Laser Mode Matcher & Overlap Lab

Compute spatial coupling efficiencies, insertion losses, and alignment tolerances between propagating laser modes and optical fibers.

Wavelength (λ, nm)

Source Mode (w1, R1)

w1 (mm)

R1 (m)

Target Mode (w2, R2)

w2 (mm)

R2 (m)

Lateral Offset (Δr, µm)

µm

Angular Tilt (θ, mrad)

mrad

Polarization Angle (Δψ, degrees)

deg

Input Laser Power (P0, mW)

Precision Mode

Efficiency vs Lateral Offset

Efficiency vs Angular Tilt

Total Coupling Overlap0.07%Insertion Loss: 31.75 dB

Coupled Optical Power0.00 mWFrom initial 5.0 mW input

Aligned Mode Overlap96.7%Mismatched spot sizes and curvatures

Lateral Offset Overlap99.2%Transverse alignment loss

Angular Tilt Overlap0.1%Wavefront tilt alignment loss

Polarization Overlap100.0%Polarization angle match

Mode Coupling Overlap Theory

\eta_0 = \frac{4}{\left( \frac{w_1}{w_2} + \frac{w_2}{w_1} \right)^2 + \left( \frac{\pi w_1 w_2}{\lambda} \right)^2 \left( \frac{1}{R_1} - \frac{1}{R_2} \right)^2}

Calculates the coupling of clean aligned spatial modes based on their waist geometries and wavefront mismatch.

\eta_{\mathrm{lateral}} = \exp\left( - \frac{2 \Delta r^2}{w_1^2 + w_2^2} \right)

Models the reduction in spatial integral overlap due to transverse displacement.

\eta_{\mathrm{angular}} = \exp\left( - \frac{2 \pi^2 w_1^2 w_2^2 \theta^2}{\lambda^2 (w_1^2 + w_2^2)} \right)

Models the reduction in spatial overlap caused by wavefront phase gradients tilting relative to target modes.