# A Novel Microstructure of 2-Bit Optical Analog to Digital Converter Based on Kerr Effect Nonlinear Nanocavities in 2D Photonic Crystal

Authors: Sulieman Ibraheem Shelash Al-Hawary; Ahmed Alkhayyat; M. Mehdi Shafieezadeh; Ngakan Ketut Acwin Dwijendra; Eman Khalaf; Iskandar Muda
Journal: Journal of Sensors
 (2023)

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## Abstract

In this paper, an all-optical analog-to-digital converter based on nonlinear with silicon materials is designed and simulated. The proposed structure consists of three nonlinear nanocavity that control the optical signal power intensity. The nonlinear material used is aluminum gallium arsenide (AlGaAs). Aluminum gallium arsenide (AlGaAs) with a linear refractive index ofn0=1.4 and a nonlinear refractive index of n2=1.5×10−17. Due to the small path length of the waveguides, the optical signals move a short distance and as a result, the power optical losses along the path are reduced and on the other hand, the speed of the structure is increased. The transmission percentage is between 90% and 100%. The overall dimensions of the structure are 324 μm2. The plane wave expansion (PWE) method is used to calculate the band structure. The two-dimensional finite difference time domain (2D-FDTD) method is used to calculate the transmission power spectrum and the simulation results.


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## Body

## 1. Introduction

Nowadays, optical technology has an essential role to play in the rapid advancement of communication and information technologies [1–8]. Tools that utilize photons rather than electrons as information carriers hold greater speeds and decrease interference light channels [9–16]. A photonic crystal consists of 2 or so materials with various coefficients of permeability, placed next to each other periodically [17–25]. This report presents a fast revision of analog to digital converters based on photonic crystals [26–33]. The mentioned photonic crystal structures hold the capacity to be integrated [34–41] and because of using engineered flaws in their crystal lattice as well as utilizing nonlinear materials, have the capability to limit the light inside [42, 43]. The all-optical analog to digital (A/D) converters available so far is very limited in terms of number [7, 44–49]. Photon crystals have absorbed a lot of attention lately due to their great flexibility in optically integrated circuits, in particular, in controlling light emission [1–3, 8, 10, 50–54]. These crystals are considered an alternate array of dielectrics having the capability of controlling the flow of light by gaps (PBGs). The photonic gap is the range of frequency that the coming light is not permitted to propagate. Those structures are a favorable choice for realizing passive as well as active optical tools. Hence, these crystals are able to be utilized to fabricate and design tools, including switches [55–57], detectors [58, 59], logic gates [3, 35, 37, 60–62], filters [63–70], optical dividers [71–74], and converters [75–79], utilize other numerous applications.Several converters offered are on the basis of the optical fibers’ nonlinear performance along with a length of about kilometers. It appears highly improbable to integrate those and all-optical converters. Analogs are provided to all-optical digital and have the ability to integrate; quantization has been done using a chalcogenide waveguide. In fact, 2-dimensional photonic crystals are composed of a range of cylinders of infinite length (dielectric) installed in a dielectric substrate (homogeneous). Photonic crystal substrates are designed in two types. The first type of dielectric rods is placed in the air bed, and the second type of air cavities are created in the dielectric bed. If a light beam hits the structure with a frequency equal to the frequency of the light gap, it is emitted without scattering inside the structure.Youssefi et al. [75] presented a new configuration for an all-optical analog-to-digital converter based on nonlinear materials has been proposed. Mehdizadeh et al. [77, 79] presented a proposed structure that is composed of a nonlinear triplexer and an optical coder. The nonlinear triplexer is for creating discrete levels in the continuous optical input signal, and the optical coder is for generating a 2-bit standard binary code out of the discrete levels coming from the nonlinear triplexer. Controlling the resonant mode of the resonant rings through optical intensity is the main objective and working mechanism of the proposed structure. The maximum delay time obtained for the proposed structure was about 5 ps and the total footprint is about 1520 μm2. In other research presented [78], a novel design for realizing all optical analog to digital converter will be proposed.Recently, in 2020, Hosseinzadeh Sani et al. proposed a 2-bit all-optical analog-to-digital converter [80]. In this converter, nonlinear ring resonators are used. The transmission power is between 65% ~90% and the structure dimensions are 777.52 μm2. In the following year, 2021, Chen et al. proposed a 5-bit all-optical analog-to-digital converter [81], in which the number of bits was important, the subparameters, such as dimensions, increased greatly and the transmission decreased greatly. Dimensions in this structure are equal to 1796 μm2. According to the work done, it can be concluded that in analog-to-digital converters, in addition to the number of bits, the amount of transmission power and the dimensions of the structure are also important [82–85].In this article, in addition to the two-bit structure, an attempt is made to reduce the dimensions of the structure, which in turn increases the speed of the structure. On the other hand, the percentage of power transmission is between 90% ~100%, which, when the percentage of transmission is 100%, it means that the power loss of the optical signal in the structure is almost 0%. The general structure of the article consists of five main sections. In the first part, photonic crystals are introduced, and the design of all converters in the photonic crystal bed is discussed. In addition, an overview of the work of the last two years has been done and the problems and challenges have been examined. In the second part, materials and methods are discussed. In this part, the nonlinear behavior of materials, and the number of different optical powers in photonic crystal structures are explained. In the third part, the proposed structure is designed. In the fourth section, the simulation results are discussed; and finally, in the fifth chapter, the conclusion is made.


