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James Clerk Maxwell (1831–1879) was one of the major contributors to physics in the nineteenth century. Although he died young, he made major contributions to the development of the kinetic theory of gases, to the understanding of color vision, and to understanding the nature of Saturn's rings. He is probably best known for having combined existing knowledge on the laws of electricity and magnetism with his insights into a complete overarching electromagnetic theory, which is...
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Generalized Maxwell projections for multi-mode network Photonics.

M Makarenko1, A Burguete-Lopez1, F Getman1

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We present a new spatio-temporal coupled mode theory for nanophotonics. This method precisely models complex optical resonator systems with many overlapping resonances, enabling faster analysis.

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Area of Science:

  • Nanophotonics
  • Optical Engineering
  • Quantum Optics

Background:

  • Controlling light at the nanoscale using optical resonant systems is crucial in nanophotonics.
  • Analyzing systems with numerous overlapping resonances presents significant challenges compared to systems with few resonances.

Purpose of the Study:

  • To develop an exact formulation of spatio-temporal coupled mode theory for complex nanophotonic systems.
  • To create a computational method for efficiently characterizing optical resonators with multiple overlapping states.

Main Methods:

  • Utilized the theory of generalized operators to formulate an exact spatio-temporal coupled mode theory.
  • Developed a fast computational technique based on first-principle simulations.

Main Results:

  • The method accurately captures the dynamics of systems with many overlapping resonances.
  • Efficiently extracts key resonator characteristics: density of states, quality factors, resonances, and linewidths.
  • Enables analysis of diverse resonator geometries and material responses.

Conclusions:

  • The developed theory and method offer a powerful tool for studying complex nanophotonic systems.
  • Facilitates both analytical and numerical investigations of light-matter interactions in resonant structures.
  • Advances the design and understanding of nanoscale optical devices.