Abstract
Polarization holography has emerged as a promising method for manipulating the amplitude, phase, and polarization states of light waves. This study proposes what we believe to be a novel design method for various all-optical logic devices, including a complete set of all-optical Boolean logic gates and a polarization-controlled 1 × 4 optical switch, utilizing polarization holography. Through the angle multiplexing technique, specially designed polarization holograms are recorded in polarization-sensitive material, transforming it into all-optical Boolean logic gates and a polarization-controlled 1 × 4 optical switch. The all-optical logic devices developed in this work function as passive diffractive optical elements, enabled by a single piece of polarization-sensitive material, eliminating the need for additional circuit control. This approach offers the advantages of a simple structure, low cost, and instantaneous response. We contend that this advancement will facilitate the expansion of the application domains of polarization holography, particularly enhancing the capabilities of all-optical information processing.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In contrast to conventional holography, polarization holography records and reconstructs not only the amplitude and phase of lightwaves but also their polarization state [1–3]. Due to its unique capability to record and reconstruct the complete information of lightwaves, polarization holography has become a prominent research area in recent years [4–6]. Tensor polarization holography theory has made significant advancements by overcoming the limitations of the paraxial approximation condition and explaining polarization holographic properties at arbitrary interference angles [7,8]. This theory has been employed to derive and verify intriguing reconstruction phenomena, including faithful reconstruction, null reconstruction, and orthogonal reconstruction [9,10]. Furthermore, these phenomena have been successfully applied to various fields, such as optical storage, optical field modulation, and micro-nano processing [11–15]. The above studies show the veracity of tensor polarization holography theory has been definitively established, and applied research based on the theory has yielded specific outcomes.
On the other hand, the advantages of all-optical information processing, which include the speed of light, parallel processing, and high reliability, have led to its widespread utilization in optical computing, optical communication, and optical networks [16,17]. Additionally, all-optical logic devices, including all-optical logic gates and optical switches, are of paramount importance for all-optical signal processing [18,19]. However, current all-optical logic devices, such as those based on semiconductor optical amplifiers (SOAs), photonic crystals (PCs), and periodically poled lithium niobates (PPLNs), still face challenges [18,20]. Although SOA-based all-optical logic devices possess the advantages of low loss, simple structure, and ease of integration with other devices, they are limited by long carrier recovery time, resulting in a low signal processing rate [21,22]. PC-based all-optical logic devices have the advantages of a simple structure and faster response. Nevertheless, they sometimes lack contrast [23,24]. PPLN-based all-optical logic devices offer fast response and low noise, but they face challenges in waveguide fabrication, the need for precise temperature control, and high optical power injection [25,26]. Polarization holography offers a promising alternative to overcome these challenges, making it attractive for all-optical logic devices. Consequently, all-optical logic devices utilizing polarization holography have also been developed [27–31]. These devices are typically regarded as having relatively simple structures, low cost, and offering an instantaneous response. However, while these methods can implement several specific logic gates, they have yet to achieve a complete set of logic gates, making it urgent to develop a method for this.
In this paper, we propose the design scheme of a complete set of all-optical Boolean logic gates and a polarization-controlled 1 × 4 optical switch. As for the all-optical Boolean logic gates, which are determined by a binary logical operation, where the “dark” and “Bright” states of input and output light signals represent the “0” and “1” of the logic states. Specifically, the implementation of the all-optical logic gates in this work is as follows: at first, in order to implement different logic gates, during the recording process, two polarization holograms are recorded in the same or different areas of a polarization-sensitive material via an angle multiplexing technique; next, during the reconstruction process (practical work), the reading waves satisfying the Bragg conditions serve as the input optical signals for the all-optical logic gates [32]. According to the Boolean logic rules, a background wave is added in the propagation direction of the reconstructed waves, they are then coherently superimposed to form the output optical signal for the all-optical logic gate. The implementation of the polarization-controlled 1 × 4 optical switch in this work proceeds as follows: During the recording process, four specially designed polarization holograms with the functions of 90° polarizer, 0° polarizer, right circular polarization detection, and left circular polarization detection are sequentially recorded onto the same area of a polarization-sensitive material via an angle multiplexing technique [33]; during the reconstruction process (practical work), changing the polarization state of the input optical signals achieves optical path switching at the output ports. These all-optical logic devices are constructed from a single piece of polarization-sensitive material (phenanthrenequinone-doped poly (methyl methacrylate) (PQ/PMMA)), with a thickness of 1.5 mm, which does not require additional circuit control and is characterized by its small size, simple structure, easy fabrication process, and low cost [34]. As a result, they can be easily integrated into various optical systems that require optical signal control. Furthermore, by adjusting the diameter of the recording waves and the dimensions of the material, all-optical logic devices of different dimensions can be designed to meet the needs of specific optical systems. Finally, as passive diffractive optical elements, their response speed is theoretically instantaneous, depending on the thickness and refractive index of the material [35,36].
