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Merge pull request #14 from DanielKotik/develop
Python package `optbeam`
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| Original file line number | Diff line number | Diff line change |
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| [bumpversion] | ||
| current_version = 1.4.2 | ||
| commit = True | ||
| tag = True | ||
| sign_tags = True | ||
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| [bumpversion:file:setup.py] | ||
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| [bumpversion:file:optbeam/__init__.py] | ||
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| [bumpversion:file:CITATION.cff] |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,136 @@ | ||
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| import math | ||
| import sys | ||
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| try: | ||
| import cython | ||
| except ModuleNotFoundError: | ||
| cython = None | ||
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| if not cython or not cython.compiled: | ||
| from math import (exp as _exp, | ||
| sqrt as _sqrt) | ||
| from cmath import exp as _cexp | ||
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| if cython and not cython.compiled: | ||
| print("\nPlease consider compiling `%s.py` via Cython: " | ||
| "`$ cythonize -3 -i %s.py`\n" % (__name__, __name__)) | ||
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| from .helpers import _complex_quad, Beam2d | ||
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| class Beam2dCartesian(Beam2d): | ||
| """...""" | ||
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| def profile(self, r): | ||
| """Field amplitude function. | ||
| Plane wave decomposition: calculate field amplitude at light source | ||
| position if not coinciding with beam waist. | ||
| """ | ||
| self._ry = r.y | ||
| self._rz = r.z | ||
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| if not self.called: | ||
| print("Calculating inital field configuration. " | ||
| "This will take some time...") | ||
| self.called = True | ||
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| try: | ||
| (result, | ||
| real_tol, | ||
| imag_tol) = _complex_quad(self if cython | ||
| and cython.compiled else self._integrand, | ||
| -self._k, self._k) | ||
| except Exception as e: | ||
| print(type(e).__name__ + ":", e) | ||
| sys.exit() | ||
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| return result | ||
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| def spectrum(self, k_y): | ||
| """Spectrum amplitude distribution function, f.""" | ||
| raise NotImplementedError | ||
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| def _phase(self, k_y, x, y): | ||
| """Phase function.""" | ||
| return x*_sqrt(self._k**2 - k_y**2) + k_y*y | ||
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| def _integrand(self, k_y): | ||
| """Integrand function.""" | ||
| return self.spectrum(k_y) * _cexp(1j*self._phase(k_y, self.x, self._ry)) | ||
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| # ----------------------------------------------------------------------------- | ||
| # specific beam implementations based on Beam2dCartesian base class | ||
| # ----------------------------------------------------------------------------- | ||
| class Gauss2d(Beam2dCartesian): | ||
| """2d Gauss beam.""" | ||
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| def __init__(self, x, params, called=False): | ||
| """...""" | ||
| self._W_y = params['W_y'] | ||
| self._norm = 2 * _sqrt(math.pi) / self._W_y | ||
| super().__init__(x, params, called) | ||
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| def profile(self, r): | ||
| """...""" | ||
| # beam profile distribution (field amplitude) at the waist of the beam | ||
| if self.x == 0: | ||
| return self._norm * _exp(-(r.y / self._W_y)**2) | ||
| else: | ||
| return super().profile(r) | ||
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| def spectrum(self, k_y): | ||
| """Spectrum amplitude function, f.""" | ||
| return self._f_Gauss(k_y, self._W_y) | ||
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| def _f_Gauss(self, k_y, W_y): | ||
| """Gaussian spectrum amplitude.""" | ||
| return _exp(-(k_y*W_y/2)**2) | ||
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| class IncAiry2d(Beam2dCartesian): | ||
| """2d incomplete Airy beam.""" | ||
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| def __init__(self, x, params, called=False): | ||
| """...""" | ||
| self._W_y = params['W_y'] | ||
| self._M = params['M'] | ||
| self._W = params['W'] | ||
| super().__init__(x, params, called) | ||
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| def profile(self, r): | ||
| """...""" | ||
| if self.x == 0: | ||
| # adjust integration boundaries | ||
| self._a = self._M-self._W | ||
| self._b = self._M+self._W | ||