## 2. Materials and Methods

In a structure utilizing nonlinear materials along with the Kerr effect, besides to determining the linear section of the material, the behavior of nonlinearity should be defined as well. The Kerr effect is a promising nonlinearity as it means a near-instantaneous intensity dependent refractive index change. Equation (1) can be used in order to acquire the nonlinear refractive index of several materials. N represents the whole value of the refractive index at a specific power. n0 represents the refractive index of the linear section of the material in question. n2 is the index of the nonlinear section of the material, changing with changes in the intensity of light (field square), parameter I represent the light signal’s intensity. The change in the refractive index named the optical chorus effect due to the fact that it seems kind of similar to the electrostatic impact of a chorus when the refractive index of a material with a static electric field’s square applied to it changes [80].
(1)n=n0+n2I.So as to attain the light field intensity, Equation (2) is used. As observed in Equation (2), the light field’ intensity differs according to the square of the field. Also, C represents the light speed in air.
(2)I=2n0ε0cEω2,(3)n2=34n02ε0cχ3.Equation (3) shows the nonlinear refractive index of the material. Decreasing or increasing both parameters can change the total refractive index of the material at a specific intensity [80].


## 3. Proposed Structure of ADC

Over the proposed structure, silicon dielectric rods with refractive index ofn1=3.6 placed in the air bed with a refractive index of ng=1. The mentioned structure is two-dimensions and a hexagonal lattice. The dielectric rods on the X-Z plate have a number of 30×30, and the lattice index value a=600nm is selected. Figure 1(a) shows the proposed structure of the all-optical analog-to-digital converter. In Figure 1(a), can be seen different states of placement of nanocavities, as it can be seen that nanocavities can be placed in different places relative to the movement of the photonic crystals. To acquire the best radius of the dielectric rods that maximize the photonic bandgap, the diagram of the photonic bandgap regarding filling (r/a) is used for the TM polarization mode utilizing the plane wave expansion (PWE) technique. The filling ratio isr/a=0.2and the widest band range is betweena/λ=0.31~0.47 [86, 87]. Figure 1(b) shows the polarization mode and bandgap for a Gaussian pulse input to the structure.Figure 1
(a) The proposed optical structure of two-bit analog-to-digital converter on the basis of nonlinear nanocavities. (b) Display the pulse signal of the input and specify the range of the bandgap.
(a)(b)


