Hi Arvind, 

I do believe that a simple criteria are:

1. dimensions of the lattice structures 

2. dielectric elements

3. refractive indices.

They all can help you to select materials that can produce band gaps that you desire. Once you find your band gaps using the Brillouin Zones, you should be able to find the desired frequencies and bandwidths you desire from those bandgaps.  

I hope this helps. Good Luck!

Dear Arvind,

The criteria as stated by Jamel might not be sufficient, depending on what is meant with 'dielectric elements'. As Jamel states you need a sufficient difference in refractive index between the two materials that create the omnidirectional reflector.

At Brewster's angle there is no reflection between layers and therefore the  mechanism that creates the bandgap dissappears, no matter how large the difference in refractive index. To avoid this, the original idea put forward is to use a third layer so that one can never reach Brewster's angle for any external angle of incidence.

Note that this implies that once you place an emitter inside the omnidirectional reflector light can always propagate through the layers; Omnidirectional reflection is something else than a complete photonic bandgap: You can get (near) 100% reflection for all angles of incidence and polarization, but the density of states (DOS) at these frequencies is finite. (in a 3D photonic bandgap the DOS goes to zero!).

You may be asking for a 1D Bragg grating with layers that alternate between negative and positive refractive index.  This means the layers alternate between having negative and positive thickness.  If designed correctly, a device with zero thickness will be omnidirectional.  In principle, you could make a Bragg grating with the same response independent of the angle of incidence.

The answer Mr. Michiel gave was very clear. In addition I suggest you to compute the band diagram on your own by programming. By changing the parameters such as refractive index, you will find the key condition for a complete band gap. The band structure of 1DPC can be easily obtained by using transfer matrix method, and do not forget to consider both TE and TM mode at the same time.

Agree with the previous answers. In addition, my advice is to check the following papers:

1. S. H. Kim and C. K. Hwangbo, Appl. Opt., 2002, 41, 3187.

2 T. J. Clement, N. Ponnampalam, H. T. Nguyen and R. G. DeCorby,

Opt. Express, 2006, 14, 1789.

It was shown that two conditions should be satisfied to achieve an omni-directional

reflection: (1) the optical contrast (difference in refractive indices of

both materials) has to be higher than 0.75 and (2) the value of high

refractive index material to be greater than 2.264.

Good luck in your calculation

Yes, I do agree with Previous answer. For both positive index layers 1-D photonic crystal the good contrast of refractive indices and proper thickness of layers can be achieved the omnidirectional bandgap.

While the left-hand right hand metamaterial the zero-phy and zero-n gap show independence of bandgap on incidence angle both for TE and TM mode.

Thanks to all @ Suggest me the chemical properties and composition of two materials necessary for 1D Photonic crystal.

It'is proper to consider the dispersion of' the refractive index of such materials, how it is possible.