Theory of coupled harmonics and its application to resonant and non-resonant electro-optic modulators

Meisam Bahadori, Yansong Yang, Ahmed E. Hassanien, Lynford L. Goddard, Songbin Gong

Research output: Contribution to journalArticlepeer-review


We present a unified theory for analyzing the frequency conversion between an RF voltage and an optical carrier in an electro-optic modulator. Our new approach results in the electro-optic coupled harmonic equation (EOCHE) that encompasses the electro-optic behavior of common types of modulators (lumped, traveling wave, and resonant) and effortlessly provides closed-form solutions for the small-signal frequency response and the large-signal intermodulation effects. In particular, the small-signal electro-optic frequency responses of lumped and traveling-wave Mach-Zehnder modulators, and resonant microring modulators are derived. We show that the concept of velocity-mismatch only applies to special cases when designing traveling-wave modulators. Therefore, to generalize the design of electro-optic modulators we propose a universal concept called the “effective RF phase” that governs how the optical power is exchanged between different RF harmonics of light. Using the EOCHE, we also propose a generalization of the widely used transfer matrix method for photonic circuits to fully capture the RF mixing effects in integrated photonic circuits, which is analogous to the steady-state AC analysis of electrical circuits. The simplicity and versatility of our approach make it a holistic tool for designing high-speed electro-optic modulators.

Original languageEnglish (US)
Article number9116832
Pages (from-to)5756-5767
Number of pages12
JournalJournal of Lightwave Technology
Issue number20
StatePublished - Oct 15 2020
Externally publishedYes


  • Coupled harmonics
  • Effective RF phase
  • Electro-optic effect
  • Lumped phase shifter
  • Mach-Zehnder interferometer
  • Microring
  • Optical modulation
  • Traveling-wave modulator

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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