# Effective occupation number of photon

• Jeffrey Yang
In summary, the conversation discusses the relationship between photon's number and photon's flux under thermal equilibrium. The occupation number is determined by the source and the photon's flux changes when it passes through an interface between two media. The equation PDOS1* ON(IN) * V1 = .PDOS2 * ON(T) * V2 + PDOS1 * ON(R) * V1 is used to describe this change, where IN, T, and R represent incidence, transmission, and reflection respectively. The concept of effective occupation number is also discussed and questioned, as well as the possibility of cancellation between reflection and velocity effects.

#### Jeffrey Yang

Hello everyone:

Here is the problem:

Under thermal equilibrium, photon's number can be described as the
photonic density of state (PDOS) * occupation number(ON).
Also, the photon's flux can be described as
PDOS * ON * effective particle velocity into certain direction ( V)

The occupation number is determined by the source, typically it will be a Boltzmann distribution characterized by the temperature and chemical potential.

When a beam scattering by an interface between media 1 and media 2, only part of incident energy can go through into the second media. If we continuously tracing the energy of the photon flux, we may can write the following equation:

PDOS1* ON(IN) * V1 = .PDOS2 * ON(T) * V2 + PDOS1 * ON(R) * V1

, where IN, T, R means incidence, transmission and reflection respectively.

This means the occupation number of photon in the media 2 will be different to the one in media 1. Is such an effective occupation number is meaningful and this consideration is correct? Does this mean that once the reflection happens the occupation number of photon in media 2 will never reach the thermodynamic limit?

Jeffrey Yang said:
This means the occupation number of photon in the media 2 will be different to the one in media 1.
You have the effect of different reflection, but you also have the different velocity. Why are you sure they won't cancel?

mfb said:
You have the effect of different reflection, but you also have the different velocity. Why are you sure they won't cancel?
If you write down the full equals, you will find that will not cancelled. The ON(T) in the second media will be a function of refractive index.