Degenerate Modes in Photonic Crystal Cavities: Examining Resonant Frequencies

[shpongle]

Can two degenerate modes have different resonant frequencies? I am asking question in context of resonance in photonic crystal cavities.

I am reviewing a paper (I have attached it).

Figure 2 (a) and (b) of this paper show modal profile for 2x2PCRR (photonic crystal ring resonator). In this figure two degenerate modes - quadruple0 and quadruple90 exist at different resonant frequencies!

This is possible? I thought degenerate modes have same energy and resonant frequency values.

 

[Greg Bernhardt]

I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?

 

[UltrafastPED]

I read "On the other hand, a pair of doubly degenerate modes at" to mean that each of the wavelengths exhibits a double degeneracy, and that there are a pair of wavelengths.

I agree that degeneracy refers to multiple modes with the same energy; the phrasing of the article is confusing.

 

[shpongle]

Many thanks for taking interest in reading the paper.

I am using using CST Microwave Studio, a commercial EM solver to simulate a simple photonic crystal given in figure 2(b) of this paper. The top crystal with a smaller cavity.

My question is:

Why do Quad0 and Quad90 occur at different wavelengths ? Quad90 is a degenerate mode of Quad0, shouldn't they occur at same wavelengths?

Also, out of curiosity, why do modes degenerate?

 

[pmacias]

I can confirm that it is possible for two degenerate modes to have different resonant frequencies in photonic crystal cavities. In fact, this phenomenon is commonly observed in photonic crystal structures due to the complex and unique behavior of light in these systems.

Degenerate modes refer to modes that have the same energy and frequency, but they can still have different spatial profiles. In the case of photonic crystal cavities, the unique structure and geometry of the cavity can result in different resonant frequencies for degenerate modes.

In Figure 2 (a) and (b) of the paper you have attached, we can see that the two degenerate modes, quadruple0 and quadruple90, have different spatial profiles and therefore, different resonant frequencies. This is due to the fact that the photonic crystal ring resonator has an asymmetrical structure, which can lead to mode splitting and different resonant frequencies for degenerate modes.

It is important to note that this phenomenon is not limited to photonic crystal cavities and can also occur in other types of resonators, such as microcavities and waveguides. Therefore, it is crucial to carefully analyze and understand the unique properties of each photonic crystal structure in order to accurately predict and control the behavior of degenerate modes.

In conclusion, it is possible for two degenerate modes to have different resonant frequencies in photonic crystal cavities. This is a result of the complex behavior of light in these structures and can be observed in various types of resonators. Further research and analysis are needed to fully understand and utilize this phenomenon in photonic applications.