/
medium.py
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medium.py
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"""
**Contains**
* Medium
"""
from sympy.physics.units import second, meter, kilogram, ampere
__all__ = ['Medium']
from sympy import Symbol, sympify, sqrt
from sympy.physics.units import speed_of_light, u0, e0
c = speed_of_light.convert_to(meter/second)
_e0mksa = e0.convert_to(ampere**2*second**4/(kilogram*meter**3))
_u0mksa = u0.convert_to(meter*kilogram/(ampere**2*second**2))
class Medium(Symbol):
"""
This class represents an optical medium. The prime reason to implement this is
to facilitate refraction, Fermat's principle, etc.
Explanation
===========
An optical medium is a material through which electromagnetic waves propagate.
The permittivity and permeability of the medium define how electromagnetic
waves propagate in it.
Parameters
==========
name: string
The display name of the Medium.
permittivity: Sympifyable
Electric permittivity of the space.
permeability: Sympifyable
Magnetic permeability of the space.
n: Sympifyable
Index of refraction of the medium.
Examples
========
>>> from sympy.abc import epsilon, mu
>>> from sympy.physics.optics import Medium
>>> m1 = Medium('m1')
>>> m2 = Medium('m2', epsilon, mu)
>>> m1.intrinsic_impedance
149896229*pi*kilogram*meter**2/(1250000*ampere**2*second**3)
>>> m2.refractive_index
299792458*meter*sqrt(epsilon*mu)/second
References
==========
.. [1] https://en.wikipedia.org/wiki/Optical_medium
"""
def __new__(cls, name, permittivity=None, permeability=None, n=None):
obj = super().__new__(cls, name)
obj._permittivity = sympify(permittivity)
obj._permeability = sympify(permeability)
obj._n = sympify(n)
if n is not None:
if permittivity is not None and permeability is None:
obj._permeability = n**2/(c**2*obj._permittivity)
if permeability is not None and permittivity is None:
obj._permittivity = n**2/(c**2*obj._permeability)
if permittivity is not None and permittivity is not None:
if abs(n - c*sqrt(obj._permittivity*obj._permeability)) > 1e-6:
raise ValueError("Values are not consistent.")
elif permittivity is not None and permeability is not None:
obj._n = c*sqrt(permittivity*permeability)
elif permittivity is None and permeability is None:
obj._permittivity = _e0mksa
obj._permeability = _u0mksa
return obj
@property
def intrinsic_impedance(self):
"""
Returns intrinsic impedance of the medium.
Explanation
===========
The intrinsic impedance of a medium is the ratio of the
transverse components of the electric and magnetic fields
of the electromagnetic wave travelling in the medium.
In a region with no electrical conductivity it simplifies
to the square root of ratio of magnetic permeability to
electric permittivity.
Examples
========
>>> from sympy.physics.optics import Medium
>>> m = Medium('m')
>>> m.intrinsic_impedance
149896229*pi*kilogram*meter**2/(1250000*ampere**2*second**3)
"""
return sqrt(self._permeability/self._permittivity)
@property
def speed(self):
"""
Returns speed of the electromagnetic wave travelling in the medium.
Examples
========
>>> from sympy.physics.optics import Medium
>>> m = Medium('m')
>>> m.speed
299792458*meter/second
>>> m2 = Medium('m2', n=1)
>>> m.speed == m2.speed
True
"""
if self._permittivity is not None and self._permeability is not None:
return 1/sqrt(self._permittivity*self._permeability)
else:
return c/self._n
@property
def refractive_index(self):
"""
Returns refractive index of the medium.
Examples
========
>>> from sympy.physics.optics import Medium
>>> m = Medium('m')
>>> m.refractive_index
1
"""
return (c/self.speed)
@property
def permittivity(self):
"""
Returns electric permittivity of the medium.
Examples
========
>>> from sympy.physics.optics import Medium
>>> m = Medium('m')
>>> m.permittivity
625000*ampere**2*second**4/(22468879468420441*pi*kilogram*meter**3)
"""
return self._permittivity
@property
def permeability(self):
"""
Returns magnetic permeability of the medium.
Examples
========
>>> from sympy.physics.optics import Medium
>>> m = Medium('m')
>>> m.permeability
pi*kilogram*meter/(2500000*ampere**2*second**2)
"""
return self._permeability
def __str__(self):
from sympy.printing import sstr
return type(self).__name__ + ': ' + sstr([self._permittivity,
self._permeability, self._n])
def __lt__(self, other):
"""
Compares based on refractive index of the medium.
"""
return self.refractive_index < other.refractive_index
def __gt__(self, other):
return not self < other
def __eq__(self, other):
return self.refractive_index == other.refractive_index
def __ne__(self, other):
return not self == other