Superior optical Kerr effects induced by two-dimensional excitons

Feng Zhou; Cacere Jelah Nieva; Dianyuan Fan; Shunbin Lu; Wei Ji

doi:10.1364/PRJ.447029

Journals >Photonics Research >Volume 10 >Issue 3 >Page 834 > Article

Photonics Research
Vol. 10, Issue 3, 834 (2022)

Superior optical Kerr effects induced by two-dimensional excitons

Feng Zhou^1、2, Cacere Jelah Nieva², Dianyuan Fan¹, Shunbin Lu^1、3、*, and Wei Ji^{1、2、4、*}

Author Affiliations

¹SZU-NUS Collaborative Innovation Center for Optoelectronic Science & Technology, International Collaborative Laboratory of 2D Materials for Optoelectronic Science & Technology of Ministry of Education, Institute of Microscale Optoelectronics (IMO), Shenzhen University, Shenzhen 518060, China

²Department of Physics, National University of Singapore, Singapore 117542, Singapore

³e-mail: shunbin_lu@szu.edu.cn

⁴e-mail: phyjiwei@nus.edu.sg

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DOI: 10.1364/PRJ.447029 Cite this Article Set citation alerts

Feng Zhou, Cacere Jelah Nieva, Dianyuan Fan, Shunbin Lu, Wei Ji. Superior optical Kerr effects induced by two-dimensional excitons[J]. Photonics Research, 2022, 10(3): 834 Copy Citation Text

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Fig. 1. Schematic of the optical Kerr effect (self-focusing or -defocusing) induced by 2PA resonant with the exciton energy (E2p). Eg is the bandgap.

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Comparison of the normalized n2 between the prediction (pink area) by Eq. (5) and the measured values (symbols) of monolayer (or few-layer) TMDs, RPP(In=1), and h-BN [25,30–34" target="_self" style="display: inline;">–34]. The envelopes of the pink area are calculated with hγ/E2p=0.05 and 0.15.

Fig. 2. Comparison of the normalized n2 between the prediction (pink area) by Eq. (5) and the measured values (symbols) of monolayer (or few-layer) TMDs, RPP(In=1), and h-BN [25,30 –34" target="_self" style="display: inline;">–34]. The envelopes of the pink area are calculated with hγ/E2p=0.05 and 0.15.

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Fig. 3. Normalized n2 dispersion of monolayer MoS2, MoSe2, WS2, and WSe2 calculated by the two excitons (purple), A exciton (red), and B exciton (blue) with hγ/E2p=0.075 eV. The symbols are the experimental data from Refs. [30 32" target="_self" style="display: inline;">–32] and scaled with Z2′=1×10−14.

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Fig. 4. Calculated n2 dispersions of (a) monolayer RPP (In=1,2,3,4) and (b) TMDs by Eq. (4) and Eq. (6). Calculated n2 dispersions of (c) monolayer RPP (In=1,2,3,4) and (d) TMDs by the two-parabolic-band model [12]. Parameters used in the calculation are displayed in Table 3 in Appendix A.

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Fig. 5. (a) Calculated n2 values as a function of photon energy (x axis) and temperature (y axis) for monolayer RPP (In=1). (b) A log-log plot of the scaled n2 in the off-resonance region versus E2p. The experimental n2 values are scaled by Z2′(n02+2)4G(x) with n0 and Z2′ listed in Table 3 in Appendix A. The solid line is the theoretical result of Eq. (4) with no adjustable parameters and a slope of −2.

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$Nonlinear refractive index, n2, as a function of photon energy (x axis) and temperature (y axis) for monolayer RPP: (a) In=2, (b) In=3, and (c) In=4. These n2 values are calculated with the averaged Z2′=1×10−14.$

Fig. 6. Nonlinear refractive index, n2, as a function of photon energy (x axis) and temperature (y axis) for monolayer RPP: (a) In=2, (b) In=3, and (c) In=4. These n2 values are calculated with the averaged Z2′=1×10−14.

