Numerical study of high-index-contrast Er:LiNbO<sub>3</sub> photonic wire lasers optically pumped at 980&#xA0;nm

Md. Sohel Mahmud Sher; Paolo Pintus; Fabrizio Di Pasquale

doi:10.1364/AO.52.004438

Applied Optics
Vol. 52,
Issue 19,
pp. 4438-4445
(2013)
•https://doi.org/10.1364/AO.52.004438

Numerical study of high-index-contrast Er:LiNbO₃ photonic wire lasers optically pumped at 980 nm

Md. Sohel Mahmud Sher, Paolo Pintus, and Fabrizio Di Pasquale

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Md. Sohel Mahmud Sher, Paolo Pintus, and Fabrizio Di Pasquale, "Numerical study of high-index-contrast Er:LiNbO₃ photonic wire lasers optically pumped at 980 nm," Appl. Opt. 52, 4438-4445 (2013)

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Abstract

For the first time [to our best knowledge] a high-index-contrast $z$ -cut ${Er : LiNbO}_{3}$ photonic wire waveguide laser, optically pumped at 980 nm wavelength, is designed for continuous-wave operation. Waveguide modes and laser characteristics are numerically computed using a developed full vectorial finite-element method based tool. In order to maximize the output power of the laser, the active cavity length and output mirror’s reflectivity have been optimized, considering different pump power and waveguide background losses. Efficient laser emission is theoretically predicted at 1531 nm wavelength for the fundamental TE mode and a value of threshold pump power as low as 0.2 mW has been computed.

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${LiNbO}_{3}$ Waveguide	Fabrication Technique	Erbium Concentrationa $[m^{- 3}]$	Laser Wavelength [nm]	Pump Wavelength [nm]	Waveguide Loss [dB/cm]	Cavity Length [mm]	Index Contrastb $Δ n$	Pump Thresholdc [mW]	Referenced
$z$ -cut	Ti-indiff.	$9 \times 10^{24}$	1532 (TE)	1477	0.3	10.5	$\sim 1.2 \times 10^{- 2}$	8 (*)	Brinkmann et al., 1991, [4]
$z$ -cut	Ti-indiff.	$1.2 \times 10^{26}$	1563 (TE)	1479	0.7	52.0	$\sim 1.2 \times 10^{- 2}$	25 13	Becker et al., 1992, [5]
$z$ -cut	Ti-indiff.	$1.2 \times 10^{26}$	1576 (TM)	1479	0.7	52.0	$\sim 1.2 \times 10^{- 2}$	25 13	Becker et al., 1992, [5]
$x$ -cut	Ti-indiff.	$1.9 \times 10^{26}$	1531 (TE)	1485	-	30.0	$\sim 1.2 \times 10^{- 2}$	10	Huang et al., 1994, [6] (**)
$z$ -cut	Ti-indiff.	$1.35 \times 10^{26}$	1531 (TE)	1484	0.18	70.0	$\sim 1.2 \times 10^{- 2}$	43	Baumann et al., 1996, [3]
$z$ -cut	Ti-indiff.	$1.35 \times 10^{26}$	1561 (TE)	1484	0.18	70.0	$\sim 1.2 \times 10^{- 2}$	20	Baumann et al., 1996, [3]
$x$ -cut	Ti-indiff.	$1.05 \times 10^{26}$	1531.4 (TE)	980	0.4 at $λ_{s}$	29.0	$\sim 1.2 \times 10^{- 2}$	52.5	Amin et al., 1996, [8]
$x$ -cut	Ti-indiff.	$1.05 \times 10^{26}$	1531.4 (TE)	980	0.55 at $λ_{p}$	29.0	$\sim 1.2 \times 10^{- 2}$	52.5	Amin et al., 1996, [8]
$z$ -cut	$MgO : {LiNbO}_{3}$ ZnO-indiff.	-	1531 (TE)	980	-	21.0	$\sim 1.9 \times 10^{- 3}$	30	Huang and Caughan, 1997, [11]
$z$ -cut	$C^{3 +}$ ion implanted	$1.0 \times 10^{26}$	1531 (TE)	980	0.2 at $λ_{s}$	20.0	$\sim 0.2$	25	Sher et al., 2011, [13] (**)
$z$ -cut	$C^{3 +}$ ion implanted	$1.0 \times 10^{26}$	1531 (TE)	980	0.3 at $λ_{p}$	20.0	$\sim 0.2$	25	Sher et al., 2011, [13] (**)
					0.3 at $λ_{s}$ , $λ_{p}$	104.0		0.15
					0.3 at $λ_{s}$ , $λ_{p}$	218.0		0.4
					1.0 at $λ_{s}$ , $λ_{p}$	58.0		0.2
$z$ -cut	Smart-cut process	$1.0 \times 10^{26}$	1531 (TE)	980	1.0 at $λ_{s}$ , $λ_{p}$	98.0	$\sim 0.7$	0.3	This work (**)
					2.0 at $λ_{s}$ , $λ_{p}$	32.0		0.3
					2.0 at $λ_{s}$ , $λ_{p}$	64.5		0.5

