Photonic local density of states and field intensity

[Jeffrey Yang]

Dear All:

I'm very confusing with the relationship between photonic local density of states and the field intensity. In thermal equilibrium, the field intensity should be proportional to the photon's number (or squared) and also be proportional to the local density of states. We know that this density of states is proportional to the n^3, where n is the refractive index. Meaning if you have larger n, you should have larger field intensity. But actually it's not. If you have larger n, meaning you have larger dielectric function, the dielectric screening will be stronger. Under a same excitation, you should have smaller field intensity.

How to under stand this point?

 

[eljose79]

Thank you for bringing up this interesting topic. I can understand your confusion regarding the relationship between photonic local density of states and field intensity.

Firstly, it is important to note that the photonic local density of states (LDOS) is a measure of the number of electromagnetic modes available for a photon to interact with in a given space. This means that a higher LDOS indicates a higher probability of photon-matter interactions.

On the other hand, field intensity is a measure of the strength of the electric or magnetic field at a given point in space. In thermal equilibrium, the field intensity is indeed proportional to the photon's number (or squared) and the local density of states. However, the relationship between the refractive index and field intensity is not as straightforward as you have described.

You are correct in stating that a higher refractive index (n) leads to a higher LDOS, which in turn indicates a higher field intensity. However, as you mentioned, a higher refractive index also means a stronger dielectric screening. This means that the electric field is partially shielded by the material, resulting in a decrease in field intensity.

To understand this better, we need to consider the concept of the effective refractive index. This takes into account the effects of both the refractive index and the dielectric screening. In materials with a high refractive index, the effective refractive index is often lower than the actual refractive index. This means that while the LDOS may be higher, the effective refractive index limits the field intensity.

In conclusion, the relationship between refractive index, LDOS, and field intensity is complex and depends on various factors such as material properties, geometry, and excitation conditions. I hope this explanation helps in understanding this point better.