For 1 D Photonic crystal, incident light wavelentgh ,for quater dielectricstack critical waveletgh ,what is the difference between them?
I am not sure to understand your question, but I think that it concerns the definition of a quarterwave stack, which is a multilayer of films with high- and low-refractive-indices, each with a thickness defined by:
di=1/ni * λ0/4.
In this short equation, di is the thickness of the layers i, ni is its index of refraction, λ0 is the central wavelength of the reflection band (what you called the critical wavelength). If you measure the reflectance of such a quarterwave stack as a function of the incident light wavelength (assuming a beam perpendicular to the surface), you will find a large reflectance band centered around λ0.
Hope that it answers your question.
The critical wavelength is the wavelength that the quarter-wave stack is designed to reflect most strongly. The incident light wavelength is the wavelength that device is actually being used or tested. It is certainly possible to use the device at a different wavelength than it was designed to operate. It would just not reflected as much of the light, if any.
Arezou,
You can use any wavelength to define your quarterwave stack, as long as you know the optical constants ni of your materials at that wavelength (assuming that they are not absorbing at that wavelength), and that you define their thicknesses di so that their individual optical thickness ni*di are equal to a quarterwave λ0/4.
For example, suppose you want to make a quarterwave stack with a reflectance band centered at λ0=500nm, using as materials SiO2 (n=1.47 at λ0=500nm) and TiO2 (n=2.32 at λ0=500nm). Then your quarterwave stack will be made of layers of SiO2 with thickness 500/4/1.47=85.0nm and TiO2 with thickness 500/4/2.32=53.9nm), starting and ending with the materials of highest index contrast with the substrate and ambient media (would be TiO2 if the stack is made on glass, in air).
with ni*di=λ0/2, the reflectance band will be centered around 2λ0; with ni*di=λ0, it will be centered around 4λ0.
If you use arbitrary thickness values for the High- and Low-index materials in the stack (and keep repeating the same thickness for the same material), you may get a reflectance band (less pronounced, narrower) around λ0=2(nHdH+nLdL).
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