Photonic Crystal Flip-Flops: Recent Developments in All Optical Memory Components

This paper reviews recent advancements in all-optical memory components, particularly focusing on various types of all-optical flip-flops (FFs) based on photonic crystal (PC) structures proposed in recent years. PCs, with their unique optical properties and engineered structures, including photonic bandgap control, enhanced light–matter interaction, and compact size, make them especially suitable for optical FFs. The study explores three key materials, silicon, chalcogenide glass, and gallium arsenide, known for their high refractive index contrast, compact size, hybrid integration capability, and easy fabrication processes. Furthermore, these materials exhibit excellent compatibility with different technologies like CMOS and fiber optics, enhancing their versatility in various applications. The structures proposed in the research leverage mechanisms such as waveguides, ring resonators, scattering rods, coupling rods, edge rods, switches, resonant cavities, and multi-mode interference. The paper delves into crucial properties and parameters of all-optical FFs, including response time, contrast ratio, and operating wavelength. Optical FFs possess significant advantages, such as high speed, low power consumption, and potential for integration, making them a promising technology for advancing optical computing and optical memory systems.


Introduction
Traditional electronic memory devices face physical and electrical limitations in terms of speed, power consumption, and integration density, necessitating the exploration of alternative technologies.Therefore, optical computing serves as a viable alternative to conventional electrical memory devices.In the rapidly evolving field of optical computing and information processing, the demand for high-speed and low-power memory components has been a driving force behind ongoing research and development efforts.
Computer memory is the ability of a system to store, retain, and recall data or instructions.It is a crucial component that enables computers and other electronic devices to perform various tasks efficiently.Memory is categorized into different types based on its characteristics, speed, capacity, and purpose.Of the two primary types of memory used in computing, Random Access Memory (RAM) is the main memory of a computer that provides fast and temporary storage for data and program instructions.It allows the CPU to access data quickly, enabling the rapid execution of tasks.RAM is volatile, which means its contents are lost when the power is turned off.Read-Only Memory (ROM) is a type of memory that stores permanent data and instructions necessary for the basic functioning of a computer or device.Unlike RAM, ROM is non-volatile, meaning its contents remain intact even when the power is off.
Computer memory systems utilize multiple flip-flops (FFs) arranged in arrays or hierarchical structures to create larger memory units.This allows for the storage and retrieval of data systematically and efficiently, in addition to more extensive data storage underlying the operation of PC FFs and explore the design considerations.Furthermore, we will highlight key advancements and novel approaches in the field, including the incorporation of nonlinear optical effects for enhanced functionality.
Numerous other research papers have been published that either reviewed [59,60] or proposed [61,62] optical memory structures, including FFs.It is evident that over time, improvements have been observed in both the simulation results and the simulation tools employed, and these aspects will be elaborated upon in the conclusion.
By examining the latest research findings and technological advancements, this paper aims to contribute to the understanding of PC FFs as crucial components in the development of all-optical memory systems.The potential benefits of these memory components, such as high-speed operation, low power consumption, and compact integration, make them promising candidates for future optical computing applications.

Fundamental Properties of Photonic Crystals in All-Optical Memory
PCs are periodic structures that exhibit a unique ability to manipulate and control the flow of light.They are composed of materials with alternating regions of high and low refractive index, forming a periodic array.This periodicity gives rise to a PBG, a range of frequencies wherein the propagation of light is forbidden, for one, two or any number of polarizations.This property makes PC particularly useful for controlling and manipulating light waves in various applications, including optical memory components such as FF.
All-optical memory components utilize materials that can change their optical properties in response to external stimuli such as heat or light; these changes allow for the encoding and storage of information in the form of light signals.
PCs can be employed in optical memory systems in different ways; one common approach is to use the PBG property of the crystal to create a structure called a "resonator" or "cavity".
A PC resonator consists of a defect within the periodic crystal lattice that introduces localized states within the PBG.These localized states can trap and confine light within the defect region.By carefully engineering the properties of the defect and the surrounding crystal structure, it is possible to create resonant modes at specific frequencies within the bandgap.To encode information, the resonator can be designed to have two or more distinct resonant modes.These modes correspond to different energy levels or states.By selectively exciting or suppressing certain modes, information can be stored as binary data (0 s and 1 s).For example, the presence or absence of a particular mode can represent a digital bit.
The advantage of using PCs in optical memory lies in their ability to confine and control light within a small volume.This confinement leads to enhanced light-matter interactions, enabling efficient read and write operations.Additionally, the PBG property ensures that the stored information is protected from external disturbances and scattering, improving the stability and reliability of the memory system.
Presented in the paper are different implementations and designs of PC-based alloptical FFs; they vary by utilizing different materials, architectures, and techniques to try and achieve the best -performing device possible.

Operating Wavelength
The operating wavelength range in optical components is a very important parameter in terms of compatibility with industry standards, for example, working at the C-band range, between 1540 nm and 1570 nm, means more compatibility with the current leading technology in the industry, the CMOS.
The operating wavelength is the optimal wavelength that is derived from the operating wavelength range.

Switching Speed
Switching speed refers to the time it takes for the optical memory device, for example, an FF, to transition between its two stable states.Switching speed is a critical parameter for optical FFs as it determines how quickly the stored information can be updated or accessed.Faster switching speeds allow for rapid data processing, high-speed communication, and efficient information storage and retrieval.The switching speed of an optical FF is influenced by several factors; one key consideration is the choice of optical components, such as waveguides, optical switches, RRs, or modulators.Another consideration is the overall design and architecture of the device, as factors such as the physical layout, the connectivity of the optical components, and signal routing mechanisms play a role in determining the overall speed of state transitions.Optimized architectures that minimize signal propagation delays and maximize light-matter interactions can help achieve faster switching speeds.

Contrast Ratio
The contrast ratio (CR) refers to the ratio between the intensity or power of the output signal in one state (such as a logical "1") compared to the intensity or power of the output signal in the opposite state (such as a logical "0").It measures the distinction or difference between the two states and is an important parameter for the performance and reliability of optical FFs.A high contrast ratio is desirable in optical components and FFs in particular, as it ensures clear differentiation between the different states, minimizing errors and improving the accuracy of information storage and retrieval.A higher contrast ratio translates to a better distinction between logical "1" and "0" states, enabling more reliable and accurate data processing.The CR is given as: where p1 and p0 are the output power levels of logic 1 and logic 0, respectively.