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| return super().profile(r) | ||
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| def spectrum(self, k_y): | ||
| """...""" | ||
| return self._f_Airy(k_y, self._W_y, self._M, self._W) | ||
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| def _f_Airy(self, k_y, W_y, M, W): | ||
| """Airy spectrum amplitude.""" | ||
| return W_y * _cexp(1.0j*(-1/3)*(k_y*W_y)**3) \ | ||
| * self._heaviside(W_y * k_y - (M - W)) \ | ||
| * self._heaviside((M + W) - W_y * k_y) | ||
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| def _heaviside(self, x): | ||
| """Theta (Heaviside step) function.""" | ||
| return 0 if x < 0 else 1 | ||
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| def _integrand(self, k_y): | ||
| """...""" | ||
| if self.x == 0: | ||
| xi = k_y | ||
| return _cexp(1.0j*(-(xi**3)/3 + (xi * self._ry/self._W_y))) | ||
| else: | ||
| # next line needs _integrand declared cpdef without nogil attribute, | ||
| # and will execute slower than repeating the super class integration | ||
| # routine function here | ||
| #return super(IncAiry2d, self)._integrand(k_y) | ||
| return self.spectrum(k_y) * _cexp(1j*self._phase(k_y, self.x, self._ry)) |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,95 @@ | ||
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| import sys | ||
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| try: | ||
| import cython | ||
| except ModuleNotFoundError: | ||
| cython = None | ||
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| if cython: | ||
| if cython.compiled: | ||
| from scipy import LowLevelCallable | ||
| else: | ||
| print("\nPlease consider compiling `%s.py` via Cython: " | ||
| "`$ cythonize -3 -i %s.py`\n" % (__name__, __name__)) | ||
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| from scipy.integrate import quad | ||
| from types import MappingProxyType | ||
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| def _real_1d_func(x, func): | ||
| """Return real part of a 1d function.""" | ||
| return func(x).real | ||
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| def _imag_1d_func(x, func): | ||
| """Return imag part of a 1d function.""" | ||
| return func(x).imag | ||
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| def _imag_1d_func_c(n, arr, func_ptr): | ||
| """Return imag part of a 1d function. | ||
| Cython implementation. | ||
| """ | ||
| # pure python formulation of: | ||
| # return (<Beam2dCartesian>func_ptr)(arr[0]).imag | ||
| return cython.cast(Beam2d, func_ptr)._integrand(arr[0]).imag | ||
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| def _real_1d_func_c(n, arr, func_ptr): | ||
| """Return real part of a 1d function. | ||
| Cython implementation. | ||
| """ | ||
| # pure python formulation of: | ||
| # return (<Beam2dCartesian>func_ptr)(arr[0]).real | ||
| return cython.cast(Beam2d, func_ptr)._integrand(arr[0]).real | ||
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| def _complex_quad(func, a, b, kwargs={}): | ||
| """Integrate real and imaginary part of the given function.""" | ||
| if cython and cython.compiled: | ||
| # pure python formulation of: cdef void *f_ptr = <void*>func | ||
| f_ptr = cython.declare(cython.p_void, cython.cast(cython.p_void, func)) | ||
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| func_capsule = PyCapsule_New(f_ptr, cython.NULL, cython.NULL) | ||
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| current_module = sys.modules[__name__] | ||
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| ll_real_1d_func_c = LowLevelCallable.from_cython(current_module, | ||
| '_real_1d_func_c', | ||
| func_capsule) | ||
| ll_imag_1d_func_c = LowLevelCallable.from_cython(current_module, | ||
| '_imag_1d_func_c', | ||
| func_capsule) | ||
| real, real_tol = quad(ll_real_1d_func_c, a, b, **kwargs) | ||
| imag, imag_tol = quad(ll_imag_1d_func_c, a, b, **kwargs) | ||
| else: | ||
| real, real_tol = quad(_real_1d_func, a, b, (func,), **kwargs) | ||
| imag, imag_tol = quad(_imag_1d_func, a, b, (func,), **kwargs) | ||
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| return real + 1j*imag, real_tol, imag_tol | ||
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| class Beam2d: | ||
| """Abstract base class.""" | ||
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| def __init__(self, x, params, called=False): | ||
| """...""" | ||
| self.x = x | ||
| self._k = params['k'] | ||
| self._params = MappingProxyType(params) # read-only view of a dict | ||
| self.called = called | ||
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| @property | ||
| def params(self): | ||
| """Beam specific parameters. | ||
| This is a read-only property. | ||
| """ | ||
| return self._params | ||
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| def _integrand(self, x): | ||
| """Integrand function over one coordinate x.""" | ||
| raise NotImplementedError |
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