Download Changing the Phase of a Light Wave

Changing the Phase of a Light
Wave
A light wave travels a distance L through a material of
refractive index n. By how much has its phase changed?
A light wave travels a distance L in vacuum. By how
much has its phase changed?
A light wave travels a distance L in vacuum. By how
much has its phase changed?
How does the amplitude depend on distance?
A light wave travels a distance L in vacuum. By how
much has its phase changed?
How does the amplitude depend on distance?
At a fixed time, E(x,t) = sin(kx + constant)
E(x1,t) = sin(k x1 + constant)
E(x2,t) = sin(k x2 + constant)
E(x1,t) = sin(k x1 + constant)
E(x2,t) = sin(k x2 + constant)
Phase of wave at x1 = k x1 + constant
Phase of wave at x2 = k x2 + constant
E(x1,t) = sin(k x1 + constant)
E(x2,t) = sin(k x2 + constant)
Phase of wave at x1 = k x1 + constant
Phase of wave at x2 = k x2 + constant
Phase difference = k x2 - k x1 = k ( x2 – x1) = k L
E(x1,t) = sin(k x1 + constant)
E(x2,t) = sin(k x2 + constant)
Phase of wave at x1 = k x1 + constant
Phase of wave at x2 = k x2 + constant
Phase difference = k x2 - k x1 = k ( x2 – x1) = k L
k = 2B/8, so that phase difference = 2B L/ 8
Coming back to our original problem, we can say that the
phase change the light undergoes in traveling a distance L
through the material is
2B L / (wavelength of light in material)
Coming back to our original problem, we can say that the
phase change the light undergoes in traveling a distance L
through the material is
2B L / (wavelength of light in material)
What is the wavelength of light in the material?
80 = wavelength of light in vacuum
8m = wavelength of light in material
80 = wavelength of light in vacuum
8m = wavelength of light in material
80 f 0 = c
8m f m = v
80 = wavelength of light in vacuum
8m = wavelength of light in material
80 f 0 = c
8m f m = v
(80 f 0) / (8m f m ) = c / v = n
80 = wavelength of light in vacuum
8m = wavelength of light in material
80 f 0 = c
8m f m = v
(80 f 0) / (8m f m ) = c / v = n
f0= fm
80 = wavelength of light in vacuum
8m = wavelength of light in material
80 f 0 = c
8m f m = v
(80 f 0) / (8m f m ) = c / v = n
f0= fm
Therefore, 80 / 8m = n
80 = wavelength of light in vacuum
8m = wavelength of light in material
80 f 0 = c
8m f m = v
(80 f 0) / (8m f m ) = c / v = n
f0= fm
Therefore, 80 / 8m = n
Or,
8m = 80 / n
The phase has changed by 2B L / 8m
The phase has changed by 2B L / 8m
= 2B L / (80 / n) = 2B n L / 80
The phase has changed by 2B L / 8m
= 2B L / (80 / n) = 2B n L / 80
In traveling a distance L in the material, the wave changes its
phase by the same amount that it would have changed if it had
traveled a distance n L in vacuum.
The phase has changed by 2B L / 8m
= 2B L / (80 / n) = 2B n L / 80
In traveling a distance L in the material, the wave changes its
phase by the same amount that it would have changed if it had
traveled a distance n L in vacuum.
n L is defined as the optical path length.
How do we represent a phase change mathematically?
In free space, the amplitude function is
E (x,t) = E0 exp[i(kx-jt + N )]
At a fixed time this is E = A eikx where A = E0 exp[i(-jt + N )]
The wave amplitude at x1 is
The wave amplitude at x2 is
ik  x1  L 
ikx2
E2  Ae
 Ae
E1  Aeikx1
E2  Aeikx2
 Aeikx1 eikL  E1 eikL
If E is the complex amplitude at the entry-face of the material,
the complex amplitude at the exit face is
E exp[i(phase change)] = E exp[2B i n L / 80 ]