Chem 249 Problem Set 1 R. Corn Spring 2007

lovelyphloxElectronics - Devices

Oct 18, 2013 (3 years and 9 months ago)

78 views

Chem 249 Problem Set 1

R. Corn

Spring 2007


Classical Description of Electromagnetic Radiation and Absorption Theory


A. Maxwell's Equations and Plane Electromagnetic Waves


1. Vector Fields and Notation

2. EM Fields and Superposition: E, B, D, H

3. Maxwel
l's Equations

4. EM Waves
-

Plane Waves

5. Polarization

6. Poynting Vector and EM Energy

7. EM Waves in Dielectrics

8. Complex Susceptibility and Absorption


B. Fresnel Calculations and Total Internal Reflection


1. Fresnel Calculations

2. Normal Incidence

Reflectance

3. Brewster's Angle

4. Total Internal Reflection

5. Metal Surfaces


C. Classical Macroscopic and Microscopic Theories of Absorption


1. Macroscopic Polarization and Susceptibility

2. Complex Index of Refraction

3. Beer's Law Absorption Coeffi
cient

4. Classical Microscopic Theory: Forced Harmonic Oscillator

5. Frequency Dependent Susceptibilities

6. Frequency Dependent Indices of Refraction



Handouts:


1. E&M1: Dielectric Constant and Frequency Dependent Susceptibility


2. E&M2: Plane Waves an
d Fresnel Equations


3. W. Hansen, J. Opt. Soc. Am. 58, 380
-
390 (1968).


Additional Readings:


1. Lorrain and Corson, Electromagnetic Fields and Waves


2. Loudon, The Frequency Dependent Susceptibility (pp. 22
-
28)


3.
http://corninfo.ps.uci.edu/calculations.html


Problems:


1. Create a spreadsheet that allows you to enter either the wavelength (nm), wavenumber
(cm
-
1), frequency (Hz), energy (in Joules) or energy (in eV) of an photon/EM wave and
con
verts it for you into the other units. (Can use Excel: very easy!) An example is:




2. Create a Igor Pro File that calculates the Reflectivity and Transmittance for p
-
polarized
and s
-
polarized light (R
p

and T
p
, R
s

and T
s
) as a function of incident angl
e from normal
incidence (0 degrees) to grazing incidence (90 degrees) in one degree increments for a
general two phase system where n
1

is real and n
2

can be complex. A printout of the
refined History text file is most useful.



3. Using, Igor Pro please cr
eate graphs of R
p
, R
s
, E
x
2
, E
y
2

and E
z
2

vs angle for three
two
-
phase systems:


i) Air/Si (n
1

= 1, n
2

= 3.0 + 0i)


ii) Air/Au (n
1

= 1, n
2

= 0.1 + 3i)


iii) Quartz/Water (n
1

= 1.51, n
2

= 1.33 + 0i).


You should let people choose the input polarization (p or

s) and where to calculate the
field: either above or below the interface.



4) Consider the general form for the frequency dependent dielectric susceptibility:




a) Please plot Im


and Re

for the cases where S = 0.05,

0

= 1000, and


= 10.
Measure the FWHM (full width at half max) for the resonant peak. How does it scale
with

?


b) Using the general form for the general form for the electric susceptibility where S =
0.05,

0

=

1000, and


= 10, please plot the real and imaginary parts of n, the complex
index of refraction (n = n
r

+ jn
i
), versus frequency. Recall that n
2

=

r

= 1 +


.