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Tunable Bandpass Filter — NiCr Heater

Center wavelength is fixed by ΔL. A NiCr thin-film heater raises the coupler temperature (thermo-optic), tuning the coupling angle and therefore only the passband width — the center never moves.

Waveguide

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

Filter spec (center fixed)

Center λ꜀ (μm, FIXED) FSR (nm) Base passband (nm, V=0) Span (× FSR) Samples

NiCr thin-film heater

ρ NiCr (Ω·m) Heater width (μm) Film thickness (μm) Thermal R_th (K/W) dn/dT (1/K)

Heater voltage V

0.00 V

Heater state & designed filter

Center λ꜀ (locked)

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Path difference ΔL

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L_DC = heater length

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Heater resistance R

—

Power P = V²/R

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Temperature rise ΔT

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Thermo-optic Δn

—

Coupler angle θ(T)

—

Passband −3 dB (base → tuned)

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Peak transmission (cross)

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Top: schematic (heater bar over both couplers). Bottom: cross port (passband) at the set voltage, with the V=0 base dashed; the center marker shows λ꜀ stays fixed while heating widens/narrows the band.

How it works

Fixed center: ΔL = m·λ꜀/n_eff (integer m) ⇒ cross peak locked at λ꜀ for all T.

NiCr heater: R = ρ·L_h/(w_h·t_h), P = V²/R, ΔT = R_th·P, Δn = (dn/dT)·ΔT.

Tunable coupler angle: θ(T) = θ_base + π·Δn·L_h/λ꜀. Cross port: P_cross = sin²(2θ)·cos²(Δφ/2).

Passband (−3 dB, absolute): PB = FSR·(2/π)·acos(√(0.5/sin²2θ)), widening to FSR/2 at θ = 45°. Only the width changes with T; λ꜀ is fixed.

Reference implementations

tunable_bandpass.py TunableBandpass.java