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fieldgenesis.py
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fieldgenesis.py
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import numpy as np
from scipy import special
import warnings
from printech import *
printer("ATTENTION: disabling RuntimeWarning often triggered due to evaluation of square roots with negative arguments")
warnings.filterwarnings("ignore", category=RuntimeWarning)
def TE_ECoregenρ(a,kFree,kz,m,nCladding,nCore):
'''
Parameters
----------
a : float
radius of the waveguide core.
kFree : float)
free space wavenumber.
kz : float
longitudinal propagation constant.
m : int
mode order, for HE modes m>=1, for TM and TE, m=0.
nCladding : float
refractive index of cladding.
nCore : float
refractive index of core.
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
Returns
-------
TE_ECoreρ : func
'''
def TE_ECoreρ(ρ):
'''
Returns the radial component of TE_ECore without the azimuthal dependence.
The azimuthal dependence depends on the parity of the field:
even -> cos(mϕ)
odd -> sin(mϕ)
Parameters
----------
ρ : float
The radial coordinate.
Returns
-------
TE_ECoreρ : real
'''
return 0
return TE_ECoreρ
def TE_ECoregenϕ(a,kFree,kz,m,nCladding,nCore):
'''
Parameters
----------
a : float
radius of the waveguide core.
kFree : float)
free space wavenumber.
kz : float
longitudinal propagation constant.
m : int
mode order, for HE modes m>=1, for TM and TE, m=0.
nCladding : float
refractive index of cladding.
nCore : float
refractive index of core.
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
Returns
-------
TE_ECoreϕ : func
'''
def TE_ECoreϕ(ρ):
'''
Returns the azimuthal component of TE_ECore without the azimuthal dependence.
The azimuthal dependence depends on the parity of the field:
even -> -sin(mϕ)
odd -> cos(mϕ)
Parameters
----------
ρ : float
The radial coordinate.
Returns
-------
TE_ECoreϕ : real
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
'''
return -(special.jv(1,np.sqrt(-kz**2 + kFree**2*nCore**2)*ρ)/special.jv(1,a*np.sqrt(-kz**2 + kFree**2*nCore**2)))
return TE_ECoreϕ
def TE_ECoregenz(a,kFree,kz,m,nCladding,nCore):
'''
Parameters
----------
a : float
radius of the waveguide core.
kFree : float)
free space wavenumber.
kz : float
longitudinal propagation constant.
m : int
mode order, for HE modes m>=1, for TM and TE, m=0.
nCladding : float
refractive index of cladding.
nCore : float
refractive index of core.
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
Returns
-------
TE_ECorez : func
'''
def TE_ECorez(ρ):
'''
Returns the transverse component of TE_ECore without the azimuthal dependence.
The azimuthal dependence depends on the parity of the field:
even -> cos(mϕ)
odd -> sin(mϕ)
Parameters
----------
ρ : float
The radial coordinate.
Returns
-------
TE_ECorez : complex
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
'''
return 0
return TE_ECorez
def TM_ECoregenρ(a,kFree,kz,m,nCladding,nCore):
'''
Parameters
----------
a : float
radius of the waveguide core.
kFree : float)
free space wavenumber.
kz : float
longitudinal propagation constant.
m : int
mode order, for HE modes m>=1, for TM and TE, m=0.
nCladding : float
refractive index of cladding.
nCore : float
refractive index of core.
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
Returns
-------
TM_ECoreρ : func
'''
def TM_ECoreρ(ρ):
'''
Returns the radial component of TM_ECore without the azimuthal dependence.
The azimuthal dependence depends on the parity of the field:
even -> cos(mϕ)
odd -> sin(mϕ)
Parameters
----------
ρ : float
The radial coordinate.
Returns
-------
TM_ECoreρ : real
'''
return special.jv(1,np.sqrt(-kz**2 + kFree**2*nCore**2)*ρ)/special.jv(1,a*np.sqrt(-kz**2 + kFree**2*nCore**2))
return TM_ECoreρ
def TM_ECoregenϕ(a,kFree,kz,m,nCladding,nCore):
'''
Parameters
----------
a : float
radius of the waveguide core.
kFree : float)
free space wavenumber.
kz : float
longitudinal propagation constant.
m : int
mode order, for HE modes m>=1, for TM and TE, m=0.
nCladding : float
refractive index of cladding.
nCore : float
refractive index of core.
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
Returns
-------
TM_ECoreϕ : func
'''
def TM_ECoreϕ(ρ):
'''
Returns the azimuthal component of TM_ECore without the azimuthal dependence.
