Are polaritons simply photons propagating in medium?

  1. In vacuum, the photon has a 4-momentum (E, p) with E^2 - p^2 = 0, i.e. it's massless. However, upon entering a medium of refractive index n, we expect that the photon retains its energy, while reducing its momentum by a factor n (due to increased wavelength). We then have for the 4-momentum of a photon in the medium (E, p/n) with E^2 - p^2 / n^2 != 0 which implies that the photon gains mass in a medium. Would it be correct to identify this particle not as a "photon in a medium" but as a polariton?

    PS I'm a particle physicist, so take it easy on me :)

    Thanks!
     
  2. jcsd
  3. DrDu

    DrDu 4,450
    Science Advisor

    As long as n is constant, the photon (or polariton) will still be massless. However n will vary with frequency and wavevector, so that the polariton can gain an effective mass as m_eff=d^2E/dp^2.
     
  4. OK, so the question is, can I identify a polariton with a particle of energy E and momentum p/n?
     
  5. Cthugha

    Cthugha 1,715
    Science Advisor

    That question is a bit difficult to answer as the usage of the word "polariton" differs in different fields. Some fields, especially some subfields in semiconductor physics reserve the term polariton for strongly coupled systems. That means that you have strong light-matter interaction and avoided crossings when plotting the dispersions. It also means that a perturbative treatment of the light-matter interaction fails. In these fields, the term "photon" is also used in the regime of weak light-matter interaction.

    However, strictly speaking a bare photon only describes the electromagnetic field in vacuum. The changes introduced by the medium can also always be described in terms of polaritons. Some fields use that stricter definition of what a polariton is.
     
  6. For my purposes, I need a word for a quasiparticle that represents a photon in an optical medium of refractive index n. That is, a particle that travels at the speed of c/n, carries energy E and momentum p/n, where E and p are energy and momentum of a photon with the same frequency propagating through vacuum. I am not particulary interested in the microscopic describtion of a medium or the strength of the coupling. All that matters it that light couples to matter and the information about the coupling is contained in one number: n. Would a "polariton" be a suitable word?
     
  7. DrDu

    DrDu 4,450
    Science Advisor

  8. I assume that you are thinking about the polaritons created by the coupling of the optical phonon field to the electromagnetic wave field. Then, I would use the word "photon-like polariton" to describe the excitation corresponding to a mass less particle. There are "phonon-like" polaritons that correspond more closely to the optical phonons. The optical phonon has a "non-zero rest mass."

    "Polaritons" have a dispersion curve consisting of two branches that are split by the coupling interactions. There is a forbidden gap in wavevector between the two branches. The boundaries of the gap are the frequencies of the transverse optical and longitudinal optical phonons.

    The dispersion curves of the polariton are very important in understanding the jargon. I am currently looking at Figure 11 on page 287 of the following reference:

    "Introduction to Solid State Physics" 7th edition by Charles Kittel (Wiley, 1996).

    A "photon-like polariton" is not really the same as a photon. Strictly speaking, a true photon can exist only in a vacuum. However, the word "photon" is often applied to those excitations in a solid that travel at a phase velocity of "c/n", where "c" is the speed of light in a vacuum and "n" is the index of refraction.

    The velocity of light in a solid is really the speed of the photon-like polariton in a vacuum. Similarly, the "optical phonons" in a solid are really "phonon-like" polaritons. The dispersion curves of the uncoupled phonon and the uncoupled photon cross. The branches are split at the point of crossing. Near the forbidden gap, polaritons have a mixed phonon-photon nature.
     
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