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I’m exploring the Lorentz oscillator model for optical dispersion, where the damping term γ
typically includes contributions from collision damping (which converts electromagnetic energy into internal energy, such as heat) and radiation damping (where energy is re-emitted by oscillating dipoles). When this model is coupled with Maxwell’s equations, it yields a steady-state solution of an attenuated monochromatic plane wave propagating through the medium. This attenuation is often interpreted as absorption, following the Lambert-Beer law.
However, I’m considering a specific scenario where the damping is entirely due to radiation damping, meaning there are no thermal losses (i.e., no energy is converted to heat). Even in this case, the model predicts an attenuated plane wave solution for the transmitted wave. Since the energy isn’t lost to heat but is instead radiated by the dipoles, and assuming lateral scattering is negligible, I’m puzzled about the fate of the energy that’s “missing” from the attenuated transmitted wave. Does this energy primarily end up in the reflected wave, or is it redistributed elsewhere in the system?
Additionally, I’ve been reflecting on how the refractive index is treated in dense media, as discussed by Feynman and Born. They derive the complex refractive index by solving macroscopic Maxwell’s equations, which is mathematically sound but, as Feynman points out, can obscure the physical intuition behind the refractive index’s origin. I suspect this approach also makes it harder to physically interpret the imaginary part of the refractive index, which is tied to absorption. I’m wondering if this imaginary part can be understood microscopically through the coherent interaction between the incident wave and the waves radiated by the dipoles—perhaps akin to Feynman’s treatment of the refractive index in gases. The Ewald-Oseen extinction theorem seems relevant here, as it describes how the incident field is extinguished and replaced by the medium’s response, but I’m unsure if it explicitly addresses the energy attenuation (or “absorption”) in this context—or perhaps I’ve overlooked something in its implications.
1.In the Lorentz oscillator model with pure radiation damping and negligible lateral scattering, where does the energy from the attenuated transmitted wave go? Is it primarily transferred to the reflected wave?
2.Can the imaginary part of the complex refractive index be physically interpreted as arising from the coherent interaction between the incident wave and the radiated waves from the dipoles?
I’m exploring the Lorentz oscillator model for optical dispersion, where the damping term γ
typically includes contributions from collision damping (which converts electromagnetic energy into internal energy, such as heat) and radiation damping (where energy is re-emitted by oscillating dipoles). When this model is coupled with Maxwell’s equations, it yields a steady-state solution of an attenuated monochromatic plane wave propagating through the medium. This attenuation is often interpreted as absorption, following the Lambert-Beer law.
However, I’m considering a specific scenario where the damping is entirely due to radiation damping, meaning there are no thermal losses (i.e., no energy is converted to heat). Even in this case, the model predicts an attenuated plane wave solution for the transmitted wave. Since the energy isn’t lost to heat but is instead radiated by the dipoles, and assuming lateral scattering is negligible, I’m puzzled about the fate of the energy that’s “missing” from the attenuated transmitted wave. Does this energy primarily end up in the reflected wave, or is it redistributed elsewhere in the system?
Additionally, I’ve been reflecting on how the refractive index is treated in dense media, as discussed by Feynman and Born. They derive the complex refractive index by solving macroscopic Maxwell’s equations, which is mathematically sound but, as Feynman points out, can obscure the physical intuition behind the refractive index’s origin. I suspect this approach also makes it harder to physically interpret the imaginary part of the refractive index, which is tied to absorption. I’m wondering if this imaginary part can be understood microscopically through the coherent interaction between the incident wave and the waves radiated by the dipoles—perhaps akin to Feynman’s treatment of the refractive index in gases. The Ewald-Oseen extinction theorem seems relevant here, as it describes how the incident field is extinguished and replaced by the medium’s response, but I’m unsure if it explicitly addresses the energy attenuation (or “absorption”) in this context—or perhaps I’ve overlooked something in its implications.
1.In the Lorentz oscillator model with pure radiation damping and negligible lateral scattering, where does the energy from the attenuated transmitted wave go? Is it primarily transferred to the reflected wave?
2.Can the imaginary part of the complex refractive index be physically interpreted as arising from the coherent interaction between the incident wave and the radiated waves from the dipoles?
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