JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III OPTOELECTRONICS AND LASER INSTRUMENTATION Previous Question Paper (February/March - 2022 - R18)

The Numerical Aperture (NA) is a dimensionless measure of the light-gathering capacity of an optical fiber. It defines the maximum angle at which light entering the fiber core can be successfully propagated through total internal reflection.

Consider a light ray entering the fiber core of refractive index n1 from air (n0 = 1) at an incident angle θ. The ray refracts into the core at an angle φ and strikes the core-cladding interface at an angle α. For total internal reflection, α must be greater than the critical angle θc, where sin(θc) = n2/n1 (n2 is the cladding refractive index).

From Snell's Law at the air-core interface: 1 sin(θ) = n1 sin(φ). Since φ = 90 - α, we have sin(θ) = n1 cos(α). Using the identity cos(α) = sqrt(1 - sin²(α)), we get sin(θ) = n1 sqrt(1 - sin²(α)). At the limit of total internal reflection, sin(α) = n2/n1. Substituting this:

This value represents the sine of the acceptance angle, defining the cone of light that the fiber can accept.

Optical fibers are primarily classified based on the refractive index profile and the number of modes of light they propagate: Step-index single-mode fiber, Step-index multi-mode fiber, and Graded-index multi-mode fiber.

1. Step-index Single-mode Fiber: This fiber has a very small core diameter (typically 8-10 µm) and a uniform refractive index. Because the core is so small, it allows only one mode of light to propagate along the axis. This eliminates modal dispersion, making it ideal for long-distance, high-bandwidth communication.

2. Graded-index Multi-mode Fiber: In this fiber, the refractive index of the core decreases parabolically from the center toward the cladding. This design causes light rays traveling longer paths in the outer regions of the core to travel faster than those near the axis. This equalization of propagation time significantly reduces modal dispersion compared to step-index multi-mode fibers, allowing for higher data rates over medium distances.