Examples#
Runnable, self-contained scripts reproducing the key conceptual
breakthroughs behind physicskit.optics – from Huygens’ 1690 wave
construction through Allen et al.’s 1992 discovery of the orbital angular
momentum of light (see Breakthroughs in Optics for the full
chronology).
See also the narrative tutorials:
Each script in this gallery is self-contained and can be run directly with
python examples/optics/<section>/<script>.py. Every script also carries
an RST module docstring as its title/description and uses # %% markers to
split narrative text from code, which is exactly what Sphinx-Gallery renders
into the pages below – the script is the source of truth for what you see,
not a copy of it.
Sections#
diffraction – scalar wave optics from Huygens through Airy: Huygens’ wavelet construction, Young’s double-slit fringes, Fresnel’s near-field diffraction theory and the Poisson/Arago spot, and Airy’s circular-aperture pattern and the diffraction limit.
ray_optics – paraxial ABCD matrix optics: Gauss’s composite-system matrix product, the two-mirror resonator stability behind Maiman’s ruby laser cavity, and Kao’s graded-index (GRIN) fiber guiding.
interference – multiple-beam interference in layered media: the Fabry-Pérot interferometer, thin-film antireflection coatings, and the band gap of a 1D photonic crystal.
nonlinear_optics – second-harmonic generation: the coherence length, quasi-phase matching and birefringent phase matching.
lasers – inside the gain medium: Schawlow and Townes’s lasing threshold, gain clamping and relaxation oscillations from the rate equations, and Haken’s Maxwell-Bloch laser with its Lorenz chaos.
gaussian_beams – complex-beam-parameter wave optics: Kogelnik and Li’s ABCD transformation of a Gaussian beam through a thin lens, Siegman’s \(M^2\) beam-quality factor, and Allen et al.’s Laguerre-Gaussian orbital-angular-momentum vortex.
quantum_optics – light in the truncated Fock basis: Wigner’s phase-space negativity, Glauber’s coherent states, the Jaynes-Cummings model’s vacuum Rabi oscillation and collapse-and-revival, Kimble/Dagenais/Mandel’s photon antibunching, and Slusher’s observation of squeezed light.
Diffraction#
Scalar wave optics from Huygens through Airy: Huygens’ wavelet construction as diffractive spreading of a pinhole, Young’s double-slit interference fringes (including an animated sweep of the near-to-far-field wavefront propagation), Fresnel’s near-field diffraction theory and the Poisson/Arago spot, Maxwell’s electromagnetic waves (the speed of light from \(\mu_0\varepsilon_0\), and Fresnel reflection from a pulse solution of Maxwell’s equations), and Airy’s circular-aperture pattern and the diffraction limit it implies.
Huygens’ wavelets: diffractive spreading of a pinhole
Gaussian beams#
Complex-beam-parameter (Gaussian) wave optics: Kogelnik and Li’s ABCD transformation of the complex beam parameter through a thin lens, Siegman’s \(M^2\) beam-quality factor for real, non-diffraction-limited beams, and the doughnut intensity and helical phase of an Allen et al. Laguerre-Gaussian orbital-angular-momentum vortex.
Kogelnik and Li: focusing a Gaussian beam through a thin lens
Allen et al.: orbital angular momentum of a Laguerre-Gaussian vortex
Interference in layered media#
Multiple-beam interference computed with the characteristic-matrix method: the Fabry-Pérot interferometer, thin-film antireflection coatings, and the band gap of a 1D photonic crystal.
The Fabry-Pérot interferometer: multiple-beam interference and finesse
Thin-film interference: the antireflection coating
Laser dynamics#
What happens inside the gain medium: the rate equations behind the lasing threshold, gain clamping and relaxation oscillations, and the Maxwell-Bloch equations whose bad-cavity instability makes a single-mode laser chaotic.
Schawlow and Townes: the lasing threshold from the laser rate equations
Haken’s laser-Lorenz analogy: Maxwell-Bloch dynamics and laser chaos
Nonlinear optics#
Second-harmonic generation: the coherence length of a phase-mismatched crystal, and the birefringent and quasi-phase-matching schemes that remove the mismatch.
Quantum optics#
Einstein’s light quanta and the photoelectric effect, and light quantized in the truncated Fock basis: Dirac’s creation/annihilation ladder operators and vacuum fluctuations, Wigner’s phase-space quasi-probability distribution and the negativity of a single-photon Fock state, Glauber’s coherent states and their Poissonian photon statistics, the Jaynes-Cummings model’s vacuum Rabi oscillation and collapse-and- revival, Kimble/Dagenais/Mandel’s photon antibunching via the Fano factor, Hanbury Brown and Twiss’s intensity-correlation bunching, and Slusher’s observation of squeezed, sub-vacuum quadrature noise.
Glauber’s coherent states: displaced vacuum, Poissonian statistics
Einstein’s light quanta and the photoelectric effect
The Hanbury Brown-Twiss effect: bunching, coherent, and antibunched light
The Jaynes-Cummings model: vacuum Rabi oscillation and collapse-and-revival
Dirac’s quantization of the electromagnetic field: ladder operators
Kimble, Dagenais, and Mandel: photon antibunching and the Fano factor
Slusher et al.: squeezed light and sub-vacuum quadrature noise
Wigner’s phase-space distribution: negativity of a Fock state
Ray optics#
Paraxial ray-transfer (ABCD) matrix optics: Gauss’s composition rule for a compound optical system as a product of elementary matrices, the two-mirror resonator stability criterion behind Maiman’s ruby laser cavity, and the sinusoidal ray confinement of Kao’s graded-index (GRIN) optical fiber.
Gauss’s ABCD formalism: a composite system as a matrix product
Graded-index fiber guiding (Kao’s low-loss optical fiber)
Two-mirror resonator stability (Maiman’s ruby laser cavity)