Physics 725 Laser Physics

Fall 2009

Catalog description:  [3 credits]
Laser operation, pumping mechanisms, resonators, optical coherence, photon statistics, non-linear optics, laser applications.
Prerequisites: PHYS 722. QUANTUM THEORY II

Textbook: "Lasers", by A. E. Siegman
Up to date reading of the textbook material is a standing homework assignment.

Recommended additional books:

1. Laser Cooling and Trapping by H.J. Metcalf and P. van der Straten
2. Laser Spectroscopy by Wolfgang Demtröder
3. The Quantum Theory of Light by Rodney Loudon
4. Atomic, Molecular & Optical Physics Handbook, Ed. G. W.F. Drake

• First class: Tue, Aug 25
• Written test #1: Th, Sept 17
• Written test #2: Th, Nov. 12 (RESCHEDULED!)
• Last class: Tue, Dec 8
• Final exam: Th, Dec 10, noon - 2:00 PM

Your grade:
5% attendance, 25% homework, 10% presentation, 20% test#1, 20% test#2, 20% final exam.

Mapping scores to letter grades:
100 : A : 92.5 : A- : 82.5 : B+: 75 :B: 67.5 :B-:57.5, etc

Tests: 
There will be two written tests and the final written exam.

Presentation:
During the semester you will be asked to make a short 15 minute presentation on laser applications of your choice.

• Correlated Spontaneous Emission Lasers (Philippe)
• The Ultimate White Light (Mahmoud)
• Magneto-optical Trap and Its Application (Kiran)
• Increasing Lifetime Of Air Plasma Channel Using Short Laser Pulses (Vijay)
• Leopard Laser NTF (Kevin)
• Laser Cooling (Rishi)
• Laser Diodes and their Application in Laser Pumping (Daniel)
• CO2 Lasers and their Applications (Nagendra)
  

Homework Assignments:  
Problem sets will be handed out or posted on this web page  typically each Tuesday and will be due one week later. No late homework will be accepted. The homework will not be graded; everyone will get the full 100% by attempting all the problems and turning them in on time. Working through these problems is essential for doing well on the tests. Up to date reading of the  textbook material  is a standing homework assignment.

Unless stated otherwise, all problems are weighted equally.

Adobe Acrobat reader may be required for viewing the Homework assignments. The reader is available here free of charge.

• HW #1 (due Sept 1st)
  
