1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Poynting theorem for light-matter coupling in an absortive medium

  1. Jun 29, 2012 #1
    Hello everybody,

    I'm focusing on the description of the coupling of a monochromatic short EM wave and on the description of the energy absorption by matter.

    The problem is the following. It is well-known that the Poynting theorem in a non-dispersive medium considers the variation of electromagnetic energy [itex]u [J.m^{-3}][/itex], the transport of power flux using Poynting vector [itex]\overrightarrow{S}=\frac{1}{2}\overrightarrow{E} \times \overrightarrow{H'}[/itex].

    Then the balance of the energy contained in the EM field is expressed by :
    [itex] \frac{\partial u}{\partial t}+\overrightarrow{\nabla}.Re\left(\overrightarrow{S}\right)=\overrightarrow{J}.\overrightarrow{E^{'}}-\omega\varepsilon_{0}.Im(\varepsilon)< \overrightarrow{E} .\overrightarrow{E} > [/itex]

    The purpose are :
    - to calculate the propagated intensity in the medium, which is, according to me calculated by [itex] I= \left\| \overrightarrow{S} \right\| = \sqrt{\overrightarrow{S}.\overrightarrow{S'}} [/itex],
    - and to calculate the thermal energy dissipated in the medium, that is expressed through the imaginary part of the dielectric function [itex] \varepsilon \in ℂ[/itex], and thus the power transmitted to the matter by thermal dissipation is given by [itex] Q_{abs}=\omega \varepsilon_{0} Im(\varepsilon) < \overrightarrow{E} . \overrightarrow{E} > [/itex]. Of course, [itex]< \overrightarrow{E} . \overrightarrow{E} > = \overrightarrow{E} . \overrightarrow{E'} [/itex], where ' means the complex conjugate.

    But the big question for me today is that the Jackson, Stratton and Landau are telling different conclusions for the same problem. I presented the Jackson approach which seems clear.

    However, Stratton and Landau explain that for harmonic field, [itex] \frac{\partial u}{\partial t}=0 [/itex], where [itex] u \in ℂ [/itex], and thus the thermal coupling with matter is given by [itex]\overrightarrow{\nabla}.\overrightarrow{S} [/itex].

    Applied to a concrete case, the [itex]\overrightarrow{\nabla}.\overrightarrow{S} [/itex] term is complex and non-symetric, despite that the system has an axial symetry. The Jackson's approach permit to obtain very symmetric distributions, which are full of physical meaning: dissipation increase in the region which the field losses its energy. However, I think that Poynting vector divergence doesn't play any absorption role in the general case (nore constant, neither harmonic but in the context of a short laser pulse).

    I ask the opinion to the forum community because this questions doesn't seem to be fixed. Some experts still disagree. I consider that almost everybody is right. The task is to understand how, e.g. find the correct form convincing everyone.

    Have a nice evening,
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted