Abstract

We have established the theoretical relation of nonlinear optical response with respect to the dielectric/nonlinear graphene/dielectric heterostructures and further demonstrated the tunable optical bistability at terahertz frequencies. It is shown that the hysteretic behavior is strongly dependent on the Fermi energy of graphene, and the threshold electric fields could be correspondingly adjusted with the continuous tuning of Fermi Energy level. It is clear that the bistable thresholds can be lowered dramatically by decreasing the Fermi energy of graphene, at the same time the optical hysteresis width is narrowed. Moreover, we have confirmed that the optical bistability can be tuned by adjusting the incident illumination angle, or by varying the thickness and permittivity of the dielectric slabs. Our contribution might provide a new avenue of fabricating graphene based optical switching device that could even operate at terahertz regime.

© 2015 Optical Society of America

1. Introduction

Optical bistability (OB) is a phenomenon characterized by certain resonant optical structures whereby it is feasible to exhibit two well-discriminated stable transmission states, depending upon the history of the input [1,2]. Such a bistable device may be useful for all-optical switching [3], optical transistor [4], and optical memory [5], and hence can be used for high-speed processing of optical signals and provide a promising alternative to their electronic counterparts [6]. Fabry-Perot cavity filled by nonlinear medium is considered as a classic nonlinear feedback configuration for achieving OB. In recent decades, researchers have focused on optimizing optical bistable devices by down-scaling the structure size, increasing the switching speed, lowering the operation power, and broadening the range of operation temperature. Both improved nonlinear materials and efficient device configurations are being sought after [1]. Recently, there has been a great deal of interest in exploring OB in nanostructures, such as, photonic crystal cavities [7], sub-wavelength metallic gratings [8], metallic gap waveguide nano-cavities [9], negative-index material [10], metamaterial [11], and nanoantenna arrays loaded with nonlinear materials [12, 13]. However, the conventional nonlinear Kerr materials display very weak nonlinear response. Hence in order to achieve large optical nonlinearity, thick nonlinear media with large Kerr nonlinear index are generally required. The bulk optical bistable device is disadvantage to application in the integrated optical element. More importantly, OB with tunable optical response is also intrinsically important for the applications in all optical devices. Based on the open and close z-scan measurement, Zhang et al. had ambiguously confirmed the large nonlinear Kerr index in graphene, which is several orders of magnitude larger than that of conventional bulk materials [14, 15]. In association with the ultrafast optical response and gate-variable optical conductivity [16, 17], graphene might be expected to open a new possibility of tunable, compact, and low threshold OB as a unique nonlinear optical material.

Graphene has attracted intensive scientific interest owing to its incredible physical properties showing great potential applications in nano-electronic devices and optoelectronic devices, and it has outstanding optical properties [18, 19], such as, strong light-graphene interaction, broadband and high-speed operation, etc. Some graphene/dielectric heterostructures are also proposed to manipulate terahertz radiations [2527]. Especially, the electrical tunability of conductivity of graphene could potentially open a new possibility of tunable optical sensor [20], metamaterials [21,22], terahertz absorber [23], and Goos-Hänchen effect [24], etc. It provides a scheme for controlling OB via suitably varying the applied voltage on graphene. Recent investigations have demonstrated that graphene and graphene related nano-materials have superior third-order nonlinear optical properties due to the linear band structure which allows for the interband optical transitions at all photon energies [28, 29]. As a result, graphene photonics have been extended to multifunction nonlinear devices including mode-locked laser [30] and optical limiter [31]. Recently, by depositing graphene with silicon photonic crystal cavity, people are able to achieve an effective nonlinear optical device that can enable ultra-low-power resonant OB, self-induced regenerative oscillations and coherent four-wave mixing [32]. We have theoretically investigated OB of reflection at the interface between graphene and Kerr-type nonlinear substrates [33] and experimentally demonstrated the OB and all-optical switching in graphene nanobubbles [34]. Peres et al., find that a single layer of graphene shows an OB in the lower THz frequency range for nonlinear graphene suspending in air [35]. Here, we investigate theoretically OB of dielectric/nonlinear graphene/dielectric heterostructures in the THz frequencies range and demonstrate the engineering of graphene nanostructures as new optical nonlinear media for generating OB. We have confirmed an approach on how to manipulate OB through engineering the Fermi energy of graphene, adjusting the incident illumination angle, and varying the thickness and permittivity of the dielectric slabs. Graphene-based optical devices with intrinsic OB allow us to explore the promise of using such nonlinear optical elements as the building block of future digital all-optical circuit.

2. Theoretical models and methods

The sandwiched structure is shown in Fig. 1, which consisted of four different layers of dielectric. Dielectric 1 with permittivity ε1 and dielectric 4 with permittivity ε4 are superstrate and substrate, respectively. The dielectric slabs 2 (ε2) and 3 (ε3) with high dielectric constants are inserted between dielectrics 1 and 4. The thicknesses of dielectric slabs 2 and 3 are d2 and d3, respectively. The graphene sheet is sandwiched between dielectric slabs 2 and 3. Without considering the external magnetic field and under the random-phase approximation, the isotropic surface conductivity of graphene σ0 is written as the sum of the intraband σintra and the interband term σinter, where

σintra=ie2kBTπh¯2(ω+i/τ)[EFkBT+2ln(eEFkBT+1)],
σinter=ie24πh¯ln|2EF(ω+iτ1)h¯2EF+(ω+iτ1)h¯|,
where ω is the frequency of the incident light, EF is the Fermi energy, τ is the electron-phonon relaxation time, and T is a temperature in K. e, and kB are the universal constants related to the electron charge, reduced Plancks constant, and Boltzmann constant, respectively. The Fermi energy EF = h̄νF (πn2D)1/2 can be electrically controlled by an applied gate voltage due to the strong dependence of the carrier density n2D on the gate voltage, where νF = 106m/s is the Fermi velocity of electrons.

 figure: Fig. 1

Fig. 1 Schematic diagram of a sandwiched structure, where the graphene sheet is inserted between two dielectric slabs. A plane wave of amplitude Ei is incident on the sandwiched structure with incident angle θ, giving rise to a reflected and a transmitted wave with amplitude ER and ET, respectively. A, B, C and D are the amplitudes of the transmitted and reflected waves inside the two dielectric slabs.

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The nonlinear conductivity coefficient σ3 for graphene is given by [14, 36],

σ3=i332e2π(eνF)2EFω3(1+iαT),
where αT is the two photon coefficient in graphene and it will not be taken into account, hence αT = 0. Here, the negative imaginary part of σ3 shows the self-focusing type nonlinear response of graphene. Obviously, both σ0 and σ3 are highly dependent on the work frequency and Fermi energy, which could provide an effective route to achieve an electrically controlled optical bistable phenomenon.

We choose the x axis to be parallel to the interface, and z axis goes along with the direction of propagation. For TE polarization, the electric and magnetic fields from medium 1 are expresses as

{E1y=Eieik1z(z+d2)eikxx+EReik1z(z+d2)eikxx,H1x=k1zμ0ωEieik1z(z+d2)eikxx+k1zμ0ωEReik1z(z+d2)eikxx,H1z=kxμ0ωEieik1z(z+d2)eikxx+kxμ0ωEReik1z(z+d2)eikxx,
where Ei and ER are the amplitudes of incident electric and reflected electric fields, respectively. kx=k0ε1sinθ, and kjz=k02εjkx2, j=1,2,3,4. θ is the incident angle, and μ0 is the magnetic permeability of free space.

In medium 2, the electric and magnetic fields are expresses as

{E2y=Aeik2zzeikxx+Beik2zzeikxx,H2x=k2zμ0ωAeik2zzeikxx+k2zμ0ωBeik2zzeikxx,H2z=kxμ0ωAeik2zzeikxx+kxμ0ωBeik2zzeikxx,
where A and B are the forward and backward electric fields in the medium 2.

In medium 3, the electric and magnetic fields are expresses as

{E3y=Ceik3zzeikxx+Deik3zzeikxx,H3x=k3zμ0ωCeik3zzeikxx+k3zμ0ωDeik3zzeikxx,H3z=kxμ0ωCeik3zzeikxx+kxμ0ωDeik3zzeikxx,
where C and D are the forward and backward electric fields in the medium 3.

