Design and optimization of a monolithically integratable InP-based optical waveguide isolator

Mathias Vanwolleghem; Philippe Gogol; Pierre Beauvillain; Wouter Van Parys; Roel Baets

doi:10.1364/JOSAB.24.000094

Journal of the Optical Society of America B
Vol. 24,
Issue 1,
pp. 94-105
(2007)
•https://doi.org/10.1364/JOSAB.24.000094

Design and optimization of a monolithically integratable InP-based optical waveguide isolator

Mathias Vanwolleghem, Philippe Gogol, Pierre Beauvillain, Wouter Van Parys, and Roel Baets

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Mathias Vanwolleghem, Philippe Gogol, Pierre Beauvillain, Wouter Van Parys, and Roel Baets, "Design and optimization of a monolithically integratable InP-based optical waveguide isolator," J. Opt. Soc. Am. B 24, 94-105 (2007)

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Abstract

The optimization design of the layer structure for a novel type of a $1.3 μ m$ monolithically integrated InP-based optical waveguide isolator is presented. The concept of this component is based on introducing a nonreciprocal loss–gain behavior in a standard semiconductor optical amplifier (SOA) structure by contacting the SOA with a transversely magnetized ferromagnetic metal contact, sufficiently close to the guiding and amplifying core of the SOA. The thus induced nonreciprocal complex transverse Kerr shift on the effective index of the guided TM modes, combined with a proper current injection, allows for forward transparency and backward optical extinction. We introduce two different optimization criteria for finding the optimal SOA layer structure, using two different figure-of-merit functions (FoM) for the device performance. The device performance is also compared for three different compositions of the ${Co}_{x} {Fe}_{1 - x}$ $(x = 0, 50, 90)$ ferromagnetic transition metal alloy system. It is found that equiatomic (or quasi-equiatomic) CoFe alloys are the most suitable for this application. Depending on the used FoM, two technologically practical designs are proposed for a truly monolithically integrated optical waveguide isolator. It is also shown that these designs are robust with respect to variations in layer thicknesses and wavelength. Finally, we have derived an analytical expression that gives a better insight in the limit performance of a ferromagnetic metal-clad SOA–isolator in terms of metal parameters.

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Composition	n	κ	$g^{'}$	$g^{″}$	$g ∕ ϵ$
${Co}_{90} {Fe}_{10}$	$4.65 \pm 0.1$	$4.82 \pm 0.03$	$- 1.7 \pm 0.2$	$- 1.05 \pm 0.1$	$- 0.0220 - 0.0387 j$
${Co}_{50} {Fe}_{50}$	$3.2 \pm 0.08$	$4.5 \pm 0.04$	$- 1.7 \pm 0.2$	$- 1.7 \pm 0.1$	$- 0.0344 - 0.0710 j$
Fe	$3.82 \pm 0.27$	$3.5 \pm 0.05$	$- 1.4 \pm 0.3$	$- 0.75 \pm 0.17$	$- 0.0324 - 0.0495 j$

Layer	Composition (Dopant, Strain ε)	Material Parameters (n, g) (Bandgap $λ_{g}$ )	Thickness
MO layer	${Co}_{90} {Fe}_{10}$	$n = 4.35 - i 4.76$	$100 nm$
	or	$g = - 1.7 + i 1.05$
	${Co}_{50} {Fe}_{50}$	$n = 3.2 - i 4.5$
	or	$g = - 1.7 + i 1.7$
	Fe	$n = 3.82 - i 3.5$
		$g = - 1.4 + i 0.75$
Absorbing	${In}_{0.54} {Ga}_{0.46} As$	$n = 3.6 - i 0.2$	$15 nm$
contact layer	Be: $3 \times 10^{19} {cm}^{- 3}$	$1.62 μ m$
Transparent	${In}_{0.81} {Ga}_{0.19} {As}_{0.41} P_{0.59}$	$n = 3.37$	$100 nm$
contact layer	Be: $1 \times 10^{19} {cm}^{- 3}$	$1.17 μ m$
Spacer layer	InP	$n = 3.203$	Optimize
Spacer layer	InP	$0.9 μ m$	Optimize
Upper SCH	${In}_{0.86} {Ga}_{0.14} {As}_{0.31} P_{0.69}$	$n = 3.34$	Optimize
Upper SCH	${In}_{0.86} {Ga}_{0.14} {As}_{0.31} P_{0.69}$	$1.05 μ m$	Optimize
Barrier ( $\times 10$ )	${In}_{0.62} {Al}_{0.3} {Ga}_{0.08} As$	$n = 3.46$	$20 nm$
Barrier ( $\times 10$ )	$ϵ = + 0.6 %$	$1.05 μ m$	$20 nm$
QW ( $\times 9$ )	${In}_{0.34} {Al}_{0.14} {Ga}_{0.52} As$	$n = 3.57 + i k$	$10 nm$
	${In}_{0.34} {Al}_{0.14} {Ga}_{0.52} As$	$k = 0.00483 \ln (\frac{6}{N_{w}} \frac{J_{tot} [in A ∕ {cm}^{2}]}{352})$
	$ϵ = - 1.25 %$	$1.3 μ m$
Lower SCH	${In}_{0.86} {Ga}_{0.14} {As}_{0.31} P_{0.69}$	$n = 3.34$	Optimize
Lower SCH	${In}_{0.86} {Ga}_{0.14} {As}_{0.31} P_{0.69}$	$1.05 μ m$	Optimize
Substrate	$InP$	$n = 3.203$
Substrate	$InP$	$0.9 μ m$

