Optical Bistability of Graphene Incorporated into All-Superconducting Photonic Crystals

Abstract

We investigated optical bistability and its temperature dependence in a composite system composed of an all-superconducting photonic crystal and graphene. The photonic crystal, constructed from two types of superconducting sheets, and which is temperature-sensitive and can greatly localize the electric field, alternately supports a defect mode in a cryogenic environment. Graphene is located at the strongest site in the electric field, so the third-order nonlinearity of graphene is enhanced tremendously, and, subsequently, low thresholds of optical bistability are achieved in the near-infrared region. The thresholds of optical bistability and the interval between the upper and lower thresholds decrease with the increase in environmental temperature, while the bistable thresholds increase with the addition of the incident wavelength. Furthermore, the critical threshold triggering optical bistability can be modulated by environment temperature and the periodic number of photonic crystals as well. The simulations may be found to be applicable for all temperature-sensitive optical switches or sensors in cryogenic environments.

1. Introduction

Optical bistability is a nonlinear effect arising from the refractive index of material dependent on the local electric field, of which one incident intensity of light corresponds to two transmitted values of light intensity, similar to hysteresis [1]. With the development of all-optical communication technology, the investigation into optical bistability has become a popular subject, with applications ranging from theories to experiments [2,3,4,5,6,7,8]. Many advanced materials and new structures for achieving optical bistability have been proposed in recent years, such as graphene [9,10,11], photonic crystals [12,13,14], hyperbolic metamaterials [15], optical waveguides [16], non-Hermitian systems [17], etc.

We know that there are obvious optical nonlinearity phenomena arising from permittivity governed by locally strong light intensity, such as regeneration based on inducing nonlinear chirps, self-phase modulation, fiber lasers, and all-optical generation [18,19,20]. The need for strong intensity presents a difficulty in realizing optical bistability. Therefore, studies in optical bistability mainly focus on decreasing the upper and lower thresholds of optical bistability and conveniently modulating optical bistability through external measures [21,22]. The upper and lower thresholds are the critical values triggering the optically bistable effects. The defect modes in photonic crystals and stationary wave resonances can be utilized to enhance local electric fields, and consequently, the third-order nonlinearity of materials is strengthened as well [21]. Low-threshold optical bistability is subsequently induced in these structures. In addition, graphene has great third-order conductance, and the conductivity of graphene depends on environment temperature, phenomenological relaxation time, and chemical potential [23,24,25,26]. In particular, the chemical potential of graphene can be tuned by iron doping and external gate voltage [27]. The literature about the research progress on graphene (arrays) and superconductor photonic crystals is listed in

Table 1. Research progress on graphene (arrays) and superconductor photonic crystals.

Structures	Authors	Optical Effects	Refs.
Graphene or graphene arrays	Wang, Z., et al. Wang, F., et al.	Spatial solitons, plasmonic supermodes, Rabi oscillations	[28,29,30,31,32,33]
Superconductor photonic crystals	Aly, X., et al. Athe, P., et al. Dong, X., et al.	Fano resonance, filters	[34,35,36,37,38]
Composite systems of graphene and superconductors	Perconte, D., et al. Liu, F., et al. Qian, L., et al.	Klein-like tunneling, Goos–Hänchen shift, optical bistability	[13,39,40]

.

Previous explorations of the optical bistability of graphene mainly concentrated on conventional materials and photonic crystals at room temperature [9,10]. However, photonic crystals composed of all-superconducting materials support Fano resonances and optical fractals, which can localize the electric field greatly under cryogenic environments, and their optical properties are sensitive to environment temperature [41]. Therefore, it is meaningful to build a photonic crystal that is all-superconducting and combined with graphene to realize the cryogenic localization of the electric field, and, further, to obtain low-threshold tunable optical bistability in a cryogenic environment.

An all-superconducting periodic photonic crystal and graphene are incorporated into a composite structure. The defect mode and its temperature dependence are explored in the system. Then, we show the localization of the electric field and enhancement of the nonlinearity of graphene around the defect mode. Optical bistability is subsequently studied by changing the temperature in the cryogenic environment and the incident wavelength. The dependence of the upper and lower thresholds of optical bistability and the interval between the upper and lower thresholds on environment temperature and the incident wavelength are studied as well. The optical bistable phenomenon could be utilized for all optical switches and temperature and wavelength sensors in a cryogenic environment.