In medium 4, the electric and magnetic fields are expresses as

{E4y=ETeik4z(zd3)eikxx,H4x=k4zμ0ωETeik4z(zd3)eikxx,H4z=kxμ0ωETeik4z(zd3)eikxx.

By using the boundary conditions at z = −d2, 0, and z = d3, we can determine the coefficients of A, B, C, D, ET, and ER. Here, at z = −d2, E1y (z = −d2) = E2y (z = −d2), H1x (z = −d2) = H2x (z = −d2); and at z = d3, E3y (z = d3) = E4y (z = d3), H3x (z = d3) = H4x (z = d3); however at z = 0, E2y (z = 0) = E3y (z = 0)H2x (z = 0) − H3x (z = 0) = σE2y (z = 0) hence the magnetic field component H2x is discontinuous due to the appearing of the graphene sheet. According to the above boundary conditions and after some complicated processes, the relation of incident electric and transmitted electric fields can be written as,

Ei=ET18(1+k2zk1z)[(1k3zk2z)Δ+Θ]eik2zd2+ET18(1k2zk1z)[(1+k3zk2z)ΔΘ]eik2zd2,
where
{Δ=(k4zk3z+1)eik3zd3+(1k4zk3z)eik3zd3,Θ=2k3zk2z(1+k4zk3z)eik3zd3μ0ωk2z(σ0+14σ3|ET|2|Δ|2)Δ.
Generally, we can assume that the incident electric field Ei is purely real and so that the transmitted electric field ET is complex. However, for simplify the discussion, here we suppose that the transmitted electric field ET is purely real and hence incident electric field Ei is complex. We define that Y = |Ei|2 and X = |ET|2, then we obtain
Y=X|Π(X)|2,
where
Π=18(1+k2zk1z)[(1k3zk2z)Δ+Θ]eik2zd2+18(1k2zk1z)[(1+k3zk2z)ΔΘ]eik2zd2.
If we consider the similar case for nonlinear graphene suspending in free space, and Eq. (10) can be simplified to Eq.(38) in Reference [35].

For TM polarization, use a similar procedure we have

Y=X|Σ(X)|2,
where Y = |Hi|2, X = |HT|2, and we assume that transmitted magnetic field HT is purely real, and
{ΔTM=(k4zk3zε3ε4+1)eik3zd3(1k4zk3zε3ε4)eik3zd3,ΘTM=k2zε2ω(σ0+14σ3X|k2zε0ε2ω|2|k3zk2zε2ε3|2|ΔTM|2)(k3zk2zε2ε3ΔTM),ΠTM=(k4k3zε3ε4+1)eik3zd3+(1k4zk3zε3ε4)eik3zd3+ΘTM,Σ=18(k2zk1zε1ε2+1)(ΠTM+k3zk2zε2ε3ΔTM)eik2zd2+(1k2zk1zε1ε2)(ΠTMk3zk2zε2ε3ΔTM)eik2zd2.
Clearly, it follows from Eqs. (10) and (12) that incident field is the multiple valued function of the transmitted field, and hence OB is appearing at the given appropriate conditions.

3. Results and discussions

Next, we discuss the role of the nonlinear graphene sheets in OB according to Eqs. (10) and (12). In the absence of the nonlinear graphene or appearing of the linear graphene, the incident electric and transmitted electric field show a linear relationship, and hence the optical bistable phenomenon does not happened. The nonlinear dependence of conductivity of graphene (Eq. (3)) can provide us the origin of OB. But, the nonlinear conductivity coefficient σ3 is inversely proportion to ω3 so that the conductivity coefficient σ3 will become very small in the high frequencies range (both infrared and visible light) and hence need more input power to excite OB. Therefore, in the present paper, we focus on the discussion of OB in the THz frequencies range for TE polarization, and OB for TM polarization can be discussed similarly.

For frequencies 2EF > h̄ω, the interband transitions in graphene are forbidden by the Pauli exclusion principle, hence σ0σintra. It is seen that the imaginary part of the linear conductivity σ0 is positive, so that the surface plasmon polarization (SPP) cannot be excited for TE-polarization. Hence, the origin of OB in the present structure for TE polarization is not from the SPP but from the interface effect due to the introduction of nonlinear graphene. Based on this principle, Peres et al., had investigated OB in the low THz frequency (0.5THz) for nonlinear graphene suspending on air for TE polarization at the normal incidence [35]. However, electrical reconfiguration is not fully achievable in their structure. This is because graphene needs to be biased from a perpendicular electrostatic field to control its conductivity. To solve the problem, we have proposed the dielectric-nonlinear graphene-dielectric sandwiched structure, as shown in Fig. 1. In this structure, we can get more means to control OB, such as, the incident angle, the thickness and the permittivity of dielectric slabs, etc. Furthermore, in Peres et al. work, it is hard to get OB at the higher frequencies (about 3THz) at the normal incidence, however OB at the higher THz frequencies can be excited in our structure.

Before analysing optical bistable behavior, we will discuss the influence of the introduction of linear graphene sheet (σ3 = 0) on the transmission of the heterostructure. To simplify the discussion, we have neglected the losses in the graphene, Re(σ0) = 0. Due to the appearing of graphene sheet, the interface effect is greatly modified, as shown in Fig. 2. The transmission coefficient is lowered markedly and the reflection coefficient is enhanced significantly because graphene sheet has an impact on the interface effect, as indicated in Eqs. (10) and (12). At the larger incident angle, the reflectance near reaches to 100%, and the total internal reflectance (TIR) can occur for θ ≥ 75°. Hence, the mode of the system can switch from transmission mode to TIR mode due to the central role of graphene in interface effect.

 figure: Fig. 2

Fig. 2 The dependencies of the transmittance and reflectance on the incident angle for the sandwich structure with the insertion of graphene sheet (a) and without graphene sheet (b). Where EF = 0.8eV, λ = 100 μm, ε1 = ε4 = 1, ε2 = ε3 = 2.25, d2=d3 = 4 μm, τ−1 = 0, and T = 300 K.

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Further, the mode of the system can switch from TIR mode back to transmission mode if the nonlinear effect of graphene sheet is included, as shown in Fig. 3. The parameters are the following: λ = 100 μm, ε1 = ε4 = 1, ε2 = ε3 = 2.25, d2=d3 = 4 μm, θ = 75°, τ−1 = 0, and T = 300 K. For EF = 0.8eV, the optical bistable hysteresis is observed from monolayer nonlinear graphene in the sandwiched structure, and a threshold electric field |Ei|up of about 9.85 × 107 V/m is required for producing the optical hysteresis loop for the monolayer graphene. We can see that the transmitted electric field gradually increases at low input electric field and then suddenly increases when the incident electric field is above 9.85 × 107 V/m. This is because the transmittance resonance could not be satisfied at low intensities but it is well achieved as the input electric field is increased up to threshold electric field |Ei|up.

 figure: Fig. 3

Fig. 3 The dependencies of the transmitted electric field (a) and transmittance (b) on the input light intensity at different Fermi energy EF of the graphene. Where θ = 75°, other parameters have the same values as those in Fig. 2.

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When the incident electric field reaches the switch-up threshold intensity, the mode of the system will switch from TIR mode to the transmission mode (Fig. 3(b)), and the reflected intensity becomes very small suddenly. In contrast, upon lowering the input electric field, the system will maintain the transmission mode, and finally switches to the TIR mode. We can seen that if switch-down electric field |Ei|down ≈ 5.58 × 107 V/m is reached, then the transmitted electric field decreases suddenly when the incident electric field is below |Ei|down. The hysteresis width Δ|Ei| = |Ei|up − |Ei|down ≈ 4.3 × 107 V/m.

