Department of Physics & Astronomy	Physics 533: Lasers (2008)
		Discussion Questions

Classical Picture of Atom-Field Interaction

Richard Wong: In the derivation of the wave equation, the book assumes that the divergence of E is zero and refers to this as a transverse or "radiation" field. Why do they make this choice? How is "transverse" associated with "radiation"?
Hadi Ebrahimnejad: made a comment regarding the cavity size for masers and it's relation to visible lasers.
Eric Vyskocil: Figure 1.2 shows a mirror with 90% reflectivity. How would such a mirror be created? Can a material be made which reflects and transmits radiation without large losses?
Rob Stead: Ch1 gives an expression for the frequency spread of the laser output. How does this translate to spread in wavelengths? What is the typical bandwidth of a HeNe Laser or a mode locked Ti:Sapphire laser with a pulse duration of 1ps?
How valid is the approximation used in deriving equation 2.47?
Steven Gou: The textbook describes lasers with wavelengths smaller than x-rays (i.e. gamma rays) difficult to achieve. Is it possible now? What are the biggest challenges? Lossy media, cavity design, etc.?
Ray Gao: Why exactly is the minimum spread of a beam limited by diffraction?
Mostafa Masnadi: --- absent ---
Ryan Lewis: Why is spontaneous emission neglected in the rate equation 1.5.1?
Tulin Okbinoglu: Why is a microwave cavity closed while visible lasers have open cavities?
Kirk Madison: Deduce what happens to the phase and group velocity near a resonance. Justify the expression for the group velocity.

Richard Wong:
Hadi Ebrahimnejad:
Eric Vyskocil:
Rob Stead:
Steven Gou:The solution to equation (3.3.1) is the steady state solution (3.3.5). However, Milonni and Eberly point out that any solution to the homogeneous case can be added to the steady state solution which then provides a transient contribution. What is the physical source or meaning of this transient contribution?
Ray Gao:
Ryan Lewis: Chapter 3.3 got me thinking about the difference between phase velocity, group velocity and how information can not travel faster than c. The smaller the index of refraction (n) is then the faster the E-field decays with distance in a material. Let's say you have, say some pulse, containing some frequency range, which is an anomalous dispersion region. My interpretation is that some frequencies may propagate faster than c, however those frequencies are attenuated the most and so they die out before they can pass ahead of the wavefront. Is this a correct interpretation?
Tulin Okbinoglu:Not all scattered waves are elastically or Rayleigh scattered, so what portion of these waves do undergo Rayleigh scattering and would this number be affected by changes in frequency and hence extinction coefficient?

Richard Wong: In 3.5, an ohmic current is introduced to model cavity losses. What are some physical mechanism for these losses? Are there clearer definition of Inhomgeneous and homogeneous broadening?
Hadi Ebrahimnejad:-
Eric Vyskocil:The introduction of the Òoscillation strengthÓ term seems to be a very ad hoc and rather sketchy move in order to force compliance between theoretical and experimental results. Was there some reason beyond Òbecause it worksÓ that f was introduced? How was it justified at the time?
Both collisions and the Doppler effect cause line broadening, although in the assumptions made during the calculations it seems that the broadening due to collisions predominates when there are many collisions but the Doppler broadening predominates when there are few or no collisions (like an ideal gas). How would we go about calculating the intermediate case? Would the extra collisions affect the Doppler broadening significantly?
Rob Stead:1) Are there any other processes other than Doppler broadening, that lead to S(_) having a non-Lorentzian profile?
2) Isn't the assumption on page 91 contradictory? "The narrower the width of S(_)...we have broadband light and broadband absorption."
3) Problem 3.5 as example of "hard-sphere approximation" and pressure broadening.
Steven Gou:With regards to equation 3.8.6, Milonni and Eberly state that the width of the lineshape function must be very narrow for broadband absorption to be approximated. I'm having trouble logically understanding that, as a more narrow lineshape function will result in a more pronouced absorption around resonance.
Ray Gao:In the end of chapter 3.5 (Milonnni), he mentions that g (as defined by eqn 3.5.9) is the classical gain coefficient, but the classical oscillator model can never achieve amplification because g is by definition always negative. So my question is, if we allow the damping constant (beta) in the classical oscillator model to become negative, this would allow g to become positive, would this represent a classical model of gain in a classical oscillator? why or why not?
Ryan Lewis: My question concerns the oscillator strength, f. I suppose the fact that it is not 1 at resonance is a failure for this classical theory. In table 3.1 they show how the value of f for hydrogen changes with frequency, but couldn't this variance just be caused by the fact that we have already made many "near resonance" approximations? I assume f is taken to be constant in later equations for the same reason, since we are assuming to be near resonance.

