Glossary entry

Acceptance angle

The maximum incidence angle at which light can enter an optical fiber or waveguide and still be guided. Geometrically related to the numerical aperture.

For a step-index fiber with core index $n_\text{core}$ and cladding index $n_\text{clad}$ , light enters through the end facet and must undergo total internal reflection at the core-cladding interface to be guided. The acceptance condition produces a maximum allowed incidence angle:

\sin\theta_\text{max} \;=\; \sqrt{n_\text{core}^2 - n_\text{clad}^2} \;=\; \text{NA},

with $\theta_\text{max}$ measured in the external medium (typically air). The acceptance cone is full-angle $2\theta_\text{max}$ centered on the fiber axis.

This defines the numerical aperture of the fiber.

Acceptance angle vs critical angle. The two concepts are linked but distinct:

Critical angle is the internal angle at the core-cladding interface (measured from the interface normal)
Acceptance angle is the external angle at the entrance facet (measured from the fiber axis)

The relationship: a ray entering at the maximum acceptance angle, refracting at the facet, and propagating internally will strike the core-cladding interface at exactly the critical angle. Any larger external angle refracts to an internal angle below the critical angle and escapes.

Fiber type	Cladding	NA	Acceptance half-angle
Single-mode telecom (SMF-28)	$\Delta = 0.36$ %	0.14	8°
Multimode 50/125	$\Delta = 1$ %	0.20	12°
Multimode 62.5/125	$\Delta = 2$ %	0.275	16°
High-NA double-clad	$\Delta =$ large	0.46	27°

Practical implications. The acceptance cone determines:

Coupling efficiency from any source — only light within the cone can be guided, so smaller acceptance cones require better collimation or lensing
Required lens NA for efficient coupling — lens output NA should match or slightly exceed fiber NA
Light spreading at fiber output — light emerging from a fiber spreads into an output cone of the same angle (reciprocity)
Bend-loss tolerance — fibers with larger NA tolerate tighter bends because the index contrast holds more strongly against the geometric distortion

The acceptance angle calculation assumes a step-index fiber with abrupt core-cladding boundary. Graded-index fibers have an effective acceptance angle that depends on radial position — light entering the center of the fiber sees the full NA, while light entering near the cladding sees a smaller effective NA because of the graded refractive index profile.

For PIC edge couplers and waveguide facets, an analogous acceptance condition applies but the analysis is mode-specific rather than ray-based.