	Refractive Index
Materials	$λ = 980 nm$	$λ = 1531 nm$
Air	1	1
${SiO}_{2}$	1.45	1.44
${LiNbO}_{3} / Er : {LiNbO}_{3}$	2.24 (ordinary)	2.21 (ordinary)
${LiNbO}_{3} / Er : {LiNbO}_{3}$	2.16 (extraordinary)	2.14 (extraordinary)

Parameters	Values	Ref.
$σ_{12}^{s}$ (at 1531 nm)	$1.25 \times 10^{- 24} m^{2} (TM)$	Huang et al. 1994 [6]
$σ_{12}^{s}$ (at 1531 nm)	$1.93 \times 10^{- 24} m^{2} (TE)$	Huang et al. 1994 [6]
$σ_{21}^{s}$ (at 1531 nm)	$1.03 \times 10^{- 24} m^{2} (TM)$	Huang et al. 1994 [6]
$σ_{21}^{s}$ (at 1531 nm)	$1.56 \times 10^{- 24} m^{2} (TE)$	Huang et al. 1994 [6]
$σ_{13}^{p}$ (at 980 nm)	$0.20 \times 10^{- 24} m^{2} (TM)$	Huang and Caughan 1996 [26]
$σ_{13}^{p}$ (at 980 nm)	$0.88 \times 10^{- 24} m^{2} (TE)$	Huang and Caughan 1996 [26]
$σ_{31}^{p}$ (at 980 nm)	$0 m^{2}$	Veasey et al., 1997 [21]
$σ_{ESA}$ (at 980 nm)	$1.0 \times 10^{- 26} m^{2}$	Veasey et al., 1997 [21]
$τ_{32}$ ( ${}^{4}{I_{11 / 2}} \to {}^{4}{I_{13 / 2}}$ )	200 μs	Veasey et al., 1997 [21]
$τ_{21}$ ( ${}^{4}{I_{13 / 2}} \to {}^{4}{I_{15 / 2}}$ )	4.3 ms	Huang et al. 1994 [6]
$N_{Er}$	$1.0 \times 10^{26} m^{- 3}$	Veasey et al., 1997 [21]
$C_{UP}$ ( $N_{Er} = 1.0 \times 10^{- 26} m^{- 3}$ )	$1.0 \times 10^{- 24} m^{3} s^{- 1}$	Veasey et al., 1997 [21]
Input mirror $R_{1}$	99.9% (at 1531 nm)	Our hypothesis
Output Bragg grating mirror $R_{2}$	0%–100% (at 1531 nm)	Our hypothesis

