 codex/transverse-cavity-mode-patterns.py

"""Ideal Hermite-Gaussian waist intensities; Python 3.14, NumPy 2.3.5, Matplotlib 3.10.7.

Run through Make in the mirrored media working directory. Each panel is normalized
by its own peak; this is a comparison of spatial shape, not equal optical power.
"""
from pathlib import Path

import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
import numpy as np
from numpy.polynomial.hermite import hermval


def field(m, n, x, y):
    """Real waist-plane field in coordinates x/w0, y/w0 (unnormalized)."""
    cm = np.zeros(m + 1)
    cn = np.zeros(n + 1)
    cm[m] = cn[n] = 1
    return hermval(np.sqrt(2) * x, cm) * hermval(np.sqrt(2) * y, cn) * np.exp(-(x*x + y*y))


def main():
    coords = np.linspace(-2, 2, 401)
    x, y = np.meshgrid(coords, coords)
    fig, axes = plt.subplots(1, 4, figsize=(10, 3.5), facecolor='white')
    fig.suptitle('Transverse cavity modes: intensity at the beam waist', fontsize=14, y=.97)
    for ax, (m, n) in zip(axes, [(0, 0), (1, 0), (2, 0), (1, 1)]):
        intensity = field(m, n, x, y)**2
        image = ax.imshow(intensity/intensity.max(), extent=(-2, 2, -2, 2), origin='lower',
                          cmap='Blues', vmin=0, vmax=1, interpolation='nearest')
        ax.set_title(f'Order ({m}, {n})', fontsize=12)
        ax.set_xlabel(r'$x/w_0$')
        ax.set_xticks([-2, 0, 2])
        ax.set_yticks([-2, 0, 2])
        ax.set_facecolor('white')
    axes[0].set_ylabel(r'$y/w_0$')
    fig.subplots_adjust(left=.055, right=.91, bottom=.22, top=.81, wspace=.30)
    cax = fig.add_axes([.93, .29, .015, .40])
    fig.colorbar(image, cax=cax, ticks=[0, .5, 1], label='Relative intensity')
    fig.text(.5, .055, 'Each panel normalized to its own peak; field phase is not shown.',
             ha='center', fontsize=10)
    fig.savefig(Path.cwd()/'transverse-cavity-mode-patterns.png', dpi=112, facecolor='white')
    plt.close(fig)


if __name__ == '__main__':
    main()