In a step-index fiber, the index of refraction undergoes a...

In a step-index fiber, the index of refraction undergoes a discontinuity (jump) at the core-cladding interface, as shown in the figure. Infrared light with wavelength $1550 \mathrm{nm}$ propagates through such a step index fiber through total internal reflection at the core-cladding interface. The index of refraction for the core at $1550 \mathrm{nm}$ is $n_{\text {core }}=1.48$ If the maximum angle $\alpha_{\max }$ at which light can be coupled into the fiber such that no light will leak into the cladding is $\alpha_{\max }=14.033^{\circ}$, calculate the percent difference between the index of refraction of the core and the index of refraction of the cladding.

In a step-index fiber, the index of refraction undergoes a discontinuity (jump) at the core-cladding interface, as shown in the figure. Infrared light with wavelength $1550 \mathrm{nm}$ propagates through such a step index fiber through total internal reflection at the core-cladding interface. The index of refraction for the core at $1550 \mathrm{nm}$ is $n_{\text {core }}=1.48$ If the maximum angle $\alpha_{\max }$ at which light can be coupled into the fiber such that no light will leak into the cladding is $\alpha_{\max }=14.033^{\circ}$,
calculate the percent difference between the index of refraction of the core and the index of refraction of the cladding.

Key Concepts

Percent Difference Calculation

Calculating the percent difference between the refractive indices of the core and cladding involves determining the relative change from the core's index to the cladding's index. This calculation is typically done by taking the difference between the two indices, dividing by the core's index, and multiplying by 100 percent. This metric helps quantify how much the cladding’s refractive index deviates from that of the core, which in turn influences the fiber’s light-guiding properties.

Numerical Aperture and Acceptance Angle

The numerical aperture (NA) of an optical fiber quantifies its ability to collect light, based on the refractive index difference between the core and cladding and the maximum acceptance angle at which light can enter the fiber. The NA is related to the sine of the maximum coupling angle and plays a central role in linking the fiber’s geometry with its optical performance.

Total Internal Reflection

Total internal reflection is the phenomenon where light is completely reflected at the boundary between two media when it strikes the interface at an angle greater than the critical angle. This is key in optical fibers because it allows light to be guided along the core without leaking into the cladding, provided the refractive index of the core is sufficiently higher than that of the cladding.

Refractive Index

The refractive index is a measure of how much light slows down as it travels through a medium compared to the speed of light in a vacuum. In the context of optical fibers, the difference in refractive index between the core and cladding determines the conditions for light propagation and confinement, affecting properties such as the numerical aperture and acceptance angle.

Step-index Fiber

A step-index fiber is an optical fiber that has a uniform refractive index in the core and a lower, constant refractive index in the cladding, with an abrupt change at the core–cladding boundary. This design is critical for directing light along the fiber using the principle of total internal reflection, which depends on the difference in refractive indices between the core and the cladding.

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