qpms/materials.h

   1 /*! \file materials.h
   2  * \brief Optical properties of materials.
   3  */
   4 #ifndef QPMS_MATERIALS_H
   5 #define QPMS_MATERIALS_H
   6 #include "qpms_types.h"
   7 #include <gsl/gsl_spline.h>
   8
   9 #ifndef SPEED_OF_LIGHT
  10 /// Speed of light in m/s.
  11 #define SPEED_OF_LIGHT (2.99792458e8)
  12 #endif
  13
  14
  15 /// Prototype for general optical property generator for isotropic materials.
  16 typedef struct qpms_epsmu_generator_t {
  17         /// Generator function.
  18         /** Implemented by:
  19          *  qpms_epsmu_const_g(),
  20          *  qpms_permittivity_interpolator_epsmu_g(),
  21          *  qpms_lorentzdrude_epsmu_g().
  22          */
  23         qpms_epsmu_t (*function) (complex double omega, const void *params);
  24         const void *params;
  25 } qpms_epsmu_generator_t;
  26
  27 /// Convenience function for generating material properties at given frequency.
  28 static inline qpms_epsmu_t qpms_epsmu_generator_eval(
  29                 qpms_epsmu_generator_t gen, complex double omega) {
  30         return gen.function(omega, gen.params);
  31 }
  32
  33 /// Constant optical property "generator" for qpms_epsmu_generator_t.
  34 qpms_epsmu_t qpms_epsmu_const_g(complex double omega, ///< Frequency ignored.
  35         const void *epsmu ///< Points to the qpms_epsmu_t to be returned.
  36         );
  37
  38 /// Gets refractive index of a material from its permeability and permittivity.
  39 /** \f[ n = \sqrt{\mu_r \varepsilon_r} \f] */
  40 static inline complex double qpms_refindex(qpms_epsmu_t em) {
  41         return csqrt(em.eps * em.mu);
  42 }
  43
  44 /// Gets wave number \a k from angular frequency and material permeability and permittivity.
  45 /** \f[ k = \frac{n\omega}{c_0}  = \frac{\omega\sqrt{\mu_r \varepsilon_r}}{c_0} \f] */
  46 static inline complex double qpms_wavenumber(complex double omega, qpms_epsmu_t em) {
  47         return qpms_refindex(em)*omega/SPEED_OF_LIGHT;
  48 }
  49
  50 /// Gets (relative) wave impedance \f$ \eta_r \f$ from material permeability and permittivity.
  51 /** \eta_r = \sqrt{\mu_r  / \varepsilon_r} \f] */
  52 static inline complex double qpms_waveimpedance(qpms_epsmu_t em) {
  53         return csqrt(em.mu / em.eps);
  54 }
  55
  56 /// A \f$ (f_j, \omega_j, \gamma_j) \f$ triple for qpms_ldparams_t.
  57 typedef struct qpms_ldparams_triple_t {
  58         double f;
  59         double omega;
  60         double gamma;
  61 } qpms_ldparams_triple_t;
  62
  63 /// Structure holding Lorentz-Drude model parameters of a material.
  64 /** \f[
  65  * \varepsilon = \varepsilon_\infty + \sum_j=0^{n-1}
  66  *    \frac{f_j \omega_p^2}{\omega_j^2-\omega^2+i\omega\gamma_j}
  67  *  \f]
  68  */
  69 typedef struct qpms_ldparams_t {
  70         complex double eps_inf; ///< Permittivity at infinity.
  71         double omega_p; ///< Plasma frequency.
  72         size_t n; ///< Number of "oscillators".
  73         qpms_ldparams_triple_t data[]; ///< "Oscillator" parameters.
  74 } qpms_ldparams_t;
  75
  76 extern const qpms_ldparams_t *const QPMS_LDPARAMS_AG; ///< Lorentz-Drude parameters from \cite rakic_optical_1998 for silver.
  77 extern const qpms_ldparams_t *const QPMS_LDPARAMS_AU; ///< Lorentz-Drude parameters from \cite rakic_optical_1998 for gold.
  78 extern const qpms_ldparams_t *const QPMS_LDPARAMS_CU; ///< Lorentz-Drude parameters from \cite rakic_optical_1998 for copper.
  79 extern const qpms_ldparams_t *const QPMS_LDPARAMS_AL; ///< Lorentz-Drude parameters from \cite rakic_optical_1998 for aluminium.
  80 extern const qpms_ldparams_t *const QPMS_LDPARAMS_CR; ///< Lorentz-Drude parameters from \cite rakic_optical_1998 for chromium.
  81 extern const qpms_ldparams_t *const QPMS_LDPARAMS_TI; ///< Lorentz-Drude parameters from \cite rakic_optical_1998 for titanium.
  82 extern const qpms_ldparams_t *const QPMS_LDPARAMS_BE; ///< Lorentz-Drude parameters from \cite rakic_optical_1998 for beryllium.