## 4. Result and Discussion

Simulating is carried out in two major sections; the initial one is applied to the inputs of the nanocavities by implementation waves to the input port. In the second section, the main outputs of the converter are investigated regarding the nanocavities outputs.Over the first section, the signal of input light signal is applied as a Gaussian pulse with various powers to the structure’s input waveguide and the frequency spectrum (normalized) with a range of specified wavelengths is defined via the charge factor r/a, as illustrated in Figure2. The normalized transmission wavelengths for the three nanocavities output ports are specified since P0 is equal to W1, in Figure 2(a), while the signal of the input light power covers the range 0<Pin<0.25P0. The waveguides did not pass through the input wavelength λ=1.55μm (Figure 2(b)). When the power of input light is implemented to the structure among the range of 0.25P0<Pin<0.5P0, the resonant frequency of the Q1 channel nanocavities transmits the input light signal’s central wavelength to the channel (corresponding). The optical signal power is within the range 0.5P0<Pin<0.75P0 according to Figure 2(c), where the transmission of the central wavelength by the nanocavities connected to the channel Q3 is done. In the last step (Figure 2(d)) while the input optical signal’s input range is 0.75P0<Pin<P0, the nanocavities resonant frequency of the Q2 channel gets past the input optical signal’s central wavelength. The wavelengths going past through main channel outputs for various normalized input power are demonstrated in Table 1.Figure 2
Normalized transmission wavelengths from the output ports when the input power is at, (a)0<Pin<0.25P0, (b) 0.25P0<Pin<0.5P0, (c) 0.5P0<Pin<0.75P0, (d) 0.75P0<Pin<P0.
(a)(b)(c)(d)Table 1
Different values of resonant wavelength for input power intensities at, (a)0<Pin<0.25P0, (b) 0.25P0<Pin<0.5P0, (c) 0.5P0<Pin<0.75P0, (d) 0.75P0<Pin<P0.
Pin (W/μm2), P0=1WQ1[λ (μm)]Q2[λ (μm)]Q3[λ (μm)]0<Pin<0.25P01.5311.5361.5410.25P0<Pin<0.5P01.5501.5561.5630.5P0<Pin<0.75P01.5421.5441.5500.75P0<Pin<P01.5451.5501.554As shown in Figure2, the nonlinear behavior of the analog-to-digital converter is demonstrated in the different input signal’s field intensities. To display those shapes, the wavelength of the input has to be arranged equally to λ=1.55μm. At each stage, the input light signal’s source power is altered. The nonlinear material utilized in nanocavities differs with respect to changes in input field strength. The signal of the input light is implemented to the input waveguide as a continuous Gaussian wave. If the input signal source power is among the range 0<Pin<0.25P0, not any of the output channels has a signal. Perform absorbs light and changes the resonance frequency. While the strength of the input signal is implemented to the structure among 0.25P0 < Pin <0.5P0, the nanowire connected to the W1 channel gets past the central λ=1.55μm. In case the input source power is within the range 0.5P0<Pin<0.75P0, the W3 channel nanocavity gets past the input signal’s central wavelength, and in the last step, the source power between 0.75P0<Pin<P0 is applied to the structure. The central wavelength to the structure’s main output is transmitted by the W2 channel. If nonlinear materials are employed in the structure, it implies that the material in question, besides holding a linear part, has a nonlinear part. The linear behavior of materials is actually a scattering action, and the materials’ nonlinear behavior shows the adsorption action, in which some desired wavelengths, the material’s nonlinear behavior neutralizes the linear behavior of the same material, and the state maintains the waveform after a while.To find the appropriate wavelengths’ range to be utilized as input wavelengths, it appears crucial to determine the normalized transmission power spectrum according to the different fields’ intensity from the output ports for particular input power. Then, so as to determine the converter’s transfer spectrum, the Fourier transform’s output