The azimuthal dependence depends on the parity of the field:
even -> -sin(mϕ)
odd -> cos(mϕ)
Parameters
----------
ρ : float
The radial coordinate.
Returns
-------
TM_ECoreϕ : real
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
'''
return 0
return TM_ECoreϕ
def TM_ECoregenz(a,kFree,kz,m,nCladding,nCore):
'''
Parameters
----------
a : float
radius of the waveguide core.
kFree : float)
free space wavenumber.
kz : float
longitudinal propagation constant.
m : int
mode order, for HE modes m>=1, for TM and TE, m=0.
nCladding : float
refractive index of cladding.
nCore : float
refractive index of core.
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
Returns
-------
TM_ECorez : func
'''
def TM_ECorez(ρ):
'''
Returns the transverse component of TM_ECore without the azimuthal dependence.
The azimuthal dependence depends on the parity of the field:
even -> cos(mϕ)
odd -> sin(mϕ)
Parameters
----------
ρ : float
The radial coordinate.
Returns
-------
TM_ECorez : complex
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
'''
return (1j*np.sqrt(-kz**2 + kFree**2*nCore**2)*special.jv(0,np.sqrt(-kz**2 + kFree**2*nCore**2)*ρ))/(kz*special.jv(1,a*np.sqrt(-kz**2 + kFree**2*nCore**2)))
return TM_ECorez
def HE_ECoregenρ(a,kFree,kz,m,nCladding,nCore):
'''
Parameters
----------
a : float
radius of the waveguide core.
kFree : float)
free space wavenumber.
kz : float
longitudinal propagation constant.
m : int
mode order, for HE modes m>=1, for TM and TE, m=0.
nCladding : float
refractive index of cladding.
nCore : float
refractive index of core.
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
Returns
-------
HE_ECoreρ : func
'''
def HE_ECoreρ(ρ):
'''
Returns the radial component of HE_ECore without the azimuthal dependence.
The azimuthal dependence depends on the parity of the field:
even -> cos(mϕ)
odd -> sin(mϕ)
Parameters
----------
ρ : float
The radial coordinate.
Returns
-------
HE_ECoreρ : real
'''
return -0.5*(special.jv(-1 + m,np.sqrt(-kz**2 + kFree**2*nCore**2)*ρ)*(-1 - (2*kFree**2*m*(nCladding**2 - nCore**2)*special.jv(m,a*np.sqrt(-kz**2 + kFree**2*nCore**2))*special.kn(m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))))/(a*(kz**2 - kFree**2*nCladding**2)*np.sqrt(-kz**2 + kFree**2*nCore**2)*(special.jv(-1 + m,a*np.sqrt(-kz**2 + kFree**2*nCore**2)) - special.jv(1 + m,a*np.sqrt(-kz**2 + kFree**2*nCore**2)))*special.kn(m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))) + np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))*(kz**2 - kFree**2*nCore**2)*special.jv(m,a*np.sqrt(-kz**2 + kFree**2*nCore**2))*(special.kn(-1 + m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))) + special.kn(1 + m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2)))))) + special.jv(1 + m,np.sqrt(-kz**2 + kFree**2*nCore**2)*ρ)*(1 - (2*kFree**2*m*(nCladding**2 - nCore**2)*special.jv(m,a*np.sqrt(-kz**2 + kFree**2*nCore**2))*special.kn(m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))))/(a*(kz**2 - kFree**2*nCladding**2)*np.sqrt(-kz**2 + kFree**2*nCore**2)*(special.jv(-1 + m,a*np.sqrt(-kz**2 + kFree**2*nCore**2)) - special.jv(1 + m,a*np.sqrt(-kz**2 + kFree**2*nCore**2)))*special.kn(m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))) + np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))*(kz**2 - kFree**2*nCore**2)*special.jv(m,a*np.sqrt(-kz**2 + kFree**2*nCore**2))*(special.kn(-1 + m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))) + special.kn(1 + m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2)))))))/special.jv(m,a*np.sqrt(-kz**2 + kFree**2*nCore**2))
return HE_ECoreρ
def HE_ECoregenϕ(a,kFree,kz,m,nCladding,nCore):
'''
Parameters
----------
a : float
radius of the waveguide core.
kFree : float)
free space wavenumber.
kz : float
longitudinal propagation constant.
m : int
mode order, for HE modes m>=1, for TM and TE, m=0.
nCladding : float
refractive index of cladding.
nCore : float
refractive index of core.