2. Complex System Composed of All-Superconducting Photonic Crystals and Graphene

The whole system is composed of all-superconducting photonic crystals and graphene. Two truncated all-superconducting photonic crystals, which are arrayed by alternative superconductors A and B along the Z-axis, form a defective photonic crystal. The defective photonic crystal is axisymmetrical to the Y-axis, and graphene G is embedded at the center of this defective photonic crystal. The composite system can be denoted by (AB)^NAGA(BA)^N, where N is a positive integer and is defined as the periodic number of photonic crystals. Figure 1 gives the schematic of the system in the case of N = 3. The multilayers are symmetric to graphene and can be viewed as a defective photonic crystal.

In the all-superconducting photonic crystal, we choose HgBa₂Ca₂Cu₃O_8+δ for lattice element A and BSCCO for lattice element B. The dielectric constants of superconductors A and B are governed by the rule

$${\epsilon }_{A,B}\left(\omega \right)=1-\frac{c^2}{{\omega }^2{\lambda }_{A,B}^2},$$

(1)

where the parameter of λ_A,B is called as the London penetration depth, ω = 2πc/λ is the angular frequency of the incident light wave, λ is the wavelength, and c is the speed of light in free space. The London penetration depth λ_A,B of HgBa₂Ca₂Cu₃O_8+δ and BSCCO are ruled by the equation

$${\lambda }_{A,B}\left(T_{\mathrm{e}m}\right)=\frac{{\lambda }_{L0}}{{\left[1-{\left(\frac{T_{em}}{T_{A,B}}\right)}^2\right]}^{1/2}}.$$

(2)

The environmental temperature is signed by T_em and the critical temperatures of superconductors A and B are labeled by T_A and T_B, respectively. For T_em = 0 K, the value of London penetration depth is given by λ_L0. Ignoring the influence of hydrostatic pressure, the characteristic parameters are T_A = 135 K and λ_L0 = 0.177 μm for superconductor HgBa₂Ca₂Cu₃O_8+δ. The characteristic parameters are T_B = 95 K and λ_L0 = 0.15 μm for material BSCCO.

The thicknesses of lattice elements A and B equate to a quarter of optical wavelength d_A,B = λ_c0/(4n_A0,B0), where the central wavelength is fixed at λ_c0 = 1.55 μm. We choose a value of temperature T_em = 120 K as the unified parameter to determine the initial refractive indices and thicknesses of A and B. Consequently, the refractive index of HgBa₂Ca₂Cu₃O_8+δ is given by n_A0 = 0.7696 and the refractive index of BSCCO is equal to n_B0 = 1.6158, respectively. The corresponding thicknesses are, respectively, d_A0 = λ_c0/(4n_A0) = 0.5035 μm and d_B0 = λ_c0/(4n_B0) = 0.2398 μm.

A light beam I_i is vertically incident in the structure on the left and transmitted from the right. The transmitted beam is denoted by I_o and the reflected beam is given by I_r.

In the terahertz band, the surface conductivity is governed by two mechanisms of electrons in graphene, viz. ${\sigma }_0\left(\omega ,\mu ,\tau ,T_{em}\right)={\sigma }_{intra}+{\sigma }_{inter}$ [42]. The intra-band transition is given by

$${\sigma }_{intra}=i\frac{e^2{k}_B{T}_{em}}{\pi {\hslash }^2(\omega +i{\tau }^{-1})}[\frac{\mu }{k_B{T}_{em}}+2\ln (\exp (-\frac{\mu }{k_B{T}_{em}})+1)].$$

(3)

The phenomenological relaxation time of electrons in the parameter is denoted by τ and the chemical potential of graphene is labeled by μ. The inter-band transition is given by

$${\sigma }_{inter}=i\frac{e^2}{4\pi \hslash }\ln [\frac{2\left|\mu \right|-\hslash (\omega +i{\tau }^{-1})}{2\left|\mu \right|+\hslash (\omega +i{\tau }^{-1})}].$$

(4)

As the light intensity is strong enough, one should consider the nonlinearity of graphene. The third nonlinear coefficient of conductivity for graphene is given by

$${\sigma }_3=-i\frac{3}{8}\frac{e^2}{\pi \hslash }{\left(\frac{e{V}_F}{\mu \omega }\right)}^2\frac{\mu }{\omega },$$

(5)

where V_F is Fermi velocity and is fixed by V_F ≈ c/300 [43].