The D Flip-Flop
In regular use cases, an FF is a sequential logic circuit that can store and manipulate binary data.The D FF, also known as a data FF, is the simplest type of FF.It has a single data input (D) and two outputs: Q (the stored value) and Q' (the complement of the stored value), as seen in Figure 1.In 2020, Saranya et al. presented a design of an all-optical clocked D FF for 1.72 Tb/s optical computing.The device is composed of 20 × 11 silicon and chalcogenide glass rods in a square lattice PC structure, with the refractive index of 3.46 and 3.1, respectively.The lattice constant a is 547 nm and the radius of the rods is 0.2a.The PBG for the silicon rods is 1327-1917 nm, and for the chalcogenide glass is 1238-1724 nm.The operating wavelength for the proposed structure is 1550 nm.
Using silicon as the refractive index, the proposed D FF has two waveguides that provide input at the first part of the design and output at the second part of the design.Connecting the two parts of these waveguides is an RR whose inner part is circular, and the outer is square.The component comprises a pair of inputs, namely, Clk and D, alongside two corresponding complementary outputs labeled as Q and Q'.The coupling rods, tinted in green, serve the purpose of linking the light signal and possess a radius of 0.14a.The stored value (Q) is updated synchronously with the CLK signal.When the CLK signal transitions from a high logic state to a low logic state, or the other way around, depending on the implementation, the current value of the D input is transferred to the output.In today's system-on-chip (Soc) designs, the D FF is most commonly used for delay, synchronization, and memory applications.
In 2020, Saranya et al. presented a design of an all-optical clocked D FF for 1.72 Tb/s optical computing.The device is composed of 20 × 11 silicon and chalcogenide glass rods in a square lattice PC structure, with the refractive index of 3.46 and 3.1, respectively.The lattice constant a is 547 nm and the radius of the rods is 0.2a.The PBG for the silicon rods is 1327-1917 nm, and for the chalcogenide glass is 1238-1724 nm.The operating wavelength for the proposed structure is 1550 nm.
Using silicon as the refractive index, the proposed D FF has two waveguides that provide input at the first part of the design and output at the second part of the design.Connecting the two parts of these waveguides is an RR whose inner part is circular, and the outer is square.The component comprises a pair of inputs, namely, Clk and D, alongside two corresponding complementary outputs labeled as Q and Q'.The coupling rods, tinted in green, serve the purpose of linking the light signal and possess a radius of 0.14a.Conversely, the scattering rods, depicted in yellow, are designed with a radius of 0.12a to prevent undesired light leakage.Figure 2   In 2020, Saranya et al. presented a design of an all-optical clocked D FF for 1.72 Tb optical computing.The device is composed of 20 × 11 silicon and chalcogenide glass rod in a square lattice PC structure, with the refractive index of 3.46 and 3.1, respectively.Th lattice constant a is 547 nm and the radius of the rods is 0.2a.The PBG for the silicon rod is 1327-1917 nm, and for the chalcogenide glass is 1238-1724 nm.The operating wave length for the proposed structure is 1550 nm.
Using silicon as the refractive index, the proposed D FF has two waveguides tha provide input at the first part of the design and output at the second part of the design Connecting the two parts of these waveguides is an RR whose inner part is circular, an the outer is square.The component comprises a pair of inputs, namely, Clk and D, along side two corresponding complementary outputs labeled as Q and Q'.The coupling rod tinted in green, serve the purpose of linking the light signal and possess a radius of 0.14a Conversely, the scattering rods, depicted in yellow, are designed with a radius of 0.12a t prevent undesired light leakage.Figure 2 displays a schematic of the proposed structure A Gaussian pulse is applied to the input with an operating wavelength of 1550 nm and a phase shift to get the desired outputs (Q, Q′).The contrast ratios for the output por Q and Q′ are calculated using Equation (1), and determined to be 11.13 dB and 3.353 dB respectively.
The fundamental configuration under consideration is evaluated utilizing both sil con and chalcogenide glass as potential refractive indexes.After careful examination, was determined that employing chalcogenide glass yielded a more favorable contrast ra tio.In this study, a 30 × 20 μm square lattice 2D PC is meticulously devised.The lattic constant a is set to 600 nm, and the rod radius is fixed at 0.2a.Specifically focusing on th chalcogenide glass refractive index, the proposed structure is adapted through the inco poration of bend waveguides.These waveguides are designed to manipulate light signa without causing any adverse impact on the optical properties of field propagation.Th revised configuration introduces three inputs, Clk, CI, and D, and establishes two output A Gaussian pulse is applied to the input with an operating wavelength of 1550 nm and a phase shift to get the desired outputs (Q, Q ).The contrast ratios for the output ports Q and Q are calculated using Equation (1), and determined to be 11.13 dB and 3.353 dB, respectively.
The fundamental configuration under consideration is evaluated utilizing both silicon and chalcogenide glass as potential refractive indexes.After careful examination, it was determined that employing chalcogenide glass yielded a more favorable contrast ratio.In this study, a 30 × 20 µm square lattice 2D PC is meticulously devised.The lattice constant a is set to 600 nm, and the rod radius is fixed at 0.2a.Specifically focusing on the chalcogenide glass refractive index, the proposed structure is adapted through the incorporation of bend waveguides.These waveguides are designed to manipulate light signals without causing any adverse impact on the optical properties of field propagation.The revised configuration introduces three inputs, Clk, CI, and D, and establishes two outputs, Q and Q'.Within the design lies a square resonator, with its innermost rods possessing a radius of 0.16a, indicated in green, surrounded by an outer circle with a radius of 0.14a, depicted in yellow.The resonant wavelength characterizing the modified structure is recorded at 1550 nm.The altered arrangement is visually depicted in Figure 3.
The contrast ratios are calculated to be 8.75 dB and 7.63 dB for the outputs Q and Q', respectively.Both silicon and chalcogenide glass were employed as the refractive index to analyze the structure.The output power of the structure is shown in Q and Q'.Within the design lies a square resonator, with its innermost rods possessing a radius of 0.16a, indicated in green, surrounded by an outer circle with a radius of 0.14a, depicted in yellow.The resonant wavelength characterizing the modified structure is recorded at 1550 nm.The altered arrangement is visually depicted in Figure 3.The contrast ratios are calculated to be 8.75 dB and 7.63 dB for the outputs Q and Q', respectively.Both silicon and chalcogenide glass were employed as the refractive index to analyze the structure.The output power of the structure is shown in  In 2017, Shaik et al. proposed a PC-based D FF scheme utilizing an MMI.This design incorporated a central MMI waveguide to facilitate the interference of the input light, while input and output ports were positioned at both ends of the MMI waveguide.Through an array of simulations, they demonstrated a contrast ratio of 9.63 dB and 5.84 dB at the Q and Q' outputs, respectively.Furthermore, the response time was measured to be under 0.29 picoseconds.The fundamental configuration of this design is depicted in orded at 1550 nm.The altered arrangement is visually depicted in Figure 3.The contrast ratios are calculated to be 8.75 dB and 7.63 dB for the outputs Q and Q', respectively.Both silicon and chalcogenide glass were employed as the refractive index to analyze the structure.The output power of the structure is shown in  In 2017, Shaik et al. proposed a PC-based D FF scheme utilizing an MMI.This design incorporated a central MMI waveguide to facilitate the interference of the input light, while input and output ports were positioned at both ends of the MMI waveguide.Through an array of simulations, they demonstrated a contrast ratio of 9.63 dB and 5.84 dB at the Q and Q' outputs, respectively.Furthermore, the response time was measured to be under 0.29 picoseconds.The fundamental configuration of this design is depicted in In 2017, Shaik et al. proposed a PC-based D FF scheme utilizing an MMI.This design incorporated a central MMI waveguide to facilitate the interference of the input light, while input and output ports were positioned at both ends of the MMI waveguide.Through an array of simulations, they demonstrated a contrast ratio of 9.63 dB and 5.84 dB at the Q and Q' outputs, respectively.Furthermore, the response time was measured to be under 0.29 picoseconds.The fundamental configuration of this design is depicted in Figure 5a.In order to achieve a delayed output, a strategic approach was employed where the input and output waveguides were extended using sharp and smooth bend waveguides, respectively.This modification aimed to enhance the delay characteristics of the structure, aligning with the primary objective of the D FF concept.The designed clocked D flip-flop (D FF) architecture comprises an arrangement of 11 × 18 silicon rods organized in a square lattice configuration set against an air background, as illustrated in Figure 5b.The structure is outfitted with two input ports, D and Clk, along with two output ports, Q and Q'.During optimization, the rod radius was fine-tuned to 0.2a, except for the edge rods situated within the MMI waveguide, which were adjusted to a radius of 0.1a.The lattice constant used for this arrangement measures 600 nm.
