In single-mode optical fiber design, the core diameter is approximately what multiple of the optical wavelength carried in the fiber?

Introduction / Context:
Single-mode fibers guide only the fundamental mode by using a small core diameter relative to the operating wavelength. Understanding the approximate relationship between core size and wavelength helps explain why single-mode fibers use cores near 8–10 micrometres for common telecom wavelengths around 1.3–1.55 micrometres. This question asks for the appropriate order-of-magnitude multiple.

Given Data / Assumptions:

• Telecom wavelengths: roughly 1.3 μm or 1.55 μm.
• Typical single-mode core diameters: roughly 8–10 μm (mode field diameter ~9–10.5 μm).
• We want an approximate multiple, not an exact formula.

Concept / Approach:
The V-number (normalized frequency) criterion governs single-mode operation: V = (2 * pi * a / λ) * NA, and single-mode occurs when V < 2.405. For typical refractive index profiles and numerical apertures used in telecom fibers, achieving V near the cutoff yields core radii a that correspond to core diameters on the order of ~8–10 μm at 1.3–1.55 μm wavelengths—roughly 6–10 times the wavelength. Therefore, “about 10 times the wavelength” is a reasonable, rounded statement that matches industry practice.

Step-by-Step Solution:

Verification / Alternative check:
ITU-T G.652 single-mode fibers list mode field diameters near 9–10.5 μm at 1.31 μm and 1.55 μm, reinforcing the “roughly ten times” characterization in common teaching texts.

Why Other Options Are Wrong:

• 10× fiber radius: nonsensical; radius vs diameter mismatch.
• 7 times the light: grammatically incorrect and imprecise.
• 3× wavelength: far too small for standard single-mode telecom fiber cores.
• None of the above: invalid because an acceptable approximation is provided.

Common Pitfalls:
Treating the multiple as exact rather than an order-of-magnitude rule; confusing core diameter with cladding diameter (usually 125 μm for standard fibers).

Final Answer:
About 10 times the wavelength of the light carried in the fiber.