2. Single-area interference recording designs for NAND, OR, XNOR, NOT, and XOR all-optical logic gates
2.1 Theoretical analysis
The design of the NAND, OR, XNOR, NOT, and XOR all-optical logic gates employed the following techniques, utilizing tensor polarization holography theory. The design diagram for the recording and reconstruction processes is presented in Fig. 1. For a simplified description, we defined θ1 and θ2 as the angles between the propagation directions of the signal wave (G+) and those of the two reference waves (G−1 and G−2). These angles are referred to as the interference angle. The s-polarization is parallel to the y-axis of the coordinate system, while the p-polarization lies in the x-z plane and is perpendicular to the propagation direction of the lightwave. As shown in Eq. (1), the s-polarization is represented by the unit vector s, the p-polarization of the G+ is represented by the unit vector p+, while the p-polarization of the reference and reading waves is represented by the unit vector p−. And the subscripts i = 1, 2 denote two reference or reading waves in different propagation directions [7,8].
Fig. 1. Design diagram of single-area preparation of NAND, OR, XNOR, NOT, and XOR all-optical logic gates. (a) Recording and (b) reconstruction processes.
During the recording process illustrated in Fig. 1(a), two specially designed polarization holograms (PHs) were sequentially recorded on the same area of the recording material via an angle multiplexing technique. The G+ was perpendicular to the material surface, while the propagation directions of the G−1 and G−2 were not fixed. According to Kogelnik’s coupled wave theory, we only need to ensure that the deviation in the interference angle between each signal wave and reference wave is greater than the Bragg angular selectivity [32]. The interference angles between the signal wave and the two reference waves are θ1 and θ2, respectively. It is noteworthy that the interference angles are the included angles between the signal and reference waves inside the material. Subsequently, during the reconstruction process illustrated in Fig. 1(b), when the two PHs were illuminated by the two reading waves (F−1 and F−2) that satisfy the Bragg condition as input optical signals, two reconstructed waves (GF1 and GF2) with the same propagation path appeared instantaneously behind the material. At this point, a background wave (B), which propagates in the same direction as the reconstructed waves, was also added. The output optical signal (O) was a coherent superposition of B, GF1, and GF2, and this O was considered the output optical signal. The G+, G−1, G−2, F−1, F−2, B, and O with linear polarization are defined as in Eq. (2):
By combining Eq. (2) with the tensor polaization holography theory, we obtained the expression for the reconstructed waves [7]:
From Eq. (3), we determined that the polarization states of the two reconstructed waves were consistent with the signal wave, demonstrating the faithful reconstruction capability of polarization holography. The polarization states of the reconstructed waves were independent of the interference angle, allowing for flexibility in choosing an appropriate interference angle for the experimental setup. Additionally, the polarization states of the reconstructed waves were independent of the exposure time, which only affected the light intensity of the reconstructed waves. This enabled flexible control of the exposure time, allowing us to adjust the light intensity of the two reconstructed waves as needed.
To realize all-optical logic gates, it is sometimes necessary to introduce a background wave in conjunction with coherent superposition theory. For instance, consider the design of a NAND logic gate. The truth table of the NAND logic gate is shown in Table 1.
As observed in Table 1, different combinations of inputs 1 and 2 result in corresponding output logic. Here, we define logic states based on the light intensity of the input and output optical signals. When the light intensity of the input and output optical signals is zero (i.e., dark), we assume that the optical signals at the input and output ports have logic states of “0”. Conversely, When the light intensity of the input and output optical signals is not zero (i.e., Bright), the optical signals at the input and outputs have logic states of “1”. Thus, we can determine the optical signals at the inputs and outputs of the designed NAND logic gate, as shown in Table 2. By combining Fig. 1, Eq. (2), Eq. (3), and Table 2, we can determine the polarization states and amplitude of input signals (F−1 and F−2) and the output optical signals (O) for the designed NAND logic gate, as shown in Table 3. The OR, XOR, and NOT all-optical logic gates use the same recording method as the NAND gates, as shown in Tables 4–6.
The XOR logic gate was designed slightly differently from the four previously mentioned logic gates. During the recording process, the recording conditions for PH1 remained unchanged, while the recording conditions for PH2 are shown in Eq. (4). During the reconstruction process, the reading wave was a p-polarization wave, and according to the tensor polarization holography theory, the expression for the reconstructed wave is shown in Eq. (5).