structure, aligning with the primary objective of the D FF concept.The designed clocked D flip-flop (D FF) architecture comprises an arrangement of 11 × 18 silicon rods organized in a square lattice configuration set against an air background, as illustrated in Figure 5b.The structure is outfitted with two input ports, D and Clk, along with two output ports, Q and Q'.During optimization, the rod radius was fine-tuned to 0.2a, except for the edge rods situated within the MMI waveguide, which were adjusted to a radius of 0.1a.The lattice constant used for this arrangement measures 600 nm.The PBG was calculated using the PWE method; the wavelength was extracted from the PBG as 1430-2120 nm, and the operating wavelength was chosen to be 1550 nm.For the envisioned configurations, output transmissions falling below 0.25 and exceeding 0.75 are designated as logic 0 and logic 1, respectively.
The time taken for the output power at port Q to transition from 0 to 90% of the average power is comprised of two constituents.The first component corresponds to the transmission delay, denoted as t1, quantified at 0.049 ps.The second facet involves the time needed to traverse from 10 to 90% of the average power, represented as t2, calculated to be 0.056 ps.These components are illustrated in Figure 6.Given the linear properties of the proposed structure's materials, the falling time extends from the average power to 10% of it, approximating t2.Consequently, the response time is determined to be 0.224 ps.Similar computations derived from the temporal evolution curve at port Q', also presented in Figure 6, reveal a response time of 0.28 ps.
The proposed configuration has been enhanced through the implementation of Lbend waveguides, depicted in Figure 5b, with the primary intention of augmenting delay or response time.On the input side, sharp L-bends are integrated to manipulate the light's propagation direction, while preserving its optical properties.Smooth L-bends are established at the output side using point defects, intended to introduce a delay to the input signal and diminish both electrical and optical interactions amid the waveguides.This is achieved through the utilization of a point defect located at the edge of the smooth Lbend, effectively acting as a cavity, and contributing to delay enhancement.
The response time of this structure, as deduced from the time-evolution curves illustrated in Figure 7 for ports Q and Q', registers at 0.76 and 0.764 picoseconds, respectively.The CR has also been evaluated using output power levels at ports Q and Q', yielding values of 9.92 dB and 5.27 dB, respectively.The PBG was calculated using the PWE method; the wavelength was extracted from the PBG as 1430-2120 nm, and the operating wavelength was chosen to be 1550 nm.For the envisioned configurations, output transmissions falling below 0.25 and exceeding 0.75 are designated as logic 0 and logic 1, respectively.
The time taken for the output power at port Q to transition from 0 to 90% of the average power is comprised of two constituents.The first component corresponds to the transmission delay, denoted as t1, quantified at 0.049 ps.The second facet involves the time needed to traverse from 10 to 90% of the average power, represented as t2, calculated to be 0.056 ps.These components are illustrated in Figure 6.Given the linear properties of the proposed structure's materials, the falling time extends from the average power to 10% of it, approximating t2.Consequently, the response time is determined to be 0.224 ps.Similar computations derived from the temporal evolution curve at port Q', also presented in Figure 6, reveal a response time of 0.28 ps.The proposed configuration has been enhanced through the implementation of L-bend waveguides, depicted in Figure 5b, with the primary intention of augmenting delay or response time.On the input side, sharp L-bends are integrated to manipulate the light's propagation direction, while preserving its optical properties.Smooth L-bends are established at the output side using point defects, intended to introduce a delay to the input signal and diminish both electrical and optical interactions amid the waveguides.This is achieved through the utilization of a point defect located at the edge of the smooth L-bend, effectively acting as a cavity, and contributing to delay enhancement.
The response time of this structure, as deduced from the time-evolution curves illustrated in Figure 7 for ports Q and Q', registers at 0.76 and 0.764 picoseconds, respectively.The CR has also been evaluated using output power levels at ports Q and Q', yielding values of 9.92 dB and 5.27 dB, respectively.In 2020, Rao et al. introduced an all-optical D FF design utilizing photonic crystal (PC) waveguides, strategically developed for optical computing and networking applications.This specific architecture was formulated through the implementation of T-shaped waveguides within a square lattice PC.Notably, the utilization of non-linear materials was deliberately avoided.The configuration featured silicon rods with a radius measuring 0.19a and a lattice constant of 0.6 μm.To facilitate light propagation, defects were skillfully introduced into the design, serving as waveguides, as visually depicted in Figure 8.At both junctions, specific rod radii were employed: rj1 at 0.18 μm, rj2 at 0.132 μm, rj3 at 0.24 μm, and the reflecting rod r1 at 0.15 μm.These variations were strategically incorporated In 2020, Rao et al. introduced an all-optical D FF design utilizing photonic crystal (PC) waveguides, strategically developed for optical computing and networking applications.This specific architecture was formulated through the implementation of T-shaped waveguides within a square lattice PC.Notably, the utilization of non-linear materials was deliberately avoided.The configuration featured silicon rods with a radius measuring 0.19a and a lattice constant of 0.6 µm.To facilitate light propagation, defects were skillfully introduced into the design, serving as waveguides, as visually depicted in Figure 8.At both junctions, specific rod radii were employed: rj1 at 0.18 µm, rj2 at 0.132 µm, rj3 at 0.24 µm, and the reflecting rod r1 at 0.15 µm.These variations were strategically incorporated to prevent undesirable back reflections into an unused input port.For instance, when the input D is set to logic 0, and both the reference and CLK inputs are at logic 1, the resultant light signal is directed away from input port D, favoring its propagation towards the output port Q'.
The waveguide situated on the left-hand side of the configuration serves as the input port designated for D. Positioned at the bottom of the structure are two vertical waveguides, functioning respectively as the reference input port R and the CLK input.Adjacent to the right edge of the design is a horizontal waveguide, allocated for use as the output port Q'.Correspondingly, the topmost position features a vertical waveguide designated as the output port Q.
to prevent undesirable back reflections into an unused input port.For instance, when the input D is set to logic 0, and both the reference and CLK inputs are at logic 1, the resultant light signal is directed away from input port D, favoring its propagation towards the output port Q'.The waveguide situated on the left-hand side of the configuration serves as the input port designated for D. Positioned at the bottom of the structure are two vertical waveguides, functioning respectively as the reference input port R and the CLK input.Adjacent to the right edge of the design is a horizontal waveguide, allocated for use as the output port Q'.Correspondingly, the topmost position features a vertical waveguide designated as the output port Q.
The operation of the all-optical D flip-flop is meticulously simulated and confirmed using OptiFDTD software, provided by OptiWave, based in Canada [66].The proposed design employs a beam-interference principle, capitalizing on a continuous wave (CW) light source with a wavelength of 1550 nm.Through simulations, the intended functionality has been successfully showcased, demonstrating all four operational states of the device.Figure 9 shows the four operation states of the D FF; by designing specific waveguide path lengths, constructive and destructive interference are achieved, resulting in the desirable operation.The operation of the all-optical D flip-flop is meticulously simulated and confirmed using OptiFDTD software, provided by OptiWave, based in Canada [66].The proposed design employs a beam-interference principle, capitalizing on a continuous wave (CW) light source with a wavelength of 1550 nm.Through simulations, the intended functionality has been successfully showcased, demonstrating all four operational states of the device.Figure 9 shows the four operation states of the D FF; by designing specific waveguide path lengths, constructive and destructive interference are achieved, resulting in the desirable operation.The waveguide situated on the left-hand side of the configuration serves as the input port designated for D. Positioned at the bottom of the structure are two vertical waveguides, functioning respectively as the reference input port R and the CLK input.Adjacent to the right edge of the design is a horizontal waveguide, allocated for use as the output port Q'.Correspondingly, the topmost position features a vertical waveguide designated as the output port Q.
The operation of the all-optical D flip-flop is meticulously simulated and confirmed using OptiFDTD software, provided by OptiWave, based in Canada [66].The proposed design employs a beam-interference principle, capitalizing on a continuous wave (CW) light source with a wavelength of 1550 nm.Through simulations, the intended functionality has been successfully showcased, demonstrating all four operational states of the device.Figure 9 shows the four operation states of the D FF; by designing specific waveguide path lengths, constructive and destructive interference are achieved, resulting in the desirable operation.The CR has been calculated using Equation ( 1) to be 13.57and 25 dB for outputs Q and Q', respectively.