	FoM I
	$t_{In P}$ (nm)	$t_{S C H, l}$ (nm)	$t_{S C H, u}$ (nm)	I $(mA ∕ (μ m \times dB))$	L (mm/dB)
Fe	420	14.8	14.8	4.793	0.326
${Co}_{50} {Fe}_{50}$	410	13.5	14.5	3.378	0.233
${Co}_{90} {Fe}_{10}$	450	12.5	13.5	7.546	0.521
	FoM $L \times I$
Fe	350	16	16	6.526	0.163
${Co}_{50} {Fe}_{50}$	330	12	15	4.658	0.113
${Co}_{90} {Fe}_{10}$	370	10.7	13.2	10.458	0.252

Composition	n	κ	$g^{'}$	$g^{″}$	$g ∕ ϵ$
${Co}_{90} {Fe}_{10}$	$4.65 \pm 0.1$	$4.82 \pm 0.03$	$- 1.7 \pm 0.2$	$- 1.05 \pm 0.1$	$- 0.0220 - 0.0387 j$
${Co}_{50} {Fe}_{50}$	$3.2 \pm 0.08$	$4.5 \pm 0.04$	$- 1.7 \pm 0.2$	$- 1.7 \pm 0.1$	$- 0.0344 - 0.0710 j$
Fe	$3.82 \pm 0.27$	$3.5 \pm 0.05$	$- 1.4 \pm 0.3$	$- 0.75 \pm 0.17$	$- 0.0324 - 0.0495 j$

Layer	Composition (Dopant, Strain ε)	Material Parameters (n, g) (Bandgap $λ_{g}$ )	Thickness
MO layer	${Co}_{90} {Fe}_{10}$	$n = 4.35 - i 4.76$	$100 nm$
	or	$g = - 1.7 + i 1.05$
	${Co}_{50} {Fe}_{50}$	$n = 3.2 - i 4.5$
	or	$g = - 1.7 + i 1.7$
	Fe	$n = 3.82 - i 3.5$
		$g = - 1.4 + i 0.75$
Absorbing	${In}_{0.54} {Ga}_{0.46} As$	$n = 3.6 - i 0.2$	$15 nm$
contact layer	Be: $3 \times 10^{19} {cm}^{- 3}$	$1.62 μ m$
Transparent	${In}_{0.81} {Ga}_{0.19} {As}_{0.41} P_{0.59}$	$n = 3.37$	$100 nm$
contact layer	Be: $1 \times 10^{19} {cm}^{- 3}$	$1.17 μ m$
Spacer layer	InP	$n = 3.203$	Optimize
Spacer layer	InP	$0.9 μ m$	Optimize
Upper SCH	${In}_{0.86} {Ga}_{0.14} {As}_{0.31} P_{0.69}$	$n = 3.34$	Optimize
Upper SCH	${In}_{0.86} {Ga}_{0.14} {As}_{0.31} P_{0.69}$	$1.05 μ m$	Optimize
Barrier ( $\times 10$ )	${In}_{0.62} {Al}_{0.3} {Ga}_{0.08} As$	$n = 3.46$	$20 nm$
Barrier ( $\times 10$ )	$ϵ = + 0.6 %$	$1.05 μ m$	$20 nm$
QW ( $\times 9$ )	${In}_{0.34} {Al}_{0.14} {Ga}_{0.52} As$	$n = 3.57 + i k$	$10 nm$
	${In}_{0.34} {Al}_{0.14} {Ga}_{0.52} As$	$k = 0.00483 \ln (\frac{6}{N_{w}} \frac{J_{tot} [in A ∕ {cm}^{2}]}{352})$
	$ϵ = - 1.25 %$	$1.3 μ m$
Lower SCH	${In}_{0.86} {Ga}_{0.14} {As}_{0.31} P_{0.69}$	$n = 3.34$	Optimize
Lower SCH	${In}_{0.86} {Ga}_{0.14} {As}_{0.31} P_{0.69}$	$1.05 μ m$	Optimize
Substrate	$InP$	$n = 3.203$
Substrate	$InP$	$0.9 μ m$

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Journal of the Optical Society of America B