Phase-sensitive four-wave mixing interferometer

Xuelei Fu; Chester Shu

doi:10.1364/OL.39.004427

Optics Letters
Vol. 39,
Issue 15,
pp. 4427-4430
(2014)
•https://doi.org/10.1364/OL.39.004427

Phase-sensitive four-wave mixing interferometer

Xuelei Fu and Chester Shu

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Xuelei Fu and Chester Shu, "Phase-sensitive four-wave mixing interferometer," Opt. Lett. 39, 4427-4430 (2014)

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Abstract

A nonlinear interferometer is constructed using a dual-pump, dual-signal four-wave mixing (FWM) process. The generated idlers are categorized into phase-insensitive and phase-sensitive (PS) outputs according to whether the power is sensitive to the phase difference of the input signals. The PS idlers are obtained from the interference of the primary idlers and are regarded as the FWM interferometer output. Potential applications include photonic exclusive-NOR and exclusive-OR operations, photonic correlators, and photonic microwave filters.

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Idler	FWM Process		Idler Power	Idler Phase	Relative Phase
I1	1-1	$P 2 + S 1 \to I 1 + P 1$	${CE}_{11} P_{S 1} \propto 4 P_{P 1} P_{P 2} P_{S 1}$	$ϕ_{I 1} = ϕ_{P 2} + ϕ_{S 1} - ϕ_{P 1}$	$Δ ϕ_{I 1} = ϕ_{S 1} - ϕ_{S 2} + 2 (ϕ_{P 2} - ϕ_{P 1})$
	1-2	$P 1 + S 2 \to I 1 + P 2$	${CE}_{12} P_{S 2} \propto 4 P_{P 1} P_{P 2} P_{S 2}$	$ϕ_{I 1} = ϕ_{P 1} + ϕ_{S 2} - ϕ_{P 2}$
I2	2-1	$2 P 1 \to I 2 + S 1$	${CE}_{21} P_{S 1} \propto P_{P 1}^{2} P_{S 1}$	$ϕ_{I 2} = 2 ϕ_{P 1} - ϕ_{S 1}$	$Δ ϕ_{I 2} = ϕ_{S 2} - ϕ_{S 1} + 2 (ϕ_{P 1} - ϕ_{P 2})$
	2-2	$2 P 2 \to I 2 + S 2$	${CE}_{22} P_{S 2} \propto P_{P 2}^{2} P_{S 2}$	$ϕ_{I 2} = 2 ϕ_{P 2} - ϕ_{S 2}$
I3	3-1	$P 1 + P 2 \to I 3 + I 4$	$\propto P_{P 1}^{2} P_{P 2}$	$ϕ_{I 3} = 2 ϕ_{P 1} - ϕ_{P 2}$	$Δ ϕ_{I 3} = ϕ_{S 2} - ϕ_{S 1} + 2 (ϕ_{P 1} - ϕ_{P 2})$
	3-2	$P 2 + S 1 \to I 3 + S 2$	$\propto 4 P_{P 2} P_{S 1} P_{S 2}$	$ϕ_{I 3} = ϕ_{P 2} + ϕ_{S 1} - ϕ_{S 2}$
I4	4-1	$P 1 + P 2 \to I 3 + I 4$	$\propto P_{P 2}^{2} P_{P 1}$	$ϕ_{I 4} = 2 ϕ_{P 2} - ϕ_{P 1}$	$Δ ϕ_{I 4} = ϕ_{S 1} - ϕ_{S 2} + 2 (ϕ_{P 2} - ϕ_{P 1})$
I4	4-2	$P 1 + S 2 \to I 4 + S 1$	$\propto 4 P_{P 1} P_{S 1} P_{S 2}$	$ϕ_{I 4} = ϕ_{P 1} + ϕ_{S 2} - ϕ_{S 1}$	$Δ ϕ_{I 4} = ϕ_{S 1} - ϕ_{S 2} + 2 (ϕ_{P 2} - ϕ_{P 1})$

Input Power (dBm)				Output Power (dBm)
$P_{P 1}$	$P_{P 2}$	$P_{S 1}$	$P_{S 2}$	$P_{I 1}$	$P_{I 2}$	Conversion Efficiency (dB)
5.50	5.60	1.90	—	$- 21.83$	$- 27.80$	${CE}_{11, dB} = - 23.73$	${CE}_{21, dB} = - 29.70$
5.50	5.60	—	1.65	$- 22.10$	$- 27.89$	${CE}_{12, dB} = - 23.75$	${CE}_{22, dB} = - 29.51$