Based on the truth table of the XOR logic gate and using the aforementioned logic rules for logic “0” and “1”, we can determine the optical signals at the inputs and outputs of the designed XOR logic gate, as shown in Table 7. By combining Fig. 1, Eqs. (2) to (5), and Table 7, we can determine the polarization states and amplitude of the input signals (F−1 and F−2) and output optical signals (O) for the designed XOR logic gate, as shown in Table 8.
The experimental setup is illustrated in Fig. 2. The laser beam emitted by the Laser 1, with a wavelength of 532?nm, was expanded into a circular beam with a uniform intensity distribution and a diameter of 5 mm by passing through a beam expander (BE) and an aperture 1 (AP1). The polarization beam splitter (PBS) and beam splitter (BS) split the expanded laser beam into a signal wave and two reference or reading waves. Half-wave plate 1 (HWP1) controlled the optical power ratio between the signal waves and the two reference or reading waves; ensuring that their powers were equal to 10?mW (51 m W/cm2). The signal wave was incident perpendicular to the surface of the material. Mirrors M2 and M3 were used to modulate the propagation direction of the two reference or reading waves to record two polarization holograms in the same area of the material. The interference angles θ1 and θ2 used in the experiment were approximately 8°.
Fig. 2. Experimental setup. Laser, 532?nm single longitudinal mode laser; BE, beam expander; AP, aperture; HWP, half-wave plate; PBS, polarizing beam splitter; BS, beam splitter; M, mirror; AT, attenuator; SH, electronic shutter; CCD, charge-coupled Device.
During the recording process, HWP3 was used to control the polarization state and phase delay of the signal wave (G+), changing it to either an s-polarization or −s-polarization wave. Aperture 1 (AT1) on the signal path was removed during the recording process. The polarization states of the reference waves (G−1 and G−2) were controlled by HWP4 and HWP2, respectively, changing them to p-polarization waves. AP2-4 were used to limit the sizes of the G+, G−1, and G−2. Simultaneously, the duration of the polarization holographic recording was controlled by cyclically switching SH1-3 between open and closed states, allowing brief observation of the two reconstructed waves (GF1 and GF2). In each cycle, the recording time was 5 s, and the observation time of the reconstructed wave was 0.5 s. The recording process was stopped when the light intensity of the two reconstructed waves became equal. During the reconstruction process, SH2 was opened to introduce a background wave (B). Furthermore, HWP3 was rotated by 90° clockwise to ensure the added background wave had a π phase delay relative to the signal wave. AT was set and rotated to adjust the light intensity of the background wave. According to Tables 3–6 and 8, the background wave must be introduced during the reconstruction process of the NAND, XNOR, and NOT logic gates, while the OR and XOR logic gates did not require a background wave. Experimental experience indicates that when the light intensity of the background wave is 8.6 times that of the reconstructed wave, the difference in light intensity between the output optical signal defined as a logic “0” and logic “1” is maximized, providing the CCD with higher tolerance. HWP2 and HWP4 were adjusted so that the polarization states of the two reading waves (F−1 and F−2), which are the input optical signals, matched those of the reference waves (G−1 and G−2).
2.3 Experimental results and discussion
Taking the NAND logic gate as an example, we observe the following behavior: When SH1 and SH3 are closed, the material is not illuminated by the F−1 and F−2, meaning the optical logic states of input ports 1 and 2 are both “0”. Consequently, there are no GF1 and GF2, and the CCD detects only B as the output optical signal, with a non-zero light intensity, indicating the optical logic state of the output port is “1”. When SH1 is opened and SH3 is closed, the material is illuminated solely by F−1. This sets the optical logic state of input port 1 to “1” and input port 2 to “0”. At this point, GF1 is present, and the CCD receives a superimposed wave of GF1 and B as the output optical signal, which again has a non-zero light intensity, indicating the optical logic state of the output port is “1”. When SH1 is closed and SH3 is opened, the material is illuminated only by the F−2, setting the optical logic state of input port 1 to “0” and input port 2 to “1”. Here, GF2 is present, and the CCD detects a superimposed wave of GF2 and B as the output optical signal, also with a non-zero light intensity, meaning the optical logic state of the output port remains “1”. Finally, when both SH1 and SH3 are opened, the material is illuminated by both F−1 and F−2 simultaneously, setting the optical logic states of input ports 1 and 2 to “1”. In this case, GF1 and GF2 are both present, and the CCD received a superimposed wave of GF1, GF2, and B as the output optical signal, which has a zero-light intensity, as shown in Table 3, indicating the optical logic state of the output port is “0”. As shown in Tables 4–9, similar analyses can be applied to OR, XNOR, NOT, and XOR logic gates by examining the input and output optical signals to determine the optical logic states of the input and output ports.
Table 9. Logic table of dual-area.
