I understand what you are trying to say, and I will use the larger band gap for my design. Is my assumption correct that the defect bands within the original bandgap are the wavelengths which will resonate in the cavity? Which means the wavelengths not in the defect bands but still in the bandgap will not resonate in the cavity but will propogate through the linear waveguide?
Also, in one of my references, it talks of a resonance condition of a cavity, which is the wavelength which will resonate in the cavity and not escape the cavity. What I am trying to do is find this resonance condition so that if I introduce a linear waveguide right after the cavity, the light will not propogate into the waveguide due to the resonance condition. I ran the PWE simulation because I assumed the defect bands would correspond to the resonance condition, but after reading your comments I am not so sure anymore. Is it possible to simulate this condition, and if so, how?
I attached an image of what I mean when I say resonance condition.