The SR Flip-flop
The SR FF, also known as the set-reset FF, is a basic FF with two inputs, S (set) and R The CR has been calculated using Equation (1) to be 13.57and 25 dB for outputs Q and Q', respectively.

The SR Flip-Flop
The SR FF, also known as the set-reset FF, is a basic FF with two inputs, S (set) and R (reset), and two outputs, Q and Q', as seen in Figure 10.The S and R inputs determine the FF state changes when the CLK signal transitions.When S = 1 and R = 0, the output is set (Q = 1) on the CLK edge.When S = 0 and R = 1, the output is reset (Q = 0).When both S and R are 0, the output remains in its current state.The SR FF is widely used for memory circuits, latches, and control systems.The CR has been calculated using Equation (1) to be 13.57and 25 dB for outputs Q and Q', respectively.

The SR Flip-flop
The SR FF, also known as the set-reset FF, is a basic FF with two inputs, S (set) and R (reset), and two outputs, Q and Q', as seen in Figure 10.The S and R inputs determine the FF state changes when the CLK signal transitions.When S = 1 and R = 0, the output is set (Q = 1) on the CLK edge.When S = 0 and R = 1, the output is reset (Q = 0).When both S and R are 0, the output remains in its current state.The SR FF is widely used for memory circuits, latches, and control systems.The lattice constant is 630 nm, and the radius of the silicon rods is equal to 0.2a; the PBG was calculated, and the operating wavelength range was extracted to be 1500-2172 nm and 851-868 nm.
The optical memory SR FF employs optical NOR gates, constructed using optical Ttype switches, PC RR, and an array of waveguides equipped with optical power drivers and Y-splitters.The optical NOR gate, designed within a 2D PC framework, is assembled by integrating two optical T-shaped switches.These switches consist of PC resonant rings along with T-type waveguides, which are formed through the introduction of specific defects into the structure of the 2D PC, as visually represented in Figure 11.The switch integrates three distinct ports: input port A, pump port C, and output port B. Connecting these ports are PC RR, and at the corners of this connection, four additional silicon rods, each with a radius of 0.3a, have been introduced.These rods are de- The switch integrates three distinct ports: input port A, pump port C, and output port B. Connecting these ports are PC RR, and at the corners of this connection, four additional silicon rods, each with a radius of 0.3a, have been introduced.These rods are depicted in green and are strategically positioned to prevent the reflection of light waves.In addition, four more rods, shown in blue, and with a radius of 0.1a, have been incorporated.These blue rods serve the dual purpose of enhancing the interaction between waves and materials within the PC RR, as well as elevating the Q-factor.This elevated Q-factor significantly influences the energy stored within the proposed PC RR.The respective blue and green colors of these rods are visually evident in Figure 11.The optical NOR gate incorporates a pair of consecutive optical T-shaped switches, employing uniform materials, lattice constants, and rod radii.These two optical T-shaped switches are designed with three ports.The initial port, referred to as the BIAS port, is situated between C and Q.It has been established by selectively removing silicon rods to facilitate the uninhibited propagation of the data signal.The remaining two input ports, labeled A and B, are introduced to establish a linkage between the data signal and the PC RR, as depicted in Figure 12.
Materials 2023, 14, x FOR PEER REVIEW 13 of 26 as feedback for NOR2.Similarly, Y2 divides the optical signal from bias port I2 into two channels, Y2A and Y2B.Y2A steers the optical signal toward port Q', and Y2B functions as feedback for NOR1, as illustrated in Figure 13.The operational wavelength for optical ports I1 and SET is set at 1600 nm, whereas for optical ports I2 and RESET, it is established at 1580 nm.The optical wave, characterized by a wavelength of 1600 nm, penetrates the arrangement through the C port, while the determination of the NOR gate's output state is governed by the inputs from the A and B ports.When either or both of the logic inputs, A and B, are in a logic 1 state, the output Q will assume a logic 0 state.Conversely, if both A and B are not in a logic 1 state, Q will transition to a logic 1 state.
The proposed optical memory SR flip-flop is depicted in Figure 13.This design encompasses two input ports, namely, SET and RESET, supplemented by additional input bias ports I1 and I2, along with two output ports, Q and Q'.The optical SR flip-flop configuration comprises two optical NOR logic gates utilizing four PC RR, namely, PC-MRR1, PC-MRR2, PC-MRR3, and PC-MRR4.These gates are interconnected by means of optical T-shaped waveguides that are linked to two Y-splitters.The division of optical power from the waveguides is achieved through optical PC Y-splitters.With a transmission efficiency of 94% and a 50:50 splitting ratio, the optical power splitter within the photonic crystal attains a balanced power distribution, resulting in each half receiving 47% of the power flow from the main waveguide.The precision of optical bends and junctions plays a pivotal role in designing the PC power splitter.The main waveguide channel Y1 partitions the optical signal from the bias port I1 into two channels, denoted as Y1A and Y1B.Y1A directs the optical signal toward port Q, while Y1B serves as feedback for NOR2.Similarly, Y2 divides the optical signal from bias port I2 into two channels, Y2A and Y2B.Y2A steers the optical signal toward port Q', and Y2B functions as feedback for NOR1, as illustrated in Figure 13.The operational wavelength for optical ports I1 and SET is set at 1600 nm, whereas for optical ports I2 and RESET, it is established at 1580 nm.
The optical input power for each input port at the active state is equal to 150 mW; the power is spread equally through the activated input ports.The proposed optical SR FF has four states and one undefined state.The set case sets the output Q to a logic 1, the reset case sets the output Q to a logic 0, and there are two no-change cases at which the output state is memorized.The states are demonstrated in Figure 14. Figure 14a describes the set case in orange color and the no-change state that occurs after in blue color.Figure 14b describes the reset case in orange color and the no-change state that occurs after in blue color.
As depicted in Figure 14, it becomes evident that the output power does not converge to a constant value, but rather exhibits oscillations.The power span corresponding to logic 0 ranges from 0 to 30 mW, while for logic 1, it spans 150 to 160 mW.Furthermore, the CR can be quantified as 4.77 dB for logic 0 and 6.99 dB for logic 1.
Figure 15a concisely presents a timing diagram encompassing a sequence of events.Simulation outcomes indicate that by manipulating the input states of the SR FF, the rise and fall response times for the proposed SR FF memory correspondingly amount to 3 ps and 1 ps, as visually demonstrated in Figure 15b.Additionally, the output response time aligns with 1.2 ps, and the switching rate attains a notable 133 GHz.
power is spread equally through the activated input ports.The proposed optical SR FF has four states and one undefined state.The set case sets the output Q to a logic 1, the reset case sets the output Q to a logic 0, and there are two no-change cases at which the output state is memorized.The states are demonstrated in Figure 14. Figure 14a describes the set case in orange color and the no-change state that occurs after in blue color.Figure 14b describes the reset case in orange color and the no-change state that occurs after in blue color.As depicted in Figure 14, it becomes evident that the output power does not converge to a constant value, but rather exhibits oscillations.The power span corresponding to logic 0 ranges from 0 to 30 mW, while for logic 1, it spans 150 to 160 mW.Furthermore, the CR can be quantified as 4.77 dB for logic 0 and 6.99 dB for logic 1.
Figure 15a concisely presents a timing diagram encompassing a sequence of events.Simulation outcomes indicate that by manipulating the input states of the SR FF, the rise and fall response times for the proposed SR FF memory correspondingly amount to 3 ps and 1 ps, as visually demonstrated in Figure 15b.Additionally, the output response time aligns with 1.2 ps, and the switching rate attains a notable 133 GHz.As depicted in Figure 14, it becomes evident that the output power does not converge to a constant value, but rather exhibits oscillations.The power span corresponding to logic 0 ranges from 0 to 30 mW, while for logic 1, it spans 150 to 160 mW.Furthermore, the CR can be quantified as 4.77 dB for logic 0 and 6.99 dB for logic 1.
Figure 15a concisely presents a timing diagram encompassing a sequence of events.Simulation outcomes indicate that by manipulating the input states of the SR FF, the rise and fall response times for the proposed SR FF memory correspondingly amount to 3 ps and 1 ps, as visually demonstrated in Figure 15b.Additionally, the output response time aligns with 1.2 ps, and the switching rate attains a notable 133 GHz.In 2018, Zamanian-Dehkordi et al. introduced an all-optical RS FF utilizing nonlinear PC configurations.This innovative design capitalizes on the nonlinear Kerr effect within the PC framework.The proposed architecture is composed of a central segment and two optical switches.The central section encompasses two interconnected resonant cavities, each resonating at distinct wavelengths: 1586 nm and 1620 nm.The fundamental PC structure is in a square lattice configuration, featuring dielectric rods immersed in an air medium.The dielectric rods possess a refractive index of 3.5, and the lattice constant a measures 575 nm.For switch 1 and switch 2, the radii of the rods are 0.2227a and 0.237a, respectively.
