Commit 714cc923 authored by Andreas Freise's avatar Andreas Freise
Browse files

adding hg2lg function, has been tested, but need to add test example

parent 0fedb516
Pipeline #1185 passed with stage
......@@ -9,7 +9,8 @@ import math
import copy
import warnings
import cmath
from scipy.special import hermite
from math import factorial
from scipy.special import hermite, jacobi
from pykat.SIfloat import SIfloat
class gauss_param(object):
......@@ -405,3 +406,48 @@ class HG_beam(object):
def hg2lg(n,m):
"""A function for Matlab which returns the coefficients and mode indices of
the LG modes required to create a particular HG mode.
Usage: coefficients,ps,ls = hg2lg(n,m)
n,m: Indces of the HG mode to re-create.
coeffcients: Complex coefficients for each order=n+m LG mode required to
re-create HG_n,m.
ps,ls: LG mode indices corresponding to coefficients.
# Mode order
N = n+m;
# Create empty vectors for LG coefficients/ indices
coefficients = np.linspace(0,0,N+1,dtype=np.complex_)
ps = np.linspace(0,0,N+1)
ls = np.linspace(0,0,N+1)
# Calculate coefficients
for j in np.arange(0,N+1):
# Indices for coefficients
l = 2*j-N
p = int((N-np.abs(l))/2)
ps[j] = p
ls[j] = l
signl = np.sign(l)
if (l==0):
signl = 1.0
# Coefficient
c = (signl*1j)**m * np.sqrt(factorial(N-m)*factorial(m)/(2**N * factorial(np.abs(l)+p)*factorial(p)))
c = c * (-1.0)**p * (-2.0)**m * scipy.special.eval_jacobi(m,np.abs(l)+p-m,p-m,0.0)
coefficients[j] = c
return coefficients, ps, ls
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