Nowadays, miniaturized optical integrated circuits make a great evolution in optical microelectronics technology. In data processing chains, the need for an ultra-fast all-optical encoder is necessary for a large data transfer. In this work, we have proposed an all-optical encoder structure based on nonlinear 2D photonic crystals with Kerr effect exploiting a nonlinear polymer material of high third-order optical susceptibility. In addition, to generate the telecommunication domain wavelength at 1.55µm, an optimization of the optical-geometry parameters has been realized. Simulations will be performed using plane wave expansion and finite difference time domain methods. The nonlinear effect allows an excellent average contrast ratio of 39.76 db, as the structure requires a very low threshold intensity estimated at 1.5 mW/µm2. The significant power transmitted to the output is equal to 99% and 0.03% of input power equivalent to logic state “1” and logic state “0” respectively. The proposed structure generates a bit rate of 1.92Tb/s, therefore able to adapt with other ultrafast all-optical circuits.
Research Article
All optical photonic crystal encoder based on nonlinear Kerr effect with ultrahigh contrast ratio and low threshold power
https://doi.org/10.21203/rs.3.rs-2748076/v1
This work is licensed under a CC BY 4.0 License
Journal Publication
published 23 Jul, 2023
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nonlinear photonics crystals (NLPCs)
ring resonator
all optical encoder
Finite-difference time-domain (FDTD)
contrast ratio
switching speed
Increasing the bit rate, the photonic band gap width, the transmission channels capacity and their transfer speed is the main goal of improving and optimizing modern communication networks and systems. Currently, the best choice is to use optical communications, which further confirms the inevitability of the migration from electronics to optics and photonics. Consequently, these specific optical networks consist of optical fibers [1, 2], waveguides [3, 4], filters [5, 6], demultiplexers [7, 8], logic gates [9–11], adders [12], decoders and encoders [13–15], sensors and biosensors [16, 17]. It has been demonstrated that all the mentioned optical devices can be realized using photonic crystals (PCs). Consequently that they can be used to realize ultra-compact devices suitable for optical integrated circuits.
Optical encoders are logic circuits with 2n input ports and n output ports. It can used to perform the reverse operation of the decoder. Only one input among n is activated at a time, which corresponds to a binary number at the output. In general, it is used in all digital systems to translate decimal values into binary in order to perform binary functions such as addition, subtraction, multiplication. They can play a substantial role in the encoding blocks of communication links. The all-optical encoder is investigated to switch the optical input signal to different output ports. Moreover, it compresses digital data for transmission and storage in optical data processing [18, 19].
In the literature, the 2DPC-based encoder is realized by various techniques, namely multimode interference [20], self-collimation effect [21], nonlinear Kerr effect [10]. Functional performance, such as bit rate, response time, switching speed, size, operating wavelength and contrast ratio were estimated.
An all-optical 4-to-2 digital encoder was proposed by Moniem [22], in this structure, he combined four resonant rings with a T waveguide to design the proposed encoder. The optical power and footprint of this encoder can reach 200 mW and 1225 µm2 respectively inside PCs. The optical intensity at the input ports and the footprint of this device are 4 W/µm2 and 880 µm2 respectively. Recently, Salimzadeh and Alipour-Banaei [25] presented an all-optical 8 to 3 encoder based on three all-optical OR gates. They used silicon rods with 10–18 m2/W for the nonlinear Kerr coefficient, which offered 15 W/µm2 at the input ports. A new all-optical reversible encoder was proposed using two ring resonators based nonlinear ellipticals ring resonator [26]. Most of the work mentioned has been done by combining nonlinear Kerr effects with PC-based resonators. As we know, for proper functioning of nonlinear structures, we need to cast large amounts of optical intensities into the input ports.
The encoders are reported with the previously mentioned techniques using linear and non-linear materials. Typically, nonlinear material-based encoder requires high input power to introduce nonlinearity although it offers high contrast ratio and narrow operating frequency. In this attempt, for better confinement the encoder based on a waveguide coupled with a nonlinear ring resonator. This structure requires a reduced input power (from 1.3 to 3 mW/µm2) compared to other structures found in the literature in order to create the nonlinear Kerr effect. Moreover, high switching speed and high contrast ratio are the major advantages of the discussed encoder. To analyze it, Plane Wave Expansion (PWE) and Finite Difference Time Domain (FDTD) [27, 28] are the two numerical methods used to estimate the propagation modes and the output spectrum, respectively.
The remainder of the article is organized as follows: In Sect. 2, we discussed the encoder description and design method, in Sect. 3, presentation and discussion of simulation results, and in Sect. 4, we have finished our work with a conclusion.
In order to confine the light signal to the desired wavelength. We have introduced a point defect in the structure, which acts as a resonant cavity. The proposed ring resonator created by modifying the material and the radius of the linear rods with nonlinear polystyrene rods. Equally, the shape of resonators as well as the location of the nonlinear rods plays a very important role to generate the wavelength of 1.5503µm belongs to the conventional C band of telecommunications.
