It has long been known that photonic science and especially photonic communications can raise the speed of technologies and producing manufacturing. More recently, photonic science has also been interested in its capabilities to implement low-precision linear operations, such as matrix multiplications, fast and effciently. For a long time most scientists taught that Electronics is the end of science but after many years and about 35 years ago had been understood that electronics do not answer alone and should have a new science. Today we face modern ways and instruments for doing tasks as soon as possible in proportion to many decays before. The velocity of progress in science is very fast. All our progress in science area is dependent on modern knowledge about new methods. In this research, we want to review the concept of a photonic neural network. For this research was selected 18 main articles were among the main 30 articles on this subject from 2015 to the 2022 year. These articles noticed three principles: 1- Experimental concepts, 2- Theoretical concepts, and, finally 3- Mathematic concepts. We should be careful with this research because mathematics has a very important and constructive role in our topics! One of the topics that are very valid and also new, is simulation. We used to work with simulation in some parts of this research. First, briefly, we start by introducing photonics and neural networks. In the second we explain the advantages and disadvantages of a combination of both in the science world and industries and technologies about them. Also, we are talking about the achievements of a thin modern science. Third, we try to introduce some important and valid parameters in neural networks. In this manner, we use many mathematic tools in some portions of this article.

翻译：众所周知，光子科学，尤其是光子通信，能够提升技术速度并推动制造生产发展。近年来，光子科学因其能快速高效地实现低精度线性运算（如矩阵乘法）而备受关注。长期以来，大多数科学家认为电子学是科学的终点，但经过多年探索，大约35年前人们认识到电子学无法独立解决问题，需要一门新科学。如今，我们面临着比以往数十年更快的任务完成方式与工具。科学进步的速度极快，我们在科学领域的一切进展都依赖于对新兴方法的现代认知。本研究旨在综述光子神经网络的概念。为此，我们从2015年至2022年间该领域的30篇核心论文中选取了18篇主要文献。这些文献关注三个原则：1）实验概念，2）理论概念，3）数学概念。我们需谨慎对待本研究，因为数学在其中起着至关重要的建构性作用！一个极具价值且新颖的研究方向是仿真。我们在本研究的某些部分使用了仿真方法。首先，我们简要介绍光子学与神经网络；其次，阐述两者在科学界、工业界及相关技术中的结合优势与不足，并讨论这一新兴科学的成就；最后，尝试介绍神经网络中的若干重要且有效的参数。本文部分内容将大量运用数学工具。