Optical Phased Array — Grating-Lobe Map

Beam Steering Controls

Target steering angle θ 30°

Element pitch d 450 nm

Wavelength λ 532 nm

Phase control resolution

Far-Field Readout

Achieved main-lobe angle

0.0°

Steering error

0.0°

Strongest grating / quantization lobe

none

Pitch / λ

0.85

Grating-free limit

0.77

How it works

Same physics as the 3D phased-array model, drawn a completely different way: instead of a rendered emitter row and a single polar curve, this is a grating-lobe map — a 2D field on a canvas grid. The horizontal axis is far-field angle θ; the vertical axis is the pitch/λ ratio d/λ swept over a whole range at once. Every pixel's brightness is the array factor

AF(θ) = (1/N) |Σ_n exp( i[k0·x_n·sinθ + φ(x_n)] )|,   k0 = 2π/λ

computed directly for that row's d/λ, holding the steering phase gradient fixed at whatever the sliders currently ask for. The bright diagonal band is the main lobe; extra bright bands that peel off it as you scan upward (larger d/λ) are grating lobes — the map makes the appearance threshold d/λ < 1/(1+|sinθ|) visible as a literal curve on the grid rather than a number you have to intuit from one snapshot.

A bright horizontal line marks the current pitch/λ row, and the live AF(θ) curve for that exact row is overlaid in a contrasting color along with tick marks for the target angle, the achieved main-lobe angle, and the strongest side lobe. The emitter strip above the map shows the N=32 phase values (hue = φ) exactly as computed for the array — a 1D object, drawn natively in 2D, not a flattened 3D render.

Emitter phase (hue = φ) Current d/λ row + AF(θ) curve Grating / quantization lobe marker

Optical Phased Array — Grating-Lobe Map (2D)