1 Introduction

Today’s advanced technology requires high-resolution information transfer to meet many needs in modern life. All-optical devices play an important role in communication networks due to their high speed of operation, low losses, low signal distortions, and small size [1, 2]. Bandgap photonic crystals block the propagation of electromagnetic waves inside them. The photonic bandgap opens up new possibilities for manipulating the electromagnetic field and building high-speed integrated circuits [3]. Photonic crystals with two-dimensional 2D or three-dimensional 3D spatial periodic variations of the dielectric constant on the order of one optical wavelength are very interesting for controlling field radiation characteristics and light propagation.

Photonic crystals can be used to realize many optical components, such as filters [4,5,6,7], demultiplexers [8,9,10,11], logic gates [12,13,14], encoders [15, 16], adders [17, 18], decoders [19,20,21,22,23] and analog/digital converters [24, 25], unidirectional absorption (1D) PPCs [26], (1D) GPCs [27], (1D) superconducting photonic crystals (SPCs) [27], and (3D) nonlinear plasma photonic crystals (PPCs) [28].

Optical decoders are necessary components in optical logic circuits and optical signal processing systems for their ability to control the output ports based on the state of the input ports. Recently, several all-optical decoders have been realized, and the optical switch is a critical component to control the output signal via the input signals using the nonlinear Kerr effect in photonic crystals [2, 3, 21]. Farhad Mehdizadeh et al. [29] proposed a new structure for an all-optical decoder. They used a nonlinear switch with 4 output ports and a power divider, and the optical intensity applied to the structure to ensure proper operation is around 20 w/µm2. Various decoders have been designed using nonlinear ring resonators [1, 2, 30, 31]. T-Daghooghi and Al [2] proposed a 2 × 4 decoder based on nonlinear resonators with a switching intensity threshold of 13 w/µm2. In another work, Alidoost Rostamizadeh and Al [1] have cascaded 3 nonlinear optical switches to realize a 2 × 4 decoder with a switching threshold of 15 w/µm2. Saeid Salimzadeh and Hamed Alipour-Banaei [31] used nonlinear ring resonators to realize a 3 × 8 decoder. In [20], the authors designed an all-optical 1 × 2 decoder based on triangular lattice photonic crystals. They used linear and point defects to control the light.

In this paper, we propose a 3 × 8 all-optical photonic crystal decoder based on nonlinear ring resonators. The proposed structure is composed of a nonlinear demultiplexer and a combiner to combine the intensities of the different input ports. In our work, we used Comsol Multiphysics to perform the necessary simulations, which is based on the FEM finite-element method [9]. The rest of the paper is organized as follows: in the next section, we will present the design process of the decoder. In the third section, we will present the simulation results, and then we will end with a conclusion in the last section.

2 Decoder design process

For the design of 3 × 8 decoder, we used the ring resonator used in the article [8]. The latter is used to build a nonlinear demultiplexer and has the same form as the demultiplexer proposed in [8] which has the role of a switch to perform the routing and switching of signals between different channels. In this work, we have applied modifications on the resonant part, so we have made a change on the radius of the rod that is located at the center of the resonator rci. The switch is made up of 54 × 23 GaAs rods embedded in the area, each with a grating constant of a = 610 nm, a rod radius of r = 120 nm, a linear refractive index of n0 = 3.37, and a nonlinear Kerr coefficient of 1.6 × 10–17 m2/w.

The photonic band diagram of our structure in TE mode is presented in Fig. 1. It can be noticed that there are two photonic bandgaps: the first one is between 0.3 < a/λ < 0.425 and the second one is between 0.725 < a/λ < 0.75, which correspond to 1435.3 nm < λ < 2033.33 nm and 813.33 nm < λ < 841.37 nm, respectively. The wavelength range of the structure encompasses a wide range of optical communication.

Fig. 1
figure 1

Photonic bandgap of the proposed structure in TE mode with square lattice

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As shown in Fig. 2, the switch is composed of an input port A, 8 outputs ports Si, a waveguide BUS and 8 waveguides DROP that are coupled with the first one by 8 resonators Ri. Each of them has a unique internal rod radius rci that is proportional to the intensity applied to the switch, where: rc1 = 366.105 nm; rc2 = 365.86 nm; rc3 = 365.58 nm; rc4 = 365.37 nm; rc5 = 365.1 nm; rc6 = 364.86 nm; rc7 = 364.62 nm; rc8 = 364.37 nm correspond to the output ports Si, with i = 1…8.

