Competition between electronic Kerr and free-carrier effects in an ultimate-fast optically switched semiconductor microcavity

Emre Yüce; Georgios Ctistis; Julien Claudon; Emmanuel Dupuy; Klaus J. Boller; Jean-Michel Gérard; Willem L. Vos

doi:10.1364/JOSAB.29.002630

Journal of the Optical Society of America B
Vol. 29,
Issue 9,
pp. 2630-2642
(2012)
•https://doi.org/10.1364/JOSAB.29.002630

Competition between electronic Kerr and free-carrier effects in an ultimate-fast optically switched semiconductor microcavity

Emre Yüce, Georgios Ctistis, Julien Claudon, Emmanuel Dupuy, Klaus J. Boller, Jean-Michel Gérard, and Willem L. Vos

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Emre Yüce, Georgios Ctistis, Julien Claudon, Emmanuel Dupuy, Klaus J. Boller, Jean-Michel Gérard, and Willem L. Vos, "Competition between electronic Kerr and free-carrier effects in an ultimate-fast optically switched semiconductor microcavity," J. Opt. Soc. Am. B 29, 2630-2642 (2012)

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Abstract

We have performed ultrafast pump–probe experiments on a GaAs–AlAs microcavity with a resonance near 1300 nm in the “Original” telecom band. We concentrate on ultimate-fast optical switching of the cavity resonance that is measured as a function of pump-pulse energy. We observe that, at low pump-pulse energies, the switching of the cavity resonance is governed by the instantaneous electronic Kerr effect and is achieved within 300 fs. At high pump-pulse energies, the index change induced by free carriers generated in the GaAs start to compete with the electronic Kerr effect and reduce the resonance frequency shift. We have developed an analytic model that predicts this competition in agreement with the experimental data. To this end, we derive the nondegenerate two- and three-photon absorption coefficients for GaAs. Our model includes a new term in the intensity-dependent refractive index that considers the effect of the probe-pulse intensity, which is resonantly enhanced by the cavity. We calculate the effect of the resonantly enhanced probe light on the refractive index change induced by the electronic Kerr effect for cavities with different quality factors. By exploiting the linear regime where only the electronic Kerr effect is observed, we manage to retrieve the nondegenerate third-order nonlinear susceptibility $χ^{(3)}$ for GaAs from the cavity resonance shift as a function of pump-pulse energy.

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Equations (49)

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Parameter	Value	Unit	Source
$N_{atm}$	$4.42 \times 10^{22}$	$atoms / {cm}^{3}$	[40]
$μ^{2}$	$6.25 \times 10^{- 43}$	$J {cm}^{3}$	[28]
$Γ_{n, l}$	$6.28 \times 10^{13}$	$rad / s$	[28]
$τ_{int}$	$150.0 \times 10^{- 15}$	$s$	a
$ω_{pr}$	7805.79	${cm}^{- 1}$	a
	$1.47 \times 10^{15}$	$Hz$	a
$I_{pr}^{*}$	0.18	$pJ / {μm}^{2}$	a
	0.2	$GW / {cm}^{2}$	a
$I_{cav}^{*}$	11.3	$pJ / {μm}^{2}$	a
	12.0	$GW / {cm}^{2}$	a
$ω_{pu}$	4166.67	${cm}^{- 1}$	a
	$7.85 \times 10^{15}$	$Hz$	a
$I_{pu}^{*}$	$1.00 \times 10^{2}$	$pJ / {μm}^{2}$	a
	93.7	$GW / {cm}^{2}$	a

Parameter	Measurement	Calculated	Unit
$χ^{(3)}$	$6.72 \times 10^{- 20}$		$m^{2} / V^{2}$
	$0.48 \times 10^{- 11}$		esu
$σ_{n g}^{(2)}$	$8.59 \times 10^{- 52}$	$1.14 \times 10^{- 50}$	${cm}^{4} s / {photon}^{2}$
$N_{eh}^{(2)}$	$3.78 \times 10^{17}$	$5.04 \times 10^{18}$	$1 / {cm}^{3}$
$β^{(2)}$	$0.10 \times 10^{- 2}$	$0.13 \times 10^{- 1}$	$cm / MW$
$σ_{l g}^{(3)}$	$4.71 \times 10^{- 83}$	$3.93 \times 10^{- 84}$	${cm}^{6} s^{2} / {photon}^{3}$
$N_{eh}^{(3)}$	$5.92 \times 10^{16}$	$4.93 \times 10^{15}$	$1 / {cm}^{3}$
$γ^{(3)}$	$0.53 \times 10^{- 3}$	$0.45 \times 10^{- 4}$	${cm}^{3} / {GW}^{2}$

Parameter	Value	Unit	Source
$N_{atm}$	$4.42 \times 10^{22}$	$atoms / {cm}^{3}$	[40]
$μ^{2}$	$6.25 \times 10^{- 43}$	$J {cm}^{3}$	[28]
$Γ_{n, l}$	$6.28 \times 10^{13}$	$rad / s$	[28]
$τ_{int}$	$150.0 \times 10^{- 15}$	$s$	a
$ω_{pr}$	7805.79	${cm}^{- 1}$	a
	$1.47 \times 10^{15}$	$Hz$	a
$I_{pr}^{*}$	0.18	$pJ / {μm}^{2}$	a
	0.2	$GW / {cm}^{2}$	a
$I_{cav}^{*}$	11.3	$pJ / {μm}^{2}$	a
	12.0	$GW / {cm}^{2}$	a
$ω_{pu}$	4166.67	${cm}^{- 1}$	a
	$7.85 \times 10^{15}$	$Hz$	a
$I_{pu}^{*}$	$1.00 \times 10^{2}$	$pJ / {μm}^{2}$	a
	93.7	$GW / {cm}^{2}$	a

Parameter	Measurement	Calculated	Unit
$χ^{(3)}$	$6.72 \times 10^{- 20}$		$m^{2} / V^{2}$
	$0.48 \times 10^{- 11}$		esu
$σ_{n g}^{(2)}$	$8.59 \times 10^{- 52}$	$1.14 \times 10^{- 50}$	${cm}^{4} s / {photon}^{2}$
$N_{eh}^{(2)}$	$3.78 \times 10^{17}$	$5.04 \times 10^{18}$	$1 / {cm}^{3}$
$β^{(2)}$	$0.10 \times 10^{- 2}$	$0.13 \times 10^{- 1}$	$cm / MW$
$σ_{l g}^{(3)}$	$4.71 \times 10^{- 83}$	$3.93 \times 10^{- 84}$	${cm}^{6} s^{2} / {photon}^{3}$
$N_{eh}^{(3)}$	$5.92 \times 10^{16}$	$4.93 \times 10^{15}$	$1 / {cm}^{3}$
$γ^{(3)}$	$0.53 \times 10^{- 3}$	$0.45 \times 10^{- 4}$	${cm}^{3} / {GW}^{2}$

Abstract

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Equations (49)

Journal of the Optical Society of America B