The recommended encoder design has an overall size equal to 313.3 µm2. This structure is designed on a square arrangement of silicon (Si) dielectric rods with refractive index of 3.46 submerged in air background. The lattice constant (a) and the radius (r) are respectively chosen at 591 nm and r = (0.18 ×a) nm, as cited in Table 1. The ring resonator of the proposed structure is optimized by two nano-resonators: yellow rods of radius r1 = (r/1.5) µm and green rods of radius r2 = (r/1.2) µm. This structure's shape and opto-geometric properties were chosen to provide the widest possible photonic band gap.
| Parameters | Numerical values |
|---|---|
| Size wafer | 39a × 23a = 313.3 µm2 |
| Lattice constant | a = 591 nm |
| Radius of linear rods | r = 0.18×a |
| Refractive index of Si | 3.46 |
| For Polystyrene (PS) Rods | 𝜀𝐿 = 2.5281 [15] |
| n2 = 1.15 × 10− 16 𝑚2/𝑊 [15] | |
| Radius of non-linear rods | r1 = r/1.5 and r2 = r/1.2 |
For an all-optical encoder (4x2), the output signal O0 and O1 are obtained according to the logic states of the four input signals I0, I1, I2 and I3 as explained on the truth table as showing in Table 2. The functional diagram of the proposed encoder is well presented in Fig. 1.
| Inputs ports | Outputs ports | ||||
|---|---|---|---|---|---|
| I0 | I1 | I2 | I3 | O0 | O1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 | 1 | 1 |
The proposed encoder consists of two cascading nonlinear ring resonators RR1 and RR2 coupled with four of the linear waveguides W1, W2, W3 and W4, characterized by the same resonant wavelength, as shown in Fig. 2.
The TE and TM band diagram represents the interval of the photonic band gap (PBG) as show in Fig. 3. Consequently, a particular set of frequencies have not been allowed to propagate through the periodic structure. [18]. In order to produce signals that are carried through the waveguide in such a way that the propagation of light is required, it is therefore possible to produce structural defects. [17]. As shown in Fig. 2, the PBG1 of the TM mode is 1340.13 to 1976.58 nm. Thus, we note that the band 2 is included between 779.68 and 802.97 nm. It is out of the proposed operating band of the proposed encoder. Thus, in our study it will not be taken into consideration.
The proposed encoder is based on a ring resonator, which functions as an optical switch. It switches between two different logic states from "ON" state to "OFF" state, and realize using one control signal port and two output signals corresponding to the drop waveguide and the bus waveguide. According to the resonance spectrum via the graph given in Fig. 4, we detect that λr equals to 1.5503 µm.
The nonlinear optical switches found in the literature take several forms depending on the resonant wavelength and their use in optical applications such as encoders [14, 15]. In our case, we have exploited polystyrene as polymeric materials with high non-linearity of the Kerr effect and their refractive index can vary proportionally depending on the intensity of the applied power [29] where:
$$n={n}_{0}+{n}_{2}\times I$$
1
n0 is the linear refractive index, n2 is the nonlinear Kerr coefficient, and I is the amount of power intensity. The influence of the refractive index on the intensity results from the susceptibility of the third-order nonlinearity χ(3) [30].
According to the fundamental theory of electromagnetism in PC, PBGs strongly depend on the refractive index of the materials that compose them. Therefore, for a nonlinear PC exhibiting a Kerr nonlinearity, the refractive index will change dynamically under the incidence of a high intensity "pump" beam, which causes the shift of the PBG. When the signal is just at the edge of the PBG, its transmission energy will change dynamically depending on the "pump" beam. In the absence of the pump signal, the signal is in high transmission bandwidth and the switch is in the "ON" state. In the nonlinear case and with the presence of a high intensity excitation, the refractive index of the nonlinear Kerr medium increases which causes the shift of the PBG towards low frequencies. The input signal is in the PBG and cannot propagate into the structure; the all-optical switch is in the “OFF” state.
To test the evolution of the proposed encoder, we use the FDTD-NL nonlinear method. The simulation of the four input signals I0, I1, I2 and I3 will be under the influence of a CW Gaussian wave of the "Unit Power" type mentioned in Rsoft's Full Wave simulator, characterized by a resonant wavelength of 1.5503 µm with a TM polarization mode.
To explain the operation mode of this encoder, the first part consists in exciting the input signal I3 at low power Iin < 1.5mW/µm2 then I0, I1 and I2 are pumped with a high power signal Iin > 1.5mW/µm2.