In order to simulate the optical properties conveniently, graphene can be equal to a dielectric slab with an equivalent dielectric constant. For the transverse magnetic polarized wave, it propagates along the Z-axis, of which H_x and H_y represent orthogonal magnetic field components and E_z is the electric field, parallel to the Z-axis. The dielectric constant of graphene can be denoted by

$${\epsilon }_g=1+i\frac{{\sigma }_0{\eta }_0}{k_0{d}_g}+i\frac{{\sigma }_3{\eta }_0}{k_0{d}_g}{\left|E_z\right|}^2,$$

(6)

which includes the nonlinear part $i\frac{{\sigma }_3{\eta }_0}{k_0{d}_g}{\left|E_z\right|}^2$. The nonlinearity dielectric constant of graphene is proportional to the local electric field intensity ${\left|E_z\right|}^2$ [17].

The whole system is a multi-layer structure and the equivalent thickness of graphene can be given by d_g = 0.33 nm. The electric and magnetic fields at the incidence and emergence terminals can be related by a transmission matrix, as follows:

$$\left(\begin{array}{c}{E}_i\\ H_i\end{array}\right)=M_1{M}_2\cdots M_l\cdots M_{\gamma }\left(\begin{array}{c}{E}_o\\ H_o\end{array}\right)=\left[\begin{array}{cc}{m}_{11}& m_{12}\\ m_{21}& m_{22}\end{array}\right]\left(\begin{array}{c}{E}_o\\ H_o\end{array}\right),$$

(7)

where the transmission matrix [m₁₁, m₁₂; m₂₁, m₂₂] can be derived by the product of all cell transmission matrices in the one-dimensional photonic crystal [44]. The transmission matrix of the ith layer is

$$M_l=\left[\begin{array}{cc}\cos {\phi }_l& -\frac{i}{{\eta }_l}\sin {\phi }_l\\ -i{\eta }_l\sin {\phi }_l& \cos {\phi }_l\end{array}\right],$$

(8)

where φ_l = 2πd_l(ε_l − sin²θ)/λ is the transmission phase and θ = 0° is the incident angle. The parameter of η_l = ε_l(ε₀/μ₀)^1/2/(ε_l − sin²θ)^1/2 is the light resistivity of each dielectric layer.

The transmission and reflection coefficients of light waves are derived by the following equations:

$$t=\frac{2{\eta }_0}{(m_{11}+m_{12}{\eta }_o){\eta }_0+(m_{21}+m_{22}{\eta }_o)}$$

(9)

and

$$r=\frac{\left(m_{11}+m_{12}{\eta }_o\right){\eta }_0-\left(m_{21}+m_{22}{\eta }_o\right)}{\left(m_{11}+m_{12}{\eta }_o\right){\eta }_0+\left(m_{21}+m_{22}{\eta }_o\right)},$$

(10)

where the light resistivity at the outputting port is η_o = η₀ = (ε₀μ₀)^1/2. The transmittance and reflectance of light waves are given by T = tt* and R = rr*, respectively.

3. Optical Bistability in All-Superconducting Photonic Crystal

It is well known that the periodic photonic crystal supports photonic bandgaps in the wave-vector space and a defect mode may arise in the bandgap in the defective photonic crystal. The defect mode is a transmission mode, of which the maximum transmittance can reach up to 1 by ignoring the material loss.

The dielectric constants of superconductors are highly dependent on environment temperature, so the transmission properties can be easily changed by modulating temperature. Figure 2a demonstrates the different transmission spectra of light waves for the three values of environment temperature T_em = 105, 120, and 135 K. The horizontal coordinate (ω − ω₀)/ω_gap represents the normalized frequency and the theory bandwidth of periodic photonic crystal is ω_gap = 4ω₀arcsin|(n_A0 − n_B0)/(n_A0 + n_B0)|²/π, where ω = 2πc/λ is the angular frequency of incident light wave and the central frequency is denoted by ω₀ = 2πc/λ_c0. The symbols λ and λ_c0, respectively, express the incident light wave wavelength and the central light wave wavelength. The vertical coordinate T represents transmittance of light waves and is derived by the transmission matrix method (TMM) [9,10].