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
Returns
-------
HE_ECoreϕ : func
'''
def HE_ECoreϕ(ρ):
'''
Returns the azimuthal component of HE_ECore without the azimuthal dependence.
The azimuthal dependence depends on the parity of the field:
even -> -sin(mϕ)
odd -> cos(mϕ)
Parameters
----------
ρ : float
The radial coordinate.
Returns
-------
HE_ECoreϕ : real
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
'''
return -0.5*(special.jv(-1 + m,np.sqrt(-kz**2 + kFree**2*nCore**2)*ρ)*(-1 - (2*kFree**2*m*(nCladding**2 - nCore**2)*special.jv(m,a*np.sqrt(-kz**2 + kFree**2*nCore**2))*special.kn(m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))))/(a*(kz**2 - kFree**2*nCladding**2)*np.sqrt(-kz**2 + kFree**2*nCore**2)*(special.jv(-1 + m,a*np.sqrt(-kz**2 + kFree**2*nCore**2)) - special.jv(1 + m,a*np.sqrt(-kz**2 + kFree**2*nCore**2)))*special.kn(m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))) + np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))*(kz**2 - kFree**2*nCore**2)*special.jv(m,a*np.sqrt(-kz**2 + kFree**2*nCore**2))*(special.kn(-1 + m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))) + special.kn(1 + m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2)))))) - special.jv(1 + m,np.sqrt(-kz**2 + kFree**2*nCore**2)*ρ)*(1 - (2*kFree**2*m*(nCladding**2 - nCore**2)*special.jv(m,a*np.sqrt(-kz**2 + kFree**2*nCore**2))*special.kn(m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))))/(a*(kz**2 - kFree**2*nCladding**2)*np.sqrt(-kz**2 + kFree**2*nCore**2)*(special.jv(-1 + m,a*np.sqrt(-kz**2 + kFree**2*nCore**2)) - special.jv(1 + m,a*np.sqrt(-kz**2 + kFree**2*nCore**2)))*special.kn(m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))) + np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))*(kz**2 - kFree**2*nCore**2)*special.jv(m,a*np.sqrt(-kz**2 + kFree**2*nCore**2))*(special.kn(-1 + m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))) + special.kn(1 + m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2)))))))/special.jv(m,a*np.sqrt(-kz**2 + kFree**2*nCore**2))
return HE_ECoreϕ
def HE_ECoregenz(a,kFree,kz,m,nCladding,nCore):
'''
Parameters
----------
a : float
radius of the waveguide core.
kFree : float)
free space wavenumber.
kz : float
longitudinal propagation constant.
m : int
mode order, for HE modes m>=1, for TM and TE, m=0.
nCladding : float
refractive index of cladding.
nCore : float
refractive index of core.
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
Returns
-------
HE_ECorez : func
'''
def HE_ECorez(ρ):
'''
Returns the transverse component of HE_ECore without the azimuthal dependence.
The azimuthal dependence depends on the parity of the field:
even -> cos(mϕ)
odd -> sin(mϕ)
Parameters
----------
ρ : float
The radial coordinate.
Returns
-------
HE_ECorez : complex
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
'''
return ((-1j)*np.sqrt(-kz**2 + kFree**2*nCore**2)*special.jv(m,np.sqrt(-kz**2 + kFree**2*nCore**2)*ρ))/(kz*special.jv(m,a*np.sqrt(-kz**2 + kFree**2*nCore**2)))
return HE_ECorez
def TE_ECladdinggenρ(a,kFree,kz,m,nCladding,nCore):
'''
Parameters
----------
a : float
radius of the waveguide core.
kFree : float)
free space wavenumber.
kz : float
longitudinal propagation constant.
m : int
mode order, for HE modes m>=1, for TM and TE, m=0.
nCladding : float
refractive index of cladding.
nCore : float
refractive index of core.
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
Returns
-------
TE_ECladdingρ : func
'''
def TE_ECladdingρ(ρ):
'''
Returns the radial component of TE_ECladding without the azimuthal dependence.
The azimuthal dependence depends on the parity of the field:
even -> cos(mϕ)
odd -> sin(mϕ)
Parameters
----------
ρ : float
The radial coordinate.
Returns
-------
TE_ECladdingρ : real
'''
return 0
return TE_ECladdingρ
def TE_ECladdinggenϕ(a,kFree,kz,m,nCladding,nCore):
'''
Parameters
----------
a : float
radius of the waveguide core.
kFree : float)
free space wavenumber.
kz : float
longitudinal propagation constant.
m : int
mode order, for HE modes m>=1, for TM and TE, m=0.
nCladding : float
refractive index of cladding.
nCore : float
refractive index of core.