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$Nonlinear refractive index, n2, as a function of photon energy (x axis) and temperature (y axis) for TMD monolayers: (a) MoS2, (b) MoSe2, (c) WS2, and (d) WSe2. These n2 values are calculated with the averaged Z2′=1×10−14.$

Fig. 7. Nonlinear refractive index, n2, as a function of photon energy (x axis) and temperature (y axis) for TMD monolayers: (a) MoS2, (b) MoSe2, (c) WS2, and (d) WSe2. These n2 values are calculated with the averaged Z2′=1×10−14.

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Fig. 8. (a) WFOM of monolayer TMDs, (b) WFOM of monolayer RPPs, (c) TFOM of monolayer TMDs, and (d) TFOM of monolayer RPPs. The gray area corresponds to the wavelength range for optical communications.

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Material	$n_{2}$ [ $\times 10^{- 12} {cm}^{2} / W$ ]	$β$ [cm/GW]	$W_{FOM}$	$T_{FOM}$	Ref.
2D RPP ( $I_{n = 4}$ )	105.5	96.3	1.02	0.14	This work
2D RPP ( $I_{n = 3}$ )	22.9	9.9	0.27	0.07	This work
2D RPP ( $I_{n = 2}$ )	7.2	1.6	0.12	0.03	This work
2D RPP ( $I_{n = 1}$ )	1.3	0.3	0.03	0.04	This work
2D ${MoS}_{2}$	1.5	5.6	0.008	0.56	This work
2D ${MoSe}_{2}$	19.1	212.5	0.07	1.72	This work
2D ${WS}_{2}$	2.7	7.7	0.02	0.45	This work
2D ${WSe}_{2}$	15.8	79.1	0.06	0.78	This work
Multilayer graphene	−800	900	0.20	1.40	[37]
$Si ⟨ 110 ⟩$	0.045	0.79	–	0.37	[45]
GaAs	0.16	10.2	–	0.10	[45]
GaAs/AlAs superlattice	0.15	1.5	–	0.87	[46]
Conjugated 3,3’-bipyridine derivative	0.0046	$< 0.01$	$> 600$	$< 0.15$	[43]

Table 1. Nonlinear Coefficients and FOMs of Materials at 1550 nm

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	$n_{2}$ [ $\times 10^{- 12} {cm}^{2} / W$ ]	$\frac{n_{2} E_{2 p}^{2}}{Z_{2}^{'} {(n_{0}^{2} + 2)}^{4}}$	$λ$ [nm]	$n_{0}$	Ref.
RPP ( $I_{n = 1}$ )	0.41	0.16	2700	2.11	[25]
RPP ( $I_{n = 2}$ )	0.45	0.11	2700	2.21	[25]
RPP ( $I_{n = 3}$ )	0.39	0.048	2700	2.41	[25]
RPP ( $I_{n = 4}$ )	0.40	0.053	2700	2.32	[25]
${MoS}_{2}$	−1.96	−1.45	800	1.84	[30]
	350	260.02	800	1.84	[38]
	1.88	1.40	1064	1.84	[38]
	−0.21	−0.15	1064	1.84	[31]
${MoSe}_{2}$	−0.12	−0.034	1064	2.10	[31]
${MoSe}_{2}$	0.20	0.058	1000	2.10	[39]
${WS}_{2}$	−1.10	−1.02	800	1.82.	[30]
	0.81	0.76	800	1.82	[32]
	58.30	54.55	1064	1.82	[40]
	128	119.77	1040	1.82	[41]
${WSe}_{2}$	−18.70	−12.27	1040	1.84	[41]
h-BN	0.12	0.30	1064	2.0	[33]
BP	860	26.73	800	2.5	[34]

Table 4. Extracted n2 Values from Experimental Data

Feng Zhou, Cacere Jelah Nieva, Dianyuan Fan, Shunbin Lu, Wei Ji. Superior optical Kerr effects induced by two-dimensional excitons[J]. Photonics Research, 2022, 10(3): 834

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