The five-pointed stars indicate the location of the defect mode with a transmittance of 1 at environment temperature T_em = 105, 120, and 135 K, respectively. For environment temperature T_em = 120 K, one can see that the defect mode denoted by a five-pointed star appears at the zero point of the horizontal coordinate (ω − ω₀)/ω_gap = 0. The corresponding wavelength is λ_c0 = 1.55 μm. For the lower temperature T_em = 105 K, the defect mode also arises in the photonic bandgap of the spectrum, and the central wavelength of the defect mode undergoes a blue shift compared with the case of T_em = 120 K. On the other hand, the defect mode is red-shifted as temperature is turned up to a higher value of T_em = 135 K. The permittivity of the superconductor decreases with the increase in environment temperature. For a fixed thickness of defect, the central wavelength therefore decreases based on the relation λ_c0 = 4d_A0n_A0 by turning down environment temperature.

To further demonstrate the profile of the photonic bandgap and the defect mode, Figure 2b gives the transmittance in the parameter space of environmental temperature and the normalized frequency. The dark blue bulk area at the center of the parameter space represents the photonic bandgap, with the defect mode indicated by an arrow located at its center. The arrows indicate the direction of the defect mode. As temperature increases, the bandgap widens and shifts towards lower frequencies. The light fringe, i.e., the defect mode, becomes narrower with increasing environmental temperature. This indicates a decrease in the resonant peak width of the defect mode.

Figure 2c plots the quality factor Q of the defect mode changing with environmental temperature. The quality factor Q is defined as Q = 1/(ω_p − ω_h), where ω_p is the according frequency of resonance and ω_h is the corresponding frequency of the half peak point of the resonant peak. For environmental temperature Tem = 90 K, the corresponding quality factor of the defect mode is ruled as Q = 1, so for other temperature values, the relative quality factor is denoted by Q/Q_Tem=90K. The quality factor increases with the increase in environmental temperature, as the value is located in the interval of (90 K, 130 K), while for T_em = 140 K, the corresponding quality factor dips slightly in comparison with the case value of T_em = 130 K. The difference |n_A − n_B0| enlarges as environmental temperature rises, which results in the stronger resonance. On the other hand, the two thicknesses and refractive indices of dielectrics A and B cannot satisfy the requirement of a quarter optical wavelength, and this mismatch becomes worse as environment temperature increases. This mismatch of thicknesses and refractive indices leads to a slight decrease in the quality factor for T_em = 140 K.

The defect mode is a longitudinal mode and the mode field power is mainly restricted in the defect layer. Figure 3a shows the intensity distribution of electric field E_z along the Z-axis. The maximum amplitude of electric field can reach up to 2.6 × 10⁷ V/m at the interface of the defect layers, which is simulated by finite-different time-domain (FDTD). The electric field power is located in the defect and the intensity rapidly decays as the coordinate parameter extends from the center zero to both sides.

To further verify these results, we simultaneously adopt the transmission matrix method (TMM), and the normalized Z-component electric field intensity varying with the Z-axis is depicted in Figure 3b. The sign of the red star labels the maximum point of the electric field intensity |E_z|, and the red line represents the graphene embedded at the interface of the two central layers AA. Consequently, the composite system can be denoted as ABABABAGABABABA. The third-order nonlinearity of graphene is proportional to the local electric field intensity; thus, the Kerr effect can be greatly enhanced by the localization of the electric field of the defect mode. Low-threshold optical bistablility may subsequently be induced based on the Kerr effect, i.e., the third-order nonlinearity of graphene.

For different periodic numbers of the defective photonic crystal, Figure 4a describes the transmittance of light waves changing with frequency. All of the defect modes, i.e., the transmission peaks labeled by the dashed box, are at the zero point of normalized frequency for N = 3, 4, and 5. However, for N = 4 or 5, a boundary transmission mode is induced near the right boundary of the bandgap. The maximum transmittance is T = 1 for each defect mode, while the resonances of these transmission peaks are different.

