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OSE 5312 FUNDAMENTALS OF OPTICAL SCIENCE
Spring 2007
Final Exam
Wednesday, April 25. 1:00 pm to 3:45 pm
Section 1
Section 1 of this exam is closed book, closed notes. Section 2 is open book, open notes.
You must turn in your answers to section 1 before you may open any books or notes.
Answer all questions. Try to use drawings & figures to help explain your answers.
Clearly state all your assumptions, definitions and approximations. The number of
points for each question is given in italics.
________________________________________________________________
Some Physical Constants:
Electron mass = 9.1 x 10-31^ kg Electron Charge = 1.6 x 10 -19^ C
Proton mass = 1.67 x 10-27^ kg ε 0 = 8.85 x 10 -12^ F/m
Boltzman’s constant, kB = 1.38x 10 -23^ J K-1^ Speed of light = 3 x 10^8 m/s
________________________________________________________________
Name: ___________________________________
Section 1
Question Score
Total /
Total from section 2 /
Exam total /
Please clearly circle your answers to questions 1-5:
- The maximum wavevector of phonons is typically (3 points) a. much smaller than the wavevector of visible light b. approximately the same as the wavevector of visible light c. much larger than the wavevector of visible light
- Lorentz oscillators generally have the highest reflection… (3 points) a. below the resonance frequency. b. just above the resonance frequency c. far above the resonance frequency
- The saturation irradiance, Isat , in a 2-level system, is defined as (4 points) a. the irradiance required to drive the absorption coefficient to zero b. the irradiance required to overcome intrinsic cavity losses c. the irradiance required to reduce the absorption coefficient to half its small-signal value
- To obtain maximum Faraday rotation of an EM wave traveling along the z direction and polarized along the y direction requires an external magnetic field along the (3 points) a. x-direction b. y-direction c. z-direction
- In a three level system, where the stimulated emission occurs between the lower two levels, increasing the lifetime τ 21 : (3 points) a. reduces the pump power required for population inversion b. reduces the maximum gain that can be obtained from the transition 2→ 1 c. makes it impossible to obtain gain from the transition 2→ 1
- A Faraday rotator uses a 10 cm long glass rod with a Verdet constant of 150 rad m-1^ T -^.
a. If it has to rotate linear polarization by 22.5º, what size of magnetic field is required? (3 points)
b. What special properties does a material have to have to exhibit:
i. Optical activity?
ii. Faraday rotation? (3 points)
- A medium with finite χ(2)^ is illuminated with two strong laser beams with wavelengths 532 nm and 355 nm. List all the wavelengths that may be generated by nonlinear mixing. (8 points)
SiO 2 (Glass - solid),
GaAs (solid).
OSE 5312 FUNDAMENTALS OF OPTICAL SCIENCE
Spring 2007
Final Exam
Wednesday, April 25. 1:00 pm to 3:45 pm
Section 2
You must turn in your answers to section 1 before you may open any books or notes.
Answer all questions. Try to use drawings & figures to help explain your answers.
Clearly state all your assumptions, definitions and approximations. The number of
points for each question is given in italics.
________________________________________________________________
Some Physical Constants:
Electron mass = 9.1 x 10-31^ kg Electron Charge = 1.6 x 10 -19^ C
Proton mass = 1.67 x 10-27^ kg ε 0 = 8.85 x 10 -12^ F/m
Boltzman’s constant, kB = 1.38x 10 -23^ J K-1^ Speed of light = 3 x 10^8 m/s
________________________________________________________________
Name: ___________________________________
Section 2
Question Score
Total /
- A glass of refractive index 1.45, is doped with atoms that have an energy difference difference between the ground state and first excited state of 1.9 eV. Both states have a degeneracy of one. (i.e. g 1 = g 2 = 1) The density of atoms is 10^18 cm-3^. The stimulated emission cross section between states is σ 12 = 6× 10 -18^ cm^2 and the lifetime of the first excited state is τ = 0.10 ms. a. At what wavelength should optical absorption due to these two states be maximum? (2 points)
b. What is the value of the absorption coefficient at the wavelength calculated in part (a), for low input irradiance? (2 points)
c. Find an expression for the absorption as a function of input irradiance. (4 points)
d. What is the absorption at an input irradiance of 1.2 kW/cm^2? (2 points)
“Cyanine” dyes are often characterized by a single dominant Lorentzian absorption line in the visible. One such dye is held in solution in a 10 μm path length optical cell. The cell is placed in a spectrometer, which reveals a single strong, absorption line, full width at half maximum 50 nm, centered on a resonance wavelength of λ 0 = 700 nm. Examination of the data reveals that at the peak of the absorption (i.e. at a wavelength of 700 nm) the transmittance is 1%. Assume the cell is perfectly antireflection coated. The solvent is completely transparent over the wavelength range of interest and its refractive index is 1.400, which may be considered to be constant over all frequencies.
a. What is the peak absorption coefficient? (4 points)
b. What is the imaginary part of the dielectric constant of the solution at the peak of the absorption? (4 points)
c. Since the absorption is a single Lorentzian line, it may be modeled using the Lorentz oscillator model, i.e.:
( ) ( ) 0 ( 0 ) 2 ( )^2
2 2 2 0
0 0
2
/ 2
χ ω p p
If we do so, what is the refractive index of the solution (i.e. dye plus solvent) at a wavelength of 725 nm? (7 points)
