1. Introduction

Picosecond optical switching devices are required in photonic switching nodes and various optical devices have been studied, which include all-optical devices [1,2]. The authors have studied on all-optical wavelength-selective switches, where switching is controlled by amplifying the optical guided wave with Raman amplifiers placed in the waveguides of the switch [3, 4]. The switch, however, requires waveguide-type efficient crystalline Raman amplifiers [5, 6]. In this paper, we propose to introduce graphene films for controlling the optical amplitudes with the similar switch architecture.

Graphene films have been extensively studied for applications to electronics and optics fields [7,8]. In the field of optics, the graphene films show excellent saturable absorption characteristics in the optical communication wavelength range, which have been applied to short pulse fiber lasers [9–11]. Graphene films have large dynamic range of absorption change controlled by incident optical intensity at picosecond response time.

In this paper, we propose an all-optical switch using saturable absorption of graphene. We discuss the switching characteristics using reported experimental data on saturable absorption by Bao et al. [12]. Picosecond response can be expected for the saturable absorption in graphene [13]. It is found that complete switching can be achieved by controlling the optical wave using nonlinear saturable absorption. The switching characteristics are theoretically analyzed and verified by FD-BPM simulation.

2. Switching by amplitude control

First, we consider an optical switch operated by controlling optical amplitude of the signal. Although most conventional switches are operated by controlling optical phase of the signal through refractive-index change, we consider optical amplitude controlled by control light through optical nonlinearity because such nonlinearity can be realized with saturable absorption of graphene. Kishikawa et al. proposed a switch architecture controlled by waveguide-type Raman amplifiers as shown in Fig. 1 [3, 4].

 

Fig. 1 Optical switch operated by controlling the gain of Raman amplifiers.

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The device consists of two cascaded interferometers whose couplers are asymmetric X-junction couplers [14–16]. The asymmetric X-junction coupler can provide 3-dB coupling over a wider wavelength range compared to a 3-dB directional coupler [4]. Waveguide-type Raman amplifiers are employed in both arms of the first interferometer. A fixed attenuator β_fix is employed in one of the arms of the second interferometer. The amplifications of the Raman amplifiers are controlled by control light having different polarization from the incident optical signal. The control light is coupled in and out with polarization beam splitters (PBSs).

The asymmetric X-junction coupler consists of three kinds of waveguides with the width of W₀, W_n, and W_w (W_n < W₀ < W_w) with small crossing angle [16, 17]. The three asymmetric X-junction couplers are aligned so that the path lengths of the two arms in each interferometer be equal. Optical electric fields of the input and output waves in the left-hand-side coupler is written as

The output fields through the switch are related to the input fields as

Therefore, amplification of the amplitude coefficient of $1+\sqrt{2}=2.414$ is required for switching. When the amplifier of α_A is amplified by 2.414 with control light, the incident light at port A_in is switched to output port A_out, whereas α_B is amplified, instead of α_A, the signal is switched to output port B_out.

Now, we consider the switching mechanism with the above switching conditions. The optical fields A_m and B_m just after the first interferometer are given by

By substituting the switching conditions given by Eqs.(5) and (6), we have the following outputs:

By attenuating the amplitude B_m with the fixed attenuator β_fix, we have the following outputs:

Thus, the optical waves incident to the third asymmetric X-junction coupler are optical waves (i) in phase and (ii) in opposite phase, with the same amplitude. Therefore, the output fields show complete switching between the two output ports as given by Eqs.(5) and (6). It is noted that the switching is performed only by controlling the optical amplitudes.

In the next step, we consider inserting an attenuator β_fix0 in front of both Raman amplifiers. The output given by Eq.(4) is now rewritten as

If β_fix0α_A ≤ 1 for ${\alpha }_A=1+\sqrt{2}$, and β_fix0α_B ≤ 1 for ${\alpha }_B=1+\sqrt{2}$, the switching can be realized with only attenuator whose attenuation coefficient should be controlled from β_fix0 to β_fix0α_A or β_fix0α_B. In the next section, we discuss how such attenuator is realized by saturable absorber.

3. Modeling of saturable absorption of monolayer graphene

We consider a sheet of monolayer graphene placed perpendicularly to the optical path as shown in Fig. 2(a). Based on an experimental result by Bao et al. [12], the transmittance T of the monolayer graphene is varied as a function of the input optical intensity as schematically illustrated in Fig. 3.

 

Fig. 2 Modeling of a sheet of monolayer graphene; (a) signal and control light perpendicularly incident to graphene, and (b) model of cascade connection of attenuator and amplifier.

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Fig. 3 Optical transmittance as a function of optical incident intensity for saturable absorption in monolayer graphene.