				Output Power (dBm)
				$P_{I 1}$				$P_{I 2}$
Input Power (dBm)				Experiment		Theory		Experiment		Theory
$P_{P 1}$	$P_{P 2}$	$P_{S 1}$	$P_{S 2}$	Max.	Min.	Max.	Min.	Max.	Min.	Max.	Min.
5.50	5.60	1.90	1.65	$- 15.90$	$- 45.67$	$- 15.94$	$- 52.11$	$- 21.72$	$- 46.35$	$- 21.82$	$- 67.54$
5.50	5.60	1.90	$- 4.00$	$- 18.07$	$- 27.45$	$- 18.37$	$- 27.68$	$- 24.12$	$- 33.88$	$- 24.20$	$- 34.05$

Idler	FWM Process		Idler Power	Idler Phase	Relative Phase
I1	1-1	$P 2 + S 1 \to I 1 + P 1$	${CE}_{11} P_{S 1} \propto 4 P_{P 1} P_{P 2} P_{S 1}$	$ϕ_{I 1} = ϕ_{P 2} + ϕ_{S 1} - ϕ_{P 1}$	$Δ ϕ_{I 1} = ϕ_{S 1} - ϕ_{S 2} + 2 (ϕ_{P 2} - ϕ_{P 1})$
	1-2	$P 1 + S 2 \to I 1 + P 2$	${CE}_{12} P_{S 2} \propto 4 P_{P 1} P_{P 2} P_{S 2}$	$ϕ_{I 1} = ϕ_{P 1} + ϕ_{S 2} - ϕ_{P 2}$
I2	2-1	$2 P 1 \to I 2 + S 1$	${CE}_{21} P_{S 1} \propto P_{P 1}^{2} P_{S 1}$	$ϕ_{I 2} = 2 ϕ_{P 1} - ϕ_{S 1}$	$Δ ϕ_{I 2} = ϕ_{S 2} - ϕ_{S 1} + 2 (ϕ_{P 1} - ϕ_{P 2})$
	2-2	$2 P 2 \to I 2 + S 2$	${CE}_{22} P_{S 2} \propto P_{P 2}^{2} P_{S 2}$	$ϕ_{I 2} = 2 ϕ_{P 2} - ϕ_{S 2}$
I3	3-1	$P 1 + P 2 \to I 3 + I 4$	$\propto P_{P 1}^{2} P_{P 2}$	$ϕ_{I 3} = 2 ϕ_{P 1} - ϕ_{P 2}$	$Δ ϕ_{I 3} = ϕ_{S 2} - ϕ_{S 1} + 2 (ϕ_{P 1} - ϕ_{P 2})$
	3-2	$P 2 + S 1 \to I 3 + S 2$	$\propto 4 P_{P 2} P_{S 1} P_{S 2}$	$ϕ_{I 3} = ϕ_{P 2} + ϕ_{S 1} - ϕ_{S 2}$
I4	4-1	$P 1 + P 2 \to I 3 + I 4$	$\propto P_{P 2}^{2} P_{P 1}$	$ϕ_{I 4} = 2 ϕ_{P 2} - ϕ_{P 1}$	$Δ ϕ_{I 4} = ϕ_{S 1} - ϕ_{S 2} + 2 (ϕ_{P 2} - ϕ_{P 1})$
I4	4-2	$P 1 + S 2 \to I 4 + S 1$	$\propto 4 P_{P 1} P_{S 1} P_{S 2}$	$ϕ_{I 4} = ϕ_{P 1} + ϕ_{S 2} - ϕ_{S 1}$	$Δ ϕ_{I 4} = ϕ_{S 1} - ϕ_{S 2} + 2 (ϕ_{P 2} - ϕ_{P 1})$

Input Power (dBm)				Output Power (dBm)
$P_{P 1}$	$P_{P 2}$	$P_{S 1}$	$P_{S 2}$	$P_{I 1}$	$P_{I 2}$	Conversion Efficiency (dB)
5.50	5.60	1.90	—	$- 21.83$	$- 27.80$	${CE}_{11, dB} = - 23.73$	${CE}_{21, dB} = - 29.70$
5.50	5.60	—	1.65	$- 22.10$	$- 27.89$	${CE}_{12, dB} = - 23.75$	${CE}_{22, dB} = - 29.51$

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Optics Letters