optics
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scripts/cm_optics.py
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105
scripts/cm_optics.py
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#!/usr/bin env python3
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from formulary import *
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from scipy.constants import Boltzmann as kB, hbar, electron_volt, elementary_charge, epsilon_0, electron_mass
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# OPTICS
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def eps_r(omega, omega0, gamma, chi, N):
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return 1 + chi + N * elementary_charge**2 /(epsilon_0 * electron_mass) * (1/(omega0**2 - omega**2 - 1j*gamma*omega))
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def eps_r_lim0(omega0, gamma, chi, N):
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return 1 + chi + N * elementary_charge**2 /(epsilon_0 * electron_mass * omega0**2)
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def eps_r_lim_infty(omega0, gamma, chi, N):
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return 1 + chi
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def dielectric_absorption():
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# values taken from adv. sc. physics ex 10/1
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fig, axs = plt.subplots(1, 2, figsize=size_formula_normal_default, sharex=True)
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omega0 = 100e12 # 100 THz
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gamma = 5e12 # 5 THz
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omegas = np.linspace(60e12, 140e12)
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chi = 5
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N = 1e25
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eps_complex = eps_r(omegas, omega0, gamma, chi, N)
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eps_real = eps_complex.copy().real
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eps_imag = eps_complex.copy().imag
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eps_real_0 = eps_r_lim0(omega0, gamma, chi, N)
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eps_real_infty = eps_r_lim_infty(omega0, gamma, chi, N)
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omegas_THz = omegas / 1e12
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anno_color = COLORSCHEME["fg2"]
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axs[0].set_ylabel(r"$\epsreal(\omega)$")
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axs[0].hlines([eps_real_0], omegas_THz[0], omegas_THz[omegas_THz.shape[0]//3], color=anno_color, linestyle="dotted")
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axs[0].hlines([eps_real_infty], omegas_THz[omegas_THz.shape[0]*2//3], omegas_THz[-1], color=anno_color, linestyle="dotted")
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axs[0].text(omegas_THz[-1], eps_real_infty, r"$\epsilon_\txr(\infty)$", ha="right", va="bottom", color=anno_color)
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axs[0].text(omegas_THz[0], eps_real_0, r"$\epsilon_\txr(0)$", ha="left", va="top", color=anno_color)
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axs[1].set_ylabel(r"$\epscomplex(\omega)$")
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vals = [eps_real, eps_imag]
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for i in range(2):
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ax = axs[i]
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val = vals[i]
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ax.set_xlabel(r"$\omega\,[\si{\tera\hertz}]$")
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ax.vlines([omega0/1e12], 0, 100, color=anno_color, linestyle="dashed")
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ax.plot(omegas_THz, val)
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vmax = val.max()
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vmin = val.min()
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margin = (vmax - vmin) * 0.05
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ax.set_ylim(vmin - margin, vmax + margin)
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return fig
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# Free e-
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@np.vectorize
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def fn(omega: float, omega_p:float, eps_infty:float, tau:float):
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eps_real = eps_infty * (1-(omega_p**2 * tau**2)/(1+omega**2 * tau**2))
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eps_imag = eps_infty * omega_p**2 * tau/(omega*(1+omega**2 * tau**2))
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eps_complex = (eps_real + 1j*eps_imag)
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n_complex: complex = np.sqrt(eps_complex)
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# n_real = n_complex.real
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# n_imag = n_complex.imag
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# return n_real, n_imag
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return n_complex
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def free_electrons_absorption():
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# values taken from adv. sc. physics ex 10/1
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fig, axs = plt.subplots(2, 2, figsize=size_formula_fill_default, sharex=True)
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omega_p = 30e12 # 30 THz
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eps_infty = 11.7
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tau = 1e-6
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omegas = omega_p * np.logspace(-1, 3, 1000, base=10, dtype=float)
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# omegas = omega_p * np.linspace(1e-1, 1e3, 1000)
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# print(omegas)
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n_complex = fn(omegas, omega_p, eps_infty, tau)
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n_real = n_complex.copy().real
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n_imag = n_complex.copy().imag
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R = np.abs((n_complex-1)/(n_complex+1))
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alpha = 2*omegas*n_imag/3e8
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for ax in axs[1,:]:
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ax.set_xlabel(r"$\omega/\omega_\text{p}$")
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ax.set_xscale("log")
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ax.set_xticks([1e-1,1e0,1e1,1e2,1e3])
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ax.set_xticklabels([0.1, 1, 10, 100, 1000])
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omegas_rel = omegas/omega_p
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axs[0,0].plot(omegas_rel, n_real)
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axs[0,0].set_yticks([0,1,2,np.sqrt(eps_infty)])
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axs[0,0].set_yticklabels([0,1,2,r"$\epsilon_\infty$"])
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axs[0,0].set_ylim(-0.2,0.2+np.sqrt(eps_infty))
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axs[0,0].set_ylabel(r"$n^\prime(\omega)$")
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axs[1,0].plot(omegas_rel, n_imag)
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axs[1,0].set_ylabel(r"$n^{\prime\prime}(\omega)$")
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axs[1,0].set_yscale("log")
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axs[0,1].plot(omegas_rel, R)
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axs[0,1].set_ylabel(r"$R(\omega)$")
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axs[1,1].plot(omegas_rel, alpha)
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axs[1,1].set_ylabel(r"$\alpha(\omega)$")
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axs[1,1].set_yscale("log")
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return fig
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if __name__ == '__main__':
