Lensed fiber

A lensed fiber has a micro-lens at its tip that focuses the divergent beam emerging from the fiber core down to a spot smaller than the fiber's mode field. This focused spot can then be coupled efficiently to small-mode targets — chip waveguide tips, laser facets — that have mode-field diameters much smaller than the bare fiber.

Why bare fiber doesn't work for chip coupling. Standard SMF-28 has mode field diameter (MFD) of 10.4 μm at 1550 nm. A typical silicon photonic inverse taper tip has effective mode diameter $\sim 2 - 3$ μm. Coupling a 10.4 μm beam to a 2.5 μm target produces 8 – 10 dB mode-mismatch loss. A lensed fiber that produces a 2.5 μm spot can match the target precisely, dropping loss to $< 1$ dB.

Lens geometries.

Specifying a lensed fiber. Standard parameters:

• Working distance (WD): distance from fiber tip to spot waist; usually 5 – 30 μm
• Spot diameter at waist: 2 – 8 μm typical
• Numerical aperture: 0.15 – 0.45, derived from spot diameter and working distance
• Polarization-maintaining or single-mode: PM lensed fibers are available for polarization-sensitive measurements
• Anti-reflection coating: typically 0.25% or 1% AR at the design wavelength

Tradeoffs in lens design. Smaller spot $\rightarrow$ tighter focus + higher coupling to small targets, but:

• Shorter Rayleigh range $\rightarrow$ tighter Z-position tolerance ($\pm 2$ μm typical for 2.5 μm spot lensed fiber, vs $\pm 15$ μm for bare fiber)
• Higher NA $\rightarrow$ tighter angular alignment tolerance
• More sensitive to lens-tip damage — sub-μm scratches or contamination destroy performance

Cost and lifetime. Commercial lensed fibers cost $200 – $1500 each, primarily reflecting precision manufacturing of the tip. Lifetime is typically 100 – 1000 alignment cycles before degradation; lab practice is to track individual fibers and replace at a measured threshold of coupling efficiency loss.

Use in pigtailing. Lensed fibers are the standard input for active-alignment pigtailing of laser diodes and silicon photonic edge couplers. The high coupling efficiency reduces the loss budget needed for the actively-aligned fiber position, allowing faster optimization and tighter mechanical positioning specifications.

Alternative: cleaved single-mode fiber with no lens is used when:

• Coupling to large-MFD targets (other SMF-28 fibers, large-mode-area fiber amplifiers)
• Coupling through a separate beam-shaping optic (free-space lens or aspheric lens)
• Low-cost applications where 5–10 dB coupling loss is acceptable

References: Kasap, Optoelectronics and Photonics: Principles and Practices (2nd ed., 2013), Ch. 12 for the optical-geometry analysis of lensed-fiber focusing.