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Is there ant relation between radius of holes, lattice constant “a” and operating wavelength while designing a PC based 2D Y junction power splitter.

### Responses (3):

• #63843 Poonam Jindal
Participant

Is there ant relation between radius of holes, lattice constant “a” and operating wavelength while designing a PC based 2D Y junction power splitter.

• #64028 Scott Newman
Moderator

The radius and lattice constant are as fundamental to your operation of a photonic crystal as the material it is made out of. The r/a ratio will control the size and location of your band gap versus wa/2pic, see the gap maps in Appendix C of the first edition of Photonic Crystals: Molding the Flow of Light.

As your operating wavelength is typically chosen to be in the center of the bandgap you look at a gap map and determine the widest gap and note that r/a and convert the wa/2pic range to as close to your desired frequency range by choosing a then from the previously noted r/a you get your required radius.

• #64063 Poonam Jindal
Participant

Thank u so much for your response Sir. I am getting a PBG for my design as 0.269228 c/a to 0.453655 c/a on the scale of wave vector k. Firstly I wanted to know how can I calculate wavelength range from this value (a = 1 micro meter the default setting). Operating wavelength of my design is 1430nm.
Secondly, How can i change the r/a ratio. I am taking r as the radius of air holes and is equal to 0.3a.
Can i optimize the value of lattice constant ‘a’ to get maximum transmission efficiency.

• #64084 Scott Newman
Moderator

Poonam,

Before I get into the other stuff I would question your units of c/a for a BG definition. Band gaps should should be in terms of frequency or normalized frequency not in terms of wave vector. Not only this but units of wavevectors are 1/m not 1/s as would be the case with c/a.

My previous comment specifically discussed the design of your base crystal. Your r/a ratio determines if you have a band gap given the materials in use. You either set a constant and scan r, calculating the band structure at each point, or you look up a band map from a reference in order to determine the r/a that gives you the largest band gap for your polarization.

With r/a set you set a = 1 and then set your r to give your r/a previously calculated. Now calculated your band structure diagram which should plot normalized frequency (wa/2pic, note we plot w/2pic) versus the wave vector. A band gap should ideally span the entire k space, otherwise your structures performance will be highly dependent on direction of propagation within the crystal. What you do is you find the primary gap (this would be the one at the lowest wa/2pic) and pick off the two values that correspond to the edges these are in wa/2pic and determine the center of these two. You then use this wa/2pic number with your operating wavelength (this should give you w) in order to solve for the a you need to use for your operating wavelength.

I will be honest this is fundamental design basics for work in photonic crystals and should be well understood before proceeding with any design work. I strongly recommend you read either the 1st or 2nd edition of “Molding the Flow of Light” by Joannopoulos, Meade, and Winn.

Scott