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Bandpass Filter — Asymmetric MZI

Set the waveguide, FSR, center wavelength and passband; the tool designs a two-directional-coupler asymmetric MZI (path difference ΔL) and plots its spectrum.

Waveguide

WG width W (μm) WG height H (μm) Δ index contrast (%) DC gap (μm)

Filter spec

Center λ꜀ (μm) FSR (nm) Passband −3 dB (nm) Span (× FSR) Samples

Designed asymmetric MZI

n_eff (at λ꜀)

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κ (at λ꜀)

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Path difference ΔL

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ΔL in wavelengths (m)

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DC1 = DC2 coupling length L_DC

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Coupler angle κ·L_DC

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FSR (achieved)

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Passband −3 dB (achieved)

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Peak transmission (cross)

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Top: schematic (DC1 — ΔL arm — DC2). Bottom: spectrum — passband on the cross port, complementary bar port; shaded band = requested passband around λ꜀, dashed line = −3 dB.

How it works

Each DC: T = [[cos(κL), −j sin(κL)], [−j sin(κL), cos(κL)]]; arm phase Δφ = (2π·n_eff/λ)·ΔL

P_bar = |cos(κL₁)cos(κL₂) − sin(κL₁)sin(κL₂)·e^−jΔφ|², P_cross = 1 − P_bar

Equal couplers ⇒ P_cross = sin²(2κL)·cos²(Δφ/2): a bandpass on the cross port.

FSR → ΔL = λ꜀²/(n_eff·FSR), snapped to ΔL = m·λ꜀/n_eff so a peak sits at λ꜀.
Passband → κ·L_DC = ½·asin(√½ / cos(π·PB/2FSR)); the absolute −3 dB width spans 0…FSR/2, with peak transmission sin²(2κL) trading off below FSR/2.

Reference implementations

band_pass_filter.py BandPassFilter.java