Spatial Beam Engineering

Create Gaussian focusing, Airy beams, and arbitrary spatial phase profiles

Beam Mode Configuration

10 mm
50 μm
20 μm
l = 1

SHG Beam Intensity Profile

Phase Profile (χ⁽²⁾ Pattern)

Beam Propagation (Side View)

Spot Size
2.5 μm
Rayleigh Range
25 μm
Divergence
5.0°
Peak Intensity
150 W/cm²
M² Factor
1.05

Intensity Cross-Section

Beam Properties

Gaussian Focusing

Classical TEM₀₀ mode with quadratic phase profile. The χ⁽²⁾ grating imparts a lens-like phase to focus or defocus the SHG beam.

Key Equation

φ(x) = πx²/(λf)

Spatial Mode Theory

Airy Beams

Self-accelerating, non-diffracting beams following a parabolic trajectory:

Ai(s) ∝ ∫exp(i(t³/3 + st))dt

Vortex Beams

Carry orbital angular momentum with helical phase:

E(r,φ) = E₀(r) exp(ilφ)