Next, we consider the dependencies of the transmitted electric field and transmittance on the input light intensity at different Fermi energy EF of the graphene, as shown in Fig. 4. From Fig. 4 we can see that the hysteretic behavior is strongly dependent on the Fermi energy of graphene. With the continuous tuning of the Fermi Energy level, the threshold electric fields |Ein|up and |Ei|down could be correspondingly adjusted. It is clear that if we increase the Fermi energy, both the switch-up threshold |Ei|up and switch-down threshold |Ei|down of the bistability move to the higher light intensity, and the optical hysteresis loop becomes large and the hysteresis width is broadened; however, if we decrease the Fermi energy, both the switch-up threshold |Ei|up and switch-down threshold |Ei|down of OB move to the lower light intensity, and the optical hysteresis loop becomes small and the hysteresis width is narrowed. These results can be confirmed from Fig. 4, where we have shown the dependencies of the threshold electric field |Ei|up and |Ei|down on the Fermi energy (0.15eV 1.2eV). OB is missing while Fermi energy EF is less that 0.15 eV, however as Fermi energy EF increases both the switch-up and switch-down threshold electric fields shift to higher electric fields quickly and the width of hysteresis loop is also enhanced markedly.

 figure: Fig. 4

Fig. 4 The dependencies of the switch-up and switch-down threshold electric fields on the Fermi energy EF of the graphene. The parameters have the same values as those in Fig. 3.

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Next, we discuss the influence of the physical properties of dielectric slabs 2 and 3 on the behavior of OB of the nonlinear graphene in the sandwiched structure. We focus on the influence of the thicknesses and the permittivities of dielectric slabs 2 and 3 on the optical bistable phenomena, as shown in Fig. 4. To simplify the discussion, we first assume that the dielectric slabs 2 and 3 have the same thicknesses and the optical bistable hysteresis has been observed as shown in Fig. 5(a). It is clear that the both switch-up threshold electric field and switch-down threshold electric field shift to higher incident electric field with the increases of the thickness.

 figure: Fig. 5

Fig. 5 The influence of the properties of dielectric slabs 2 and 3 on the optical bistable phenomenon for (a) different thicknesses of dielectric slabs 2 and 3, and (b) different permittivities of dielectrics 2 and 3. Where ε2 = ε3 = 2.25 in (a) and d2=d3 = 4 μm in (b), other parameters have the same values as those in Fig. 3.

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In the meantime, the width of hysteresis loop is also enhanced. Moreover, Fig. 5(b) gives the influence of the permittivities of dielectric slabs 2 and 3 on the optical bistable phenomena. Here we also assume that the dielectric slabs 2 and 3 have the same permittivity. We can find that larger dielectric constant materials will lead to the increases of the threshold electric fields and the enhancement of the width of hysteresis loop. These results remind us that we can control OB by changing the surroundings of the sandwiched structure.

Besides the material properties in the sandwiched structure, OB is also strongly dependent on the behavior of the incident angles, the results are shown in Fig. 6. The mode of system switches from transmission mode to TIR mode at the larger incident angle due to the occurring of graphene and the mode of system switches back from TIR mode to transmission mode due to the influence of the nonlinear conductivity of graphene under the larger incident electric field. This process leads to the generating of OB at the large incident angle, as shown in Fig. 6(a) where we find that OB is missing for small incident angle (such as 30°) due to the lacking of TIR mode. Even if the incident angle increases to 60°, the hysteresis is not evident and the width of hysteresis loop is narrowed compared to the result for θ = 75°. Moreover, from Eq. (3) we know that the nonlinear conductivity of graphene σ3 is a inverse proportion to the third power of frequency, and hence σ3 is proportional to the work wavelength. Therefore, longer wavelength will obviously enhance the nonlinearity of graphene, and hence lower the threshold electric fields, as shown in Fig. 6(b).

 figure: Fig. 6

Fig. 6 The influence of the properties of incident light on the optical bistable phenomena for (a) different incident angle, and (b) different work wavelength. Where λ2 = 100 μm in (a) and θ = 75° in (b), other parameters have the same values as those in Fig. 3.

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In the previous study, the damping rate τ−1 has been neglected, in fact, it should be considered in discussing OB. More importantly, we find that damping rate τ−1 will play a great role in OB, as shown in Fig. 7. Figs. 7(a) and (b) give the dependencies of the transmitted electric field and transmittance on the input electric field at different electron-phonon relaxation time τ of the graphene for wavelength λ = 100um. Where θ = 75°, EF = 0.8eV, and the other parameters have the same values as those in Fig. 3. Figs. 7(c) and (d) give the dependencies of the transmitted electric field and transmittance on the input electric field at different electron-phonon relaxation time τ of the graphene but for wavelength λ = 60um. It is clear that the damping rate τ−1 can modified markedly the hysteresis behavior. Here the transmittances are lowered with the increasing of the damping rate τ−1. Hence, in order to excite OB it is need more input light intensity due to the energy loss in the graphene sheet. Moreover, it is demonstrated that the large damping rate τ−1 can cause the missing of the hysteresis loop. For λ = 100um, hysteresis loop is vanished for τ = 100 fs, however for λ = 60um, hysteresis loop is vanished for τ = 50 fs. These differences are directly linked to the dependence of the nonlinear conductivity σ3 on the wavelength of the incident light, as indicated in Eq. (3). Through the analysis of the above, we can find that optical bistable phenomena are still happened if the damping rate τ−1 is not too seriously in spite of the transmittance is lowered.

 figure: Fig. 7

Fig. 7 The dependencies of the transmitted electric field and transmittance on the input electric field at different electron-phonon relaxation time τ of the graphene for wavelength λ = 100um in (a and b) and λ = 60um in (c and d). The parameters have the same values as those in Fig. 3.

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4. Conclusion

In summary, we have theoretically investigated the exotic optical bistable phenomena of the light transmitted through a sandwiched structure with the introduction of nonlinear graphene. It is found that the hysteretic response occurs at some conditions. It is very important that the hysteretic effects can be electrically controlled through electrical or chemical modification of the charge carrier density of the graphene. Moreover, we demonstrated that the hysteretic responses strongly depend on the surrounding of the sandwiched structure and the properties of incident light. Graphene optical bistable devices appear to be particularly promising because of giant optical nonlinearities, tunable optical property, ultra-fast response times and infinite small thickness permitting, and the construction of miniaturized devices in integrated optics. They could potentially open a new possibility of all-optical switching, optical transistor, optical logic, and optical memories.

Acknowledgments

This work is partially supported by the Natural Science Foundation of SZU (Grant Nos. 201452), the Science and Technology Project of Shenzhen (grant Nos. JCYJ20140828163633996), and the Scientific Research Foundation for the returned Overseas Chinese Scholar, State Education Ministry.

References and links

1. H. M. Gibbs., Optical Bistability: Controlling Light with Light. (Academic Press, 1985).

2. E. Abraham and S. D. Smith, “Optical bistability and related devices,” Rep. Prog. Phys. 45, 815–885 (1982). [CrossRef]  

3. D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel’kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003). [CrossRef]   [PubMed]  

4. G. Assanto, Z. Wang, D. J. Hagan, and E. W. VanStryland, “All-optical modulation via nonlinear cascading in type II second-harmonic generation,” Appl. Phys. Lett. 67, 2120–2122 (1995). [CrossRef]  

5. H. Nihei and A. Okamoto, “Photonic crystal systems for high-speed optical memory device on an atomic scale,” Proc. SPIE 4416, 470–473 (2001). [CrossRef]  

6. L. S. Yan, A. E. Willner, X. X. Wu, A. L. Yi, B. Antonella, Z. Y. Chen, and H. Y. Jiang, “All-optical signal processing for ultrahigh speed optical systems and networks,” J. Lightwave Technol. 30, 3760–3770 (2012). [CrossRef]  

7. F. Y. Wang, G. X. Li, H. L. Tam, K. W. Cheah, and S. N. Zhu, “Optical bistability and multistability in one-dimensional periodic metal-dielectric photonic crystal,” Appl. Phys. Lett. 92, 211109 (2008). [CrossRef]  

8. C. Min, P. Wang, C. Chen, Y. Deng, Y. Lu, H. Ming, T. Ning, Y. Zhou, and G. Yang, “All optical switching in subwavelength metallic grating structure containing nonlinear optical materials,” Opt. Lett. 33, 869–871 (2008). [CrossRef]   [PubMed]  

9. Y. Shen and G. P. Wang, “Optical bistability in metal gap waveguide nanocavities,” Opt. Express 16, 8421–8426 (2008). [CrossRef]   [PubMed]  