${LiNbO}_{3}$ Waveguide	Fabrication Technique	Erbium Concentrationa $[m^{- 3}]$	Laser Wavelength [nm]	Pump Wavelength [nm]	Waveguide Loss [dB/cm]	Cavity Length [mm]	Index Contrastb $Δ n$	Pump Thresholdc [mW]	Referenced
$z$ -cut	Ti-indiff.	$9 \times 10^{24}$	1532 (TE)	1477	0.3	10.5	$\sim 1.2 \times 10^{- 2}$	8 (*)	Brinkmann et al., 1991, [4]
$z$ -cut	Ti-indiff.	$1.2 \times 10^{26}$	1563 (TE)	1479	0.7	52.0	$\sim 1.2 \times 10^{- 2}$	25 13	Becker et al., 1992, [5]
$z$ -cut	Ti-indiff.	$1.2 \times 10^{26}$	1576 (TM)	1479	0.7	52.0	$\sim 1.2 \times 10^{- 2}$	25 13	Becker et al., 1992, [5]
$x$ -cut	Ti-indiff.	$1.9 \times 10^{26}$	1531 (TE)	1485	-	30.0	$\sim 1.2 \times 10^{- 2}$	10	Huang et al., 1994, [6] (**)
$z$ -cut	Ti-indiff.	$1.35 \times 10^{26}$	1531 (TE)	1484	0.18	70.0	$\sim 1.2 \times 10^{- 2}$	43	Baumann et al., 1996, [3]
$z$ -cut	Ti-indiff.	$1.35 \times 10^{26}$	1561 (TE)	1484	0.18	70.0	$\sim 1.2 \times 10^{- 2}$	20	Baumann et al., 1996, [3]
$x$ -cut	Ti-indiff.	$1.05 \times 10^{26}$	1531.4 (TE)	980	0.4 at $λ_{s}$	29.0	$\sim 1.2 \times 10^{- 2}$	52.5	Amin et al., 1996, [8]
$x$ -cut	Ti-indiff.	$1.05 \times 10^{26}$	1531.4 (TE)	980	0.55 at $λ_{p}$	29.0	$\sim 1.2 \times 10^{- 2}$	52.5	Amin et al., 1996, [8]
$z$ -cut	$MgO : {LiNbO}_{3}$ ZnO-indiff.	-	1531 (TE)	980	-	21.0	$\sim 1.9 \times 10^{- 3}$	30	Huang and Caughan, 1997, [11]
$z$ -cut	$C^{3 +}$ ion implanted	$1.0 \times 10^{26}$	1531 (TE)	980	0.2 at $λ_{s}$	20.0	$\sim 0.2$	25	Sher et al., 2011, [13] (**)
$z$ -cut	$C^{3 +}$ ion implanted	$1.0 \times 10^{26}$	1531 (TE)	980	0.3 at $λ_{p}$	20.0	$\sim 0.2$	25	Sher et al., 2011, [13] (**)
					0.3 at $λ_{s}$ , $λ_{p}$	104.0		0.15
					0.3 at $λ_{s}$ , $λ_{p}$	218.0		0.4
					1.0 at $λ_{s}$ , $λ_{p}$	58.0		0.2
$z$ -cut	Smart-cut process	$1.0 \times 10^{26}$	1531 (TE)	980	1.0 at $λ_{s}$ , $λ_{p}$	98.0	$\sim 0.7$	0.3	This work (**)
					2.0 at $λ_{s}$ , $λ_{p}$	32.0		0.3
					2.0 at $λ_{s}$ , $λ_{p}$	64.5		0.5

	Refractive Index
Materials	$λ = 980 nm$	$λ = 1531 nm$
Air	1	1
${SiO}_{2}$	1.45	1.44
${LiNbO}_{3} / Er : {LiNbO}_{3}$	2.24 (ordinary)	2.21 (ordinary)
${LiNbO}_{3} / Er : {LiNbO}_{3}$	2.16 (extraordinary)	2.14 (extraordinary)

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Applied Optics