To view these defect modes more clearly, we plot the profiles in the vicinity of resonances and zoom in locally, as shown in Figure 4b. One can see that the half-width of the resonant peak shrinks as the periodic number of the photonic crystal increases, which manifests as the resonance becoming stronger for the structure with a larger N. The photonic crystal can be viewed as a resonant cavity, of which the defect is equivalent to a cavity body. The finite periodic structure (AB)^N and (BA)^N equate to two reflectors of the resonant cavity. Since the system (AB)^NAA(BA)^N can be extended, the selectivity of longitudinal mode reflectance becomes better with increasing N. Consequently, the electric field localization of the defect mode could be greatly enhanced by adding the number of layers. The strong localization of the electric field may enhance the third-order nonlinearity of graphene. However, the frequent propagation forward and reflectivity back of light in the photonic crystal with a large periodic number may induce significant optical losses, which affects the transmittance of the defect mode. All things considered, we here choose N = 3, 4, and 5 as the system parameters to explore the optical properties.

A necessary but not sufficient condition is to require the incident light wavelength the be red-detuned to the defect mode. The resonant wavelength is λ = 1.55 μm for T_em = 120 K, as mentioned before; therefore, we set the incident wavelength to λ = 1.572 μm, which is red-detuned to λ = 1.55 μm. One can observe a transmission peak with negative gradient for T_em = 119 K, which manifests as one incident light intensity corresponding to three values of transmittance, as I_i is located between 32.66 TW/cm² and 112.33 TW/cm², resulting in three corresponding curves. The transmittance changes with the incident light intensity along with the bottom curve as I_i increases from 0 to 112.33 TW/cm², while the dependence of transmittance on the incident light intensity submits to the upper curve relation as I_i decreases from ∞ to 32.66 TW/cm². The middle curve with negative gradient does not exist in real physics, but this property indicates that optical bistability may be induced. For T_em = 120 K, the curve gradient of the transmission peak is also negative and optical bistability can result as well. However, no transmission peak with negative gradient can be found for T_em = 121 K, indicating that bistable phenomena cannot be derived in this case.

Figure 5b depicts the transmitted intensity of light waves changing with incident intensity of light waves for T_em = 119, 120, and 121 K. There is an S-shaped segment in each curve for T_em = 119 and 120 K. The negative curve segment does not actually exist in physics. In other words, one incident intensity of light corresponds two transmitted intensities, which is called the optical bistable phenomenon. For the case of T_em = 119 K, the transmitted intensity of light increases with the increase in the incident intensity of light, as the light intensity is weak and the transmitted intensity jumps upward at I_i = 112.33 TW/cm², which is defined as the upper threshold of optical bistability, while the transmitted intensity decreases by decreasing the incident intensity from a large value, and I_o abruptly decreases at I_i = 32.66 TW/cm², which is defined as the lower threshold of optical bistability. For T_em = 120 K, the profile of the S-shape shrinks and the upper and lower thresholds of optical bistability are lower than the corresponding values in the case of T_em = 119 K; meanwhile, the interval between the upper threshold and the lower threshold reduces. There is no S-shaped segment in the input–output relationship curve for T_em = 121 K, indicating that optical bistability cannot be induced in this case.

Temperature can influence the wavelength of the defect mode, and the equivalent refractive index of graphene is governed by the local electric field; the optical intensity of light is strong enough, so the transmitted light intensity is a function of temperature and incident intensity considering the third-order nonlinearity of graphene for a strong incident light wave. Figure 5c gives the transmitted intensity varying with the incident intensity by changing temperature simultaneously. One can see that the S-shaped curve arises as the environmental temperature decreases and the profile of the S-shape appears more and more obviously by lowering environment temperature.

Figure 5d demonstrates the modulation of the upper and lower thresholds of optical bistability through changing environment temperature. The thresholds of optical bistability decrease with the increase in environment temperature. The interval between the upper and lower thresholds shrinks as temperature rises, and the optical bistability phenomenon disappears as environmental temperature T_em > 120.1 K.

As the environmental temperature is fixed, there is a cluster of input–output relationship curves for different incident wavelengths. Figure 6a gives the transmitted optical intensity of light waves while changing incident light intensity for λ = 1.568, 1.57, 1.572, and 1.574 μm. The environment temperature is set as T_em = 120 K and the periodic number is N = 3; in this case, the resonant wavelength of the defect mode is λ = 1.55 μm. One can see that there is no S-shaped segment in the input–output relationship curve for λ = 1.568 μm, which is red-detuned to the resonant wavelength. By increasing the incident wavelength, the detuning is larger and the S-shaped profile becomes more obvious.

