Interactive Introduction to Optics

The objective is to review some principles in optics and how light interacts with matter.

Classical Propagation

A simple model to understand the propagation of light in matter is to consider matter as a collection of dipoles.

$$ m_0\frac{d^2x}{dt^2} + m_0\gamma\frac{dx}{dt} + m_0\omega_0^2x = -e \varepsilon $$

where $m_0$ is the electron mass, $\gamma$ the damping rate, $e$ the electric charge and $\varepsilon$ the electric field of the light wave driving the dipole.

All the effect of the interaction with matter, can be encoded in what is known as the complex dielectric function

$$\epsilon(\omega)= \frac{Ne^2}{\epsilon_0 m_0}\frac{\gamma\omega}{(\omega_0^2-\omega^2)+ (\gamma\omega)^2}$$



In [6]:

    
from sympy import *
import sympy.plotting as p
init_printing()
%pylab inline









    



Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].
For more information, type 'help(pylab)'.



In [18]:

    
x = symbols('x')
omega, gamma, omega_0 = symbols('omega, gamma, omega_0', positive = True, real = True)
p.plot(x, x**2, x**3, (x,-5,5))
epsilon = symbols('epsilon', cls=Function)
epsilon = gamma*omega/((omega_0**2-omega**2)+ (gamma*omega)**2)
epsilon









    












    Out[18]:





$$\frac{\gamma \omega}{\gamma^{2} \omega^{2} - \omega^{2} + \omega_{0}^{2}}$$



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