Using the PWE method, two PBG were found for each switch at TM mode; the operating wavelength range for switch 1 is at 1489-2186 nm and 1058-1134 nm, and the operating wavelength range for switch 2 is at 1562-2255 nm and 1065-1190 nm.
The core section is shown in Figure 16 and is composed of two cross-connected resonant cavities with a nonlinear elliptical defect shown in blue color.IN1 and IN2 are inputs and Q and Q' are the output ports.
The rods constituting the foundational structure, illustrated in gray, possess a refractive index of 3.5.The red rods are characterized by a lattice constant of 575 nm and a radius equivalent to 0.15a.The elliptical defects, marked by radii of 0.29a and 0.31a, have a nonlinear coefficient of 9 × 10 −17 m 2 W . Simulations reveal the absence of a PBG in the TM mode, while two distinct PBGs emerge in the TE mode: one spans 1389-2061 nm and the other occupies 783-805 nm.Upon introducing varying wavelengths into IN1 and IN2, it becomes evident that the cavities exhibit resonant modes at 1620 and 1586 nm.These resonant wavelengths enable the emission of light from the core section.
nant cavities with a nonlinear elliptical defect shown in blue color.IN1 and IN2 are inputs and Q and Q' are the output ports.
The rods constituting the foundational structure, illustrated in gray, possess a refractive index of 3.5.The red rods are characterized by a lattice constant of 575 nm and a radius equivalent to 0.15a.The elliptical defects, marked by radii of 0.29a and 0.31a, have a nonlinear coefficient of 9 10 . Simulations reveal the absence of a PBG in the TM mode, while two distinct PBGs emerge in the TE mode: one spans 1389-2061 nm and the other occupies 783-805 nm.Upon introducing varying wavelengths into IN1 and IN2, it becomes evident that the cavities exhibit resonant modes at 1620 and 1586 nm.These resonant wavelengths enable the emission of light from the core section.The final design for the RS FF is shown in Figure 17; the device has two input ports, set and reset, two bias ports B1 and B2, and two output ports Q and Q'.RR1 and RR2 symbolize the representation of two RRs for each of the switches.There are five different states that were simulated.The final design for the RS FF is shown in Figure 17; the device has two input ports, set and reset, two bias ports B1 and B2, and two output ports Q and Q'.RR1 and RR2 symbolize the representation of two RRs for each of the switches.There are five different states that were simulated.Figure 18 illustrates the time response diagrams, showcasing a continuous presentation of all simulated states of the FF.The optical power applied to the input ports is set at 100 mW.Modification in the input logic states results in a rise time of 3.1 ps for Q and 3 Figure 18 illustrates the time response diagrams, showcasing a continuous presentation of all simulated states of the FF.The optical power applied to the input ports is set at 100 mW.Modification in the input logic states results in a rise time of 3.1 ps for Q and 3 ps for Q', correspondingly.The fall time for these transitions is 1 ps.Rise and fall times denote the intervals required to shift between the amplitude values of 10% and 90%, and vice versa, respectively.Consequently, the maximum response time is recorded at 3.1 ps, while the switching speed registers 320 GHz.The normalized power margins for logic 1 and 0 are obtained at 65% and 7%, respectively.Figure 18 illustrates the time response diagrams, showcasing a continuous presentation of all simulated states of the FF.The optical power applied to the input ports is set at 100 mW.Modification in the input logic states results in a rise time of 3.1 ps for Q and 3 ps for Q', correspondingly.The fall time for these transitions is 1 ps.Rise and fall times denote the intervals required to shift between the amplitude values of 10% and 90%, and vice versa, respectively.Consequently, the maximum response time is recorded at 3.1 ps, while the switching speed registers 320 GHz.The normalized power margins for logic 1 and 0 are obtained at 65% and 7%, respectively.In this diagram the output power does not converge to a constant value, it oscillates.This issue is mainly due to reflection at the core section of the resonant cavity and due to In this diagram the output power does not converge to a constant value, it oscillates.This issue is mainly due to reflection at the core section of the resonant cavity and due to the nature of the nonlinear resonant cavity.The suggested design enhances the switching speed at the expense of optical power, yet the operational efficacy of the proposed structures demands a higher optical power compared to other suggested designs.
In 2022, Soma et al. proposed a design of 2D PC-based ultra-compact optical RS FF.The FF is designed using two NOR gates, PC waveguides, four silicon RRs, four input ports, and two output ports.The structure consists of hexagonal silicon rods in an air background with a lattice constant a of 630 nm, rod radius of 0.2a, and operating wavelength of 1550 nm.
Figure 19 shows the proposed structure of the RS FF constructed using a 2D hexagonal lattice PC; the lattice structure is constructed using 55 × 34 silicon rods with air as a background.The PBG is calculated using the PWE method, and the operating wavelength range is extracted from the PGB to be 1316-1978 nm.
The proposed configuration involves the interconnection of two NOR gates.The initial NOR gate is responsible for receiving the reset input and the reference input "B".It is created by utilizing two ring resonators (PCRR3 and PCRR4) along with a T-type waveguide.The outcome of the first NOR gate is divided into two using Y splitter ports.One branch is directed towards output port Q, while the other serves as feedback to the input of the NOR gate.
The second NOR gate is designed to handle the set input and the reference input a.This is achieved by employing two different ring resonators (PCRR1 and PCRR2) in combination with a T-type waveguide.Similar to the first NOR gate, the output of the second NOR gate is divided into two using Y splitter ports.One of these outputs is collected from output port Q', and the other is routed back to the input of the first NOR gate as feedback.
ports, and two output ports.The structure consists of hexagonal silicon rods in an air background with a lattice constant a of 630 nm, rod radius of 0.2a, and operating wavelength of 1550 nm.
Figure 19 shows the proposed structure of the RS FF constructed using a 2D hexagonal lattice PC; the lattice structure is constructed using 55 × 34 silicon rods with air as a background.The PBG is calculated using the PWE method, and the operating wavelength range is extracted from the PGB to be 1316-1978 nm.The proposed configuration involves the interconnection of two NOR gates.The initial NOR gate is responsible for receiving the reset input and the reference input "B".It is created by utilizing two ring resonators (PCRR3 and PCRR4) along with a T-type waveguide.The outcome of the first NOR gate is divided into two using Y splitter ports.One branch is directed towards output port Q, while the other serves as feedback to the input of the NOR gate.
The second NOR gate is designed to handle the set input and the reference input a.This is achieved by employing two different ring resonators (PCRR1 and PCRR2) in combination with a T-type waveguide.Similar to the first NOR gate, the output of the second NOR gate is divided into two using Y splitter ports.One of these outputs is collected from output port Q', and the other is routed back to the input of the first NOR gate as feedback.
The outputs from Q and Q' of each NOR gate are also looped back to the input of both NOR gates through Y splitter connections.The operational wavelength for the optical source applied to the inputs is 1550 nm, and the intensity of the optical signal used is 1 arbitrary unit (a.u.).If the intensity of the optical signal surpasses 0.5 a.u., it is interpreted as logic 1, while a signal with an intensity below 0.5 a.u. is considered logic 0.
The operational characteristics of the newly proposed FF are evaluated across various states using the FDTD method.From the simulation outcomes, it is determined that the contrast ratio at the output ports Q and "Qbar" measures 8.7 dB and 4 dB, respectively.The response time for Q is approximately 1.2 ps, while for "Qbar" it is around 2.6 ps.The outputs from Q and Q' of each NOR gate are also looped back to the input of both NOR gates through Y splitter connections.The operational wavelength for the optical source applied to the inputs is 1550 nm, and the intensity of the optical signal used is 1 arbitrary unit (a.u.).If the intensity of the optical signal surpasses 0.5 a.u., it is interpreted as logic 1, while a signal with an intensity below 0.5 a.u. is considered logic 0.
The operational characteristics of the newly proposed FF are evaluated across various states using the FDTD method.From the simulation outcomes, it is determined that the contrast ratio at the output ports Q and "Qbar" measures 8.7 dB and 4 dB, respectively.The response time for Q is approximately 1.2 ps, while for "Qbar" it is around 2.6 ps.
Additionally, the physical dimensions of the proposed FF are smaller, spanning 28 µm by 28 µm, when compared to what is reported in the previous literature, as outlined in the paper.This compact size is complemented by its fast-switching frequency.

