Martino Ferrari
03b63ba03a
Full implementation of Laguerre-Gauss modal reconstruction for gyrotron beam diagnostics, per the approved design spec, plus tests, docs, and a runnable end-to-end example. Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
104 lines
3.2 KiB
Python
104 lines
3.2 KiB
Python
import numpy as np
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import pytest
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from he11lib.modes import LGBasis
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W0 = 5e-3 # 5 mm waist
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Z0 = 0.5 # waist at 0.5 m
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WAVELENGTH = 1.76e-3 # ~170 GHz gyrotron
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def make_grid(w, half_widths_in_w=6.0, n=300):
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extent = half_widths_in_w * w
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coords = np.linspace(-extent, extent, n)
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dx = coords[1] - coords[0]
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x, y = np.meshgrid(coords, coords)
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return x, y, dx
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def test_beam_radius_at_waist_equals_w0():
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basis = LGBasis(w0=W0, z0=Z0, wavelength=WAVELENGTH)
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assert basis.beam_radius(Z0) == pytest.approx(W0)
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def test_beam_radius_at_one_rayleigh_range():
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basis = LGBasis(w0=W0, z0=Z0, wavelength=WAVELENGTH)
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zR = np.pi * W0**2 / WAVELENGTH
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assert basis.beam_radius(Z0 + zR) == pytest.approx(W0 * np.sqrt(2))
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def test_gouy_phase_zero_at_waist():
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basis = LGBasis(w0=W0, z0=Z0, wavelength=WAVELENGTH)
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assert basis.gouy_phase(Z0, p=0, l=0) == pytest.approx(0.0)
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assert basis.gouy_phase(Z0, p=1, l=2) == pytest.approx(0.0)
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def test_gouy_phase_at_one_rayleigh_range_for_fundamental():
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basis = LGBasis(w0=W0, z0=Z0, wavelength=WAVELENGTH)
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zR = np.pi * W0**2 / WAVELENGTH
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# order (2p+|l|+1) = 1 for p=0,l=0; atan(1) = pi/4
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assert basis.gouy_phase(Z0 + zR, p=0, l=0) == pytest.approx(np.pi / 4)
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def test_fundamental_mode_matches_analytic_gaussian_at_waist():
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basis = LGBasis(w0=W0, z0=Z0, wavelength=WAVELENGTH)
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x, y, _ = make_grid(W0, n=50)
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r2 = x**2 + y**2
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field = basis.field(x, y, Z0, p=0, l=0)
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expected_intensity_shape = np.exp(-2 * r2 / W0**2)
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intensity = np.abs(field) ** 2
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# shapes should match up to a constant normalization factor
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ratio = intensity / expected_intensity_shape
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ratio_center = ratio[len(ratio) // 2, len(ratio) // 2]
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np.testing.assert_allclose(ratio / ratio_center, 1.0, atol=1e-6)
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def test_mode_is_normalized_at_waist():
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basis = LGBasis(w0=W0, z0=Z0, wavelength=WAVELENGTH)
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x, y, dx = make_grid(W0, n=400)
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field = basis.field(x, y, Z0, p=0, l=0)
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total_power = np.sum(np.abs(field) ** 2) * dx**2
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assert total_power == pytest.approx(1.0, rel=2e-3)
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def test_mode_is_normalized_away_from_waist():
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basis = LGBasis(w0=W0, z0=Z0, wavelength=WAVELENGTH)
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z = Z0 + 0.2
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w_z = basis.beam_radius(z)
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x, y, dx = make_grid(w_z, n=400)
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field = basis.field(x, y, z, p=1, l=2)
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total_power = np.sum(np.abs(field) ** 2) * dx**2
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assert total_power == pytest.approx(1.0, rel=2e-3)
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def test_modes_are_orthogonal():
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basis = LGBasis(w0=W0, z0=Z0, wavelength=WAVELENGTH)
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z = Z0 + 0.1
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w_z = basis.beam_radius(z)
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x, y, dx = make_grid(w_z, n=400)
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field_a = basis.field(x, y, z, p=0, l=0)
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field_b = basis.field(x, y, z, p=1, l=0)
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inner_product = np.sum(field_a * np.conj(field_b)) * dx**2
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assert abs(inner_product) < 1e-3
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def test_project_recovers_known_coefficients():
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basis = LGBasis(w0=W0, z0=Z0, wavelength=WAVELENGTH)
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z = Z0 + 0.15
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w_z = basis.beam_radius(z)
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x, y, dx = make_grid(w_z, n=400)
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true_coeffs = {(0, 0): 0.8 + 0.1j, (1, 0): 0.2 - 0.3j}
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field = basis.field_superposition(x, y, z, true_coeffs)
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recovered = basis.project(field, x, y, dx, z, modes=list(true_coeffs.keys()))
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for mode, coeff in true_coeffs.items():
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assert recovered[mode] == pytest.approx(coeff, abs=5e-3)
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