10. N. M. Litchinitser, I. R. Gabitov, and A. I. Maimistov, “Optical bistability in a nonlinear optical coupler with a negative index channel,” Phys. Rev. Lett. 99, 113902 (2007). [CrossRef]   [PubMed]  

11. P. Y. Chen, M. Farhat, and A. Alu, “Bistable and self-tunable negative-index metamaterial at optical frequencies,” Phys. Rev. Lett. 106, 105503 (2011). [CrossRef]   [PubMed]  

12. P. Y. Chen and A. Alu, “Optical nanoantenna arrays loaded with nonlinear materials,” Phys. Rev. B 82, 235405 (2010). [CrossRef]  

13. F. Zhou, Y. Liu, Z. Y. Li, and Y. Xia, “Analytical model for optical bistability in nonlinear metal nano-antennae involving Kerr materials,” Opt. Express 18, 13337–13344 (2010). [CrossRef]   [PubMed]  

14. E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105, 097401 (2010). [CrossRef]   [PubMed]  

15. H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37, 1856–1858 (2012). [CrossRef]   [PubMed]  

16. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004). [CrossRef]   [PubMed]  

17. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009). [CrossRef]  

18. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011). [CrossRef]   [PubMed]  

19. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010). [CrossRef]  

20. E. Simsek, “Improving tuning range and sensitivity of localized SPR sensors with graphene,” Photon. Technol. Lett. 25, 867–870 (2013). [CrossRef]  

21. B. Vasić, M. M. Jakovljević, G. Isić, and R. Gajić, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 103, 011102 (2013).

22. L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011). [CrossRef]   [PubMed]  

23. A. Andryieuski and A. V. Lavrinenko, “Graphene metamaterials based tunable terahertz absorber: effective surface conductivity approach,” Opt. Express 21, 9144–9155 (2013). [CrossRef]   [PubMed]  

24. L. Jiang, Q. Wang, Y. Xiang, X. Dai, and S. Wen, “Electrically tunable Goos-Hänchen shift of light beam reflected from a graphene-on-dielectric surface,” IEEE Photonic J. 5, 6500108 (2013). [CrossRef]  

25. Y. C. Fan, Z. Y. Wei, H. Q. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88, 241403 (2013). [CrossRef]  

26. Y. C. Fan, F. L. Zhang, Q. Zhao, Z. Y. Wei, and H. Q. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014). [CrossRef]   [PubMed]  

27. C. S. R. Kaipa, A. B. Yakovlev, G. W. Hanson, Y. R. Padooru, F. Medina, and F. Mesa, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Phys. Rev. B 85, 245407 (2012). [CrossRef]  

28. R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano. Lett. 11, 5159–5164 (2011). [CrossRef]   [PubMed]  

29. J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21, 2430–2435 (2009). [CrossRef]  

30. Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Tang, and K. P. Loh, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009). [CrossRef]  

31. G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics 5, 554–560 (2011). [CrossRef]  

32. T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photon. 6, 554–559 (2012). [CrossRef]  

33. Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104, 051108 (2014). [CrossRef]  

34. Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, (2015), , “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. doi: [CrossRef]  

35. N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. P. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90, 125425 (2014). [CrossRef]  

36. S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J Phys: Condens. Matter. 20, 384204 (2008).

References

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  1. H. M. Gibbs., Optical Bistability: Controlling Light with Light. (Academic Press, 1985).
  2. E. Abraham and S. D. Smith, “Optical bistability and related devices,” Rep. Prog. Phys. 45, 815–885 (1982).
    [Crossref]
  3. D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel’kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
    [Crossref] [PubMed]
  4. G. Assanto, Z. Wang, D. J. Hagan, and E. W. VanStryland, “All-optical modulation via nonlinear cascading in type II second-harmonic generation,” Appl. Phys. Lett. 67, 2120–2122 (1995).
    [Crossref]
  5. H. Nihei and A. Okamoto, “Photonic crystal systems for high-speed optical memory device on an atomic scale,” Proc. SPIE 4416, 470–473 (2001).
    [Crossref]
  6. L. S. Yan, A. E. Willner, X. X. Wu, A. L. Yi, B. Antonella, Z. Y. Chen, and H. Y. Jiang, “All-optical signal processing for ultrahigh speed optical systems and networks,” J. Lightwave Technol. 30, 3760–3770 (2012).
    [Crossref]
  7. F. Y. Wang, G. X. Li, H. L. Tam, K. W. Cheah, and S. N. Zhu, “Optical bistability and multistability in one-dimensional periodic metal-dielectric photonic crystal,” Appl. Phys. Lett. 92, 211109 (2008).
    [Crossref]
  8. C. Min, P. Wang, C. Chen, Y. Deng, Y. Lu, H. Ming, T. Ning, Y. Zhou, and G. Yang, “All optical switching in subwavelength metallic grating structure containing nonlinear optical materials,” Opt. Lett. 33, 869–871 (2008).
    [Crossref] [PubMed]
  9. Y. Shen and G. P. Wang, “Optical bistability in metal gap waveguide nanocavities,” Opt. Express 16, 8421–8426 (2008).
    [Crossref] [PubMed]
  10. N. M. Litchinitser, I. R. Gabitov, and A. I. Maimistov, “Optical bistability in a nonlinear optical coupler with a negative index channel,” Phys. Rev. Lett. 99, 113902 (2007).
    [Crossref] [PubMed]
  11. P. Y. Chen, M. Farhat, and A. Alu, “Bistable and self-tunable negative-index metamaterial at optical frequencies,” Phys. Rev. Lett. 106, 105503 (2011).
    [Crossref] [PubMed]
  12. P. Y. Chen and A. Alu, “Optical nanoantenna arrays loaded with nonlinear materials,” Phys. Rev. B 82, 235405 (2010).
    [Crossref]
  13. F. Zhou, Y. Liu, Z. Y. Li, and Y. Xia, “Analytical model for optical bistability in nonlinear metal nano-antennae involving Kerr materials,” Opt. Express 18, 13337–13344 (2010).
    [Crossref] [PubMed]
  14. E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105, 097401 (2010).
    [Crossref] [PubMed]
  15. H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37, 1856–1858 (2012).
    [Crossref] [PubMed]
  16. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
    [Crossref] [PubMed]
  17. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
    [Crossref]
  18. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
    [Crossref] [PubMed]
  19. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
    [Crossref]
  20. E. Simsek, “Improving tuning range and sensitivity of localized SPR sensors with graphene,” Photon. Technol. Lett. 25, 867–870 (2013).
    [Crossref]
  21. B. Vasić, M. M. Jakovljević, G. Isić, and R. Gajić, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 103, 011102 (2013).
  22. L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
    [Crossref] [PubMed]
  23. A. Andryieuski and A. V. Lavrinenko, “Graphene metamaterials based tunable terahertz absorber: effective surface conductivity approach,” Opt. Express 21, 9144–9155 (2013).
    [Crossref] [PubMed]
  24. L. Jiang, Q. Wang, Y. Xiang, X. Dai, and S. Wen, “Electrically tunable Goos-Hänchen shift of light beam reflected from a graphene-on-dielectric surface,” IEEE Photonic J. 5, 6500108 (2013).
    [Crossref]
  25. Y. C. Fan, Z. Y. Wei, H. Q. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88, 241403 (2013).
    [Crossref]
  26. Y. C. Fan, F. L. Zhang, Q. Zhao, Z. Y. Wei, and H. Q. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014).
    [Crossref] [PubMed]
  27. C. S. R. Kaipa, A. B. Yakovlev, G. W. Hanson, Y. R. Padooru, F. Medina, and F. Mesa, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Phys. Rev. B 85, 245407 (2012).
    [Crossref]
  28. R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano. Lett. 11, 5159–5164 (2011).
    [Crossref] [PubMed]
  29. J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21, 2430–2435 (2009).
    [Crossref]
  30. Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Tang, and K. P. Loh, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
    [Crossref]
  31. G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics 5, 554–560 (2011).
    [Crossref]
  32. T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photon. 6, 554–559 (2012).
    [Crossref]
  33. Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104, 051108 (2014).
    [Crossref]
  34. Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, (2015), , “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. doi:
    [Crossref]
  35. N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. P. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90, 125425 (2014).
    [Crossref]
  36. S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J Phys: Condens. Matter. 20, 384204 (2008).