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export(free_electrons_absorption(), "cm_optics_absorption_free_electrons")
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export(dielectric_absorption(), "cm_optics_absorption_dielectric")
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@ -149,57 +149,6 @@ def test():
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# OPTICS
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@np.vectorize
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def fn(omega: float, omega_p:float, eps_infty:float, tau:float):
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eps_real = eps_infty * (1-(omega_p**2 * tau**2)/(1+omega**2 * tau**2))
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eps_imag = eps_infty * omega_p**2 * tau/(omega*(1+omega**2 * tau**2))
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eps_complex = (eps_real + 1j*eps_imag)
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n_complex: complex = np.sqrt(eps_complex)
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# n_real = n_complex.real
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# n_imag = n_complex.imag
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# return n_real, n_imag
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return n_complex
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def free_electrons_absorption():
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# values taken from adv. sc. physics ex 10/1
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fig, axs = plt.subplots(2, 2, figsize=size_formula_fill_default, sharex=True)
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omega_p = 30e12 # 30 THz
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eps_infty = 11.7
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tau = 1e-6
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omegas = omega_p * np.logspace(-1, 3, 1000, base=10, dtype=float)
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# omegas = omega_p * np.linspace(1e-1, 1e3, 1000)
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# print(omegas)
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n_complex = fn(omegas, omega_p, eps_infty, tau)
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n_real = n_complex.copy().real
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n_imag = n_complex.copy().imag
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R = np.abs((n_complex-1)/(n_complex+1))
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alpha = 2*omegas*n_imag/3e8
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for ax in axs[1,:]:
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ax.set_xlabel(r"$\omega/\omega_\text{p}$")
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ax.set_xscale("log")
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ax.set_xticks([1e-1,1e0,1e1,1e2,1e3])
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ax.set_xticklabels([0.1, 1, 10, 100, 1000])
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omegas_rel = omegas/omega_p
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axs[0,0].plot(omegas_rel, n_real)
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axs[0,0].set_yticks([0,1,2,np.sqrt(eps_infty)])
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axs[0,0].set_yticklabels([0,1,2,r"$\epsilon_\infty$"])
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axs[0,0].set_ylim(-0.2,0.2+np.sqrt(eps_infty))
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axs[0,0].set_ylabel(r"$n^\prime(\omega)$")
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axs[1,0].plot(omegas_rel, n_imag)
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axs[1,0].set_ylabel(r"$n^{\prime\prime}(\omega)$")
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axs[1,0].set_yscale("log")
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axs[0,1].plot(omegas_rel, R)
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axs[0,1].set_ylabel(r"$R(\omega)$")
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axs[1,1].plot(omegas_rel, alpha)
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axs[1,1].set_ylabel(r"$\alpha(\omega)$")
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axs[1,1].set_yscale("log")
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return fig
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@ -207,5 +156,4 @@ if __name__ == '__main__':
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# export(test(), "cm_sc_charge_carrier_density")
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export(schottky_barrier(), "cm_sc_devices_metal-n-sc_schottky")
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# export(charge_carrier_density(), "cm_sc_charge_carrier_density")
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# export(free_electrons_absorption(), "cm_sc_optics_free_electrons")
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@ -9,7 +9,11 @@ import matplotlib as mpl
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mpl.rcParams["font.family"] = "serif"
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mpl.rcParams["mathtext.fontset"] = "stix"
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mpl.rcParams["text.usetex"] = True
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mpl.rcParams['text.latex.preamble'] = r'\usepackage{amsmath}\usepackage{siunitx}'
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mpl.rcParams['text.latex.preamble'] = f'''
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\\usepackage{{amsmath}}
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\\usepackage{{siunitx}}
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\\input{{{os.path.abspath("../src/util/math-macros.tex")}}}
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'''
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if __name__ == "__main__": # make relative imports work as described here: https://peps.python.org/pep-0366/#proposed-change
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@ -20,7 +20,7 @@
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\complex{\epsilon}_\txr(0) &\to 1+\chi + \frac{Ne^2}{\epsilon_0 m_\txe \omega_0^2} \\
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\complex{\epsilon}_\txr(\infty) &= \epsilon_\infty = 1+\chi
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}
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\TODO{plot}
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\fig{img/cm_optics_absorption_dielectric.pdf}
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\end{formula}
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\begin{formula}{clausius-mosotti}
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\begin{formula}{absorption}
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\desc{Free charge carrier absorption}{Exemplary values}{$\omega_\txp$ \fRef{::plasma_frequency}, \QtyRef{refraction_index_real}, \QtyRef{refraction_index_complex}, \QtyRef{absorption_coefficient}, $R$ \fRef{ed:optics:reflectivity}}
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\desc[german]{Freie Ladungsträger}{Beispielwerte}{}
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\fig{img/cm_sc_optics_free_electrons.pdf}
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\fig{img/cm_optics_absorption_free_electrons.pdf}
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\TODO{Include equations? aus adv sc ex 10/1c}
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\end{formula}
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@ -87,8 +87,8 @@
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\eq{W_{1\to2} = \frac{2\pi}{\hbar} \abs{M_{12}}^2 \delta(E_1-E_2+\hbar\omega)}
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\end{formula}
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\begin{formula}{emission}
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\desc{Absorption}{}{}
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\desc[german]{Absorption}{}{}
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\desc{Emission}{}{}
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\desc[german]{Emission}{}{}
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\eq{W_{2\to1} = \frac{2\pi}{\hbar} \abs{M_{12}}^2 \delta(E_1-E_2-\hbar\omega)}
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\end{formula}
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\TODO{stimulated vs spontaneous}
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