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Optical bistability of graphene embedded in parity-time-symmetric photonic lattices

Dong Zhao, Shaolin Ke, Yonghong Hu, Bing Wang, and Peixiang Lu

Open Access Open Access

Abstract

We investigate the optical bistability of graphene in parity-time-symmetric (PT-symmetric) photonic lattices incorporated with a defect at terahertz frequencies. The field localization of the defect mode can strengthen the nonlinearity of graphene to achieve low-threshold bistability. The nonlinearity is further enhanced, and the bistability threshold decreases, by increasing the gain-loss factor in the PT-symmetric structure. The interval of upper and lower bistability thresholds is broadened as the exceptional points split. Moreover, we show the phase transition between bistability and nonbistability by modulating the incident wavelength and chemical potential of graphene. The study may find great applications in all-optical switches and optical storage.

© 2019 Optical Society of America

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Figures (8)
Fig. 1.
Fig. 1. Schematic of PT-symmetric photonic lattices incorporated with graphene. For dielectrics A, B, A′, and B′, the thicknesses are a quarter of optical wavelength. The graphene is embedded in the center of defect layer C. The refractive indices of dielectrics A, B, A′, B′, and C are na=1.38+iq, nb=2.35−iq, na′=1.38−iq, nb′=2.35+iq, and nc=1.5, respectively.

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Fig. 2.
Fig. 2. (a), (b) Transmittance and reflectance spectrum for three different Bragg periodic numbers N=3, 4, and 5, respectively. (c) Electric field intensity (|Ez|2) distribution of the DM for N=4. The incident wavelength is λ=30.68  μm. The chemical potential of graphene is μ=0.15  eV in (a)–(c).

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Fig. 3.
Fig. 3. (a), (b) Dependence of transmittance and transmitted intensity on incident light intensity for three different Bragg periodic numbers, respectively. The wavelength of incidence light λ=30.9  μm.

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Fig. 4.
Fig. 4. (a) Reflectance of light incident from the left. (b) Reflectance of light incident from the right. (c) Transmittance of light. (d) Q factor of PT-symmetric photonic lattices and EPs splitting. The Bragg periodic number N=4.

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Fig. 5.
Fig. 5. (a), (c) Dependence of transmittance and transmitted intensity on the gain-loss factor and the incident intensity of light, respectively. (b) The maximum of transmittance and corresponding incident intensity varying with the gain-loss factor. (d) Bistability threshold varying with the gain-loss factor. (a)–(d) are with the incident wavelength λ=31  μm. The Bragg periodic number N=4, and the chemical potential μ=0.15  eV.

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Fig. 6.
Fig. 6. (a) Upper and lower thresholds of bistability varying with the wavelength of incident light. The Bragg periodic number N=4, and the gain-loss factor q=0.1. (b) Phase transition of bistability to nonbistability in the parameter space spanned by the wavelength detuning and gain-loss factor.

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Fig. 7.
Fig. 7. (a) Phase transition of bistability to nonbistability in the parameter space of the chemical potential and gain-loss factor. (b), (c), (d) Bistability threshold varying with the chemical potential for three different gain-loss factors q=0, 0.05, and 0.1, respectively. The wavelength of incident light λ=31  μm.

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Fig. 8.
Fig. 8. (a), (b), (d), (e) Transmittance and reflectance for light impinging upon the PT-symmetric photonic lattices, respectively. (c) Electric field intensity (|Ez|2) distribution of CPA laser state. Gain is only considered in dielectrics for (a)–(c), while loss is only included in dielectrics for (d) and (e).

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Equations (6)

Equations on this page are rendered with MathJax. Learn more.

σ(1)(ω,μ,τ,T)=−ie2(ω+iτ−1)πℏ2[∫−∞+∞|ε|(ω+iτ−1)2∂fd(ε)∂εdε−∫0+∞∂fd(−ε)−∂fd(ε)(ω+iτ−1)2−4(ε/ℏ)2dε],
σintra=ie2kBTπℏ2(ω+iτ−1)[μkBT+2ln(exp(−μckBT)+1)].
σinter=ie24πℏln[2|μ|−ℏ(ω+iτ−1)2|μ|+ℏ(ω+iτ−1)].
(ElHl)=(cos ϕl−iηl sin ϕl−iηl sin ϕlcos ϕl)(El+1Hl+1),
t=2η1m11η1+m12η1ηN+1+m21+m22η1,
r=m11η1+m12η1ηN+1−m21−m22ηN+1m11η1+m12η1ηN+1+m21+m22ηN+1,
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