The S-shaped profile moves right by turning up the incident wavelength, which demonstrates the threshold increase, and the interval between the upper and lower threshold rises, as shown in Figure 6b. It shows that optical bistability arises as λ > 1.5689 μm and the thresholds of optical bistability increase with the increase in the incident wavelength, so the generation of optical bistability and its thresholds are both modulated by changing the incident wavelength.

Lowering temperature to T_em = 119 K and keeping the value constant, Figure 6c plots a cluster of optical bistability curves for different incident wavelengths. For the incident wavelength λ = 1.556 μm, the relation between the transmitted intensity of light and the incident intensity is not bistable. Increasing the incident wavelength to λ = 1.558, 1.56, and 1.562 μm, there are S-shapes in the relationship curves of transmitted intensity of light and incident intensity. As the incident wavelength increases, the thresholds increase as well; meanwhile, the interval between the upper and lower thresholds also enlarges, of which these characteristics can be viewed in Figure 6d more evidently. Otherwise, it shows that the optical bistability arises while the incident wavelength is set as λ > 1.5571 μm for T_em = 119 K. This peculiarity manifests as the critical value of the incident wavelength for optical bistability changing with the environment temperature.

Figure 7a gives the transmitted intensity of light changing with the incident intensity of light for the periodic number N = 4. One can see that there is not optical bistability for the incident wavelength λ = 1.562 μm and optical bistability arises by increasing the incident wavelength to λ = 1.564, 1.566, and 1.568 μm. Compared with the case for N = 3, the layers of the structure have increased, so the localization of the electric field has also been enhanced. More layers for the system mean more transmissions forward and reflections back of the light beams, which leads to an increase in the optical loss, since graphene is passive. Therefore, the transmitted intensity of light for the system of N = 4 is lower by a magnitude compared to the light intensity of the case of N = 3.

Figure 7b describes the upper and lower thresholds of optical bistability changing the incident wavelength for N = 4. By increasing the incident wavelength, the optical bistability occurs as λ > 1.5641 μm, which is the critical value for the incident wavelength to trigger optical bistability for N = 4. The critical value λ = 1.5641 μm for N = 4 is lower than the critical value λ = 1.5689 μm for N = 3. This provides evidence that the localization of the electric field of N = 4 is stronger than that of N = 3 from another aspect. Otherwise, similar to the case of N = 3, the upper and lower thresholds, and the interval between the upper and lower thresholds, increase with the increase in the incident wavelength.

Previous works have concentrated on optical bistability at room temperature, or their systems are partially constructed by superconductors. We here combine full superconductors with graphene and investigate optical bistability in a cryogenic environment. Compared with the previous structures, the tunability of optical bistability in our system is superior through modulating the environment temperature.

We here induce optical bistability, utilizing electric field localization of longitudinal modes, while the propagating modes in optical fibers or wave-guides are transverse. The familiar optical NLEs, such as solitons and supermodes, can be realized in optical fibers or wave-guides, which results from the localization of the electric field of transverse modes [28,29,30,31,45,46,47,48].

One can explore topological photonics, unidirectional transmission, solitons, and supermodes in superconducting wave-guides or photonic crystals. Furthermore, metamaterials, such as hyperbolic metamaterials, can be composed of superconductors and other materials, and some singular optical effects may be induced in the systems.

4. Conclusions

In conclusion, optical bistability is explored in an all-superconducting photonic crystal and graphene combined system. Two superconductors are alternatively arrayed to form all-superconducting defect photonic crystals, with graphene embedded at the center in the cryogenic environment. A defect mode is induced in this composite system, wherein the central wavelength of the defect mode makes a blue shift as the environment temperature increases. The defect mode can greatly localize the electric field around the center, thereby tremendously enhancing the nonlinearity of graphene. The localization of the electric field could also be promoted by changing the environment temperature. Consequently, low-threshold optical bistability has been realized, since an incident light beam is sufficiently strong. The thresholds of optical bistability decrease with increasing environment temperature. By warming the structure, the interval between the upper and lower thresholds of optical bistability decrease as well, while for a fixed value of environment temperature, the bistability thresholds and the interval between the upper and lower thresholds increase with the increase in the incident wavelength. Otherwise, a larger critical incident wavelength to achieve optical bistability is needed for higher environment temperature. Additionally, by adding the periodic number of photonic crystals, the critical incident wavelength to trigger optical bistability increases. This exploration could find applications for temperature-controlled optical switches and sensors in a cryogenic environment.