gaussian_beams.py 5.81 KB
 Daniel Brown committed Dec 05, 2013 1 2 3 import pykat.exceptions as pkex import numpy import math  4 import copy  Daniel Brown committed Dec 05, 2013 5 6 7 8 9 10 11 12 13 14 15 16 17  class gauss_param(object): """ Gaussian beam complex parameter gauss_param is effectively a complex number with extra functionality to determine beam parameters. defaults to 1064e-9m for wavelength and refractive index 1 usage: q = gauss_param(w0=w0, z=z) q = gauss_param(z=z, zr=zr) q = gauss_param(wz=wz, rc=rc)  18  q = gauss_param(q=a) # where a is a complex number  Daniel Brown committed Dec 05, 2013 19 20 21 22 23 24 25 26 27 28 29 30 31  or change default wavelength and refractive index with: q = gauss_param(wavelength, nr, w0=w0, zr=zr) """ def __init__(self, wavelength=1064e-9, nr=1, *args, **kwargs): self.__q = None self.__lambda = wavelength self.__nr = nr if len(args) == 1: self.__q = args[0]  32 33 34 35 36  elif len(kwargs) == 1: if "q" in kwargs: self.__q = complex(kwargs["q"]) else:  Daniel Brown committed Dec 09, 2013 37  raise pkex.BasePyKatException("Must specify: z and w0 or z and zr or rc and wz or q, to define the beam parameter")  38   Daniel Brown committed Dec 05, 2013 39 40 41 42 43 44 45 46 47 48  elif len(kwargs) == 2: if "w0" in kwargs and "z" in kwargs: q = float(kwargs["z"]) + 1j *float(math.pi*kwargs["w0"]**2/(self.__lambda/self.__nr) ) elif "z" in kwargs and "zr" in kwargs: q = float(kwargs["z"]) + 1j *float(kwargs["zr"]) elif "rc" in kwargs and "wz" in kwargs: one_q = 1 / kwargs["rc"] - 1j * self.__lamda / (math.pi * self.__nr * kwargs["wz"]**2) q = 1/one_q else:  Daniel Brown committed Dec 09, 2013 49  raise pkex.BasePyKatException("Must specify: z and w0 or z and zr or rc and wz or q, to define the beam parameter")  Daniel Brown committed Dec 05, 2013 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70  self.__q = q else: raise pkex.BasePyKatException("Incorrect usage for gauss_param constructor") @property def wavelength(self): return self.__lambda @property def nr(self): return self.__nr @property def q(self): return self.__q @property def z(self): return self.__q.real @property def zr(self): return self.__q.imag @property  Andreas Freise committed Jan 09, 2014 71  def w(self):  Daniel Brown committed Dec 12, 2013 72  return self.w0 * math.sqrt(1 + (self.__q.real/self.__q.imag)**2)  Daniel Brown committed Dec 05, 2013 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97  @property def w0(self): return math.sqrt(self.__q.imag * self.__lambda / (self.__nr * math.pi)) @property def Rc(self): if self.__q.real != 0: return abs(self.__q) / self.__q.real else: return float("inf") def conjugate(self): return gauss_param(self.__lambda, self.__nr, self.__q.conjugate()) def __complex__(self): return self.__q def __str__(self): return str(self.__q) def __mul__(self, a): return gauss_param(self.__lambda, self.__nr, self.__q * complex(a)) def __imul__(self, a):  Daniel Brown committed Dec 15, 2013 98  self.__q *= complex(a)  Daniel Brown committed Dec 05, 2013 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134  return self __rmul__ = __mul__ def __add__(self, a): return gauss_param(self.__lambda, self.__nr, self.__q + complex(a)) def __iadd__(self, a): self.__q += complex(a) return self __radd__ = __add__ def __sub__(self, a): return gauss_param(self.__lambda, self.__nr, self.__q - complex(a)) def __isub__(self, a): self.__q -= complex(a) return self __rsub__ = __sub__ def __div__(self, a): return gauss_param(self.__lambda, self.__nr, self.__q / complex(a)) def __idiv__(self, a): self.__q /= complex(a) return self def __pow__(self, q): return gauss_param(self.__lambda, self.__nr, self.__q**q) def __neg__(self, q): return gauss_param(self.__lambda, self.__nr, -self.__q) def __eq__(self, q):  Daniel Brown committed Dec 11, 2013 135 136 137 138 139 140 141 142 143 144  return complex(q) == self.__q @property def real(self): return self.__q.real @real.setter def real(self, value): self.__q.real = SIfloat(value) @property def imag(self): return self.__q.imag @imag.setter  145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186  def imag(self, value): self.__q.imag = SIfloat(value) class HG_gauss_beam(object): def __init__(self, qx, qy=None, n=0, m=0): self._qx = copy.deepcopy(qx) self._2pi_qrt = math.pow(2.0/math.pi, 0.25) if qy == None: self._q0 = copy.deepcopy(qx) else: self._q0 = copy.deepcopy(qy) self.n = n self.m = m self._calc_constants() @property def n(self): return self._n @n.setter def n(self,value): self._n = float(value) self._calc_constants() @property def m(self): return self._m @m.setter def m(self,value): self._m = float(value) self._calc_constants() def _calc_constants(self): self.__xpre_const = math.pow(2.0/math.pi, 0.25) self.__xpre_const *= math.sqrt(1/(2**self._n * math.factorial(self._n))) self.__xpre_const *= math.sqrt(1j*self._qx.imag / self._qx) self.__xpre_const *= math.pow((1j*self._qx.imag * self._qx.conjugate)/(-1j*self._qx.imag * self._qx), self._n/2.0) self.__ypre_const = math.pow(2.0/math.pi, 0.25) self.__ypre_const *= math.sqrt(1/(2**self._m * math.factorial(self._m))) self.__ypre_const *= math.sqrt(1j*self._qy.imag / self._qy) self.__ypre_const *= math.pow((1j*self._qy.imag * self._qy.conjugate)/(-1j*self._qy.imag * self._qy), self._m/2.0)  Daniel Brown committed Dec 15, 2013 187 188 189  def Unm(self, n, m, x, y): # need to finish... return self.__xpre_const  190   Andreas Freise committed Jan 09, 2014 191