optics

# Optics ## What I Do I provide comprehensive optics tools including geometrical optics, wave optics, interferometry, polarization, laser physics, and nonlinear optics for physics and engineering applications. ## When to Use Me - Optical system design - Interferometer analysis - Laser cavity design - Thin film coatings - Fiber optics - Nonlinear optics ## Core Concepts - **Geometrical Optics**: Ray tracing, ABCD matrices - **Wave Optics**: Diffraction, interference - **Polarization**: Jones vectors, Mueller matrices - **Laser Physics**: Cavity modes, gain, linewidth - **Interferometry**: Michelson, Fabry-Perot - **Thin Films**: Coating design, reflectivity - **Nonlinear Optics**: SHG, Raman, Kerr - **Fiber Optics**: Waveguides, dispersion ## Code Examples ### Ray Tracing (ABCD Matrix) ```python import numpy as np def translation_matrix(d): return np.array([[1, d], [0, 1]]) def thin_lens_matrix(f): return np.array([[1, 0], [-1/f, 1]]) def interface_matrix(n1, n2): return np.array([[1, 0], [0, n1/n2]]) def propagate_ray(ABCD, ray): y, theta = ray return np.dot(ABCD, ray) def transfer_matrix_system(matrices): M = np.eye(2) for M_i in matrices: M = M_i @ M return M f1, f2 = 50, -30 # mm d1, d2 = 20, 40 # mm M_lens1 = thin_lens_matrix(f1) M_drift1 = translation_matrix(d1) M_lens2 = thin_lens_matrix(f2) M_drift2 = translation_matrix(d2) M_total = M_drift2 @ M_lens2 @ M_drift1 @ M_lens1 print(f"System matrix:\n{M_total}") ``` ### Interferometry ```python def michelson_interference(delta, I0=1): return I0 * np.cos(delta / 2)**2 def fabry_perot_transmission(free_spectral_range, finesse, nu): delta = 2 * np.pi * nu / free_spectral_range return 1 / (1 + finesse**2 * np.sin(delta/2)**2) def coherence_length(c, delta_nu): return c / delta_nu def visibility(I_max, I_min): return (I_max - I_min) / (I_max + I_min) def thin_film_reflectivity(n_film, n_substrate, n_air, d, wavelength): n1, n2, n3 = n_air, n_film, n_substrate phi = 4 * np.pi * n2 * d / wavelength r12 = (n1 - n2) / (n1 + n2) r23 = (n2 - n3) / (n2 + n3) return (r12 + r23 * np.exp(1j*phi))**2 / (1 + r12 * r23 * np.exp(1j*phi))**2 d = 500e-9 # 500 nm film lam = 600e-9 R = thin_film_reflectivity(1.38, 1.5, 1.0, d, lam) print(f"Film reflectivity: {abs(R)**2:.4f}") ``` ### Laser Physics ```python def laser_threshold_gain(g_th, losses): return g_th + losses def cavity_mode_spacing(c, n, L): return c / (2 * n * L) def output_coupling(T, L_internal): return T / (T + L_internal) def laser_linewidth(nu, P, tau_cavity, hnu): from scipy.constants import h return nu * h * nu / (4 * np.pi * P * tau_cavity) def rate_equations(N2, N1, sigma_e, sigma_a, V, phi, Wp): dN2 = Wp - (N2 - N1) * sigma_e * phi / V - N2 / tau dphi = (N2 - N1) * sigma_e * phi / V - phi / tau_cavity return dN2, dphi c = 3e8 n = 1.5 L = 0.5 # m delta_nu = cavity_mode_spacing(c, n, L) print(f"FSR: {delta_nu:.0f} Hz") ``` ### Polarization ```python def jones_vector(theta, delta): return np.array([np.cos(theta), np.exp(1j * delta) * np.sin(theta)]) def jones_matrix_linear_polarizer(angle): c = np.cos(angle)**2 s = np.sin(angle)**2 cs = np.cos(angle) * np.sin(angle) return np.array([[c, cs], [cs, s]]) def jones_matrix_retarder(delta, fast_axis_angle=0): return np.array([ [np.cos(delta/2) + 1j*np.sin(delta/2)*np.cos(2*fast_axis_angle), 1j*np.sin(delta/2)*np.sin(2*fast_axis_angle)], [1j*np.sin(delta/2)*np.sin(2*fast_axis_angle), np.cos(delta/2) - 1j*np.sin(delta/2)*np.cos(2*fast_axis_angle)] ]) def stokes_parameters(S0, S1, S2, S3): return np.array([S0, S1, S2, S3]) def mueller_matrix_linear_polarizer(P): return np.array([ [1, P, 0, 0], [P, P**2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0] ]) delta = np.pi # Half-wave plate print(f"Jones matrix:\n{jones_matrix_retarder(delta)}") ``` ### Diffraction ```python def fraunhofer_intensity(k, a, z, I0=1): beta = k * a / (2 * z) sinc = np.sin(beta) / beta return I0 * sinc**2 def fresnel_diffraction(z, lambda_, w): from scipy.special import fresnel u = np.sqrt(2 / (lambda_ * z)) * w S, C = fresnel(u) return 0.5 * ((0.5 + C)**2 + (0.5 + S)**2) def grating_equation(d, theta_m, lambda_): return np.sin(theta_m) = m * lambda_ / d def resolve_two_points(theta, lambda_, D): return 1.22 * lambda_ / D * np.sin(theta) def numerical_aperture(n, theta_max): return n * np.sin(theta_max) D = 0.1 # 10 cm aperture lam = 500e-9 resolution = 1.22 * lam / D print(f"Angular resolution: {resolution:.2e} rad") ``` ## Best Practices 1. **Paraxial Approximation**: Check validity for given NA 2. **Aberrations**: Consider spherical, chromatic aberrations 3. **Coherence**: Consider spatial and temporal coherence 4. **Polarization**: Account for polarization effects 5. **Alignment**: Minimize misalignment errors ## Common Patterns ```python # Gaussian beam propagation def gaussian_beam_w0(wavelength, w0): k = 2 * np.pi / wavelength zR = np.pi * w0**2 / wavelength return k, zR ``` ## Core Competencies 1. Geometrical optics and ray tracing 2. Wave optics and diffraction 3. Laser physics and cavities 4. Interferometry 5. Polarization optics