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Laser Resonator Stability

This example analyzes the stability of an optical cavity by propagating a Gaussian beam through optical elements using ABCD matrices.

How to Run

cargo run -p physics_examples --example laser_resonator_stability

Physics Overview

A laser cavity traps light between mirrors. For a stable mode to exist, the diffraction of the beam (spreading) must be counteracted by the focusing of lenses or curved mirrors.

We model the beam using the Complex Beam Parameter $q(z)$: $$ \frac{1}{q(z)} = \frac{1}{R(z)} - i \frac{\lambda}{\pi w(z)^2} $$

  • $R(z)$: Radius of curvature of the wavefront.
  • $w(z)$: Beam spot size (radius).

Propagation through an optical element (Matrix M) transforms $q$: $$ q_{out} = \frac{A q_{in} + B}{C q_{in} + D} $$

Causal Chain

  1. Beam Initialization: Start with a defined waist $w_0$.
  2. Drift: Propagate through free space.
  3. Lens: Focus through a thermal lens.
  4. Stability Check: The gaussian_q_propagation wrapper automatically verifies the physical invariant Im(q) > 0. If the cavity is unstable, the beam size diverges (imaginary part goes to zero/negative in math), triggering a Causal Error.

Key APIs

  • deep_causality_physics::photonics::gaussian_q_propagation
  • deep_causality_physics::photonics::{AbcdMatrix, ComplexBeamParameter}
  • deep_causality_physics::photonics::lens_maker