The experimental images of the input and output optical signals, captured using a CCD, are shown in Fig. 3. The optical logic is determined by the light intensity of these signals. The normalized light intensity of the output optical signals was calculated based on the average grey value of the experimental image at the output, as indicated by the red numbers in Fig. 3. The optical logic at the input ports can be inferred from the presence of reading waves illuminating the material. The optical logic at the output port is determined by the light intensity of the output optical signal. Specifically, when the normalized light intensity is less than 0.2, the optical signal at the output port is considered dark, corresponding to an optical logic of “0”. Conversely, when the normalized light intensity exceeds 0.2, the optical signal at the output port is considered bright, corresponding to an optical logic of “1”. According to these logic rules, the operation of the NAND, OR, XNOR, NOT, and XOR all-optical logic gates is successfully realized.
Fig. 3. Experimental images. (a)-(e) depict NAND, OR, XNOR, NOT, and XOR all-optical logic gates, respectively, where the red values on the output images represent the normalized diffraction efficiencies of the respective output ports.
3. Dual-area interference recording designs for NOR and AND all-optical logic gates
3.1 Theoretical analysis
The design scheme of single-area interference recording is not applicable for the all-optical NOR and AND logic gates [31]. Consequently, the design scheme of dual-area interference recording is employed to implement these two all-optical logic gates.
During the recording process illustrated in Fig. 4(a), the material to be recorded was divided into two areas: Area 1 and Area 2. The polarization states of signal wave (G+), reference wave 1 (G−1), reference wave 2 (G−2) are shown in Eq. (6).
Fig. 4. Design diagram of dual-area preparation of NOR and AND all-optical logic gates. (a) Recording and (b) reconstruction processes.
During the reconstruction process illustrated in Fig. 4(b), the reading wave 1 (F−1) and reading wave 2 (F−2), which serve as the input optical signals, were divided and directed onto Area 1 and Area 2, respectively. The input optical signals on Area 1 and Area 2 together determined the optical logic at the input ports. Two detectors were used to receive the reconstructed waves from Area 1 and Area 2 as output optical signals, which together determined the optical logic at the output port. The polarization states of reading wave 1 (F−1), reading wave 2 (F−2), reconstructed wave 1 (GF1), reconstructed wave 2 (GF2), background wave (B), and output optical signal (O) are shown in Eq. (7) [7].
The final input and output logic states were established by analyzing the combined light intensities of the input and output optical signals in both Area 1 and Area 2, as depicted in Table 9.
In Table 9, when the bright and dark states of Area 1 and Area 2 were identical, i.e., either both areas had zero light intensity or neither had zero light intensity, which represented logic “1”. Conversely, when the bright and dark states of Area 1 and Area 2 differed, i.e., one area had zero light intensity while the other had not zero, which represented logic “0”. For ease of design, we used the logic rules specified in lines 2 and 3 of Table 9. Area 1 did not require the recording of polarization holograms and remained dark, while Area 2 recorded two polarization holograms via an angle multiplexing technique. Based on these logic rules and the truth table of the NOR gate, the optical signals at the inputs and outputs of the designed NOR logic gate are shown in Table 10.
Table 10. Optical signals of the designed NOR logic gate.
Similar to the implementation of NAND gates, the use of a background lightwave (B) was necessary for NOR gates to perform logical operations, as depicted in Fig. 4(b). By combining Eqs. (7) and Table 10, we determined the polarization states and amplitude of the input optical signals (F−1 and F−2) and output optical signal (O) of the designed NOR logic gate, as shown in Table 11. By integrating the truth table of the AND gate with the logic rules from Table 9, we can determine the polarization states and amplitude of the input (F−1 and F−2) and the output optical signal (O) for the designed AND logic gate, as shown in Table 12.
Table 11. The polarization states and amplitude of input and output optical signals of the NOR logic gates.
Table 12. The polarization states and amplitude of input and output optical signals of the AND logic gates.
3.2 Experimental results and discussion
The experimental setup for designing NOR and AND gates is shown in Fig. 2. Given that recording polarization holograms in Area 1 was unnecessary, G−1, G−2, and G+ were directed through AP2-4 to partition the recording area into Area 1 and Area 2. The recording process for NOR gates followed similar steps to those for NAND gates, while the process for AND gates paralleled those for OR gates. During the reconstruction process, SH2 is controlled to open and close depending on whether the background lightwaves needs to be introduced according to Tables 11 and 12, and the optical signals at the input ports were regulated by alternately opening and closing SH1 and SH3. The CCD subsequently captured the experimental images of the input and output optical signals, as shown in Fig. 5.
Fig. 5. Experimental images. (a)-(b) depict NOR and AND all-optical logic gates, respectively, where the red values on the output images represent the normalized diffraction efficiencies of the respective output ports.