2014 (3)

Y. C. Fan, F. L. Zhang, Q. Zhao, Z. Y. Wei, and H. Q. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014).
[Crossref] [PubMed]

Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104, 051108 (2014).
[Crossref]

N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. P. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90, 125425 (2014).
[Crossref]

2013 (5)

E. Simsek, “Improving tuning range and sensitivity of localized SPR sensors with graphene,” Photon. Technol. Lett. 25, 867–870 (2013).
[Crossref]

B. Vasić, M. M. Jakovljević, G. Isić, and R. Gajić, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 103, 011102 (2013).

A. Andryieuski and A. V. Lavrinenko, “Graphene metamaterials based tunable terahertz absorber: effective surface conductivity approach,” Opt. Express 21, 9144–9155 (2013).
[Crossref] [PubMed]

L. Jiang, Q. Wang, Y. Xiang, X. Dai, and S. Wen, “Electrically tunable Goos-Hänchen shift of light beam reflected from a graphene-on-dielectric surface,” IEEE Photonic J. 5, 6500108 (2013).
[Crossref]

Y. C. Fan, Z. Y. Wei, H. Q. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88, 241403 (2013).
[Crossref]

2012 (4)

C. S. R. Kaipa, A. B. Yakovlev, G. W. Hanson, Y. R. Padooru, F. Medina, and F. Mesa, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Phys. Rev. B 85, 245407 (2012).
[Crossref]

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photon. 6, 554–559 (2012).
[Crossref]

L. S. Yan, A. E. Willner, X. X. Wu, A. L. Yi, B. Antonella, Z. Y. Chen, and H. Y. Jiang, “All-optical signal processing for ultrahigh speed optical systems and networks,” J. Lightwave Technol. 30, 3760–3770 (2012).
[Crossref]

H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37, 1856–1858 (2012).
[Crossref] [PubMed]

2011 (5)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

P. Y. Chen, M. Farhat, and A. Alu, “Bistable and self-tunable negative-index metamaterial at optical frequencies,” Phys. Rev. Lett. 106, 105503 (2011).
[Crossref] [PubMed]

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics 5, 554–560 (2011).
[Crossref]

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano. Lett. 11, 5159–5164 (2011).
[Crossref] [PubMed]

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref] [PubMed]

2010 (4)

P. Y. Chen and A. Alu, “Optical nanoantenna arrays loaded with nonlinear materials,” Phys. Rev. B 82, 235405 (2010).
[Crossref]

F. Zhou, Y. Liu, Z. Y. Li, and Y. Xia, “Analytical model for optical bistability in nonlinear metal nano-antennae involving Kerr materials,” Opt. Express 18, 13337–13344 (2010).
[Crossref] [PubMed]

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105, 097401 (2010).
[Crossref] [PubMed]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

2009 (3)

J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21, 2430–2435 (2009).
[Crossref]

Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Tang, and K. P. Loh, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[Crossref]

2008 (4)

S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J Phys: Condens. Matter. 20, 384204 (2008).

F. Y. Wang, G. X. Li, H. L. Tam, K. W. Cheah, and S. N. Zhu, “Optical bistability and multistability in one-dimensional periodic metal-dielectric photonic crystal,” Appl. Phys. Lett. 92, 211109 (2008).
[Crossref]

C. Min, P. Wang, C. Chen, Y. Deng, Y. Lu, H. Ming, T. Ning, Y. Zhou, and G. Yang, “All optical switching in subwavelength metallic grating structure containing nonlinear optical materials,” Opt. Lett. 33, 869–871 (2008).
[Crossref] [PubMed]

Y. Shen and G. P. Wang, “Optical bistability in metal gap waveguide nanocavities,” Opt. Express 16, 8421–8426 (2008).
[Crossref] [PubMed]

2007 (1)

N. M. Litchinitser, I. R. Gabitov, and A. I. Maimistov, “Optical bistability in a nonlinear optical coupler with a negative index channel,” Phys. Rev. Lett. 99, 113902 (2007).
[Crossref] [PubMed]

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

2003 (1)

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel’kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
[Crossref] [PubMed]

2001 (1)

H. Nihei and A. Okamoto, “Photonic crystal systems for high-speed optical memory device on an atomic scale,” Proc. SPIE 4416, 470–473 (2001).
[Crossref]

1995 (1)

G. Assanto, Z. Wang, D. J. Hagan, and E. W. VanStryland, “All-optical modulation via nonlinear cascading in type II second-harmonic generation,” Appl. Phys. Lett. 67, 2120–2122 (1995).
[Crossref]

1982 (1)

E. Abraham and S. D. Smith, “Optical bistability and related devices,” Rep. Prog. Phys. 45, 815–885 (1982).
[Crossref]

Abraham, E.

E. Abraham and S. D. Smith, “Optical bistability and related devices,” Rep. Prog. Phys. 45, 815–885 (1982).
[Crossref]

Akimov, A. V.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel’kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
[Crossref] [PubMed]

Alu, A.

P. Y. Chen, M. Farhat, and A. Alu, “Bistable and self-tunable negative-index metamaterial at optical frequencies,” Phys. Rev. Lett. 106, 105503 (2011).
[Crossref] [PubMed]

P. Y. Chen and A. Alu, “Optical nanoantenna arrays loaded with nonlinear materials,” Phys. Rev. B 82, 235405 (2010).
[Crossref]

Andryieuski, A.

Antonella, B.

Assanto, G.

G. Assanto, Z. Wang, D. J. Hagan, and E. W. VanStryland, “All-optical modulation via nonlinear cascading in type II second-harmonic generation,” Appl. Phys. Lett. 67, 2120–2122 (1995).
[Crossref]

Bai, X.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano. Lett. 11, 5159–5164 (2011).
[Crossref] [PubMed]

Bao, Q.

H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37, 1856–1858 (2012).
[Crossref] [PubMed]

Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Tang, and K. P. Loh, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, (2015), , “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. doi:
[Crossref]

Bechtel, H. A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref] [PubMed]

Bian, F.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano. Lett. 11, 5159–5164 (2011).
[Crossref] [PubMed]

Blau, W. J.

J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21, 2430–2435 (2009).
[Crossref]

Bludov, Y. V.

N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. P. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90, 125425 (2014).
[Crossref]

Bonaccorso, F.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

Castro Neto, A. H.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[Crossref]

Cheah, K. W.

F. Y. Wang, G. X. Li, H. L. Tam, K. W. Cheah, and S. N. Zhu, “Optical bistability and multistability in one-dimensional periodic metal-dielectric photonic crystal,” Appl. Phys. Lett. 92, 211109 (2008).
[Crossref]

Chen, C.

Chen, H.

Y. C. Fan, Z. Y. Wei, H. Q. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88, 241403 (2013).
[Crossref]

Chen, J.

Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, (2015), , “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. doi:
[Crossref]

Chen, P. Y.

P. Y. Chen, M. Farhat, and A. Alu, “Bistable and self-tunable negative-index metamaterial at optical frequencies,” Phys. Rev. Lett. 106, 105503 (2011).
[Crossref] [PubMed]

P. Y. Chen and A. Alu, “Optical nanoantenna arrays loaded with nonlinear materials,” Phys. Rev. B 82, 235405 (2010).
[Crossref]

Chen, Z. L.

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics 5, 554–560 (2011).
[Crossref]

Chen, Z. Y.

Chua, L. L.

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics 5, 554–560 (2011).
[Crossref]

Clark, J.

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics 5, 554–560 (2011).
[Crossref]

Coleman, J. N.

J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21, 2430–2435 (2009).
[Crossref]

Dai, X.

Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104, 051108 (2014).
[Crossref]

L. Jiang, Q. Wang, Y. Xiang, X. Dai, and S. Wen, “Electrically tunable Goos-Hänchen shift of light beam reflected from a graphene-on-dielectric surface,” IEEE Photonic J. 5, 6500108 (2013).
[Crossref]

Deng, Y.