The T Flip-Flop
The T FF, also known as a toggle FF, is an extension of the D FF.It has a single input called T and two outputs Q and Q', as shown in Figure 20.The T input determines whether the FF state toggles or remains unchanged when the CLK signal transitions.The T FF is often used for frequency division, counters, and control circuitry.Additionally, the physical dimensions of the proposed FF are smaller, spanning 28 μm by 28 μm, when compared to what is reported in the previous literature, as outlined in the paper.This compact size is complemented by its fast-switching frequency.

The T Flip-flop
The T FF, also known as a toggle FF, is an extension of the D FF.It has a single input called T and two outputs Q and Q', as shown in Figure 20.The T input determines whether the FF state toggles or remains unchanged when the CLK signal transitions.The T FF is often used for frequency division, counters, and control circuitry.In 2021, M. Valliammai et al. offered a new design for an all-optical chalcogenide T FF utilizing a PC waveguide.The structure of the FF comprises chalcogenide rods arranged in a square lattice on an air substrate.The lattice constant a is maintained at 600 nm, the rod radius is set to 0.19a, the small rod's radius "re" is equal to 0.1a, and the operating wavelength is 1550 nm.
Figure 21 shows the structure of the T FF, which is formed by combining an XOR gate with a D FF.This construction involves incorporating an array of chalcogenide rods arranged in a square lattice, consisting of 26 × 13 rods, exposed to an air substrate.In 2021, M. Valliammai et al. offered a new design for an all-optical chalcogenide T FF utilizing a PC waveguide.The structure of the FF comprises chalcogenide rods arranged in a square lattice on an air substrate.The lattice constant a is maintained at 600 nm, the rod radius is set to 0.19a, the small rod's radius "re" is equal to 0.1a, and the operating wavelength is 1550 nm.
Figure 21 shows the structure of the T FF, which is formed by combining an XOR gate with a D FF.This construction involves incorporating an array of chalcogenide rods arranged in a square lattice, consisting of 26 × 13 rods, exposed to an air substrate.In 2021, M. Valliammai et al. offered a new design for an all-optical chalcogenide T FF utilizing a PC waveguide.The structure of the FF comprises chalcogenide rods arranged in a square lattice on an air substrate.The lattice constant a is maintained at 600 nm, the rod radius is set to 0.19a, the small rod's radius "re" is equal to 0.1a, and the operating wavelength is 1550 nm.
Figure 21 shows the structure of the T FF, which is formed by combining an XOR gate with a D FF.This construction involves incorporating an array of chalcogenide rods arranged in a square lattice, consisting of 26 × 13 rods, exposed to an air substrate.The proposed structure consists of three input ports, T, Cl (control input logic), and CLK, as well as two output ports, Q and Q'.To confirm the toggle logic operation, the actual input bits are energized in the form of a light beam through the T input port.Specifically, the Cl input port represents the former state and appears at the output of the T FF, represented as Q.The CLK input port is activated with logical 1.The XOR receives inputs from the Cl and T ports to create logic values for "D".The D FF section takes inputs from the CLK port and the output of the XOR section is utilized as an input signal.The implementation of a clocked D FF introduces a delay or acts as a buffer for its input signal.
In Figure 22, the contrast ratio is depicted as a measure to illustrate the power level difference between the optical logic 0 and logic 1 states.The power level P0, which varies below 0.28, represents the optical logic 0 state through the Q port.Similarly, the power level P1, above the value of 0.89, signifies the optical logic 0 state through the Q' port.from the CLK port and the output of the XOR section is utilized as an input signal.The implementation of a clocked D FF introduces a delay or acts as a buffer for its input signal.
In Figure 22, the contrast ratio is depicted as a measure to illustrate the power level difference between the optical logic 0 and logic 1 states.The power level P0, which varies below 0.28, represents the optical logic 0 state through the Q port.Similarly, the power level P1, above the value of 0.89, signifies the optical logic 0 state through the Q' port.The effectiveness of this design is evaluated through mathematical analysis using the FDTD technique.The use of chalcogenide glass material proves beneficial in achieving a high contrast ratio, which enables clear differentiation between the logic 0 and logic 1 The effectiveness of this design is evaluated through mathematical analysis using the FDTD technique.The use of chalcogenide glass material proves beneficial in achieving a high contrast ratio, which enables clear differentiation between the logic 0 and logic 1 states.