As shown in Table 9, considering the logic rules between light intensity and the operation of all-optical logic gates, the light intensity difference between “dark” and “light” should be as large as possible to provide higher tolerance for the detector in practical applications. In our experiments, based on the principle of coherent light superposition, we designed the light intensity of the background wave to be 8.6 times that of the reconstructed waves. Additionally, we set a gray scale threshold to reduce the interference of ambient light [31]. These measures result in a discrepancy between the experimental diffraction efficiency shown in Fig. 5 and the theoretical values presented in Tables 11 and 12. The normalized light intensity of the output optical signals was derived from the average gray value of the experimental image at the output, indicated by the red numbers in Fig. 5. The optical logic at the input ports was easily judged by whether reading waves illuminated Area 1 and Area 2 of the material. Similarly, the optical logic at the output port was determined by the light intensity of the output optical signals in Area 1 and Area 2. When the normalized light intensity was less than 0.2, the output optical signal in the respective area was considered dark; when the normalized light intensity exceeded 0.2, the output optical signal was considered bright. As shown in Table 9, the final input and output logic was determined by combining the different light intensities of the input and output optical signals in Area 1 and Area 2. Following these logic rules, the operation of the NOR and AND all-optical logic gates is successfully realized.
4. Polarization-controlled 1 × 4 optical switch
4.1 Theoretical analysis
We employed following techniques to design a polarization-controlled 1 × 4 optical switch based on tensor polarization holography theory. During the recording process, four specially designed polarization holograms (PHs) were recorded sequentially at the same area of the recording material via an angle multiplexing technique. PHs1-4 functioned similar to those of a polarizer with an angle of 90° between the transmission axis and horizontal direction (90° polarizer), a polarizer with an angle of 0° between the transmission axis and horizontal direction (0° polarizer), a right circular polarization detector, and a left circular polarization detector, respectively [33,37]. The reference wave (G−) was perpendicular to the material surface, and the propagation directions of the four signal waves (G + 1, G + 2, G + 3, and G + 4) for recording the four PHs were tailored according to experimental requirements. Additionally, the interference angles between the four signal waves and reference wave were θ1, θ2, θ3, and θ4, respectively. It is noteworthy that the interference angles were the included angles between the signal and reference waves inside the material. Subsequently, during the reconstruction process, upon the illumination of the four PHs by the reading wave (F–) satisfying the Bragg condition, four distinct reconstructed waves (GF1, GF2, GF3, and GF4) with no crosstalk among them appeared behind the material.
Moreover, during the reconstruction process, PHs1-4 recorded on the recording material functioned similarly to the 90° polarizer, 0° polarizer, right circular polarization detector, and left circular polarization detector. Considering a reading wave with p-polarization. Because the function of PH1 was similar to that of the 90° polarizer, the light intensity of GF1 was 0. The function of PH2 was similar to that of the 0° polarizer; therefore, the light intensity of GF2 was not 0. The function of PH3 was similar to that of the right circular polarization detector, and the reading wave with p-polarization contained left circular polarization components; hence, the light intensity of GF3 was not 0. The function of PH4 was similar to that of the left circular polarization detector, and the reading wave with p-polarization contained right circular polarization components; therefore, the light intensity of GF4 was not 0. These observations were consistent for reading waves with s-, right circular, and left circular polarization. Consequently, during the reconstruction process, the reconstruction phenomenon is shown in Fig. 6.
Fig. 6. Schematic of the working principle of the optical switch utilizing the tensor polarization holography theory.
4.2 Experimental setup and procedure
The experimental setup used to fabricate the optical switch with a laser wavelength of 532?nm and coherence length of 50 m is shown in Fig. 7.
Fig. 7. Experimental setup for fabricating the optical switch. BE: beam expansion, APE: aperture, M: mirror, HWP: half-wave plate, QWP: quarter-wave plate, PBS: polarization beam splitter, POL: polarizer, SH: shutter, PM: power meter, and CCD: charge-coupled device. (a) Recording and (b) reconstruction processes.
Initially, the laser beam was expanded using a BE into a circular beam with uniform intensity distribution and a diameter of 5 mm. Subsequently, the expanded beam passed through PBS1, where the reflected and transmitted beams were used as the signal and reference (or reading) waves, respectively. HWP1 was employed to control the optical power ratio between the reflected and transmitted beams, ensuring both had powers of 51.0?mW/cm2. The polarization states of the signal waves were adjusted using a combination of HWP2 and QWP1, while the polarization states of the reference or reading waves were modified using HWP3 and QWP2. The recording material used in the experiment was PQ/PMMA, with dimensions of 51 × 54 × 1.5 mm (thickness) and a PQ concentration of 1 wt.% [34].