is taken. The power spectrum which is normalized within the wavelengths’ range that meet our desired power distribution circumstances, is shown in Figure3. The input power ratio is broken down into four sections. As shown in Figure 4(a), when the input wave signal strength is placed within the range of section 1, the amount of transmission power seen at all 3 nano-cavities outputs reaches nearly 12% (Q1 = 4%, Q2 = 2%, Q3 = 6%). Figure 4(b) shows that the range of input signal power is set within the power range of section 2. In this case, the power transmitted to channel Q1 has a value of 100% of the input as well as the output power of Q2 and Q3 channels are almost 0% (Q2 = 0%, Q3 = 0%). In case the input power range is in section 3, the power transmitted to Q3 channel is 92% of the power of the input, and the powers seen in Q1 and Q2 channels are nearly equal to 8% (Q1 = 4%, Q2 = 5%) (Figure 4(c)). In the last section, which is shown in Figure 4(d), the power range is in section 4, where the Q2 channel output power is 91%. In addition, the output power of Q1 and Q3 channels is roughly 9% (Q1 = 4%, Q3 = 5%). As observed in the results, due to utilizing the nano-cavities as a hexagonal structure and utilizing non-linear materials in the spots needed for wave transmission, and utilizing proper radii of coupled dielectrics between waveguides and nano-cavities, it has been found that the amount of power loss in the channels that are not used is quite low and the amount of power transferred from the desired channel’s input to output is considerable and with inconsequential losses (Table 2).Figure 3
The behavior of the electric field for different input intensities at, (a) 0 < Pin <0.25P0, (b) 0.25P0 < Pin <0.5P0, (c) 0.5P0 < Pin <0.75P0, (d) 0.75 P0 < Pin < P0.
(a)(b)(c)(d)Figure 4
Normalized transmission power spectrum from the output ports of transducer resonant nano-cavities at central wavelengthλ =1.55 μm.
(a)(b)(c)(d)Table 2
Normalized output power in different power intensities.
Pin (W/μm2), P0=1WQ1 (%)Q2 (%)Q3 (%)0 <Pin <0.25P04260.25P0 < Pin <0.5P0100000.5P0 < Pin <0.75P035920.75P0 < Pin <P04915As shown in Figure5, the proposed structure’s input power diagram is plotted regarding output power for the three channels. When the power is in the first section, the received coding will be “00”. If the range of the power is set in the second section, the amount of power in the outputs is Q1=1, Q2=0, and Q3=0, which indicates the coding of “01”. In case the range of the power is within the third section, the amount of power in the outputs is Q1 = 0, Q2 = 0 and Q3 = 1, which represent the coding of “10”, and in the last section, when the power interval is in the fourth part, the amount of power in the outputs is Q1 = 0, Q2 = 1 and Q3 = 0, which indicate the “11” coding. Thus, the outputs of the cover structure are four logic modes for an analog-to-digital bit converter.Figure 5
The diagram of the input power of the proposed structure based-on output power.Comparison of important parameters of the analog-to-digital dual-bit converter with recent articles are illustrated in Table3.Table 3
Comparison of important parameters of the analog-to-digital dual-bit converter with recent articles.
WorksS (μm2)Transfers (%)YearsRef [75]449762012Ref [77]1520—2017Ref [78]924802017Ref [79]806602018Ref [80]777.52902020This work32490—


## 5. Conclusion

In this work, the proposed structure consists of three nanocavities with nonlinear materials. Due to the small size of the photonic crystal substrate, there is no integration problem. The main function of the structure is based on nonlinear nanocavities made of aluminum gallium arsenide (AlGaAs). These parameters are obtained for the proposed structure with dimensions of 324μm2. The output power spectrum that produces the converter logic is calculated using the finite difference time domain method (FDTD). The speed of input power to output waveguides allows this structure to be used in applications with high signal processing speed and accuracy.



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