Semiclassical Atom-Field Interaction: Quantum Mechanical Atoms in Classical Fields

Richard Wong:1. I do understand how the k come about in Bloch's theorem from the idea that only the probability (conjugate square) has to be strictly periodic with the period of the potential. Is there a more intuitive physical interpretation of that?
2. How far can we push this approach that we use for simple one or two body systems? Can you briefly go into some of the techniques people use to solve many-body quantum systems?
Hadi Ebrahimnejad: - none -
Eric Vyskocil:For electrons in an atomic atom, we know that there are occupancy restrictions on the number of electrons that may occupy an energy level. Considering that for a solid there are not discrete energy levels, but energy bands, how do we calculate the occupancy?
Rob Stead: example question on the harmonic oscillator ladder operators.
Steven Gou: In chapter 5, Milonni and Eberly illustrate that the probability density of an oscillator becomes more classical at higher n values. Is there a physical reason for this?
Ray Gao: Can you drive transitions between quantum states with a spatially invariant but time dependent potential?
Ryan Lewis:How long did it take before it was realized that Schrodinger's wave mechanics were equivalent to Heisenberg's matrix mechanics?

Heisenberg was first with matrix mechanics, about half a year before Schroedinger, and it was Schroedinger who showed they were equivalent about 3 months after he published his paper on the Schroedinger equation.
Ueber das Verhaeltnis der Heisenberg Born Jordanischen Quantenmechanik zu der meinen / On the Relation Between the Quantum Mechanics of Heisenberg, Born, and Jordan, and that of Schroedinger, Annalen der Physik. Leipzig 79 (1926) 734;

Richard Wong: The book briefly talked about parity selection rules for allowed transitions. How does it work?
Hadi Ebrahimnejad: My question regards two level system. In the book, it is argued that when the frequency of the incident radiation is nearly the energy difference between two eigenstates, just these two states can be taken into consideration. But, as we treat the field as a continuous source of energy leading to transitions, the above assumption doesn't look necessary. It seems that an implicit assumption of quantization of the radiation makes the above assumption plausible, which is really the case.
Eric Vyskocil: In Section 6.4 on page 192 it is stated that "the c's are 'slow variables' (compared with the a's)" however, equation (6.3.12a) explicitly states that a1 and c1 are equal. While I can see that c2 would be slow compared to a2, is there something that I am missing concerning the relationship between a1 and c1 that would make c1 slower?
Rob Stead: - none -
Steven Gou:- none -
Ray Gao: regarding the density matrix formulation, since a mixed state cannot be represented by any single state vector but a density matrix, does a mixed state contain more quantum mechanical 'information' than a pure state?
Ryan Lewis: - none -

