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I used to work on fast algorithms for solving acoustical wave equation, e.g., as explained in https://en.wikipedia.org/wiki/Wave_equation. Now I am working in a semiconductor company, and we study optics. As I searched, e.g., as explained in http://faculty.washington.edu/lylin/EE485W04/Ch2.pdf, I didn't find much difference between acoustical wave equation and optical wave equation, except the difference between speed of sound and speed of light. As we know, in acoustics, wave equation is derived from conservation of mass and conservation of momentum of the medium of sound propagation, gas. Does light have a similar medium that satisfies conservation of mass and conservation of momentum? Does it mean an acoustic solver can be applied to studying optics just by changing the speed of sound to speed of light?

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The "wave equation" is the same for both but the acoustic is a scalar while the EM is vectorial type. Depending on the medium and/or scattering obstacles the several components (6 = 3 Electric field + 3 Magnetic field) may interact and then it becomes a lot more complicated problem than just the scalar case.

Per @Jagerber48, if the medium is simple (homogeneous, isotropic and lossless) and interactions between the components at the scattering boundaries are negligible then the vector equation separates into scalar equations and the acoustic solver should work for you. EM component mixing, ie., the vector behavior, is important if you want to see sub-wavelength details of the field very near the scattering object.

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  • $\begingroup$ I’d add, or ask you to add in the answer, that in non-complicated media, the vector optical wave equation can be reduced to a scalar wave equation, in which case the acoustic solver could be used for the optical waves. $\endgroup$
    – Jagerber48
    Commented Feb 14, 2022 at 15:08
  • $\begingroup$ Of course you would have to know the physical criteria for when that reduction is possible. $\endgroup$
    – Jagerber48
    Commented Feb 14, 2022 at 15:09

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