Dijkhuis, J. I.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel’kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
[Crossref] [PubMed]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

Fan, Y. C.

Y. C. Fan, F. L. Zhang, Q. Zhao, Z. Y. Wei, and H. Q. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014).
[Crossref] [PubMed]

Y. C. Fan, Z. Y. Wei, H. Q. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88, 241403 (2013).
[Crossref]

Farhat, M.

P. Y. Chen, M. Farhat, and A. Alu, “Bistable and self-tunable negative-index metamaterial at optical frequencies,” Phys. Rev. Lett. 106, 105503 (2011).
[Crossref] [PubMed]

Ferrari, A. C.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

Friend, R. H.

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics 5, 554–560 (2011).
[Crossref]

Gabitov, I. R.

N. M. Litchinitser, I. R. Gabitov, and A. I. Maimistov, “Optical bistability in a nonlinear optical coupler with a negative index channel,” Phys. Rev. Lett. 99, 113902 (2007).
[Crossref] [PubMed]

Gajic, R.

B. Vasić, M. M. Jakovljević, G. Isić, and R. Gajić, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 103, 011102 (2013).

Geim, A. K.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[Crossref]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

Geng, B.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref] [PubMed]

Gibbs., H. M.

H. M. Gibbs., Optical Bistability: Controlling Light with Light. (Academic Press, 1985).

Girit, C.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref] [PubMed]

Godbout, N.

Goh, R. G. S.

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics 5, 554–560 (2011).
[Crossref]

Golubev, V. G.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel’kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
[Crossref] [PubMed]

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

Gu, T.

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photon. 6, 554–559 (2012).
[Crossref]

Guinea, F.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[Crossref]

Guo, J.

Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104, 051108 (2014).
[Crossref]

Hagan, D. J.

G. Assanto, Z. Wang, D. J. Hagan, and E. W. VanStryland, “All-optical modulation via nonlinear cascading in type II second-harmonic generation,” Appl. Phys. Lett. 67, 2120–2122 (1995).
[Crossref]

Hale, P. J.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105, 097401 (2010).
[Crossref] [PubMed]

Hanson, G. W.

C. S. R. Kaipa, A. B. Yakovlev, G. W. Hanson, Y. R. Padooru, F. Medina, and F. Mesa, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Phys. Rev. B 85, 245407 (2012).
[Crossref]

Hao, Z.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref] [PubMed]

Hasan, T.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

Hendry, E.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105, 097401 (2010).
[Crossref] [PubMed]

Hernandez, Y.

J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21, 2430–2435 (2009).
[Crossref]

Ho, P. K. H.

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics 5, 554–560 (2011).
[Crossref]

Hone, J.

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photon. 6, 554–559 (2012).
[Crossref]

Horng, J.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref] [PubMed]

Isic, G.

B. Vasić, M. M. Jakovljević, G. Isić, and R. Gajić, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 103, 011102 (2013).

Jakovljevic, M. M.

B. Vasić, M. M. Jakovljević, G. Isić, and R. Gajić, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 103, 011102 (2013).

Jauho, A. P.

N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. P. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90, 125425 (2014).
[Crossref]

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

Jiang, H. Y.

Jiang, L.

L. Jiang, Q. Wang, Y. Xiang, X. Dai, and S. Wen, “Electrically tunable Goos-Hänchen shift of light beam reflected from a graphene-on-dielectric surface,” IEEE Photonic J. 5, 6500108 (2013).
[Crossref]

Jiang, X.

Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, (2015), , “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. doi:
[Crossref]

Ju, L.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref] [PubMed]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

Kaipa, C. S. R.

C. S. R. Kaipa, A. B. Yakovlev, G. W. Hanson, Y. R. Padooru, F. Medina, and F. Mesa, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Phys. Rev. B 85, 245407 (2012).
[Crossref]

Kerst, R.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel’kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
[Crossref] [PubMed]

Kockaert, P.

Kurdyukov, D. A.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel’kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
[Crossref] [PubMed]

Kwong, D. L.

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photon. 6, 554–559 (2012).
[Crossref]

Lavrinenko, A. V.

Li, G. X.

F. Y. Wang, G. X. Li, H. L. Tam, K. W. Cheah, and S. N. Zhu, “Optical bistability and multistability in one-dimensional periodic metal-dielectric photonic crystal,” Appl. Phys. Lett. 92, 211109 (2008).
[Crossref]

Li, H. Q.

Y. C. Fan, F. L. Zhang, Q. Zhao, Z. Y. Wei, and H. Q. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014).
[Crossref] [PubMed]

Y. C. Fan, Z. Y. Wei, H. Q. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88, 241403 (2013).
[Crossref]

Li, S.

Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, (2015), , “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. doi:
[Crossref]

Li, Z. Y.

Liang, X.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref] [PubMed]

Lim, G. K.

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics 5, 554–560 (2011).
[Crossref]

Litchinitser, N. M.

N. M. Litchinitser, I. R. Gabitov, and A. I. Maimistov, “Optical bistability in a nonlinear optical coupler with a negative index channel,” Phys. Rev. Lett. 99, 113902 (2007).
[Crossref] [PubMed]

Liu, M.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

Liu, Y.

Lo, G. Q.

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photon. 6, 554–559 (2012).
[Crossref]

Loh, K. P.

Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Tang, and K. P. Loh, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, (2015), , “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. doi:
[Crossref]

Lotya, M.

J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21, 2430–2435 (2009).
[Crossref]

Lu, X.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano. Lett. 11, 5159–5164 (2011).
[Crossref] [PubMed]

Lu, Y.

Maimistov, A. I.

N. M. Litchinitser, I. R. Gabitov, and A. I. Maimistov, “Optical bistability in a nonlinear optical coupler with a negative index channel,” Phys. Rev. Lett. 99, 113902 (2007).
[Crossref] [PubMed]

Martin, M.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref] [PubMed]

Massar, S.

Mazurenko, D. A.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel’kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
[Crossref] [PubMed]

McMillan, J. F.

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photon. 6, 554–559 (2012).
[Crossref]

Medina, F.

C. S. R. Kaipa, A. B. Yakovlev, G. W. Hanson, Y. R. Padooru, F. Medina, and F. Mesa, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Phys. Rev. B 85, 245407 (2012).
[Crossref]

Mesa, F.

C. S. R. Kaipa, A. B. Yakovlev, G. W. Hanson, Y. R. Padooru, F. Medina, and F. Mesa, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Phys. Rev. B 85, 245407 (2012).
[Crossref]

Mikhailov, S. A.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105, 097401 (2010).
[Crossref] [PubMed]

S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J Phys: Condens. Matter. 20, 384204 (2008).

Min, C.

Ming, H.

Moger, J.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105, 097401 (2010).
[Crossref] [PubMed]

Morozov, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

Ng, W. H.

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics 5, 554–560 (2011).
[Crossref]

Ni, Z.

Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Tang, and K. P. Loh, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Nihei, H.

H. Nihei and A. Okamoto, “Photonic crystal systems for high-speed optical memory device on an atomic scale,” Proc. SPIE 4416, 470–473 (2001).
[Crossref]

Ning, T.

Novoselov, K. S.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[Crossref]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

Okamoto, A.

H. Nihei and A. Okamoto, “Photonic crystal systems for high-speed optical memory device on an atomic scale,” Proc. SPIE 4416, 470–473 (2001).
[Crossref]

Padooru, Y. R.

C. S. R. Kaipa, A. B. Yakovlev, G. W. Hanson, Y. R. Padooru, F. Medina, and F. Mesa, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Phys. Rev. B 85, 245407 (2012).
[Crossref]

Peres, N. M. R.

N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. P. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90, 125425 (2014).
[Crossref]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[Crossref]

Petrone, N.

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photon. 6, 554–559 (2012).
[Crossref]

Pevtsov, A. B.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel’kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
[Crossref] [PubMed]

Ping, L. K.

Polavarapu, L.

Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Tang, and K. P. Loh, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Santos, J. E.

N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. P. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90, 125425 (2014).
[Crossref]

Savchenko, A. K.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105, 097401 (2010).
[Crossref] [PubMed]

Sel’kin, A. V.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel’kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
[Crossref] [PubMed]

Shen, Y.