Richard Wong: - none -
Hadi Ebrahimnejad:- none -
Eric Vyskocil:On page 201, Milonni states that elastic collisions do not affect the populations rho11 and rho22, but does not explain fully why this is. Why do elastic collisions not affect those populations but inelastic do?
Rob Stead: 1) In M & E it is explained that flipping the Bloch Vector from "due South to due North" corresponds to the generation of a population inversion. What is the analogue of flipping the vector from "East to West"?
2) Verdeyen suggests that the process of stimulated emission (and later, the relaxation processes) are "hidden in the right hand side of equation 14.6.8" Does this literally mean hidden, or are there certain tems there that should be immediately recogniseable as stimulated emission? I can appreciate that it emerges through the analysis, but the equation seems somewhat concealing. A discussion on the meaning of the terms in this section and how they relate to the various processes going on in the laser medium might be useful/interesting for all.
Steven Gou: Is Equation 6.5.14 incomplete? It takes into account population leaving the 2 state system into other levels of the atom but does not seem to include a rate at which population is transferred into the 2 states from the other states. Is there a justification for this omission?
What is meant by coherence as described in Levenson 2.1? Why can't an incoherent ensemble be described by a wavefunction such as Equation L2.1.4 if it is just an addition of a random phase?
Ray Gao: If we have a single 2-level atom with only 1 electron in an EM field and ignore decoherence, can its rabi oscillations decay? (or is rabi oscillation well defined at all for only 1 electron?)
Ryan Lewis: On the topic of collisional relaxation I have a question about the inelastic transfer probabilities to energy levels other than levels 1 and 2 (the gamma 1 and 2 factors in 6.5.18). The text claims that these are usually very small. I am wondering if there ARE cases where they could be significant?

Richard Wong:My question has to do with metastable states. I understand, rather abstractly, that some transitions have slow rates (Amn) because the matrix element of rmn is small. In the case of parity selection, some of these matrix element would be 0. Is this always true? Is it possible to have a more concrete interpretation as to how some excited states tend to have longer lifetime than others?
Hadi Ebrahimnejad:One can imagine that with collisions, the energy emitted or absorbed by an atom can be slightly different from the energy difference between the ground an excited states; however, how do we understand the case of spontaneous emission or absorption where the spectrum of light emitted or absorbed includes frequencies which are not equal to the energy splitting between the ground and excited states?
Eric Vyskocil: On page 227 near the bottom, Milonni states that while the 'radiative broadening' of a line is generally immutable, that laser radiation can be narrower than the 'natural' linewidth of the laser transition. I am curious what benefits there are to creating lasers with linewidths that small and how they are achieved.
Rob Stead: 1) At the bottom of page 214 M+E explain how equation 7.3.3 describes how, eventually, the entire population is taken out of states one and two due to elastic colisions. Presumably this is not the case if state 1 is the ground state, and the rates in equation 6.5.13 are modified?
Steven Gou:1) In equation (7.4.5), the formula is for cross section that only depends on incident wavelength and states that this simple formula is independent of the properties of the atom. However, this equation is arrived at after assuming resonance: w{21}=w. Doesn't this determine the incident wavelength and thus determine cross section?
2) In appendix 7.A, they refer to the "strength" of a transition. I'm not sure what this is referring to.
Ray Gao:Can stimulated emission and absorption rates be not the same for an atom in single monochromatic wave (for the same transition)?
Ryan Lewis: -none-

Semiclassical Laser Theory

Richard Wong:This question did not come directly from the readings. I started thinking about how polarization would evolve in a medium. From what I understand, we are got the result that the light emitted from the 2 level system would have the same polarization as the incoming light, with a possible phase lag. Tracing it back, I think this may be due to conservation of momentum, and just lacking a source of energy in that polarization. However, classically speaking, is it possible that collisions can change the orientation and thus the polarization of the excited atoms, so that they decay into light with a different polarization? I am not certain, but I can vaguely imagine a quantum analogue to orientation changing collision. Has this somehow been included via the orientation averaging?
Hadi Ebrahimnejad:- none -
Eric Vyskocil:Early in 8.4 in accounting for the effect other atoms have on the system it is stated that background atoms are far from resonance. Why is this necessarily true?
Rob Stead:- none -
Steven Gou:- none -
Ray Gao:Is there a valid bloch sphere to represent mixed states? (as discussed in my notes)
Ryan Lewis:At the very beginning of sec 8.4, equation 8.4.1 actually, I'm a bit confused as to the meaning of ro(sub 21)-bar. I believe the bar means that we are talking about background atoms that we assume are not near resonance, so are we also assuming then that the atoms have 2 levels of some arbitrary spacing? i.e what is this 2-1 subscript all about?

