer coating is 250 µm. Jacket colors are used to recognize cables easily. For example, yellow color jacket identifies single mode fiber Orange color is used for multimode fiber cable. Aqua colored 50 m cables from Lucent Technologies has 10 G b/s. Department of Telecommunication, MUET UET Jamshoro 9
Optical Fiber SMF and MMF Department of Telecommunication, MUET UET Jamshoro 10
Transmission of Light through Optical Fibers The transmission of light along optical fibers depends not only on the nature of light, but also on the structure of the optical fiber. Two theories are used to describe how light is transmitted along the optical fiber. Ray theory, uses the concepts of light reflection and refraction and treat light as a simple ray. The advantage of the ray approach is that you get a clearer picture of the propagation of light along a fiber. The ray theory is used to approximate the light acceptance and guiding properties of optical fibers. Mode theory, treats light as electromagnetic waves. The mode theory describes the behavior of light within an optical fiber. The mode theory is useful in describing the optical fiber properties of absorption, attenuation, and dispersion. Department of Telecommunication, MUET UET Jamshoro 11
Ray Theory Two types of rays propagate along an optical fiber, meridional rays and skew rays. Meridional rays pass through the axis of the optical fiber. Meridional rays are used to illustrate the basic transmission properties of optical fibers. Skew rays are rays that travel through an optical fiber without passing through its axis. Department of Telecommunication, MUET UET Jamshoro 12
Rays Theory Department of Telecommunication, MUET UET Jamshoro 13
Snell s Law When a ray is incident on the interface between two media of differing refractive indices, refraction takes place. Snell's law defines the relationship between refractive indices and the light ray angles: n sin n sin 1 1 2 2 n n sin sin 1 2 2 1 Department of Telecommunication, MUET UET Jamshoro 14
Principle of Total Internal Reflection When light is incident upon a medium of lesser index of refraction, the ray is bent away from the normal, so the exit angle is greater than the incident angle. Such reflection is commonly called "internal reflection". At some angle of incidence θ 1, the angle of refraction θ 2 is 90 degrees. That angle is termed as critical angle. Critical angle can be defined as the angle of incidence beyond which rays of light entering less denser medium are not refracted but totally reflected. If θ 1 is greater than the critical angle then the ray returns or is refracted back into the high refractive index medium. n2 sin c n Department of Telecommunication, MUET UET Jamshoro 15 1
Total Internal Reflection Department of Telecommunication, MUET UET Jamshoro 16
Total Internal Reflection The light in a fiber-optic cable travels through the core (hallway) by constantly bouncing from the cladding (mirrorlined walls), a principle called Total Internal Reflection. Department of Telecommunication, MUET UET Jamshoro 17
Total Internal Reflection Department of Telecommunication, MUET UET Jamshoro 18
Transmission of light through perfect optical fiber Department of Telecommunication, MUET UET Jamshoro 19
Relative Refractive Index (Δ) It defines the difference in the core and cladding refractive indices. n n n n n 2 2 1 2 1 2 2 1 2 2n1 n1 n1 Department of Telecommunication, MUET UET Jamshoro 20
Relative Refractive Index- example Department of Telecommunication, MUET UET Jamshoro 21
Acceptance Angle The acceptance angle (θ a ) is the largest or maximum incident angle at which a guided ray can be coupled within the fiber. Department of Telecommunication, MUET UET Jamshoro 22
Acceptance Angle Department of Telecommunication, MUET UET Jamshoro 23
Numerical Aperture This defines a relationship between acceptance angle and the refractive indices of three media: core, cladding, and air. This relationship is termed as Numerical Aperture. This is a more generally used term. Department of Telecommunication, MUET UET Jamshoro 24
Numerical Aperture The ray enters the fiber from a medium (air) of refractive index n0, and the fiber core has a refractive index n1, which is slightly greater than the cladding refractive index n2. Using Snell s law: n 0 sin θ 1 = n 1 sin θ 2 (1) Considering the right-angled triangle ABC indicated in Figure (given on previous slide), then: φ = π 2 θ 2 (2) Replacing θ 2 by ϕ, equation (2) becomes n 0 sin θ 1 = n 1 cos φ (3) Using the trigonometrical relationship: sin 2 φ + cos 2 φ = 1 Department of Telecommunication, MUET UET Jamshoro 25