Fig. 2
figure 2

The optical switch structure based on nonlinear ring resonators

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As can be seen from Fig. 2, the basis for designing a switch with 8-output ports is to design 8 ring resonators, each of which has different geometric properties from the other to specify its resonance wavelength, as already mentioned in the article [8]. Therefore, we obtained these values of inner radius of each resonator from a parametric study, and it is necessary that these values result in a uniform spacing between the resonance wavelengths, because in the rest of our work, we will excite the switch by a wavelength equal to 1.55 µm with different intensities, and the difference between them is uniform with a step of 150 w/µm2. It is worth mentioning that each time we change the input intensity, the output port changes.

Resonators R1…R8 resonate according to the amount of intensity applied to the switch input, i.e., changing the input intensity changes the wavelength output due to dielectric nonlinearity, in general, n = n0 + n1I which defines by the Kerr effect, such that n0, n1 are, respectively, the linear refractive index and the nonlinear Kerr coefficient, and I is the input signal intensity [32].

Before finalizing the final decoder structure, a very important structure for the correct operation of the decoder is the combiner. This is designed on the basis of GaAs linear dielectric rods with the same geometrical switch parameters. The combiner has one excitation port E and three input ports A1, A2, and A3.

The combiner structure is composed of 3 splitters and 3 OR logic gates. The first logic gate is between port E and A3, the second logic gate is between the waveguide coming from port A1 and A2, and the third logic gate is between port A1 and A2 as shown in Fig. 3.

Fig. 3
figure 3

Optical combiner used in the proposed decoder

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We used 2 splitters at port A1 to divide the input power over 4, and we used a single splitter at port A2 to divide the power over 2. We use the splitters to avoid power level similarity at the output of the combiner because, in the absence of this device, we will have the cases:(E = 1, A1 = 1, A2 = 0, A3 = 0) = (E = 1, A1 = 0, A2 = 1, A3 = 0) = (E = 1, A1 = 1, A2 = 0, A3 = 1), where “1” indicates the activated port and “0” indicates the disabling port. In the regions D1, D2, D3, we added three rods of radius rr = 42.7 nm to guide the maximum power to the combiner output, as shown in Fig. 3.

The final proposed 3 × 8 decoder scheme is depicted in Fig. 4. We can notice that the final structure is a fusion of a switch and a mixer to obtain a decoder with 3 inputs and 8 outputs.

Fig. 4
figure 4

The final structure of the proposed 3 × 8 decoder

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3 Simulation results and discussion

The proposed final decoder structure was simulated in TE mode using COMSOL Multiphysics software, which is based on the finite-element method FEM. First, we started with the simulation of a nonlinear demultiplexer, then we injected a range of wavelengths [1.5422–1.5525 µm] on the input of the latter with an intensity of 100 w/µm2. Figure 5 shows the simulation result of nonlinear DEMUX, we obtained 8 resonance wavelengths λ1 = 1.55 µm, λ2 = 1.549 µm, λ3 = 1.548 µm, λ4 = 1.547 µm, λ5 = 1.546 µm, λ6 = 1.545 µm, λ7 = 1.544 µm, λ8 = 1. 543 µm and a normalized transmission efficiency of 97.5%, 96%, 93%, 90.5%, 88%, 99%, 96.5%, 99% for the output ports S1…8, respectively, which confirms the good performance of the resonators at wavelength separation. Table 1 summarizes the demultiplexer results.

Fig. 5
figure 5

Output spectra of nonlinear demultiplexer

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Table 1 The demultiplexer results
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From Table 1 and Fig. 5, we can notice that the demultiplexer works properly, and has very good results, such as the transmission efficiency is high and between 88%, 99%, and the spacing between channels or between output spectra being uniform, its value is 1 nm, which responds to the power variation applied on the nonlinear demultiplexer, and during the course of a switch test, we will change the intensity by step of 150 w/µm2.