During the recording process, the propagation direction of the signal waves was adjusted by varying the position and rotation of reflector M3 so that the signal and reference waves enabling the formation of four specially designed PHs at distinct interference angles. The PHs were recorded sequentially in the same area of the PQ/PMMA sample. According to Kogelnik's coupled wave theory, to ensure that the deviations of the interference angles between each signal and reference wave exceeded the Bragg angular selectivity, the interference angles for the four PHs were set to θ1 = 7.21°, θ2 = 10.63°, θ3 = 15.26°, and θ4 = 18.15° [32]. The exposure response coefficient (A/B), which depends solely on the material at the initial exposure stage, was measured in advance [38]. The A/B value for the PQ/PMMA samples used in this study at the initial exposure stage (i.e., at exposure energy less than 30 J/cm2) was approximately 7.0. The conditions utilized for recording these four specially designed PHs are shown in Table 13.
Table 13. Conditions used for recording the four polarization holograms.
The recording process was divided into four steps, and a polarization hologram was recorded in each step. During the recording of each polarization hologram, SH2 remained open. Concurrently, by cyclically switching SH1 and SH3 between open and closed states, we controlled the polarization holographic recording time and briefly observed the reconstructed wave. Each cycle consisted of a 5 s recording period and a 0.5 s observation period for the reconstructed wave. This brief observation of the reconstructed wave did not damage the hologram. Subsequently, the polarization states of the reconstructed waves were captured and analyzed using PM1 and PM2, as illustrated in Fig. 7. When the power ratio of the p- and s-polarization components or polarization angle of the reconstructed wave matched that listed in line 5 of Table 13, the polarization hologram recording at this step was deemed complete. Polarization holograms 1-4 were recorded sequentially as shown in Table 13.
4.3 Experimental results and discussion
During the reconstruction process, SH1 remained closed, SH2 remained open, and SH3 was removed. By controlling HWP3 and QWP2, the p-, s-, left-handed circular, and right-handed circular polarization waves were obtained. When these four polarization waves illuminated the recorded material, four non-crosstalk reconstructed waves emerged behind the material. The CCDs positioned behind the material captured these reconstructed waves. The experimental results are shown in Fig. 8.
Fig. 8. The reconstructed images and their corresponding normalized diffraction efficiencies for the reading waves, utilizing four distinct polarization states during the reconstruction process. (a)-(d) illustrate the reading waves with p-polarization, s-polarization, right-handed circular polarization, and left-handed circular polarization, respectively.
In Fig. 8. The red numbers represent the normalized diffraction efficiency of GF received at the O1, O2, O3, and O4 output ports, respectively. This efficiency was calculated from the average grey value of the reconstructed images at the output ports. Moreover, the reconstructed image depicted in Fig. 8 revealed that the light intensity signals received at the output ports were contrasted. However, a specific error between the experimental and theoretical values of the normalized diffraction efficiency was observed, which may be attributed to the following factor: the initial value of A/B used in the experiment was 7.0, determined through preliminary experiments. Due to systematic error in the experimental setup, this measured value may slightly differ from the actual initial A/B value of the material, potentially introducing errors in subsequent experiments [33]. However, according to the experimental results shown in Fig. 8, the error between the experimental and theoretical values was within an acceptable range. These results demonstrated that the device could switch the optical path of the output port by changing the polarization state of the input optical signal. Consequently, the experimental data verified the feasibility of designing an optical switch utilizing tensor polarization holography theory.
5. Conclusions
This study presents a comprehensive design scheme for all-optical Boolean logic gates and a polarization-controlled 1 × 4 optical switch utilizing the tensor polarization holography theory. The proposed all-optical logic device exhibits a simple structure, low cost, and instantaneous response. Although the light intensity of the output optical signals by the designed all-optical logic device is relatively weak, only on the order of µW, the experiments were conducted in a controlled darkroom environment to minimize potential interference from ambient light and ensure the experimental results remain valid and reliable. It is noteworthy that the input optical signals for the designed all-optical logic gates are not constrained to the p-polarization state; rather, optical signals of any polarization state can be utilized. This versatility is achieved through employing small-angle interference to ensure orthogonality between the polarization states of the signal wave and the input optical signal, while maintaining consistency between the polarization state of the reference wave and the input optical signal [39]. Furthermore, the designed optical switch imposes specific criteria on the accuracy of the polarization state of the input optical signal. It is assumed that the optical switch functions properly when the ratio of the minimum diffraction efficiency of the reconstructed wave, defined as “0” at the output, to the diffraction efficiency of the reconstructed wave, defined as “1” at the output, exceeds 15. According to simulation, the following tolerances are observed: when the input optical signal is a p- or s-polarization wave, the allowable difference in polarization angle between the actual input and the ideal input is within 10.52°; similarly, when the input optical signal is a right- or left-handed circular polarization wave, the permissible difference in ellipticity between the actual input and the ideal input is within 0.240.