Richard Wong:The book says that the three/four level pump schemes are only rough models. What are some of the main ways can real lasers deviate from these models? How much impact to they have on our analysis of them?
Hadi Ebrahimnejad:- none -
Eric Vyskocil:Section 10.12 deals with what is termed 'spatial hole burning' where the gain coefficient g(v) has minimums and maximum values inside the cavity. What effect does spatial hole burning have on laser operation? We have assumed that losses only occur at the mirrors and it appears mathematically impossible for the gain coefficient to become negative. So why can we not just calculate some net gain coefficient over the cavity and ignore the spatial hole burning?
Rob Stead: i) What is the effect of spatial hole buning on the average gain coefficient provied by a laser medium? Ie: compute the integral wrt z of g(nu) both without and in the presence of spatial hole burning. (Obviously, some assumptions will have to be made in this case)
ii) How might one overcome the effect of spatial hole burning? Obviously leading to a brief discussion of linear vs ring cavities.
Steven Gou: A 3 level laser with laser transition between 2 to 1 is discussed in the text. What about a 3 level laser with laser transition between 3 to 2? Wouldn't this be better?
Ray Gao: on the top of page 295 of Milloni, he drops the d/dz term in the rate equation arguing that I does not vary with z very much. But the concept of gain is based on the laser propagating through the medium so how can we justify this? when does this argument break down (at what cavity length scales?)
Ryan Lewis: - none -

Richard Wong:
Hadi Ebrahimnejad: My question is regarding the section 11.10. Milonni argues that the main source of finite band width of radiation coming out of laser is the spontaneous emission. He says that this radiation bears no relation to cavity waves, and it is incoherent with respect to stimulated emitted light. It also has an inherent Lorenzian-like frequency distribution. But, I think that its phase incoherency and finite width are not separate from each other. Like any sinusoidal signal when imposed a time dependency to its phase constant can be expanded on a band of frequencies in addition to it central frequency.
Eric Vyskocil: Sections 11.8 and 11.9 discuss the topics of the spectral hold burning in the gain curve and frequency pulling, respectively. In 11.8 Figure 11.9 indicates that there will be two holes burned in the Doppler profile symmetric about the center. Does frequency pulling affect the positions of the holes that are burned?
Rob Stead: i) Fig 11.7 and spatial hole burning in lasers with liquid gain media: I was under the impression that all dye lasers circulated the dye so as to avoid depletion of the gain medium. Presumably, in these cases one avoids spatial hole burning, even in linear cavities?
ii) Equation 11.9.6
I'm a little confused here. The equations give the cavity bandwidth, nu(c), as being dependent on the individual longitudinal laser modes, nu(m), but presumably the cavity bandwidth must be single valued? Hopefully I can figure this one out. Maybe it's nearly bed time!!
Steven Gou: -none-
Ray Gao: -none-
Ryan Lewis: If your laser has no preferred polarization, then I'm wondering if it is polarized? My guess is yes, that when the laser is running one polarization should "wash" the others out because of feedback, but if there is no preferred polarization then does that mean when you turn the laser on each time the polarization could be different?

