ECE 437 – Fiber and Integrated Optics
Homework Assignment #1; Due 11
th
February, Thursday 5PM
1. Frequency Invariance during reflection and refraction
It is a common observation that for
most
materials
the frequency of the monochromic
light (hence the color of the light) does not
change as light passes through or reflects
from surfaces of linear media (constant
dielectric coefficient). This property is
characteristic of media with linear
polarization (constant dielectric coefficient).
Assuming that incident beam is polarized in
the plane of incidence (TM polarization),
prove that for linear media the frequencies of
incident, reflected, refracted beams are the
same.
Hint: Apply any of the boundary conditions at
the interface
2. Reflection and Refraction at dielectric interface
Using the boundary conditions for electromagnetic fields at boundary, derive the amplitude
reflection and transmission coefficients for an electromagnetic wave that is polarized with the
electric field
parallel
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 '04
 LIPSON
 Frequency, refractive index, photonic chip. 4. Group and Phase, incident power. Hint, smallest incident angle, cos cos cos, plane wave solution

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