In this work, for steps of logic operation of the suggested optical encoder are clearly explained by exploiting the nonlinear Kerr effect technique. They are organized as follows:
3.1 First case (when I0 = “1” and I1 = I2 = I3 = “0”):
In this case, we want to obtain a logic state “0” in the two outputs O0 and O1, also well presented in the Fig. 5-a. For this, we inject an intense input signal Iin > 1.5mW/µm2, we notice that an absence of resonance in the two resonators RR1 and RR2 due to wavelength shift. As shown in Fig. 5-b, the signal is totally reflected, which causes a weak output transmission and we detect a weak signal equal 6.26×10− 4% of Pin for O0 and 2.4×10− 3% of Pin for O1.
3.2 Second case (when I1 = “1” and I0 = I2 = I3 = “0”):
Similarly, as shown in Fig. 6-a, with the present of a higher intensity, we will have the same reasoning as that of the first case. As a result, this signal ensures the modification of the refractive index of the nonlinear PS rods of the resonator. Following the Kerr effect, the latter presents a shift in wavelength towards high values, and no signal will be coupled to the resonators and all optical signal will drive to port O1. The amount of power estimated at 97.6% of Pin. Which considered as a high logic state equal to “1”. This logical state is showing in Fig. 6-b.
3.3 Third case (when I2 = “1” and I0 = I1 = I3 = “0”):
In this case, as show in figure 7.a, the input signal I2 is started with a high power. Due to the nonlinear Kerr effect, the simulation result submits to the same reasoning as that of the second case. Thus, the entire input signal will flow to port O0. The amount of power transmitted to the output O0 equal to 97.6 % of Pin, detecting a logic state “1”.The response diagrams of this case is presented in figure 7.b.
3.4 Third case (when I3 = “1” and I0 = I1 = I2 = “0”):
This is the case where the encoder operates in linear mode. The input signal I3 is excited from a low intensity power, which will be lower than the threshold value of the resonator, i.e. I3 < 1.5mW/µm2. The structure resonates for the adjusted resonant wavelength through the ring resonators RR1 and RR2 with λr = 1.5503 µm. Consequently, all the power accumulates inside the ring resonator and injects through the drop waveguide by coupling with the ring resonators as show in Fig. 8.a. In this state, no change in refractive index of the materials. Thus, a high signal will be detected at the output ports respectively O0 and O1 of the optical encoder, a large amount of light will be obtained and equal to 102% of Pin, which is considered as logic “1” as show in Fig. 8.b.
Table 3 summarizes the simulation results obtained for each logic state applied to inputs I0, I1, I2 and I3 normalized as Pin. The normalized power values (in %) are determined according to the Pin input signal.
|
Inputs ports (Intensity in mW/µm2) |
Outputs ports |
||||||
|---|---|---|---|---|---|---|---|
|
O0 |
O1 |
||||||
|
I0 |
I1 |
I2 |
I3 |
Logic state |
Power value % |
Logic state |
Power value % |
|
> 1.5 |
0 |
0 |
0 |
0 |
6.26 ×10− 4 |
0 |
2.24 ×10− 3 |
|
0 |
> 1.5 |
0 |
0 |
0 |
1.78 ×10− 3 |
1 |
97.6 |
|
0 |
0 |
> 1.5 |
0 |
1 |
97.6 |
0 |
1.78 ×10− 3 |
|
0 |
0 |
0 |
< 1.5 |
1 |
102 |
1 |
102 |
The performance of this structure, such as the contrast ratio (CR), and the bit rate (BR) will be calculated numerically [6, 26, 27]. The CR is determined by Eq. (2):
P1 and P0 are the normalized power for “1” and “0” logic state respectivelly.
The bit rate is the inverse of the response time (RT), which is calculated according to Eq. (3):
The value t11 is the transmission delay required by the structure from 0 to 0.1% of the average output power Pavg for the logic output 1, the second is the time t12 required between 0 to 90% of the Pavg value [6, 21]. We note that the average power Pavg or called the peak power is the quantity of power transmitted at the output of logic state “1”. Thus, these values are determined directly from the graph of correspoding cas: I1 = I2 = I3 = “1”, as shown in the corresponding figures respectivelly (Fig. 6; Fig. 7 and Fig. 8).
The numerical simulation results including the average values of the contrast ratio and the bit rate are respectively about 39.76 db and 1.92 Tb/s.
The essential role of the proposed encoder is to block the passage of light only at a well-defined wavelength, in our case λr = 1550.3 nm. This resonance wavelength can be modified to ensure the passage of the two outputs O0 and O1 from an “ON” state to the “OFF” state by exploiting the nonlinear Kerr effect. Indeed, the speed of switching between two logic states is very important, this advantage allows us to design new all-optical encoders in order to improve their performance, such as the reduction of the excitation intensity in the input ports estimated at 0.15 mW/µm2. Therefore, a high intensity contrast obtained at the outputs equal to 39.76 dB and a data transmission speed reaches 1.92 Tb/s. Besides, integration of optical encoder with other optical circuits could be proposed as future work, such as on arithmetic logic unit, also to build optical integrated circuit for various applications.
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No competing interests reported.