gaussian_beams.py 5.79 KB
Newer Older
1
2
3
import pykat.exceptions as pkex
import numpy
import math
4
import copy
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
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's avatar
Daniel Brown committed
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
                
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's avatar
Daniel Brown committed
49
                raise pkex.BasePyKatException("Must specify: z and w0 or z and zr or rc and wz or q, to define the beam parameter")
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
                
            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
    def wz(self):
72
        return self.w0 * math.sqrt(1 + (self.__q.real/self.__q.imag)**2)
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
98
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
    
    @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):
        self.__q += complex(a)
        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):
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
187
188
189
190
    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)
                
    def Unm(self, n, m, x, y):    
        return self.__xpre_const * special