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When optical incident signal is weak with intensity P_s,in, graphene film shows a low transmittance $T_{\mathit{low}}^{(1)}$. By adding intense control light with intensity P_c,in, where wavelength or polarization is assumed to be different from that of the signal light, the trasmittance increases to $T_{\mathit{high}}^{(1)}$ due to saturable absorption phenomena. The transmission coefficients for optical amplitude corresponding to the transmittance $T_{\mathit{low}}^{(1)}$ and $T_{\mathit{high}}^{(1)}$ are given by $t_{\mathit{low}}^{(1)}=\sqrt{T_{\mathit{low}}^{(1)}}$ and $t_{\mathit{high}}^{(1)}=\sqrt{T_{\mathit{high}}^{(1)}}$, respectively. The optical saturable absorption of a sheet of monolayer graphene can be modeled as a cascade connection of an attenuator having transmission coefficient $t_{\mathit{low}}^{(1)}$ and an amplifier having amplitude amplification coefficient α⁽¹⁾ as shown in Fig. 2(b). The amplification coefficient is α⁽¹⁾ = 1 without control light, whereas ${\alpha }^{(1)}=t_{\mathit{high}}^{(1)}/t_{\mathit{low}}^{(1)}$ with control light.

From the reported experimental result [12], we find $T_{\mathit{low}}^{(1)}=0.309$ and $T_{\mathit{high}}^{(1)}=0.8$ for light peak power of 3 mW/μm² and 10 mW/μm², respectively. Therefore, we obtain $t_{\mathit{low}}^{(1)}=0.556$ and ${\alpha }^{(1)}=t_{\mathit{high}}^{(1)}/t_{\mathit{low}}^{(1)}=\sqrt{0.8/0.309}=1.608$. This value α⁽¹⁾ is smaller than the value α = 2.414 required for switching as discussed in the previous section.

Next, we consider saturable absorption through two-stage monolayer graphene as shown in Fig. 4(a). The reason why two-stage monolayer graphene is considered instead of two-layer graphene is because selected fabrication of two-layer graphene over a wide area is considered to be not easy. Saturable absorption experiments have been reported only for monolayer graphene or graphene of a few layer structure including one to four, for example [12]. From the viewpoint of time response, monolayer graphene may be preferable because carrier lifetime may be shorter in monolayer graphene than that in multilayer graphene [12]. Therefore, we adopt two-stage monolayer graphene to evaluate the saturable absorption by using reported experimental data. Although absorption through two sheets of graphene for the signal light is larger than that of a single sheet of graphene, the amplitude of the optical signal can be controlled over a larger dynamic range. The incident signal light is attenuated through the first-stage graphene to $P_{s,\mathit{out}}^{(1)}=T_{\mathit{low}}^{(1)}{P}_{s,\mathit{in}}$ without control light. This signal light is then incident to the second-stage graphene. When the signal light is weak enough, the transmittance $T_{\mathit{low}}^{(2)}$ of the second-stage graphene for $P_{s,\mathit{out}}^{(1)}$ is considered to be approximated as $T_{\mathit{low}}^{(1)}\simeq T_{\mathit{low}}^{(2)}$. [18]. Therefore, the signal light is further attenuated to $P_{s,\mathit{out}}^{(2)}=T_{\mathit{low}}^{(1)}{T}_{\mathit{low}}^{(2)}{P}_{s,\mathit{in}}\simeq {\left(T_{\mathit{low}}^{(1)}\right)}^2{P}_{s,\mathit{in}}$.

 

Fig. 4 Modeling of two sheets of monolayer graphene; (a) signal and control light perpendicularly incident to graphene, and (b) model of cascade connection of attenuators and amplifiers.

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Now, we add control light with intensity P_c,in. The control light is attenuated to $P_{c,\mathit{out}}^{(1)}=T_{\mathit{high}}^{(1)}{P}_{c,\mathit{in}}$ through the first-stage graphene. The transmittance of the second-stage graphene for the incident light $P_{s,\mathit{out}}^{(1)}+P_{c,\mathit{out}}^{(1)}$ is decreased to $T_{\mathit{high}}^{(2)}$. Then the transmission coefficient for amplitude of the second-stage graphene is $t_{\mathit{high}}^{(2)}=\sqrt{T_{\mathit{high}}^{(2)}}$. The second-stage graphene can be modeled as a cascade connection of an attenuator having transmission coefficient $t_{\mathit{low}}^{(1)}$ and an amplifier having amplitude amplification coefficient α⁽²⁾ as shown in Fig. 4(b). The amplification coefficient is α⁽²⁾ = 1 without control light, whereas ${\alpha }^{(2)}=t_{\mathit{high}}^{(2)}/t_{\mathit{low}}^{(2)}\simeq t_{\mathit{high}}^{(2)}/t_{\mathit{low}}^{(1)}$ with control light.