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
Returns
-------
TE_ECladdingϕ : func
'''
def TE_ECladdingϕ(ρ):
'''
Returns the azimuthal component of TE_ECladding without the azimuthal dependence.
The azimuthal dependence depends on the parity of the field:
even -> -sin(mϕ)
odd -> cos(mϕ)
Parameters
----------
ρ : float
The radial coordinate.
Returns
-------
TE_ECladdingϕ : real
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
'''
return -(special.kn(1,(np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))*ρ)/a)/special.kn(1,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))))
return TE_ECladdingϕ
def TE_ECladdinggenz(a,kFree,kz,m,nCladding,nCore):
'''
Parameters
----------
a : float
radius of the waveguide core.
kFree : float)
free space wavenumber.
kz : float
longitudinal propagation constant.
m : int
mode order, for HE modes m>=1, for TM and TE, m=0.
nCladding : float
refractive index of cladding.
nCore : float
refractive index of core.
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
Returns
-------
TE_ECladdingz : func
'''
def TE_ECladdingz(ρ):
'''
Returns the transverse component of TE_ECladding without the azimuthal dependence.
The azimuthal dependence depends on the parity of the field:
even -> cos(mϕ)
odd -> sin(mϕ)
Parameters
----------
ρ : float
The radial coordinate.
Returns
-------
TE_ECladdingz : complex
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
'''
return 0
return TE_ECladdingz
def TM_ECladdinggenρ(a,kFree,kz,m,nCladding,nCore):
'''
Parameters
----------
a : float
radius of the waveguide core.
kFree : float)
free space wavenumber.
kz : float
longitudinal propagation constant.
m : int
mode order, for HE modes m>=1, for TM and TE, m=0.
nCladding : float
refractive index of cladding.
nCore : float
refractive index of core.
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
Returns
-------
TM_ECladdingρ : func
'''
def TM_ECladdingρ(ρ):
'''
Returns the radial component of TM_ECladding without the azimuthal dependence.
The azimuthal dependence depends on the parity of the field:
even -> cos(mϕ)
odd -> sin(mϕ)
Parameters
----------
ρ : float
The radial coordinate.
Returns
-------
TM_ECladdingρ : real
'''
return (nCore**2*special.kn(1,(np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))*ρ)/a))/(nCladding**2*special.kn(1,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))))
return TM_ECladdingρ
def TM_ECladdinggenϕ(a,kFree,kz,m,nCladding,nCore):
'''
Parameters
----------
a : float
radius of the waveguide core.
kFree : float)
free space wavenumber.
kz : float
longitudinal propagation constant.
m : int
mode order, for HE modes m>=1, for TM and TE, m=0.
nCladding : float
refractive index of cladding.
nCore : float
refractive index of core.
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
Returns
-------
TM_ECladdingϕ : func
'''
def TM_ECladdingϕ(ρ):
'''
Returns the azimuthal component of TM_ECladding without the azimuthal dependence.
The azimuthal dependence depends on the parity of the field:
even -> -sin(mϕ)
odd -> cos(mϕ)
Parameters
----------
ρ : float
The radial coordinate.
Returns
-------
TM_ECladdingϕ : real
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
'''
return 0
return TM_ECladdingϕ
def TM_ECladdinggenz(a,kFree,kz,m,nCladding,nCore):
'''
Parameters
----------
a : float
radius of the waveguide core.
kFree : float)
free space wavenumber.
kz : float
longitudinal propagation constant.
m : int
mode order, for HE modes m>=1, for TM and TE, m=0.
nCladding : float
refractive index of cladding.
nCore : float
refractive index of core.
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
Returns
-------
TM_ECladdingz : func
'''
def TM_ECladdingz(ρ):
'''
Returns the transverse component of TM_ECladding without the azimuthal dependence.
The azimuthal dependence depends on the parity of the field:
even -> cos(mϕ)
odd -> sin(mϕ)
Parameters
----------
ρ : float
The radial coordinate.
Returns
-------
TM_ECladdingz : complex
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
'''
return ((-1j)*np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))*nCore**2*special.kn(0,(np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))*ρ)/a))/(a*kz*nCladding**2*special.kn(1,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))))
return TM_ECladdingz
def HE_ECladdinggenρ(a,kFree,kz,m,nCladding,nCore):
'''
Parameters
----------
a : float
radius of the waveguide core.
kFree : float)
free space wavenumber.
kz : float
longitudinal propagation constant.
m : int
mode order, for HE modes m>=1, for TM and TE, m=0.
nCladding : float
refractive index of cladding.
nCore : float
refractive index of core.
