quantum-photon-filtering-sim

Photon Filtering with a Fabry–Pérot Interferometer

This project simulates how a Fabry–Pérot interferometer (FPI) acts as a filter for photons, using both classical optics and a quantum single-photon model. The simulations are written in Python with NumPy and Matplotlib.

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Overview

Classical Simulation

• Models a Gaussian input spectrum passing through an FPI.
• Demonstrates frequency domain filtering by overlaying the Airy function transmission curve with the input and output spectrum.
• Time-domain response shows the ring-down behavior of the cavity (exponential decay caused by multiple reflections and transmissions).

Figure 1: Frequency domain filtering with Gaussian input and FPI transmission overlay.

Figure 2: Time-domain cavity ring-down.

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Quantum Simulation

• Models a single-photon Gaussian wavepacket passing through the FPI.
• Frequency-domain filtering again overlays the Airy function with the photon’s input/output spectra (normalized).
• Time-domain response shows the photon’s survival time in the cavity, plotted on a log scale to emphasize exponential decay.

Figure 3: Single-photon spectrum filtered by the Fabry–Pérot interferometer.

Figure 4: Photon lifetime in the FPI cavity.

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Adjustable Parameters

Several physical parameters can be tuned in the code:

• Mirror reflectivity R

  • Higher R → narrower transmission peaks, longer photon lifetime, slower ring-down.
  • Lower R → broader transmission, faster decay, less filtering.

• Cavity length L

  • Determines the Free Spectral Range (FSR) = c / (2nL).
  • Longer cavity → smaller FSR (closer resonances).
  • Shorter cavity → larger FSR (wider spacing of resonances).

• Photon pulse width σₜ

  • Sets the photon’s frequency bandwidth (σf ≈ 1/(2πσt)).
  • Shorter pulses (small σₜ) → broader frequency spectrum.
  • Longer pulses (large σₜ) → narrower frequency spectrum.

• Wavelength λ₀

  • Sets the photon’s carrier frequency (f₀ = c / λ₀).
  • Changing λ₀ moves the system into different optical regimes (visible, telecom, IR, etc.).

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What This Shows

• Classical optics view: FPIs act as narrowband filters, with transmission described by the Airy function.
• Quantum optics view: A photon wavepacket experiences the same filtering; its spectral content is shaped by the FPI and in the time domain it exhibits an exponential decay (ring-down) associated with cavity lifetime.
• Relevance to quantum computing: FPIs and similar resonant structures are widely used in quantum optics for single-photon filtering, frequency stabilization, and mode selection.