From the reported experimental result [12], we find $P_{s,\mathit{out}}^{(1)}+P_{c,\mathit{out}}^{(1)}=T_{\mathit{high}}^{(1)}\left(P_{s,\mathit{in}}+P_{c,\mathit{in}}\right)=8\text{mW}/\mu {\text{m}}^2$ for P_s,in + P_c.in=10 mW/μm², and then $t_{\mathit{high}}^{(2)}/t_{\mathit{low}}^{(1)}\simeq \sqrt{0.75/0.309}\simeq 1.558$. As the result, the two-stage graphene is regarded as a cascade connection of an attenuator having transmission coefficient ${\left(t_{\mathit{low}}^{(1)}\right)}^2={0.556}^2=0.309$ and an amplifier having amplitude amplification coefficient α = α⁽¹⁾α⁽²⁾, where α = 1 and α = 1.608 × 1.558 = 2.505 without and with control light, respectively.

Optical switch architecture containing two-stage graphene in both arms of the first interferometer is shown in Fig. 5. Although amplification of the amplitude coefficient of 2.414 is required for switching, the two-stage graphene films can provide α = α⁽¹⁾α⁽²⁾ = 2.505 from the experimentally reported data. Therefore, a control power of 10mW/μm² is considered to be a little too large for switching. Although the switching is accompanied by an insertion loss of ${\left(t_{\mathit{low}}^{(1)}\right)}^2$, complete switching can be achieved. When ${\left(t_{\mathit{low}}^{(1)}\right)}^2=0.309$, the insertion loss is calculated to be −10log0.309²=10.2(dB).

 

Fig. 5 Switch architecture consisting of two-stage interferometers having two-stage monolayer graphene in both arms in the first interferometer.

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In fabrication of the structure of vertically inserted graphene in the optical waveguides, a thin film with monolayer graphene on both sides can be inserted in a narrow gap formed with a dicing saw and fixed with epoxy adhesive [19, 20]. To reduce the radiation loss, the gap should be as narrow as possible, for example, a few tens micrometers. The supporting thin film for graphene sheets can be a polyimid film [20].

4. FD-BPM simulation

The switching operation is numerically simulated by FD-BPM. We consider a two-dimensional slab waveguide model. The core and cladding regions have refractive indices of n_c = 1.461 and n_s = 1.45, respectively. The waveguide widths of the fundamental, narrow and wide waveguides of the asymmetric X-junctions are W₀ = 3.0μm, W_n = 2.6 μm and W_w = 3.4 μm, respectively. Optical waves are assumed to be TE mode. The lengths of the X-junction coupler and the parallel waveguides are L_x = 16mm and L_p = 1mm, respectively. The total length is 50 mm. The distance of the input ports is D = 23 μm. The total length can be shortened by employing curved waveguides.

The switching operation at λ = 1550nm is confirmed as shown in Fig. 6, where squared electric fields |E|² are plotted. In the simulation, amplification is equivalently simulated just by increasing the electric field by multiplying the gain coefficient α_i at a plane located at the end of the waveguide region for the arms containing graphene sheets. Therefore, in the simulation, the optical waveguides denoted by dotted lines in Fig. 5 for coupling the control light were not modeled. In an actual device, the control light can be coupled using polarization depending coupler when the control light is assumed to propagate in TM mode. In a similar manner, the attenuator is modeled by multiplying the electric field by ${\left(t_{\mathit{low}}^{(1)}\right)}^2$ at the end of the arms containing graphene sheets or β_fix at the beginning of the attenuators. The normalized out-put intensities are summarized in Table I, where analytical results discussed in section 2 are also shown. Extinction ratio in switching is found to be 24.7 dB and 24.6 dB for switching to B_out and A_out, respectively, for the simulated result. The simulated results agree well with the analysis with the ideal model.

Table 1. Comparison of optical output intensities between theoretical analysis and smula-tion.

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Fig. 6 Optical intensities along the switch obtained by FD-BPM simulation: (a) switched to output port B_out by inserting control light to lower arm (α_A = 1, ${\alpha }_B=1+\sqrt{2}$) and (b) switched to output port A_out by inserting control light to upper arm ( ${\alpha }_A=1+\sqrt{2}$, α_B = 1).

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5. Conclusion

An all-optical switch using saturable absorption of graphene was proposed. Since only attenuation is used in controlling the guided wave, an insertion loss of 10.2 dB is inevitable. However, complete switching between the two output ports can be achieved. The switching can be as fast as picosecond-order response because of the fast response of saturable absorption in graphene. Although the graphene sheets have to be inserted in the waveguides, an all optical switch can be fabricated with a variety of materials such as silica glass, silicon and LiNbO₃. From the viewpoint of fabrication process, graphene loaded waveguide is preferable compared to the waveguide with parpendicularly inserted graphene since graphene insertion in the waveguide cross-section is technically more difficult than forming loaded graphene on the waveguide. Also, inserting graphene perpendicularly in the optical waveguide may suffer from excess loss due to radiation at the waveguide gap. We will experimentally measure saturable absorption in detail with these two kinds of waveguides including graphene film to realize the proposed switch device.