Optical fiber design – Refractive index requirement for total internal reflection In a step-index optical fiber, what must be the relationship between the refractive indices of the cladding and the core for guided propagation?

Introduction:
Total internal reflection confines light within an optical fiber core. The refractive index step between core and cladding provides the waveguide action. This question tests the fundamental requirement for guiding.

Given Data / Assumptions:

• Step-index fiber with core index n1 and cladding index n2.
• Launch from air; numerical aperture depends on n1 and n2.
• Negligible absorption and scattering for the concept discussion.

Concept / Approach:

Total internal reflection requires light to travel from a higher-index medium to a lower-index medium at the core–cladding boundary. Therefore, n1 > n2. This ensures that rays hitting the interface above the critical angle are reflected back into the core, establishing guided modes whose effective indices lie between n1 and n2.

Step-by-Step Solution:

Verification / Alternative check:

Mode theory shows axial propagation constants β satisfying n2 k0 < β < n1 k0, only possible when n1 > n2.

Why Other Options Are Wrong:

Equal or higher cladding index would leak light; specifying “nearly 1” or “very low” ignores the necessary relation to the core index.

Common Pitfalls:

Confusing the air index with cladding index; assuming high numerical aperture requires extreme n2 values (it only requires a suitable difference n1 − n2).

Final Answer:

cladding index less than that of core.