  83 extern const qpms_ldparams_t *const QPMS_LDPARAMS_NI; ///< Lorentz-Drude parameters from \cite rakic_optical_1998 for nickel.
  84 extern const qpms_ldparams_t *const QPMS_LDPARAMS_PD; ///< Lorentz-Drude parameters from \cite rakic_optical_1998 for polonium.
  85 extern const qpms_ldparams_t *const QPMS_LDPARAMS_PT; ///< Lorentz-Drude parameters from \cite rakic_optical_1998 for platinum.
  86 extern const qpms_ldparams_t *const QPMS_LDPARAMS_W ; ///< Lorentz-Drude parameters from \cite rakic_optical_1998 for tungsten.
  87
  88 /// Lorentz-Drude permittivity.
  89 complex double qpms_lorentzdrude_eps(complex double omega, const qpms_ldparams_t *);
  90
  91 /// Lorentz-Drude optical properties, with relative permeability set always to one.
  92 qpms_epsmu_t qpms_lorentzdrude_epsmu(complex double omega, const qpms_ldparams_t *);
  93
  94 /// Lorentz-Drude optical properties, with relative permeability set always to one, compatible with qpms_epsmu_generator_t.
  95 qpms_epsmu_t qpms_lorentzdrude_epsmu_g(
  96                 complex double omega,
  97                 const void *ldparams ///< Lorentz-Drude parameters, in reality const qpms_ldparams_t *.
  98                 );
  99
 100
 101 /// Interpolator of tabulated optical properties.
 102 // TODO use gsl_interp instead of gsl_spline.
 103 typedef struct qpms_permittivity_interpolator_t {
 104         double *wavelength_m; ///< Wavelength array (in meters).
 105         double *n; ///< Refraction index array.
 106         double *k; ///< Attenuation coefficient array.
 107         gsl_interp *interp_n; ///< Refraction index interpolator object.
 108         gsl_interp *interp_k; ///< Attenuation coeff interpolator object.
 109         size_t size; ///< Size of n[], k[], and wavelength_m[].
 110         // I could add gsl_interp_accel, but that is not necessary.
 111 } qpms_permittivity_interpolator_t;
 112
 113 /// Creates a permittivity interpolator from tabulated wavelengths, refraction indices and extinction coeffs.
 114 qpms_permittivity_interpolator_t *qpms_permittivity_interpolator_create(const size_t incount,
 115                 const double *wavelength_m, ///< Tabulated vacuum wavelength in metres, in strictly increasing order.
 116                 const double *n, ///< Tabulated refraction indices at omega.
 117                 const double *k, ///< Tabulated extinction coefficients.
 118                 const gsl_interp_type *iptype ///< GSL interpolator type
 119                 );
 120
 121 /// Creates a permittivity interpolator from an yml file downloaded from refractiveindex.info website.
 122 qpms_permittivity_interpolator_t *qpms_permittivity_interpolator_from_yml(
 123                 const char *path, ///< Path to the yml file.
 124                 const gsl_interp_type *iptype ///< GSL interpolator type
 125                 );
 126
 127 /// Evaluates interpolated material permittivity at a given angular frequency.
 128 complex double qpms_permittivity_interpolator_eps_at_omega(
 129                 const qpms_permittivity_interpolator_t *interp, double omega_SI);
 130
 131 /// Evaluates interpolated material permittivity at a given angular frequency, qpms_epsmu_generator_t compatible version.
 132 /** Permeability is always set to one. Imaginary part of omega is discarded.
 133  */
 134 qpms_epsmu_t qpms_permittivity_interpolator_epsmu_g(
 135                 complex double omega, ///< Angular frequency. The imaginary part is ignored!
 136                 const void * interpolator ///< Interpolator of type qpms_permittivity_interpolator_t
 137                 );
 138
 139 /// Returns the minimum angular frequency supported by the interpolator.
 140 double qpms_permittivity_interpolator_omega_min(
 141                 const qpms_permittivity_interpolator_t *ip);
 142
 143 /// Returns the minimum angular frequency supported by the interpolator.
 144 double qpms_permittivity_interpolator_omega_max(
 145                 const qpms_permittivity_interpolator_t *ip);
 146
 147 /// Destroy a permittivity interpolator.
 148 void qpms_permittivity_interpolator_free(qpms_permittivity_interpolator_t *interp);
 149
 150 /// Relative permittivity from the Drude model.
 151 static inline complex double qpms_drude_epsilon(
 152                 complex double eps_inf, ///< Relative permittivity "at infinity".
 153                 complex double omega_p, ///< Plasma frequency \f$ \omega_p \f$ of the material.
 154                 complex double gamma_p, ///< Decay constant \f$ \gamma_p \f$ of the material.
 155                 complex double omega ///< Frequency \f$ \omega \f$ at which the permittivity is evaluated.
 156                 ) {
 157         return eps_inf - omega_p*omega_p/(omega*(omega+I*gamma_p));
 158 }
 159
 160
 161 #endif //QPMS_MATERIALS_H