Gaussian Beams and Optical resonators

Richard Wong: 1. What are some of the applications where focusing the beam to a very small spot is important? Are there specific examples of these in your lab?
2. In deriving all the resonator properties, we make no reference to the gain medium, in terms of refractive index and shape. Are their effects generally insignificant? Are the any conditions that has to be satisfied for this to happen?
Hadi Ebrahimnejad:-none-
Eric Vyskocil:section 11.12 regarding obtaining a single mode from multiple modes there is a discussion about ways to introduce loss mechanisms that discriminate again all modes but one. I believe in class previously we discussed adding another gain medium with spatial holes that introduce losses to all but certain frequencies of oscillations. Are there benefits to using this method rather than the Fabry-Perot etalon?
Rob Stead:-none-
Steven Gou:With regards to resonator stability, the plane parallel resonator is said to be impractical due to slight misalignments causing instability. I'm wondering if the stability equations can give any information about stability with regards to alignment.
Ray Gao:Since spherical waves satisfy the Helmholtz equation, can't we have spherical waves modes in a resonator if we allow the radius of curvature at the mirrors to match the radius of curvature of the spherical waves?
Ryan Lewis:-none-

Time Domain Dynamics of Laser Oscillation

Richard Wong:Q switching is a really interesting idea. To have the shape of a pulse, there would be a range of longitudinal modes; are there likely more transverse mode as well? Also with all these modes, does the spread in frequency give rise to dispersion that significantly lengthen the pulse? If so, can we also use anomalous dispersion to compress the pulse further?
Hadi Ebrahimnejad: We saw that relaxation oscillations behave as a damped harmonic oscillator. Is it ever the case that the oscillations are critically or over-damped?
Eric Vyskocil:Why is it that Q-switched lasers only deliver stable output if they oscillate at a single frequency?
Rob Stead:A comment regarding tomorrow, I personally find that the mathematical approach of Verdeyen section 9.3 clouds the detail of what is actually happening. However, I do think the example towards the end of section 9.4 is very useful. I'd be happy if we spent some time discussing this rather than my example question above.
Steven Gou:-none-
Ray Gao:Can a Q-switched pulsed laser be more efficient (in terms of total # of photons lost) compared to its cw counterpart (exactly the same specs but without the Q-switch). Consider Q-switching based on changing mirror reflectivity. In a cw laser, we can assume a constant rate of photons being lost at the mirrors. In the Q-switched version, when the Q-switch is "off" (the storing energy phase), there is very few photons in the cavity and few being lost, when the Q-switch is "on", photon flux increases rapidly and many photons are lost at the mirrors. It is plausible to consider a case where the photons in the Q-switched laser undergoes fewer number of roundtrips on average in the cavity than the cw laser thus being more efficient? ... under the condition that the total mirror loss of the cw laser equals the time-averaged total loss of the Q-switched laser.
Ryan Lewis:-none-

Richard Wong:-none-
Hadi Ebrahimnejad:-none-
Eric Vyskocil:It states in 12.7 that Q switching may include many modes, but the Chapter 4 notes stated that to have stability for Q switching it had to have a single mode only. What am I confusing?
Rob Stead:-none-
Steven Gou:-none-
Ray Gao: Can AM mode locking be used for arbitrary pulse shaping by "customizing" the shape (hence the transfer function of the laser pulse) of the AM pulse? And a comment: In Miloni pg 387, he compared mode-locking by AM modulation to hyugens pendulums But I find this misleading since Hyugen's pendulums are a coupled oscillator phenomenon while active AM mode locking is a driven oscillator. For example, In Verdeyen 9.5, it is shown that you can have AM modulation mode locking in an homogenously broadened medium when only a single cavity exists naturally.
Ryan Lewis:-none-

Richard Wong:-none-
Hadi Ebrahimnejad:-none-
Eric Vyskocil:-none-
Rob Stead:-none-
Steven Gou:-none-
Ray Gao:-none-
Ryan Lewis:-none-

Richard Wong:-none-
Hadi Ebrahimnejad:-none-
Eric Vyskocil:-none-
Rob Stead:-none-
Steven Gou:-none-
Ray Gao:-none-
Ryan Lewis:-none-

Non-linear optical effects

Final presentations