In the second step, we test the switch by the wavelength 1.55 µm, and we notice that there is an intensity variation in the input port of the switch. Therefore, we have 100 w/µm2 injected to the switch when all the input port of the combiner are all disable, and when the combiner’s input ports are (A1 = 1, A2 = 0, A3 = 0), (A1 = 0, A2 = 1, A3 = 0), (A1 = 1, A2 = 1, A3 = 0), (A1 = 0, A2 = 0, A3 = 1), (A1 = 1, A2 = 0, A3 = 1), (A1 = 0, A2 = 1, A3 = 1), (A1 = 1, A2 = 1, A3 = 1), the power injected to the switch are 250 w/µm2, 400 w/µm2, 550 w/µm2, 700 w/µm2, 850 w/µm2, 1000 w/µm2, and 1150 w/µm2, respectively.

From Fig. 6a–h, it can be seen that each time the input intensity is changed, only one output port will be active, and the wave will shift from one port to another due to the nonlinearity of the material, such that the refractive index depends on the intensity and depends on the following formula n = n0 + n1I. The transmission coefficients are: 99%, 94.7%, 94.9%, 87%, 90%, 94%, 92%, and 93.9%, for ports S1…S8, respectively. The insertion loss and maximum cross talk of the output ports are calculated using the following formulas, respectively: 10log (Pin/Pout), 10log ((Plow)/Phigh) [29]. Such that the insertion loss values are between − 0.043 and − 0.6 dB, and the maximum cross talk is between − 7.96 and − 14.62 dB. The switch simulation results are presented in Table 2.

Fig. 6
figure 6figure 6

Distribution of the optical waves inside the nonlinear demultiplexer with different input intensities. a I = 100 w/µm2, b I = 250 w/µm2, c I = 400 w/µm2, d I = 550 w/µm2, e I = 700 w/µm2, f I = 850 w/µm2, g I = 1000 w/µm2, h I = 1150 w/µm2

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Table 2 The switch simulation results
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Finally, we simulate the final 3 × 8 decoder structure. The wavelength 1.55 µm injected into the input ports for our structure to be activated. We excited the E port by an intensity of 100 w/µm2 and the other input ports by an intensity of 600 w/µm2. The test of this decoder passes through 8 cases with different power levels in order not to collide with similar cases. In each case, the excitation port will be activated, and the power level that reaches the switch port will be changed proportionally to the changes in the input port state. As a result, we can observe that the wave changes the output port that will take it because of the effect of nonlinearity.

The wave applied on the decoder couples with a single resonator and will be guided to the waveguide DROP that is connected with this resonator to activate the desired port Si. Our device will be activated when we activate the excitation port E even if the other input ports are deactivated (an active port is in logical state 1, and a deactivated port is in logical state 0). Figures 7, 8, 9, 10, 11, 12, 13, and 14 represent the simulation results of our structure.

Fig. 7
figure 7

Distribution of the optical wave for E = 1, A1 = A2 = A3 = 0. Case 1: (E is ON, A1, A2, A3 are OFF) = > S1 is ON

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Fig. 8
figure 8

Distribution of the optical wave for E = A1 = 1, A2 = A3 = 0. Case 2: (E, A1 are ON, A2, A3 are OFF) = > S2 is ON

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Fig. 9
figure 9

Distribution of the optical wave for E = A2 = 1, A1 = A3 = 0. Case 3: (E, A2 are ON, A1, A3 are OFF) = > S3 is ON

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Fig. 10
figure 10

Distribution of the optical wave for E = A1 = A2 = 1, A3 = 0. Case 4: (E, A1, A2 are ON, A3 are OFF) = > S4 is ON

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Fig. 11
figure 11

Distribution of the optical wave for E = A3 = 1, A1 = A2 = 0. Case 5: (E, A3 are ON, A1, A2 are OFF) =  > S5 is ON

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Fig. 12
figure 12

Distribution of the optical wave for E = A1 = A3 = 1, A2 = 0. Case 6: (E, A1, A3 are ON, A2 is OFF) = > S6 is ON

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Fig. 13
figure 13

Distribution of the optical wave for E = A2 = A3 = 1, A1 = 0. Case 7: (E, A2, A3 are ON A1 is OFF) = > S7 is ON

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Fig. 14
figure 14

Distribution of the optical wave for E = A1 = A2 = A3 = 1. Case 8: (E, A1, A2, A3 are ON) = > S8 is ON

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In the first case, port E is activated while the other ports A1, A2, and A3 are deactivated, resulting in an intensity of 100 w/µm2 at the switch input. The optical wave is propagated and coupled with the resonator R1, then exits to port S1, which will be activated and the other output ports will be deactivated. Therefore, when (E = 1, A1 = A2 = A3 = 0) = > (S1 = 1, S2…8 = 0).

