Working Through Yariv's Optical Waves in Crystals
Yariv's Optical Waves in Crystals is one of those books that everyone in photonics references but very few people actually finish working through cover to cover. The problems are where most people hit a wall. The theory sections are dense but manageable if you already have some background in electrodynamics and crystal optics. The end-of-chapter problems, though, they require a different kind of patience. You need to know when to approximate, when to push through a messy integral, and when to step back and realize you've been setting up the coordinate system wrong the entire time. There are a handful of solution documents floating around, and I've seen the term Joburgore used in a few student forums as a label for one particular compilation. I'm not going to link to anything directly since these circulate on file-sharing platforms and change addresses constantly, but if you search for that phrase alongside the problem numbers from your edition you should land on something usable. The key is matching it to your edition. Yariv went through at least two major printings and the problem numbers shift between them. I once spent an afternoon cross-referencing solutions only to realize I was looking at chapter 5 problems from the 1985 edition while my homework was from the 1991 reprint. Two different numbering schemes for essentially the same material. Here's the thing nobody tells you about these books: the solutions are almost always presented in a way that skips the part where the author figures out which approach to take in the first place. Yariv himself writes in a very compressed style. When you're working through a problem on coupled-mode theory for electro-optic interaction in a uniaxial crystal, the solution will show you the final amplitude equations and the phase-matching condition, but it won't walk you through how he arrived at dropping certain coupling terms. That's the gap you need to fill.
My general approach is to work the problem on my own first, even if I can't finish it. Then I look at the solution, not to copy it, but to identify the single step where my derivation diverged from theirs. That's usually where the actual learning happens. In one case with problem 7.4 involving nonlinear wave mixing in lithium niobate, I kept getting a factor of two mismatch in the effective nonlinear coefficient. The solution didn't explain why. I ended up going back to the original Agrawal paper from 1978 that Yariv cites, and the discrepancy came down to a convention difference in how the nonlinear polarization is defined. Some authors include the degeneracy factor in the coefficient, others pull it out into the equation. Once I matched conventions, the answer fell into place.
Common Problems and Where People Get Stuck
Chapter 3 on light propagation in anisotropic media is where most students start having real trouble. The index ellipsoid derivation is straightforward if you know your tensor algebra, but the moment you need to find the allowed polarization modes for an arbitrary propagation direction, things get messy. I've seen people waste days on problems involving the walk-off angle because they kept trying to use Cartesian components instead of working in the principal plane. The trick is to rotate your coordinate system so that the propagation direction lies in one of the principal planes. It reduces the eigenvalue problem from a full 3x3 matrix to something you can actually solve by hand. Another recurring issue is the treatment of magneto-optic effects in chapter 8. The Faraday rotation derivations assume a weak-field limit that's easy to miss if you're not careful. I worked through a problem set where the external magnetic field was strong enough that the second-order term in the permeability expansion was no longer negligible. None of the available solutions I found caught that. You have to go back to the fundamental Maxwell equations and re-derive the dispersion relation without making that approximation. It adds about four extra lines to the calculation but changes the final result noticeably.
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When a Solutions Document Isn't Enough
The hardest chapter in the book is chapter 10 on acoustic-optic interaction. The solutions that circulate online for this chapter are notoriously patchy. A lot of them just restate the Bragg condition and move on without actually solving the wave equation with the acoustic perturbation. If you're struggling here, supplement the solutions with the original Raman-Nath and Bhatnagar papers that Yariv references. The experimental details in those older papers often contain the physical intuition that gets lost in the textbook formulation. I found that reading Bhatnagar's 1963 paper on acoustic wave propagation in anisotropic crystals took me about three hours but clarified more than two weeks of working through the textbook problems alone. Also worth noting: not every problem in the book has a clean analytical solution. Some of the later problems in chapter 11 on integrated optic devices are set up so that you need to run a numerical simulation. I've seen solution documents that present closed-form answers for these when no such answer exists. If a solution looks suspiciously clean for a problem involving mode coupling in a graded-index waveguide, it probably glosses over the approximation. Run a quick finite-difference beam propagation check to verify.
A Few Practical Notes on Working Through This Book
Keep a separate notebook for derivations. Yariv's notation shifts slightly between sections, and what he calls the electro-optic coefficient r41 in one chapter becomes gamma in another. Writing things out by hand helps you track these changes. It also forces you to slow down enough to notice when a solution document has swapped indices or dropped a complex conjugate. I've caught at least three errors in widely circulated solution sets this way. Don't try to do all the problems. The book has more end-of-chapter exercises than any single course can cover. Pick the ones that match the topics your professor emphasizes and skip the rest. The problems on photorefractive effects in chapter 12, for example, are interesting but rarely assigned in a standard graduate course. I spent two weeks on them once and it was pure time investment with no return for my grade. If you're stuck on a specific problem and can't find a solution anywhere, post the problem number and your edition year on the relevant optics forums. People there tend to help, but make sure you show your work first. The ones who just ask for the answer without any attempt usually get ignored.
