What is a good basis for coupled modes in a resonator?

In summary, the conversation discusses an electro-optical modulator and its Hamiltonian, which includes all modes and a parameter 𝜙0. The question is posed about a good set of basis for the system, particularly when the index m is restricted to an upper bound. It is clarified that the b's are raising/lowering operators and the index m can run through positive and negative integers, as it is a matter of choice.
  • #1
Supantho Raxit
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TL;DR Summary
When trying to solve the Hamiltonian for coupled modes, what set of commutating operators can we use?
Suppose, there is an electro-optical modulator that can couple the neighboring modes in an optical ring resonator. The Hamiltonian for the system
Screen Shot 2020-11-22 at 12.56.00 AM.png


looks something like this^^ (see the attached image). Here we sum over all modes m and 𝜙0 is a parameter. What will be a good set of basis for the system? Suppose, we somehow restrict m to some upper bound m_max. What will be a good set of basis then?
 
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  • #2
Since nobody else is answering... are the bs raising/lowering operators? Does the index m run through positive and negative integers?
 
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Likes Supantho Raxit
  • #3
Yes, the b's are raising/lowering operators, and index m does run through positive and negative integers. The latter is a matter of choice since we can label our "sites" as we wish.
 

FAQ: What is a good basis for coupled modes in a resonator?

1. What is a resonator?

A resonator is a device that is designed to produce or amplify a specific frequency or range of frequencies. It is typically made up of a cavity or chamber with reflecting walls and a source of energy, such as an electrical signal or sound wave.

2. What are coupled modes in a resonator?

Coupled modes in a resonator refer to the interaction between multiple resonant modes within the cavity. This can occur when the resonator has multiple sources of energy or when the cavity has multiple modes of vibration.

3. Why is having a good basis for coupled modes important?

A good basis for coupled modes is important because it allows for better control and understanding of the resonator's behavior. It can help optimize the efficiency and performance of the resonator, as well as prevent unwanted interactions between modes.

4. How can a good basis for coupled modes be achieved?

A good basis for coupled modes can be achieved through proper design and tuning of the resonator. This may involve adjusting the geometry and dimensions of the cavity, as well as carefully selecting the energy sources and their frequencies.

5. What are some applications of coupled modes in resonators?

Coupled modes in resonators have a wide range of applications, including in lasers, microwave cavities, and acoustic devices. They are also commonly used in scientific research, such as in studying the properties of materials and for precise measurements of frequency and wavelength.

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