The JK Flip-Flop
The JK FF is an extension of the SR FF; it has two inputs, J (set) and K (reset), and two outputs, Q and Q', as shown in Figure 23.The J and K inputs determine how the FF state changes when the CLK signal transitions.When J = 1 and K = 0, the output is set (Q = 1) on the CLK edge.When J = 0 and K = 1, the output is reset (Q = 0).When both J and K are 1, the output toggles (Q = Q' or Q' = Q).The effectiveness of this design is evaluated through mathematical analysis using the FDTD technique.The use of chalcogenide glass material proves beneficial in achieving a high contrast ratio, which enables clear differentiation between the logic 0 and logic 1 states.

The JK Flip-flop
The JK FF is an extension of the SR FF; it has two inputs, J (set) and K (reset), and two outputs, Q and Q', as shown in Figure 23.The J and K inputs determine how the FF state changes when the CLK signal transitions.When J = 1 and K = 0, the output is set (Q = 1) on the CLK edge.When J = 0 and K = 1, the output is reset (Q = 0).When both J and K are 1, the output toggles (Q = Q' or Q' = Q).In 2021, a clocked JK FF design was proposed by K. Rao et al. using an advanced air-hole type PC.The structure of the FF is based on the principles of MMI.The proposed JK FF structure consists of an arrangement of 15 × 21 poles organized in a square grid within an air medium.The lattice constant a is 500 nm, while the rod radius is set at 0.5a.The operating wavelength for this design is chosen as 1650 nm.The coupling length, denoted as Lc, of the MMI waveguide is derived from the scattering characteristics of the waveguide, and is specifically set to 8.2a.
The structure of the JK FF, as depicted in Figure 24, comprises a waveguide or MMI region.The MMI area is designed to support a significant number of modes and is connected to input and output waveguides at its front and back ends.These additional waveguides facilitate the transmission and retrieval of light to and from the main MMI waveguide, enabling the operation of the JK FF.
The JK FF consists of three input ports, namely, J, K, and CLK, as well as two output ports, Q and Q'.The J and K ports are responsible for receiving the input bit patterns, while the CLK port is used for the positive-level triggered CLK input.The outputs, Q and Q', represent the resulting binary values generated by the FF.
The photonic band structure is utilized to determine the PBG regions of the crosssection of the PC where the waveguide is constructed.The band structure and scattering behavior are determined using the PWE method.
The determination of the coupling length (Lc) in the system involves considering four possible guided modes: the essential mode, first-order mode, second-order mode, and third-order mode.The guided modes in the PC-based MMI waveguide are determined based on the working point, which depends on the working frequency.At the working point of a equivalent to 0.367, corresponding parameters for the guided modes are obtained and recorded in Table 1, where b is the generated constant of the requested mode.operating wavelength for this design is chosen as 1650 nm.The coupling length, denoted as Lc, of the MMI waveguide is derived from the scattering characteristics of the waveguide, and is specifically set to 8.2a.
The structure of the JK FF, as depicted in Figure 24, comprises a waveguide or MMI region.The MMI area is designed to support a significant number of modes and is connected to input and output waveguides at its front and back ends.These additional waveguides facilitate the transmission and retrieval of light to and from the main MMI waveguide, enabling the operation of the JK FF.The JK FF consists of three input ports, namely, J, K, and CLK, as well as two output ports, Q and Q'.The J and K ports are responsible for receiving the input bit patterns, while the CLK port is used for the positive-level triggered CLK input.The outputs, Q and Q', represent the resulting binary values generated by the FF.
The photonic band structure is utilized to determine the PBG regions of the crosssection of the PC where the waveguide is constructed.The band structure and scattering behavior are determined using the PWE method.
The determination of the coupling length (Lc) in the system involves considering four possible guided modes: the essential mode, first-order mode, second-order mode, and third-order mode.The guided modes in the PC-based MMI waveguide are determined based on the working point, which depends on the working frequency.At the working point of a equivalent to 0.367, corresponding parameters for the guided modes are obtained and recorded in Table 1, where b is the generated constant of the requested mode.The coupling length (Lc) is determined by the essential mode and the second-order mode, ensuring the proper coupling of the three information signals.At this coupling length, the MMI waveguide's output port receives more power, while the other output port receives lower or insignificant power.When a single information port is activated, a single image occurs at multiples of the beat length, which is approximated as the coupling length (Lc) in the structure.The coupling length is set at 8.2a, obtained from the spacing between the focal points of the extreme edge bars in the MMI waveguide multiplied by half of the rod radius.
Figure 25 displays the response time of the JK FF for each test case.The coupling length (Lc) is determined by the essential mode and the second-order mode, ensuring the proper coupling of the three information signals.At this coupling length, the MMI waveguide's output port receives more power, while the other output port receives lower or insignificant power.When a single information port is activated, a single image occurs at multiples of the beat length, which is approximated as the coupling length (Lc) in the structure.The coupling length is set at 8.2a, obtained from the spacing between the focal points of the extreme edge bars in the MMI waveguide multiplied by half of the rod radius.
Figure 25 displays the response time of the JK FF for each test case.Table 2 presents the final contrast ratio results for each output of the JK FF.Table 2 presents the final contrast ratio results for each output of the JK FF.The results show that the contrast ratios at Q' and Q are 8.657 and 6.24 dB, respectively.Additionally, the output time response is measured at 0.27 ps.The structure exhibits a very low response time.Its simplicity, high contrast ratio, power output, and quick response time make it highly suitable for integration into optical circuits.

Conclusions
This paper investigates various structures of all-optical FFs based on PC.The four types of FFs studied are D FF, SR FF, T FF, and JK FF.The key parameters evaluated include response time, contrast ratio, footprint, operating wavelength range, and operating wavelength, as seen in Table 3, which summarizes all the structures discussed in this paper.The contrast ratio range observed in these structures is 6.91-16.68dB, ensuring reliable differentiation between logic 0 and logic 1 states.The operating wavelength range is 1550-1650 nm, falling within the C and L bands, crucial for optical communication systems like telecommunications networks and fiber optic links.The footprint range for the alloptical FFs is 38.85-836 µm 2 , which enables it to be integrated on a large-scale all-optical chip.The response time range is 0.063-3.1 picoseconds.The all-optical FFs' structures are designed using RRs, waveguides, Y-splitters, and MMIs, employing PC technology and leveraging the optical interference effect.Different lattice types, square or hexagonal, and with and without non-linear materials, are used.Point defects, like scattering rods or coupling rods, are introduced to achieve the desired FF operation.In a study published in 1999 by V. Stojanovic et al., an analysis of FFs was conducted using a set of rules to ensure fair and realistic comparisons between high-speed FFs built using different architectures [72].The findings indicate that the response time of these FFs falls within the bracket of 180 to 630 picoseconds, which is considerably slower compared to the earlier mentioned range of 0.063 to 3.1 picoseconds.This substantial difference of 2 to 4 orders of magnitude underscores the remarkable capability of optical components, highlighting their superior potential in terms of operational speed when compared to conventional electrical components.
Different technologies have been proposed to make optical FFs; in a study published in 2005 by R. Clavero et al., an all-optical FF was proposed that is based on a single semiconductor optical amplifier-based Mach-Zehnder interferometer (SOA-MZI) [73].Based on the simulations the authors performed, the response time of the structure is lower than 1 ns.In 2003, H.J.S Dorren et al. studied nonlinear polarization rotations in SOAs and how they can be applied to all-optical FFs [74].The conclusion the paper presents is that an FF using their proposed mechanism can achieve a response time of around 100 picoseconds.A clear difference in speed can be observed when comparing the mentioned examples of all-optical FFs in different technologies to the structures in this review paper, which are all designed using PC technology.Based on the comparison made in this paper, a design can be chosen for different optical computing applications, depending on the preferable trade-off between its parameters.For example, devices with smaller footprints might be preferable to use in high-density integration applications, devices with high contrast ratios might be used in highly accurate optical computing, devices with specific operating wavelengths might be used in certain optical communication systems, etc.In conclusion, this paper highlights the significant advantages of optical FFs, making them a promising technology for advancing optical computing and optical memory systems.