Shen, Y. R.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref] [PubMed]

Shen, Z.

Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Tang, and K. P. Loh, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Simsek, E.

E. Simsek, “Improving tuning range and sensitivity of localized SPR sensors with graphene,” Photon. Technol. Lett. 25, 867–870 (2013).
[Crossref]

Smith, S. D.

E. Abraham and S. D. Smith, “Optical bistability and related devices,” Rep. Prog. Phys. 45, 815–885 (1982).
[Crossref]

Soukoulis, C. M.

Y. C. Fan, Z. Y. Wei, H. Q. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88, 241403 (2013).
[Crossref]

Sun, Z.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

Tam, H. L.

F. Y. Wang, G. X. Li, H. L. Tam, K. W. Cheah, and S. N. Zhu, “Optical bistability and multistability in one-dimensional periodic metal-dielectric photonic crystal,” Appl. Phys. Lett. 92, 211109 (2008).
[Crossref]

Tan, H. W.

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics 5, 554–560 (2011).
[Crossref]

Tang, D.

Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104, 051108 (2014).
[Crossref]

Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Tang, and K. P. Loh, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Ulin-Avila, E.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

van der Zande, A.

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photon. 6, 554–559 (2012).
[Crossref]

VanStryland, E. W.

G. Assanto, Z. Wang, D. J. Hagan, and E. W. VanStryland, “All-optical modulation via nonlinear cascading in type II second-harmonic generation,” Appl. Phys. Lett. 67, 2120–2122 (1995).
[Crossref]

Vasic, B.

B. Vasić, M. M. Jakovljević, G. Isić, and R. Gajić, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 103, 011102 (2013).

Vasilevskiy, M. I.

N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. P. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90, 125425 (2014).
[Crossref]

Venkatesan, T.

Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, (2015), , “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. doi:
[Crossref]

Virally, S.

Wang, E.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano. Lett. 11, 5159–5164 (2011).
[Crossref] [PubMed]

Wang, F.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref] [PubMed]

Wang, F. Y.

F. Y. Wang, G. X. Li, H. L. Tam, K. W. Cheah, and S. N. Zhu, “Optical bistability and multistability in one-dimensional periodic metal-dielectric photonic crystal,” Appl. Phys. Lett. 92, 211109 (2008).
[Crossref]

Wang, G. P.

Wang, J.

J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21, 2430–2435 (2009).
[Crossref]

Wang, P.

Wang, Q.

L. Jiang, Q. Wang, Y. Xiang, X. Dai, and S. Wen, “Electrically tunable Goos-Hänchen shift of light beam reflected from a graphene-on-dielectric surface,” IEEE Photonic J. 5, 6500108 (2013).
[Crossref]

Wang, W.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano. Lett. 11, 5159–5164 (2011).
[Crossref] [PubMed]

Wang, Y.

Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Tang, and K. P. Loh, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Wang, Z.

G. Assanto, Z. Wang, D. J. Hagan, and E. W. VanStryland, “All-optical modulation via nonlinear cascading in type II second-harmonic generation,” Appl. Phys. Lett. 67, 2120–2122 (1995).
[Crossref]

Wei, Z. Y.

Y. C. Fan, F. L. Zhang, Q. Zhao, Z. Y. Wei, and H. Q. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014).
[Crossref] [PubMed]

Y. C. Fan, Z. Y. Wei, H. Q. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88, 241403 (2013).
[Crossref]

Wen, S.

Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104, 051108 (2014).
[Crossref]

L. Jiang, Q. Wang, Y. Xiang, X. Dai, and S. Wen, “Electrically tunable Goos-Hänchen shift of light beam reflected from a graphene-on-dielectric surface,” IEEE Photonic J. 5, 6500108 (2013).
[Crossref]

Willner, A. E.

Wong, C. W.

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photon. 6, 554–559 (2012).
[Crossref]

Wu, R.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano. Lett. 11, 5159–5164 (2011).
[Crossref] [PubMed]

Wu, X. X.

Xia, Y.

Xiang, Y.

Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104, 051108 (2014).
[Crossref]

L. Jiang, Q. Wang, Y. Xiang, X. Dai, and S. Wen, “Electrically tunable Goos-Hänchen shift of light beam reflected from a graphene-on-dielectric surface,” IEEE Photonic J. 5, 6500108 (2013).
[Crossref]

Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, (2015), , “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. doi:
[Crossref]

Xu, Q. H.

Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Tang, and K. P. Loh, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, (2015), , “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. doi:
[Crossref]

Yakovlev, A. B.

C. S. R. Kaipa, A. B. Yakovlev, G. W. Hanson, Y. R. Padooru, F. Medina, and F. Mesa, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Phys. Rev. B 85, 245407 (2012).
[Crossref]

Yan, L. S.

Yan, S.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano. Lett. 11, 5159–5164 (2011).
[Crossref] [PubMed]

Yang, G.

Yi, A. L.

Yin, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

Yu, M.

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photon. 6, 554–559 (2012).
[Crossref]

Zentgraf, T.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

Zettl, A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref] [PubMed]

Zhang, F. L.

Zhang, H.

H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37, 1856–1858 (2012).
[Crossref] [PubMed]

Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Tang, and K. P. Loh, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Zhang, K.

Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, (2015), , “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. doi:
[Crossref]

Zhang, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

Zhang, Y.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano. Lett. 11, 5159–5164 (2011).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

Zhao, J.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano. Lett. 11, 5159–5164 (2011).
[Crossref] [PubMed]

Zhao, Q.

Zhou, F.

Zhou, Y.

Zhu, S. N.

F. Y. Wang, G. X. Li, H. L. Tam, K. W. Cheah, and S. N. Zhu, “Optical bistability and multistability in one-dimensional periodic metal-dielectric photonic crystal,” Appl. Phys. Lett. 92, 211109 (2008).
[Crossref]

Ziegler, K.

S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J Phys: Condens. Matter. 20, 384204 (2008).

Adv. Funct. Mater. (1)

Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q. H. Xu, D. Tang, and K. P. Loh, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

Adv. Mater. (1)

J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21, 2430–2435 (2009).
[Crossref]

Appl. Phys. Lett. (4)

Y. Xiang, X. Dai, J. Guo, S. Wen, and D. Tang, “Tunable optical bistability at the graphene-covered nonlinear interface,” Appl. Phys. Lett. 104, 051108 (2014).
[Crossref]

B. Vasić, M. M. Jakovljević, G. Isić, and R. Gajić, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 103, 011102 (2013).

G. Assanto, Z. Wang, D. J. Hagan, and E. W. VanStryland, “All-optical modulation via nonlinear cascading in type II second-harmonic generation,” Appl. Phys. Lett. 67, 2120–2122 (1995).
[Crossref]

F. Y. Wang, G. X. Li, H. L. Tam, K. W. Cheah, and S. N. Zhu, “Optical bistability and multistability in one-dimensional periodic metal-dielectric photonic crystal,” Appl. Phys. Lett. 92, 211109 (2008).
[Crossref]

IEEE Photonic J. (1)

L. Jiang, Q. Wang, Y. Xiang, X. Dai, and S. Wen, “Electrically tunable Goos-Hänchen shift of light beam reflected from a graphene-on-dielectric surface,” IEEE Photonic J. 5, 6500108 (2013).
[Crossref]

J Phys: Condens. Matter. (1)

S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J Phys: Condens. Matter. 20, 384204 (2008).

