I want to find the photonic band gap of a crystal in COMSOL. The wavelength in free space is 632nm and the refractive index of material (Gold) is n=.18836 and absorption k=3.4034.
refractive index will remain constant and I want to find the photonic bandgap.What should be the dimension of the lattice constant?
What is the relation between the lattice constant and photonics stop band .Will i get the stopband around the incident wavelength 632 nm.
Thanks in advance.
Hi Anisuzzaman
Great question. For a face-centred cubic-based photonic crystal, such as an opal or inverse opal, the relationship between the PBG wavelength (in nm) along a particular direction [hkl] in the photonic crystal, the lattice constant (a in nm) and the average refractive index of the photonic crystal (navg) is straightforward.
PBG (in nm) along [hkl] = 2 * dhkl * navg
dhkl (in nm) = a (in nm) / squareroot (h2 + k2 + l2)
Thus
PBG (in nm) along [hkl] = 2 * a * navg / squareroot (h2 + k2 + l2)
also, a = squareroot 2 * D (where D is the diameter in nm of the spheres used to construct the fcc lattice), so the equation above is more commonly rewritten in the form
PBG (in nm) along [hkl] = 2 * squareroot 2 * D * navg / squareroot (h2 + k2 + l2)
Thanks for your answer.To get the photonic band gap,i need to give two input in the eigen value solve:Lattice constant (a) and the k vector.K vector is found from the irreducible brullion zones.What should be the lattice vector if the free space wavelength is 650 nm.
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