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
Returns
-------
HE_ECladdingρ : func
'''
def HE_ECladdingρ(ρ):
'''
Returns the radial component of HE_ECladding without the azimuthal dependence.
The azimuthal dependence depends on the parity of the field:
even -> cos(mϕ)
odd -> sin(mϕ)
Parameters
----------
ρ : float
The radial coordinate.
Returns
-------
HE_ECladdingρ : real
'''
return -0.5*(a*np.sqrt(-kz**2 + kFree**2*nCore**2)*(special.kn(-1 + m,(np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))*ρ)/a)*(-1 - (2*kFree**2*m*(nCladding**2 - nCore**2)*special.jv(m,a*np.sqrt(-kz**2 + kFree**2*nCore**2))*special.kn(m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))))/(a*(kz**2 - kFree**2*nCladding**2)*np.sqrt(-kz**2 + kFree**2*nCore**2)*(special.jv(-1 + m,a*np.sqrt(-kz**2 + kFree**2*nCore**2)) - special.jv(1 + m,a*np.sqrt(-kz**2 + kFree**2*nCore**2)))*special.kn(m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))) + np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))*(kz**2 - kFree**2*nCore**2)*special.jv(m,a*np.sqrt(-kz**2 + kFree**2*nCore**2))*(special.kn(-1 + m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))) + special.kn(1 + m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2)))))) - (1 - (2*kFree**2*m*(nCladding**2 - nCore**2)*special.jv(m,a*np.sqrt(-kz**2 + kFree**2*nCore**2))*special.kn(m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))))/(a*(kz**2 - kFree**2*nCladding**2)*np.sqrt(-kz**2 + kFree**2*nCore**2)*(special.jv(-1 + m,a*np.sqrt(-kz**2 + kFree**2*nCore**2)) - special.jv(1 + m,a*np.sqrt(-kz**2 + kFree**2*nCore**2)))*special.kn(m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))) + np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))*(kz**2 - kFree**2*nCore**2)*special.jv(m,a*np.sqrt(-kz**2 + kFree**2*nCore**2))*(special.kn(-1 + m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))) + special.kn(1 + m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))))))*special.kn(1 + m,(np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))*ρ)/a)))/(np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))*special.kn(m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))))
return HE_ECladdingρ
def HE_ECladdinggenϕ(a,kFree,kz,m,nCladding,nCore):
'''
Parameters
----------
a : float
radius of the waveguide core.
kFree : float)
free space wavenumber.
kz : float
longitudinal propagation constant.
m : int
mode order, for HE modes m>=1, for TM and TE, m=0.
nCladding : float
refractive index of cladding.
nCore : float
refractive index of core.
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
Returns
-------
HE_ECladdingϕ : func
'''
def HE_ECladdingϕ(ρ):
'''
Returns the azimuthal component of HE_ECladding without the azimuthal dependence.
The azimuthal dependence depends on the parity of the field:
even -> -sin(mϕ)
odd -> cos(mϕ)
Parameters
----------
ρ : float
The radial coordinate.
Returns
-------
HE_ECladdingϕ : real
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
'''
return -0.5*(a*np.sqrt(-kz**2 + kFree**2*nCore**2)*(special.kn(-1 + m,(np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))*ρ)/a)*(-1 - (2*kFree**2*m*(nCladding**2 - nCore**2)*special.jv(m,a*np.sqrt(-kz**2 + kFree**2*nCore**2))*special.kn(m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))))/(a*(kz**2 - kFree**2*nCladding**2)*np.sqrt(-kz**2 + kFree**2*nCore**2)*(special.jv(-1 + m,a*np.sqrt(-kz**2 + kFree**2*nCore**2)) - special.jv(1 + m,a*np.sqrt(-kz**2 + kFree**2*nCore**2)))*special.kn(m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))) + np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))*(kz**2 - kFree**2*nCore**2)*special.jv(m,a*np.sqrt(-kz**2 + kFree**2*nCore**2))*(special.kn(-1 + m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))) + special.kn(1 + m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2)))))) + (1 - (2*kFree**2*m*(nCladding**2 - nCore**2)*special.jv(m,a*np.sqrt(-kz**2 + kFree**2*nCore**2))*special.kn(m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))))/(a*(kz**2 - kFree**2*nCladding**2)*np.sqrt(-kz**2 + kFree**2*nCore**2)*(special.jv(-1 + m,a*np.sqrt(-kz**2 + kFree**2*nCore**2)) - special.jv(1 + m,a*np.sqrt(-kz**2 + kFree**2*nCore**2)))*special.kn(m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))) + np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))*(kz**2 - kFree**2*nCore**2)*special.jv(m,a*np.sqrt(-kz**2 + kFree**2*nCore**2))*(special.kn(-1 + m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))) + special.kn(1 + m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))))))*special.kn(1 + m,(np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))*ρ)/a)))/(np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))*special.kn(m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))))
return HE_ECladdingϕ
def HE_ECladdinggenz(a,kFree,kz,m,nCladding,nCore):
'''
Parameters
----------
a : float
radius of the waveguide core.