J. Lightwave Technol. (1)

Nano. Lett. (1)

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano. Lett. 11, 5159–5164 (2011).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref] [PubMed]

Nat. Photon. (1)

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photon. 6, 554–559 (2012).
[Crossref]

Nat. Photonics (2)

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics 5, 554–560 (2011).
[Crossref]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

Nature (1)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (3)

Photon. Technol. Lett. (1)

E. Simsek, “Improving tuning range and sensitivity of localized SPR sensors with graphene,” Photon. Technol. Lett. 25, 867–870 (2013).
[Crossref]

Phys. Rev. B (4)

C. S. R. Kaipa, A. B. Yakovlev, G. W. Hanson, Y. R. Padooru, F. Medina, and F. Mesa, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Phys. Rev. B 85, 245407 (2012).
[Crossref]

Y. C. Fan, Z. Y. Wei, H. Q. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88, 241403 (2013).
[Crossref]

P. Y. Chen and A. Alu, “Optical nanoantenna arrays loaded with nonlinear materials,” Phys. Rev. B 82, 235405 (2010).
[Crossref]

N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. P. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90, 125425 (2014).
[Crossref]

Phys. Rev. Lett. (4)

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105, 097401 (2010).
[Crossref] [PubMed]

N. M. Litchinitser, I. R. Gabitov, and A. I. Maimistov, “Optical bistability in a nonlinear optical coupler with a negative index channel,” Phys. Rev. Lett. 99, 113902 (2007).
[Crossref] [PubMed]

P. Y. Chen, M. Farhat, and A. Alu, “Bistable and self-tunable negative-index metamaterial at optical frequencies,” Phys. Rev. Lett. 106, 105503 (2011).
[Crossref] [PubMed]

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel’kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91, 213903 (2003).
[Crossref] [PubMed]

Proc. SPIE (1)

H. Nihei and A. Okamoto, “Photonic crystal systems for high-speed optical memory device on an atomic scale,” Proc. SPIE 4416, 470–473 (2001).
[Crossref]

Rep. Prog. Phys. (1)

E. Abraham and S. D. Smith, “Optical bistability and related devices,” Rep. Prog. Phys. 45, 815–885 (1982).
[Crossref]

Rev. Mod. Phys. (1)

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[Crossref]

Science (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

Other (2)

H. M. Gibbs., Optical Bistability: Controlling Light with Light. (Academic Press, 1985).

Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, (2015), , “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. doi:
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Schematic diagram of a sandwiched structure, where the graphene sheet is inserted between two dielectric slabs. A plane wave of amplitude Ei is incident on the sandwiched structure with incident angle θ, giving rise to a reflected and a transmitted wave with amplitude ER and ET, respectively. A, B, C and D are the amplitudes of the transmitted and reflected waves inside the two dielectric slabs.
Fig. 2
Fig. 2 The dependencies of the transmittance and reflectance on the incident angle for the sandwich structure with the insertion of graphene sheet (a) and without graphene sheet (b). Where EF = 0.8eV, λ = 100 μm, ε1 = ε4 = 1, ε2 = ε3 = 2.25, d2=d3 = 4 μm, τ−1 = 0, and T = 300 K.
Fig. 3
Fig. 3 The dependencies of the transmitted electric field (a) and transmittance (b) on the input light intensity at different Fermi energy EF of the graphene. Where θ = 75°, other parameters have the same values as those in Fig. 2.
Fig. 4
Fig. 4 The dependencies of the switch-up and switch-down threshold electric fields on the Fermi energy EF of the graphene. The parameters have the same values as those in Fig. 3.
Fig. 5
Fig. 5 The influence of the properties of dielectric slabs 2 and 3 on the optical bistable phenomenon for (a) different thicknesses of dielectric slabs 2 and 3, and (b) different permittivities of dielectrics 2 and 3. Where ε2 = ε3 = 2.25 in (a) and d2=d3 = 4 μm in (b), other parameters have the same values as those in Fig. 3.
Fig. 6
Fig. 6 The influence of the properties of incident light on the optical bistable phenomena for (a) different incident angle, and (b) different work wavelength. Where λ2 = 100 μm in (a) and θ = 75° in (b), other parameters have the same values as those in Fig. 3.
Fig. 7
Fig. 7 The dependencies of the transmitted electric field and transmittance on the input electric field at different electron-phonon relaxation time τ of the graphene for wavelength λ = 100um in (a and b) and λ = 60um in (c and d). The parameters have the same values as those in Fig. 3.

Equations (13)

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

σ intra = i e 2 k B T π h ¯ 2 ( ω + i / τ ) [ E F k B T + 2 ln ( e E F k B T + 1 ) ] ,
σ inter = i e 2 4 π h ¯ ln | 2 E F ( ω + i τ 1 ) h ¯ 2 E F + ( ω + i τ 1 ) h ¯ | ,
σ 3 = i 3 32 e 2 π ( e ν F ) 2 E F ω 3 ( 1 + i α T ) ,
{ E 1 y = E i e i k 1 z ( z + d 2 ) e i k x x + E R e i k 1 z ( z + d 2 ) e i k x x , H 1 x = k 1 z μ 0 ω E i e i k 1 z ( z + d 2 ) e i k x x + k 1 z μ 0 ω E R e i k 1 z ( z + d 2 ) e i k x x , H 1 z = k x μ 0 ω E i e i k 1 z ( z + d 2 ) e i k x x + k x μ 0 ω E R e i k 1 z ( z + d 2 ) e i k x x ,
{ E 2 y = A e i k 2 z z e i k x x + B e i k 2 z z e i k x x , H 2 x = k 2 z μ 0 ω A e i k 2 z z e i k x x + k 2 z μ 0 ω B e i k 2 z z e i k x x , H 2 z = k x μ 0 ω A e i k 2 z z e i k x x + k x μ 0 ω B e i k 2 z z e i k x x ,
{ E 3 y = C e i k 3 z z e i k x x + D e i k 3 z z e i k x x , H 3 x = k 3 z μ 0 ω C e i k 3 z z e i k x x + k 3 z μ 0 ω D e i k 3 z z e i k x x , H 3 z = k x μ 0 ω C e i k 3 z z e i k x x + k x μ 0 ω D e i k 3 z z e i k x x ,
{ E 4 y = E T e i k 4 z ( z d 3 ) e i k x x , H 4 x = k 4 z μ 0 ω E T e i k 4 z ( z d 3 ) e i k x x , H 4 z = k x μ 0 ω E T e i k 4 z ( z d 3 ) e i k x x .
E i = E T 1 8 ( 1 + k 2 z k 1 z ) [ ( 1 k 3 z k 2 z ) Δ + Θ ] e i k 2 z d 2 + E T 1 8 ( 1 k 2 z k 1 z ) [ ( 1 + k 3 z k 2 z ) Δ Θ ] e i k 2 z d 2 ,
{ Δ = ( k 4 z k 3 z + 1 ) e i k 3 z d 3 + ( 1 k 4 z k 3 z ) e i k 3 z d 3 , Θ = 2 k 3 z k 2 z ( 1 + k 4 z k 3 z ) e i k 3 z d 3 μ 0 ω k 2 z ( σ 0 + 1 4 σ 3 | E T | 2 | Δ | 2 ) Δ .
Y = X | Π ( X ) | 2 ,
Π = 1 8 ( 1 + k 2 z k 1 z ) [ ( 1 k 3 z k 2 z ) Δ + Θ ] e i k 2 z d 2 + 1 8 ( 1 k 2 z k 1 z ) [ ( 1 + k 3 z k 2 z ) Δ Θ ] e i k 2 z d 2 .
Y = X | Σ ( X ) | 2 ,
{ Δ T M = ( k 4 z k 3 z ε 3 ε 4 + 1 ) e i k 3 z d 3 ( 1 k 4 z k 3 z ε 3 ε 4 ) e i k 3 z d 3 , Θ T M = k 2 z ε 2 ω ( σ 0 + 1 4 σ 3 X | k 2 z ε 0 ε 2 ω | 2 | k 3 z k 2 z ε 2 ε 3 | 2 | Δ T M | 2 ) ( k 3 z k 2 z ε 2 ε 3 Δ T M ) , Π T M = ( k 4 k 3 z ε 3 ε 4 + 1 ) e i k 3 z d 3 + ( 1 k 4 z k 3 z ε 3 ε 4 ) e i k 3 z d 3 + Θ T M , Σ = 1 8 ( k 2 z k 1 z ε 1 ε 2 + 1 ) ( Π T M + k 3 z k 2 z ε 2 ε 3 Δ T M ) e i k 2 z d 2 + ( 1 k 2 z k 1 z ε 1 ε 2 ) ( Π T M k 3 z k 2 z ε 2 ε 3 Δ T M ) e i k 2 z d 2 .

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