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Acousto-optics in thin-film Lithium Niobate

Over the course of my Ph.D., I’ve made a number of different acousto-optic devices: waveguides for stimulated Brillouin scattering; cavity optomechanics; piezoelectric transducers; intramodal and intermodal modulators; and, finally, acousto-optic deflectors. And, except for the transducers, there’s always a g to calculate, and they’re all similar but slightly different. What started as a mess of vector algebra in 2014 now has a slick form ħgij = −i<ψi | ∂δχ |ψj>  that makes it easy to build off and extend. I wrote the first two chapters of this thesis hoping to bring some of the simple algebraic beauty of quantum mechanics to waveguides. I show that the symmetries of the operators in the dynamics are easier to see if we package the fields in a state vector, Ψ, and that these symmetries, like H = H , give us orthogonality. With that, I derive coupled mode equations like Equation 16 for resonators and waveguides which describe the dynamics of the acousto-optic devices I developed over the course of my Ph.D.. While you can find waveguide-focused orthogonality relations for microwaves [193], optics [199], and mechanics [12, 13]; Brillouin physics [235]; and cavity optomechanics [170, 11] in the literature, it’s hard to find it in one place, in one language. I hope that with these tools, the next wave of grad students will boldly couple what only physicsts at Bell Labs in the 70’s have coupled before them.

In Chapter 4, I discuss the physics and design of piezoelectric transducers. The main thrust of my research is on integrated acousto-optic modulators, and you can’t use sound to modulate light if you can’t efficiently generate sound. The efficient nanomechanical waveguide transducers (Chapter 9, Reference [34]) Yanni and I made were a key breakthrough. They allowed me to make collinear AOMs with the highest reported figure of merit to date (Chapter 11) and Wentao and I (mostly Wentao) to make integrated, resonant AOMs in pursuit of quantum microwave-to-optical conversion [81]. These transducers called for a novel design approach, reviving some tools beautifully described by Auld [12, 13], and pushing me to reckon with the nebulous piezoelectric coupling coefficient, k2 . I’ve done what I can in Chapter 4 to package that reckoning so that no poor soul will ever have to reckon in the manner I reckoned again. In it, you’ll find a definition of k2 that’s general and physical. I hope you’ll find a definition that’s delightful.

The rest of the thesis is a collection of my published works. There is some technical rhyme and reason to them which I hope to capture in the Introduction, Chapter 1. But the real rhyme and reason dates back to electricity with Mrs. Drankwalter; to Halliday and Resnick; to building submarines with Mr. Barton; to Dave Pritchard and Wolfgang’s lab; to John Belcher, Faraday, and the stress tensor; to Huffman Prairie; and to the simple idea that with his machines, man can do the impossible.

Christopher J. Sarabalis
Stanford University
Publication Date
August, 2021
Type of Dissertation
Ph.D. Applied Physics