In the second case, we turn on port A1 and leave A2 and A3 off, the intensity that is injected into A1 will be divided on 2, twice successively, to result in a power of about 150 w/µm2 which will combine with the intensity from port E (100 w/µm2). Therefore, we get an intensity of 250 w/µm2 at the switch input, in this case, the resonator R2 will be resonated and the port S2 will be activated. When (E = A1 = 1, A2 = A3 = 0) = > (S2 = 1, S1 = S3…8 = 0).

In the third case, port A2 is switched on and ports A1 and A3 stay off, this time the intensity is divided by 2. Therefore, we will combine an intensity level equal to 300 w/µm2 with the intensity coming from port E, which results in an intensity of 400 w/µm2 at the switch. The resonator R3 will be resonated, and the port S3 will turn to an activated state. In other words, when (E = A2 = 1, A1 = A3 = 0) = > (S3 = 1, S1 = S2 = S4…8 = 0).

Fourth case, we activate A1, A2, and A3 port is deactivated, and the intensity reaching the switch input is 550 w/µm2 (100 w/µm2 + 150 w/µm2 + 300 w/µm2). The optical wave will reach the resonator R4 and then propagate to the port S4 to activate it. (E = A1 = A2 = 1, A3 = 0) = > (S4 = 1, S1,2,3 = S5…8 = 0).

Fifth case, we activate A3 and deactivate A1 and A2. The intensity injected at port A3 will not split and will combine with the intensity injected at port E, so we get a power of 700 w/µm2 at the switch input. The resonator R5 will resonate and direct the wave to the port S5, so this last one will be activated while the others are turned off. (E = A3 = 1, A1 = A3 = 0) = > (S5 = 1, S1…4 = S6,7,8 = 0).

Sixth case, ports A1 and A3 are activated, A2 is deactivated, and the power intensity that will arrive at the switch input is 850 w/µm2 (100 w/µm2 + 150 w/µm2 + 600 w/µm2). The wave will fall on the resonator R6, so the port S6 will be activated. (E = A1 = A3 = 1, A2 = 0) = > (S6 = 1, S1…5 = S7,8 = 0).

In the seventh case, when A2 and A3 are switched on, and A1 is switched off, we obtain an intensity at the switch level equal to 1000 w/µm2 (100 w/µm2 + 300 w/µm2 + 600 w/µm2). In this case, the resonator R7 will guide the light wave to the port S7 to activate it. (E = A2 = A3 = 1, A1 = 0) = > (S7 = 1, S1…6 = S8 = 0).

The last test, we activate all the input ports (A1, A2, A3). The power that will arrive at the input of switch is 1150 w/µm2 (100 w/µm2 + 150 w/µm2 + 300 w/µm2 + 600 w/µm2). The wave will propagate to the port S8 via the resonator R8. (E = A1 = A2 = A3 = 1) = > (S8 = 1, S1…7 = 0).

Table 3 shows the logical state of the decoder.

Table 3 The logical state of the 3 × 8 decoder
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Table 4 presents a comparison of the proposed decoder with other previously proposed decoders.

Table 4 Comparison of the proposed decoder with other previously proposed decoders
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Many 2 × 4 decoders have been realized in the literature [22, 29], and [33], but there have been few works on the design of a 3 × 8 decoder. Table 3 shows that in [31, 34], the authors designed a 3 × 8 decoder based on photonic crystals working around 1.55 m. Our 3 × 8 decoder, about 682.64 µm2, smaller than the decoder size proposed in [34], works at the third window of telecommunications 1.55 µm, so it can be used in the next all-optical application.

4 Conclusion

In this paper, we present and discuss the design steps and simulation results of an all-optical 3 × 8 decoder. The final structure is composed of a combiner and an optical switch. The switch is realized by combining 8 nonlinear resonators. Since the resonance wavelength of the resonator is very sensitive to the refractive index of the dielectric rods, and the refractive index of the dielectric materials depends on the optical power intensity, we controlled the switch behavior via the optical power intensity. The wavelength switching is done by changing the power intensity by a step of 150 w/µm2. The insertion loss is between 0.043 and 0.6 dB, and the maximum crosstalk is between − 7.96 and − 14.62 dB. The final structure has good potential to be used in optical communication systems.