Numerical Aperture Eq. (3) may be written in the form: n 0 sin θ 1 = n 1 1 sin 2 φ 1 2 (4) Consider the limiting case for total internal reflection. For this ϕ becomes equal to critical angle θ c. sin φ c = sin φ = n 2 n 1 (5) In this case, θ 1 also becomes the acceptance angle for the fiber θ a. Combining these, equation (4) becomes: n 0 sin θ a = n 1 2 n 2 2 1 2 (6) Equation (6) relates acceptance angle to refractive indices. Department of Telecommunication, MUET UET Jamshoro 26
Numerical Aperture This equation also serves as the basis for the definition of the important optical fiber parameter, the numerical aperture (NA). The numerical aperture (NA) is a measurement of the ability of an optical fiber to capture light. The NA is also used to define the acceptance cone of an optical fiber. NA = n 0 sin θ a = n 1 2 n 2 2 1 2 Since the NA is often used with the fiber in air where n 0 is unity, it is simply equal to sin ϴ a. Department of Telecommunication, MUET UET Jamshoro 27
Numerical Aperture The NA may also be given in terms of the relative refractive index difference Δ between the core and the cladding which is defined as: n n n n 2 2 1 2 1 2 2 2n1 n1 Combining this equation with the equation: NA n sin a n n 2 2 0 1 2 NA n 1 2 Department of Telecommunication, MUET UET Jamshoro 28
Meridional Rays Meridional rays can be further classified as: Bound Rays Bound rays remain in the core and propagate along the axis of the fiber. Bound rays propagate through the fiber by total internal reflection. Unbound Rays Unbound rays are refracted out of the fiber core. Department of Telecommunication, MUET UET Jamshoro 29
Skew Rays Any ray entering the fiber in a point other than the center of the core is skew ray. Skew rays propagate down the fiber in a helical path The θ as (for skew rays) θ a (meridional rays). Skew rays are often used in the calculation of light acceptance in an optical fiber. Department of Telecommunication, MUET UET Jamshoro 30
Skew Rays The addition of skew rays increases the amount of light capacity of a fiber. In a multimode fiber, most rays are skew rays. The addition of skew rays also increases the amount of loss in a fiber. Skew rays tend to propagate near the edge of the fiber core. It may be observed from Figure (on previous slide) that the helical path traced through the fiber gives a change in direction of 2γ at each reflection, where γ is the angle between the projection of the ray in two dimensions and the radius of the fiber core at the point of reflection. Department of Telecommunication, MUET UET Jamshoro 31
Skew Rays To calculate the acceptance angle for skew ray, consider the Figure given below. Skew ray is incident at point A at an angle θ s to the normal at the fiber end face. Department of Telecommunication, MUET UET Jamshoro 32
Skew Rays The ray is refracted at the air core interface before traveling to the point B in the same plane. The angles of incidence and reflection at the point B are ϕ, which is greater than the critical angle for the core cladding interface. θ is the angle between the ray and a line AT drawn parallel to the core axis. Now cos φ = RBΤ AB = RBΤ BT BTΤ AB cos γ sin θ = cos φ cos γ sin θ = 1 sin 2 1 2 Using limiting condition when ϕ becomes ϕ c i.e. sin φ c = Τ n 2 n1 Department of Telecommunication, MUET UET Jamshoro 33
Skew Rays From this equation: cos γ sin θ cos φ c = 1 n 2 2 sin θ = cos φ c cos γ Using Snell s law at the point A, we can write: n 0 sin θ a = n 1 sin θ Replacing sinθ, we can calculate θ as, sin θ as = n 1 cos φ c n 0 cos γ = n 1 n 0 cos γ 1 n 2 2 n 1 2 1 2 = n 1 2 1 2 1 n 0 cos γ n 1 2 n 2 2 1 2 Replacing n 0 =1 (for air) and n 2 2 1 n 1 2 2 = NA: θ as = sin 1 NA cos γ Department of Telecommunication, MUET UET Jamshoro 34
Example-2.1 A silica optical fiber with a core diameter large enough to be considered by ray theory analysis has a core refractive index of 1.5 and a cladding refractive index of 1.47. Determine: a) Critical angle b) NA c) angle in the air ϴ air Solution: ϴ c =sin -1 (n 2 /n 1 )= sin -1 (1.47/1.5)=78.5 0. NA n n ϴ air =Sin -1 NA=17.4 0 2 2 1 2 2 2 NA (1.5) (1.47) 0.3 Department of Telecommunication, MUET UET Jamshoro 35
Example-2.3 An optical fiber in air has an NA of 0.4. Compare the acceptance angle for meridional rays with that for skew rays which change direction by 100 at each reflection. Solution: The acceptance angle for meridional rays: as NA 23.6 1 1 sin ( ) sin (0.4) The skew rays change direction by 100 at each reflection, therefore γ = 50. Using eq: 1 NA 1 0.4 as sin sin cos cos 50 38.5 Department of Telecommunication, MUET UET Jamshoro 36