The all-optical logic devices we have designed, utilizing the tensor polarization holography theory, not only deepens our understanding of polarization holography but also broadens its applicability. These devices hold significant potential for use in various optical systems requiring optical signal control, including fields such as optical communications and networks. Looking forward, the implementation of liquid crystal spatial light modulators could facilitate the recording of spatially distributed polarization holograms in recording materials, thereby enabling functions analogous to those of metamaterials [40–42]. This advancement opens exciting avenues for future research and innovation in optics and photonics.
Funding
National Key Research and Development Program of China (2018YFA0701800); National Natural Science Foundation of China (U22A2080); Project of Fujian Province Major Science and Technology (2020HZ01012).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are available from the authors upon reasonable request.
References
1. X. Lin, J. Liu, J. Hao, et al., “Collinear holographic data storage technologies,” Opto-Electron. Adv. 3(3), 190004 (2020). [CrossRef]
2. J. Hao, X. Lin, Y. Lin, et al., “Lensless complex amplitude demodulation based on deep learning in holographic data storage,” Opto-Electron. Adv. 6(3), 220157 (2023). [CrossRef]
3. L. Nikolova and P. S. Ramanujam, Polarization holography (Cambridge University, 2009).
4. Q. Xu, X. Zhang, Y. Xu, et al., “Polarization-controlled surface plasmon holography,” Laser Photonics Rev. 11(1), 1600212 (2017). [CrossRef]
5. L. D. Sio, D. E. Roberts, Z. Liao, et al., “Digital polarization holography advancing geometrical phase optics,” Opt. Express 24(16), 18297–18306 (2016). [CrossRef]
6. L. Rong, W. Xiao, F. Pan, et al., “Speckle noise reduction in digital holography by use of multiple polarization holograms,” Chin. Opt. Lett. 8(7), 653–655 (2010). [CrossRef]
7. K. Kuroda, Y. Matsuhashi, R. Fujimura, et al., “Theory of polarization holography,” Opt. Rev. 18(5), 374–382 (2011). [CrossRef]
8. P. Qi, J. Wang, H. Song, et al., “Faithful reconstruction condition of linear polarization holography,” Acta Opt. Sin. 40(23), 2309001 (2020). [CrossRef]
9. J. Wang, X. Tan, P. Qi, et al., “Linear polarization holography,” Opto-Electron. Sci. 1(2), 210009 (2022). [CrossRef]
10. R. Wei, J. Zang, Y. Liu, et al., “Review on polarization holography for high density storage,” Opto-Electron. Eng. 46(3), 180598 (2019). [CrossRef]
11. J. Zang, G. Kang, P. Li, et al., “Dual-channel recording based on the null reconstruction effect of orthogonal linear polarization holography,” Opt. Lett. 42(7), 1377–1380 (2017). [CrossRef]
12. J. Zang, F. Fan, Y. Liu, et al., “Four-channel volume holographic recording with linear polarization holography,” Opt. Lett. 44(17), 4107–4110 (2019). [CrossRef]
13. L. Huang, Y. Zhang, Q. Zhang, et al., “Generation of a vector light field based on polarization holography,” Opt. Lett. 46(18), 4542–4545 (2021). [CrossRef]
14. T. Ye, J. Wang, J. Liu, et al., “Generation of vector beams based on diffraction characteristics of a linear polarization hologram in coaxial recording,” Opt. Express 31(5), 7764–7773 (2023). [CrossRef]
15. X. Xu, Y. Zhang, H. Song, et al., “Generation of circular polarization with an arbitrarily polarization reading wave,” Opt. Express 29(2), 2613–2623 (2021). [CrossRef]
16. A. Mohebzadeh-Bahabady and S. Olyaee, “Designing an ultracompact all-optical 4-to-2 encoder and investigating its optical power consumption,” Appl. Opt. 59(8), 2409–2415 (2020). [CrossRef]
17. L. Wu, T. Fan, S. Wei, et al., “All-optical logic devices based on black arsenic-phosphorus with strong nonlinear optical response and high stability,” Opto-Electron. Adv. 5(1), 200046 (2022). [CrossRef]
18. H. Qi, Z. Du, X. Hu, et al., “High performance integrated photonic circuit based on inverse design method,” Opto-Electron. Adv. 5(10), 210061 (2022). [CrossRef]
19. Y. Huang, T. Xiao, S. Chen, et al., “All-optical controlled-NOT logic gate achieving directional asymmetric transmission based on metasurface doublet,” Opto-Electron. Adv. 6(7), 220073 (2023). [CrossRef]
