Waveguiding Light: Questions on Allowed Modes & Energy Distribution

[fisico30]

I have a question about waveguides:

Say your input is an electromagnetic field of a certain time frequency, energy distribution, polarization. Its time frequency is above the cut-off frequency of many of the allowed modes of the waveguide.

The allowed modes are orthogonal functions (whatever they are: TE, TM, TEM). Is that always true? Can the set of allowed modes be an non-orthogonal set?

Once we inject the input beam in the waveguide, Does its energy distributes

a)in all the allowed modes with equal energy.

b)only in those modes that, by superposition, would recreate the initial input field field the best (initial_field= a*mode1+b*mode2+c*mode3+...). (it would only be approximate since we don't have an infinite amount of basis terms to work with but just the allowed ones.

c)Or can the energy even be all channeled in just one of the modes somehow, higher than the fundamental one?

d)none of the above.

Thanks again

 

[Valerie Park]

.The answer to your question is d) none of the above. The energy of an electromagnetic field in a waveguide is distributed among all of the allowed modes, but the amount of energy in each mode depends on the particular characteristics of the input field (time frequency, energy distribution, polarization). Generally, the higher modes tend to absorb less energy than the lower modes, and the energy can be distributed unevenly among the modes. In addition, the total energy of the field may be absorbed or reflected at the boundaries of the waveguide, so the energy of the field may not be conserved.

 

[astrokreng]

I would like to start by clarifying some basic concepts related to waveguides. A waveguide is a structure that is used to guide electromagnetic waves, such as light, along a specific path. This path is determined by the dimensions and properties of the waveguide, and it can be used to manipulate and control the propagation of light.

Now, to address your questions about allowed modes and energy distribution in a waveguide:

1. Are the allowed modes always orthogonal?

The answer to this question is not a simple yes or no. It depends on the type of waveguide and the specific conditions. In general, the most commonly used waveguides, such as rectangular or circular waveguides, have orthogonal modes. However, there are cases where non-orthogonal modes can also be allowed, such as in photonic crystal waveguides. It is important to note that the orthogonality of modes is not a requirement for a waveguide to function, but it can simplify the analysis and design of the waveguide.

2. How does the energy distribute in a waveguide?

The energy distribution in a waveguide is determined by the input field and the properties of the waveguide, such as its dimensions and material. In general, the energy will distribute among all the allowed modes, with each mode carrying a certain amount of energy. The distribution of energy among the modes can vary depending on the input field and the specific properties of the waveguide.

3. Can the energy be channeled in just one mode?

Yes, it is possible for all the energy to be channeled in just one mode. This is known as the fundamental mode, and it is the mode with the lowest cut-off frequency. However, this is not always the case and the energy distribution can vary depending on the input field and the properties of the waveguide.

In summary, the distribution of energy in a waveguide is a complex phenomenon that depends on various factors. The allowed modes can be orthogonal or non-orthogonal, and the energy can be distributed among all the allowed modes or concentrated in just one mode. it is important to carefully analyze and understand these factors in order to accurately predict and control the behavior of light in a waveguide. I hope this response has helped clarify your questions.