kFree : float)
free space wavenumber.
kz : float
longitudinal propagation constant.
m : int
mode order, for HE modes m>=1, for TM and TE, m=0.
nCladding : float
refractive index of cladding.
nCore : float
refractive index of core.
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
Returns
-------
HE_ECladdingz : func
'''
def HE_ECladdingz(ρ):
'''
Returns the transverse component of HE_ECladding without the azimuthal dependence.
The azimuthal dependence depends on the parity of the field:
even -> cos(mϕ)
odd -> sin(mϕ)
Parameters
----------
ρ : float
The radial coordinate.
Returns
-------
HE_ECladdingz : complex
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
'''
return ((-1j)*np.sqrt(-kz**2 + kFree**2*nCore**2)*special.kn(m,(np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))*ρ)/a))/(kz*special.kn(m,np.sqrt(a**2*(kz**2 - kFree**2*nCladding**2))))
return HE_ECladdingz
def TE_HCoregenρ(a,kFree,kz,m,nCladding,nCore):
'''
Parameters
----------
a : float
radius of the waveguide core.
kFree : float)
free space wavenumber.
kz : float
longitudinal propagation constant.
m : int
mode order, for HE modes m>=1, for TM and TE, m=0.
nCladding : float
refractive index of cladding.
nCore : float
refractive index of core.
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
Returns
-------
TE_HCoreρ : func
'''
def TE_HCoreρ(ρ):
'''
Returns the radial component of TE_HCore without the azimuthal dependence.
The azimuthal dependence depends on the parity of the field:
even -> cos(mϕ)
odd -> sin(mϕ)
Parameters
----------
ρ : float
The radial coordinate.
Returns
-------
TE_HCoreρ : real
'''
return (kz*special.jv(1,np.sqrt(-kz**2 + kFree**2*nCore**2)*ρ))/(kFree*special.jv(1,a*np.sqrt(-kz**2 + kFree**2*nCore**2)))
return TE_HCoreρ
def TE_HCoregenϕ(a,kFree,kz,m,nCladding,nCore):
'''
Parameters
----------
a : float
radius of the waveguide core.
kFree : float)
free space wavenumber.
kz : float
longitudinal propagation constant.
m : int
mode order, for HE modes m>=1, for TM and TE, m=0.
nCladding : float
refractive index of cladding.
nCore : float
refractive index of core.
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
Returns
-------
TE_HCoreϕ : func
'''
def TE_HCoreϕ(ρ):
'''
Returns the azimuthal component of TE_HCore without the azimuthal dependence.
The azimuthal dependence depends on the parity of the field:
even -> -sin(mϕ)
odd -> cos(mϕ)
Parameters
----------
ρ : float
The radial coordinate.
Returns
-------
TE_HCoreϕ : real
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
'''
return 0
return TE_HCoreϕ
def TE_HCoregenz(a,kFree,kz,m,nCladding,nCore):
'''
Parameters
----------
a : float
radius of the waveguide core.
kFree : float)
free space wavenumber.
kz : float
longitudinal propagation constant.
m : int
mode order, for HE modes m>=1, for TM and TE, m=0.
nCladding : float
refractive index of cladding.
nCore : float
refractive index of core.
Reference
---------
Snyder, Allan W, and John Love. Optical Waveguide Theory, 1983.
Returns
-------
TE_HCorez : func
'''
def TE_HCorez(ρ):
'''
Returns the transverse component of TE_HCore without the azimuthal dependence.
The azimuthal dependence depends on the parity of the field:
even -> cos(mϕ)
odd -> sin(mϕ)
Parameters