  1. The inner cover of the textbook lists Nobel prize awards relevant to lasers up to 1981. Continue this list through 2008 (may be we will extend it in Dec. 2009?). You may want to use the Nobel Foundation web-site: nobelprize.org.
  2. (1.1.1) Problem 1 on page 5 [spectrum].
• HW #2 (due Sept 8th)
  1.  Given the intensity I of a laser beam, find the amplitude E of the electric field.  For I=1 mW/cm^2 what is the numerical value of E in V/cm?
  2. Find a number of photons incident per unit time on a surface normal to a laser beam. Express your result in terms of intensity I, beam area A and wavelength of the beam. Compute this number for  I=1 mW/cm^2, A=1 cm^2 and lambda=780 nm.
• HW #3 (due Sept 15th)
  1. (1.4.1) Problem 1 on page 35 [typical Boltzmann ratios].
  2. (1.5.1) Problem 1 on page 38 [laser pumping scheme++].
  3. (1.7.1)  Problem 1 on page 59 [Fraunhofer aperture diffraction patterns].
• HW #4 (due Sept 29th)
  1. (2.1.2) Problem 2 on page 89 [Q-factor for CEO]
  2. (2.1.3) Problem 3 on page 89 [Decay rate for CEO]
  3. (2.3.1) Problem 1 on page 101 [Dephasing in a solid]
  4. (2.4.5) Problem 5 on page 109 [Range of validity of the resonance approx.]
• HW #5 (due Oct 6th)
  1. (3.1.1) Problem 1 on page 126 [Hydrogen atom oscillator strength]
  2. (3.2.1) Problem 3 on page 135 [Derivative spectroscopy and gas pressure]
  3. Decide on the topic of your 15 minute in-class presentation. Write a one-page (typed ) summary of your presentation and send it to me via e-mail and also include a printed copy with your homework.
• HW #6 (due Oct 13th)
  1. (3.3.2) Problem 2 on page 143 [Computer plots of oscillating QM charge distributions].  Mathematica may be especially useful here. (see function Animate[]). It is available online through UNR DataWorks. Here is a short tutorial: MmkaQMLecture and the Mathematica notebook: MmkaQMLecture.nb.
  2. (3.4.2)  Problem 2 on page 149 [Tensor response of anisotropic 2D oscillator]
  3.  (3.7.1) Problem 1 on page 174 [Inhomogeneous broadening with a lorentzian]
• HW #7 (due Oct 20th)
  1. [25pts] (4.3.1) Problem 1 on page 194 [ Thermal equilibration]
  2. [75 pts] (Research problem) A two-level system is driven by a train of identical on/off pulses of radiation. A single pulse is described as
     W12 = W>0 for t=0,Tp and W12 = 0 for t=Tp,Tr.
     Here Tr is the repetition time and Tp is the on-time for the pulse. For example, the second pulse will be on for t=Tr, Tr+Tp
     (a) Qualitatively describe various regimes of time-evolution for delta N(t)
     (b) How Figure 4.13 would look like as a function of various parameters?  Choose numerical parameters to highlight the regimes of part (a) and plot population difference as a function of time. Although the problem has an analytical solution, you may wish to solve Eq.(63) numerically. 
• HW #8 (due Oct 27th)
  1. (6.1.3) Problem 3 on page 251 [cascade pumping of a four-level system]
  2. (6.1.5) Problem 5 on page 251 [Laser refrigeration]
  3. (6.2.1) Problem 1 on page 256 [Transient response in the simplified laser-pumping model]
• HW #9 (due Nov 3rd)
  1. (7.2.1) Problem 1 on page 275 [Read through the end of Sec. 7.2; double-Lorentzian]
  2. (7.4.1) Problem 1 on page 284 [Amplification bandwidth for a Gaussian lineshape]
  3. (7.4.5) Problem 5 on page 285 [Cascaded amplifier + absorber]
  4. (7.5.4) Problem 4 on page 292 [Energy storage in a Nd:YAG rod]
• HW #10 (due Nov 10th)
  1. (7.6.2) Problem 2 on page 269 [Saturation lineshape for the reactive part of a homogeneous two-level transition]
  2. With your favorite plotting software reproduce Fig. 7.13 (Amplifier output versus input for two different values of small-signal gain) by numerically solving Eq.(7.81)
  3. (7.7.3) Problem 3 on page 304 [Signal penetration depth]
• HW #11 (due Nov 17th)
  1. With your favorite plotting software, reproduce plots on Fig 11.10 (a) using 10% internal power loss per round trip. Discuss the differences compared to the original Fig. (2% loss),
  2. (11.6.1) Problem 1 on page 447 [Reflection gain of a regenerative amplifier]
  3. (11.7.1) Problem 1 on page 454 [Power transmission halfway between axial modes]
• HW #12 (due Nov 24th)
  1. (12.2.2) Problem 2 on page 471 [Laser cavity design]
  2. (12.3.1) Problem 1 on page 483 [Optimum coupling analysis for a unidirectional ring-cavity laser]
  3. (12.3.4) Problem 4 on page 484 [Laser oscillator with both saturable loss and saturable gain]
• HW #13 (due Dec 8th)
  1. (a) Derive time-evolution equations [an analog of the time-dependent Schrodinger equation (TDSE)] for the density matrix of two-level system driven by periodic electromagnetic field.  Use the rotating wave approximation to simplify your result.
     (b) Neglecting the spontaneous emission, recover the TDSE from your density matrix equations.
  2. What is distance (numerical value) required to bring a beam of two-level atoms to a milliKelvin temperature from room temperature? Assume mass of 133Cs atom, lifetime of 10 ns, wavelength of transition 500 nm,  and that the slowing laser operates in a saturation regime for the atomic transition.
  3. Compare the steady state solutions for a driven two-level system in the density-matrix formulation and in the CEO formulation of the Siegman textbook.
  4. Explicitly compute quantities qr and qi for (a) traveling  and (b) standing waves.
  5. (No extra credit): Evaluate your professor following these instuctions (Constructive suggestions are always appreciated!)

Misc material:

• NIST Atomic Spectra Database
• Mathematica is available online through UNR DataWorks. Here is a short tutorial: MmkaQMLecture and the Mathematica notebook: MmkaQMLecture.nb.
• Here is a Mathematica rendered output related to your HW #6 problem 3.3.2. (Oscillating Dipoles)