20. S. Jiao, J. Liu, L. Zhang, et al., “All-optical logic gate computing for high-speed parallel information processing,” Opto-Electron. Sci. 1(9), 220010 (2022). [CrossRef]
21. K. E. Stubkjae, “Semiconductor optical amplifier-based all-optical gates for high-speed optical processing,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1428–1435 (2000). [CrossRef]
22. M. Zhang, W. Ling, and Y. Peida, “All optical XOR logic gates: technologies and experiment demonstrations,” IEEE Commun. Mag. 43(5), S19–S24 (2005). [CrossRef]
23. A. Salmanpour, S. Mohammadnejad, and A. Bahrami, “Photonic crystal logic gates: an overview,” Opt. Quantum Electron. 47(7), 2249–2275 (2015). [CrossRef]
24. H. M. E. Hussein, T. A. Ali, and N. H. Rafat, “A review on the techniques for building all-optical photonic crystal logic gates,” Opt. Laser Technol. 106, 385–397 (2018). [CrossRef]
25. Y. L. Lee, B. Yu, T. J. Eom, et al., “All-optical AND and NAND gates based on cascaded second-order nonlinear 3 waveguide,” Opt. Express 14(7), 2776–2782 (2006). [CrossRef]
26. J. Wang, J. Sun, and Q. Sun, “Single-PPLN-based simultaneous half-adder, half-subtracter, and OR logic gate: proposal and simulation,” Opt. Express 15(4), 1690–1699 (2007). [CrossRef]
27. X. Yang, C. Zhang, S. Qi, et al., “All-optical Boolean logic gate using azo-dye doped polymer film,” Optik 116(6), 251–254 (2005). [CrossRef]
28. R. Forsati, S. Ebrahimi, K. Navi, et al., “Implementation of all-optical reversible logic gate based on holographic laser induced grating using azo-dye doped polymers,” Opt. Laser Technol. 45, 565–570 (2013). [CrossRef]
29. C. Li, L. Cao, J. Li, et al., “Polarization-based all-optical logic operations in volume holographic photopolymer,” In Proceeding of SPIE Holography, Diffractive Optics, and Applications VI, 24–29 (2014).
30. R. Xia, C. Wang, T. Chen, et al., “Design of an all-optical logic sequence generator based on polarization holographic gratings,” Chin. Opt. Lett. 17(8), 082302 (2019). [CrossRef]
31. D. Zhang, P. Qi, J. Wang, et al., “All-optical AND and NOR logic gates based on polarization holography,” In International Workshop on Holography and Related Technologies (IWH2022 & 2023), 84–88 (2024).
32. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48(9), 2909–2947 (1969). [CrossRef]
33. P. Qi, J. Wang, Y. Yang, et al., “Simultaneously characterized Stokes parameters of a lightwave utilizing the tensor polarization holography theory,” Opt. Express 30(26), 47264–47279 (2022). [CrossRef]
34. Y. Liu, Z. Li, J. Zang, et al., “The optical polarization properties of phenanthrenequinone-doped Poly (methyl methacrylate) photopolymer materials for volume holographic storage,” Opt. Rev. 22(5), 837–840 (2015). [CrossRef]
35. Q. Jiang, G. Jin, and L. Cao, “When metasurface meets hologram: principle and advances,” Adv. Opt. Photonics 11(3), 518–576 (2019). [CrossRef]
36. N. A. Rubin, Z. Shi, and F. Capasso, “Polarization in diffractive optics and metasurfaces,” Adv. Opt. Photonics 13(4), 836–970 (2021). [CrossRef]
37. Y. Zhang, Q. Zhang, X. Jiang, et al., “Circular polarization detector based on polarization holography,” Opt. Lett. 47(22), 5941–5944 (2022). [CrossRef]
38. J. Wang, P. Qi, A. Lin, et al., “Exposure response coefficient of polarization-sensitive media using tensor theory of polarization holography,” Opt. Lett. 46(19), 4789–4792 (2021). [CrossRef]
39. P. Qi, J. Wang, X. Yuan, et al., “Diffraction characteristics of a linear polarization hologram in coaxial recording,” Opt. Express 29(5), 6947–6956 (2021). [CrossRef]
40. H. Gao, X. Fan, W. Xiong, et al., “Recent advances in optical dynamic meta-holography,” Opto-Electron. Adv. 4(11), 210030 (2021). [CrossRef]
41. P. Cheben, J. H. Schmid, R. Halir, et al., “Recent advances in metamaterial integrated photonics,” Adv. Opt. Photonics 15(4), 1033–1105 (2023). [CrossRef]
42. L. Y. Beliaev, O. Takayama, P. N. Melentiev, et al., “Photoluminescence control by hyperbolic metamaterials and metasurfaces: a review,” Opto-Electron. Adv. 4(8), 210031 (2021). [CrossRef]
