# Michelson Interferometric Methods for Full Optical Complex Convolution
## 4 Applications  
As per the simulation and experimental results, the proposed RCCM is a powerful developing tool for accelerating computationally algorithms, realizing the Fourier transformation in optics passively by using a single lens. We can foresee many applications based on this employment. One of the possible implementations of the featured algorithm is in Montgomery modular multiplication [25; 26]. Montgomery modular multiplication is a computational method that efficiently performs modular multiplication operations of extremely large integers [27; 28]. Here, \(a\), \(b\), and \(c\) denote large integers, \(R\) is chosen to be a power of two greater than \(m\), \(a^{\prime}=aR\) mod \(m\) and \(b^{\prime}=bR\) mod \(m\). \(M=-\text{m}^{-1}\) mod \(R\) and \(c^{\prime}\) denote the corresponding calculated modular production in the Montgomery domain. With the employment of RCCM, the calculation of Equation (4) can be accelerated significantly, only limited by the refresh rate of the SLMs (and resolution) [29]. \[c^{\prime}=\frac{a^{\prime}b^{\prime}+(a^{\prime}b^{\prime}M\mod R)m}{R} \tag{4}\]  
Moreover, we introduce a pioneering approach to data processing and security, focusing on optical hashing and compression techniques inspired by the SWIFFT hashing algorithm, a notable contender in the NIST SHA-3 competition [9]. Traditional computing hardware, particularly in electronic domains, faces significant challenges such as delays and high energy consumption, issues that are exacerbated in heterogeneous systems like electronic-photonic accelerators due to inefficient domain crossings [30; 31; 32; 33]. Our approach leverages the inherent advantages of free-space optical processing, such as parallel computation, rapid tensor multiplication, and efficient Fourier transformations. Figure 5: Detailed comparison of modulation techniques in CIFAR-10 neural network performance. (**a**) Complex modulation (RCCM) performance: Achieved a top accuracy of 51.98%, highlighting the effectiveness of combining amplitude and phase modulations in neural network applications. Color intensity indicates prediction frequency, with darker blue representing higher frequency and lighter shades lower frequency. (**b**) Amplitude modulation performance: Reached an accuracy of 50.83%, demonstrating its capability, though slightly less effective than complex modulation. (**c**) Phase modulation performance: Yielded the lowest accuracy of 47.87%, indicating its impact and limitations when used independently in neural networks. (**d**) Neural network architecture: Depicts the detailed architecture of the simulated neural network, providing insights into the structural elements that contribute to the performance differences observed in the modulation techniques. These characteristics make optical systems well suited for complex data processing tasks. The RCCM utilizes these advantages to potentially enhance processing speeds significantly compared to traditional optical machine learning accelerators. This improvement is achieved by replacing conventional high-resolution cameras with faster, signal-triggered CMOS detector arrays. The RCCM's capability for simultaneous phase and amplitude modulation enables several potential applications. In image recognition, it could process multiple images concurrently by encoding them onto different regions of the wavefront, potentially increasing throughput in large-scale recognition tasks. For data security, the RCCM could implement advanced optical hashing algorithms, utilizing both amplitude and phase information to create more robust encryption schemes, as shown in Figure 6. This approach could enhance data compression efficiency and security, offering new possibilities in optical computing and secure communications. In the realm of large-scale convolution computing, the RCCM's ability to perform complex convolutions optically could significantly reduce the computational load on electronic systems.