N×N wavelength (de)multiplexer — two slab star couplers connected by an array of waveguides with a constant path increment ΔL. The phase order m and ΔL fix the dispersion; the focal length fl sets the channel spacing on the output star.
Waveguide (EIM TE, silica core, lower-Δ cladding)
AWG channel spec
Array geometry
Spectrum window
Layout (GDS export)
D_slab (effective)
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Min bend radius (computed)
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Min straight (computed)
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Layers — 1: AWG array waveguides · 2: input port · 3: output ports · 10: slab star couplers.
Coordinates in μm (1 dbu = 1 nm). PATH width = WG width W with round end-caps (pathtype 2).
Designed AWG parameters
Waveguide effective index n_eff_a
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Slab effective index n_eff_s (TE)
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Group index n_g
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Phase order m
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Path difference ΔL
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Free spectral range FSR
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Focal length f_l (Rowland)
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Total angular sweep on star
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Channel positions on output face
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Top: schematic — input port → input slab (Rowland) → array of N_a waveguides with path increment ΔL → output slab → output ports. Bottom: transmission spectrum at each output port (centred on λ꜀).
How it works
Phase order & path difference: ΔL = m · λ꜀ / n_eff_a. The integer m is the diffraction order seen by every adjacent pair of array waveguides.
Free spectral range: FSR_λ = λ꜀² / (n_g · ΔL). n_g is the group index of the array waveguide (n_g = n_eff − λ · dn_eff/dλ).
Focal length (Rowland circle): f_l = (n_eff_s · d_aw · d_io · n_eff_a) / (m · n_g · Δλ_ch). Sets the linear dispersion x_i = f_l · θ_i on the output star face.
Output port i transmission: T_i(λ) = |Σ_k A_k · exp(j·k·Δφ_i(λ))|² / (Σ A_k)², where Δφ_i = β·ΔL + 2π·n_eff_s·d_aw·θ_i/λ, β = 2π·n_eff_a/λ, θ_i = (i − (N_ch+1)/2)·d_io/f_l.