Fiber Optic Parameters Calculator
Compute the numerical aperture, acceptance cone half-angle, or critical angle of an optical fiber from its core and cladding refractive indices. Used by fiber installers, photonics students, and optical engineers.
About this calculator
An optical fiber guides light by total internal reflection at the core-cladding interface. The numerical aperture (NA) quantifies how wide a cone of light the fiber will accept and propagate. The formula is: NA = √(n_core² − n_cladding²) / n_medium, where n_core and n_cladding are the refractive indices of the fiber core and cladding respectively, and n_medium is the refractive index of the surrounding medium (1.0 for air). The acceptance angle (half-angle of the acceptance cone) is: θ_accept = arcsin(NA). The critical angle for total internal reflection inside the fiber is: θ_c = arcsin(n_cladding / n_core). A higher NA means the fiber collects more light but typically supports more modes and exhibits greater modal dispersion, limiting bandwidth over long distances. Single-mode fibers have NA values around 0.10–0.14, while multimode fibers range from 0.2 to 0.5.
How to use
Consider a step-index multimode fiber with n_core = 1.48, n_cladding = 1.46, and n_medium = 1.0 (air). Step 1: NA = √(1.48² − 1.46²) / 1.0 = √(2.1904 − 2.1316) = √0.0588 ≈ 0.2425. Step 2: Acceptance angle = arcsin(0.2425) ≈ 14.03°. Step 3: Critical angle = arcsin(1.46 / 1.48) = arcsin(0.9865) ≈ 80.5°. Enter n_core = 1.48, n_cladding = 1.46, and n_medium = 1.0, then select your desired output — the calculator handles all three modes.
Frequently asked questions
What does numerical aperture mean for an optical fiber and why does it matter?
The numerical aperture is a dimensionless measure of a fiber's light-gathering ability and the range of angles over which it accepts light efficiently. A higher NA allows you to couple light from broader sources more easily — useful in multimode applications like medical imaging and short-range data links. However, higher NA also means more modes propagate, increasing modal dispersion and reducing bandwidth over long distances. In single-mode telecommunications fiber, a low NA is deliberately chosen to restrict the fiber to guiding only one mode, enabling very high bandwidths over kilometers.
How does the refractive index difference between core and cladding affect fiber performance?
The fractional refractive index difference Δ = (n_core² − n_cladding²) / (2 n_core²) drives almost every key fiber parameter. A larger Δ gives a higher NA, a wider acceptance cone, stronger light confinement, and more propagating modes — but it also increases modal dispersion and can make the fiber more sensitive to bending losses. Conversely, a very small Δ (typically 0.003 for single-mode telecom fiber) confines light to a single mode, minimizes dispersion, but makes coupling alignment far more critical. Choosing the right Δ is a fundamental trade-off in fiber design.
Why does the external medium refractive index appear in the numerical aperture formula?
The NA formula describes how a ray in the external medium enters the fiber end-face and couples into the guided core modes. Because Snell's law at the fiber entrance involves n_medium × sin θ_accept = NA_fiber, a denser external medium (n_medium > 1) effectively increases the angle from which light can be launched into a fiber with a given intrinsic NA. In practice most fibers are used in air (n_medium = 1.0), but fiber sensors immersed in liquids or integrated with solid-state detectors may have n_medium significantly greater than 1, changing the effective acceptance angle.