Ring Resonator: Spectrogram & Phasor View

Modulator Drive

Reverse bias |V_R| 0.0 V

Optical Input

Laser detuning Δλ 0 pm

Bus–ring coupling κ 0.10

Live Readout

Resonance λ_res

1550.000 nm

Output T

100.0%

Extinction

0.0 dB

Loaded Q

—

Round-trip settling rate |r·a|

—

How it works

This is a 2D-native companion to the 3D ring-modulator scene. Instead of a rendered torus, the same all-pass ring transfer function is shown two ways that only make sense as flat fields, not as objects in space:

Spectrogram (left) — a live 2D field T(λ, t): wavelength runs across, time scrolls down. Each new row is a full transmission spectrum re-evaluated from the closed-form ring transfer function, so the resonance dip's motion under bias/detuning changes is literally visible as a bending stripe, not two separate line charts.
Phasor view (right) — the intracavity complex field is time-stepped round trip by round trip using the coupled-wave recursion E_ring[n] = iκ·s_in + r·a·e^iφ·E_ring[n−1], drawn on the complex (Re, Im) plane. This reproduces genuine cavity build-up/decay dynamics — something the closed-form-per-frame 3D scene never computes — and directly shows the Q-vs-bandwidth trade-off: low κ spirals in slowly (high Q, narrow linewidth), high κ snaps to its new steady state almost immediately (low Q, wide linewidth).

T(λ) = (a² − 2ar·cosφ + r²) / (1 − 2ar·cosφ + (ar)²)
E_ring[n] = iκ·s_in + r·a·e^(iφ)·E_ring[n-1]     (equivalent recursion)
φ(λ) ≈ −2π L n_g (λ − λ_res) / λ0²
Δλ_res(V) = k_n·V·λ0 / n_g      (free-carrier plasma dispersion)

Reverse bias still red-shifts λ_res, switching the notch out from under the fixed laser line; Auto NRZ still drives the same on/off bit pattern through an RC-like electro-optic response, but now you can watch the ring's stored field actually spiral to its new equilibrium each time the bit flips.

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Silicon Ring-Resonator Modulator — Spectrogram & Phasor View