Figure 1 .
Figure 1.(a) Block diagram and (b) truth table of a D FF.

Figure 1 .
Figure 1.(a) Block diagram and (b) truth table of a D FF.
displays a schematic of the proposed structure.

Figure 1 .
Figure 1.(a) Block diagram and (b) truth table of a D FF.

Figure 4 .
The blue colored line describes the state where D = 0, Clk = 1 and CI = 1.The orange colored line describes the state where D = 1, Clk = 1 and CI = 0.

Figure 4 .
The blue colored line describes the state where D = 0, Clk = 1 and CI = 1.The orange colored line describes the state where D = 1, Clk = 1 and CI = 0.

Figure 4 .
Figure 4. Normalized intensity of D FF at (a) port Q' and (b) port Q [63].

Figure 4 .
The blue colored line describes the state where D = 0, Clk = 1 and CI = 1.The orange colored line describes the state where D = 1, Clk = 1 and CI = 0.

Figure 4 .
Figure 4. Normalized intensity of D FF at (a) port Q' and (b) port Q [63].

Figure 4 .
Figure 4. Normalized intensity of D FF at (a) port Q' and (b) port Q [63].

Materials 2023 , 26 Figure 6 .
Figure 6.Normalized intensity at the output of the basic clocked D FF at port Q and Q' [64].Figure 6. Normalized intensity at the output of the basic clocked D FF at port Q and Q' [64].

Figure 6 .
Figure 6.Normalized intensity at the output of the basic clocked D FF at port Q and Q' [64].Figure 6. Normalized intensity at the output of the basic clocked D FF at port Q and Q' [64].

Figure 6 .
Figure 6.Normalized intensity at the output of the basic clocked D FF at port Q and Q' [64].

Figure 7 .
Figure 7. Time evolving curves of the modified clocked D FF at port Q and Q' [64].

Figure 7 .
Figure 7. Time evolving curves of the modified clocked D FF at port Q and Q' [64].

Figure 8 .
Figure 8. Structure of proposed PC based all-optical D FF [65].

Figure 8 .
Figure 8. Structure of proposed PC based all-optical D FF [65].

Figure 8 .
Figure 8. Structure of proposed PC based all-optical D FF [65].

Figure 10 .
Figure 10.(a) Block diagram and (b) truth table of an SR FF.In 2021, Hassan et al. presented an efficient and compact SR FF optical memory-based PC platform.The proposed design is based on two optical NOR logic gates which use two-dimensional PC with a square lattice of silicon dielectric rods in an air background.The lattice constant is 630 nm, and the radius of the silicon rods is equal to 0.2a; the PBG was calculated, and the operating wavelength range was extracted to be 1500-2172 nm and 851-868 nm.The optical memory SR FF employs optical NOR gates, constructed using optical Ttype switches, PC RR, and an array of waveguides equipped with optical power drivers and Y-splitters.The optical NOR gate, designed within a 2D PC framework, is assembled by integrating two optical T-shaped switches.These switches consist of PC resonant rings along with T-type waveguides, which are formed through the introduction of specific defects into the structure of the 2D PC, as visually represented in Figure11.

Figure 10 . 26 Figure 11 .
Figure 10.(a) Block diagram and (b) truth table of an SR FF.In 2021, Hassan et al. presented an efficient and compact SR FF optical memory-based PC platform.The proposed design is based on two optical NOR logic gates which use two-dimensional PC with a square lattice of silicon dielectric rods in an air background.The lattice constant is 630 nm, and the radius of the silicon rods is equal to 0.2a; the PBG was calculated, and the operating wavelength range was extracted to be 1500-2172 nm and 851-868 nm.The optical memory SR FF employs optical NOR gates, constructed using optical T-type switches, PC RR, and an array of waveguides equipped with optical power drivers and Y-splitters.The optical NOR gate, designed within a 2D PC framework, is assembled by integrating two optical T-shaped switches.These switches consist of PC resonant rings along with T-type waveguides, which are formed through the introduction of specific defects into the structure of the 2D PC, as visually represented in Figure 11.Materials 2023, 14, x FOR PEER REVIEW 12 of 26

Figure 11 .
Figure 11.The proposed optical T-switch based on PC RR [67].

Figure 13 .
Figure 13.The proposed structure of optical SR FF based on 2D PC [67].

Figure 13 .
Figure 13.The proposed structure of optical SR FF based on 2D PC [67].

Figure 14 .
Figure 14.The output power (a) at port Q and (b) at port Q' [67].

Figure 15 .
Figure 15.(a) Timing diagram for different SR FF states, (b) normalized intensity at the output of the SR FF [67].

Figure 15 .
Figure 15.(a) Timing diagram for different SR FF states, (b) normalized intensity at the output of the SR FF [67].

Figure 15 .
Figure 15.(a) Timing diagram for different SR FF states, (b) normalized intensity at the output of the SR FF [67].

Figure 16 .
Figure 16.The core section of the proposed device [68].

Figure 16 .
Figure 16.The core section of the proposed device [68].

Figure 17 .
Figure 17.The final structure of the proposed RS FF [68].

Figure 17 .
Figure 17.The final structure of the proposed RS FF [68].

Figure 18 .
Figure 18.Time response of the structure with reset and set inputs [68].

Figure 18 .
Figure 18.Time response of the structure with reset and set inputs [68].

Figure 20 .
Figure 20.(a) Block diagram and (b) truth table of a T FF.

Figure 20 .
Figure 20.(a) Block diagram and (b) truth table of a T FF.

Figure 20 .
Figure 20.(a) Block diagram and (b) truth table of a T FF.

Figure 21 .Figure 21 .
Figure 21.Light propagation in the "11" state of the T FF [70].The proposed structure consists of three input ports, T, Cl (control input logic), and CLK, as well as two output ports, Q and Q'.To confirm the toggle logic operation, the actual input bits are energized in the form of a light beam through the T input port.Specifically, the Cl input port represents the former state and appears at the output of the T FF, represented as Q.The CLK input port is activated with logical 1.The XOR receives inputs from the Cl and T ports to create logic values for "D".The D FF section takes inputs

Figure 23 .
Figure 23.(a) Block diagram and (b) truth table of a JK FF.In 2021, a clocked JK FF design was proposed by K. Rao et al. using an advanced airhole type PC.The structure of the FF is based on the principles of MMI.The proposed JK FF structure consists of an arrangement of 15 × 21 poles organized in a square grid within

Figure 23 .
Figure 23.(a) Block diagram and (b) truth table of a JK FF.

Figure 25 .
Figure 25.Response time of FF for change in output [71].

Figure 25 .
Figure 25.Response time of FF for change in output [71].

Table 3 .
Comparison of all works discussed in this paper.

of Structure Mechanisms and Effects Response Time (psec) Contrast Ratio (dB) Footprint (µm 2 )
* Parameters for Si rods.** Parameters for chalcogenide glass rods.