Determination of optical Kerr nonlinearity of a photonic bandgap structure by Z-scan measurement

Jisoo Hwang; J. W. Wu

doi:10.1364/OL.30.000875

Determination of optical Kerr nonlinearity of a photonic bandgap structure by Z-scan measurement

Jisoo Hwang and J. W. Wu

Optics Letters
Vol. 30,
Issue 8,
pp. 875-877
(2005)
•https://doi.org/10.1364/OL.30.000875

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Jisoo Hwang and J. W. Wu, "Determination of optical Kerr nonlinearity of a photonic bandgap structure by Z-scan measurement," Opt. Lett. 30, 875-877 (2005)

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Abstract

Through analysis of the dispersion relation in a photonic bandgap structure, the effective optical Kerr nonlinearity that determines a Z-scan profile particularly near the stop-band edges, is derived. Near and inside the stop band, the nonlinear optical phase change that originates from an off-resonant response is converted into a change in nonlinear optical intensity through Bragg reflection. The Z-scan measurement of a cholesteric liquid-crystal photonic bandgap structure confirmed that off-resonant Kerr nonlinearity is responsible for the characteristic open-aperture Z-scan profiles near the stop-band edges.

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Parameter	Three-Dimensional fcc PC	One-Dimensional CLC PC
$n_{a}$ (or $n_{b}$ )	Refractive index of nanospheres (or background medium)	Refractive index parallel (or perpendicular) to the local director of nematics forming the CLC
G	$2 π α ∕ a$ (a is a lattice constant, $α = \sqrt{3}$ , 2 for $Γ \to L$ , $Γ \to X$ )	$4 π ∕ p$ (p is the pitch, for normal incidence)
$ε_{0}^{L}$	${[n_{a}^{(0)}]}^{2} f + {[n_{b}^{(0)}]}^{2} (1 - f)$ ^a	$\frac{1}{2} {{[n_{a}^{(0)}]}^{2} + {[n_{b}^{(0)}]}^{2}}$
$ε_{0}^{N L}$	$2 [n_{a}^{(0)} n_{a}^{(2)} f + n_{b}^{(0)} n_{b}^{(2)} (1 - f)]$	$[n_{a}^{(0)} n_{a}^{(2)} + n_{b}^{(0)} n_{b}^{(2)}]$
$U_{\hat{G}}^{L}$	$- \frac{2}{α^{3} π^{2}} (\sin ξ - ξ \cos ξ) {{[n_{a}^{(0)}]}^{2} - {[n_{b}^{(0)}]}^{2}}$ , $(ξ^{3} = \frac{3}{2} α^{3} π^{2} f)$	$\frac{1}{2} {{[n_{a}^{(0)}]}^{2} - {[n_{b}^{(0)}]}^{2}}$
$U_{\hat{G}}^{N L}$	$- \frac{4}{α^{3} π^{2}} (\sin ξ - ξ \cos ξ) [n_{a}^{(0)} n_{a}^{(2)} - n_{b}^{(0)} n_{b}^{(2)}]$	$[n_{a}^{(0)} n_{a}^{(2)} - n_{⊥}^{(0)} n_{⊥}^{(2)}]$

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