Yuri Evgenievich Drobotov

Free-space optical transceiver modules require precise lens assembly to achieve efficient laser-to-fiber coupling. However, optical coupling efficiency is highly sensitive to axial spacing, optical component parameters, and alignment conditions, making conventional parameter tuning time-consuming and inefficient. In this study, a simulation-assisted deep reinforcement learning (DRL) framework is proposed for lens assembly optimization in free-space optical transceiver modules. A dual-lens optical coupling system consisting of a laser diode, a collimating lens, a coupling lens, an optical isolator, and a single-mode fiber was established using a ray-tracing optical simulation environment. A deep deterministic policy gradient agent based on an actor–critic architecture was employed to search the continuous assembly parameter space and maximize the optical coupling efficiency. Under the common benchmark, all five methods produced solutions close to the independent reference efficiency. BO and PSO required the fewest evaluations to reach the 0.95η_REF and 0.99η_REF targets, whereas DDPG showed greater run-to-run variability. To further clarify the influence of reward design on optimization behavior, seven reward-weighting conditions spanning efficiency-only to stability-only formulations were investigated to examine the influence of reward composition on the DDPG optimization behavior. The reward-efficiency analysis indicates that an overemphasis on a single objective may lead to ineffective optimization behavior, whereas the equal-weight condition produced a visually more concentrated coupling-efficiency trajectory in the representative run; however, additional repeated-run and tolerance analyses are required to establish improved stability. These results demonstrate the potential of the proposed simulation-based framework for evaluating optimization strategies in optical design and lens assembly, while further experimental and hardware-level validation is required to assess its applicability to practical optical packaging.

The multidimensional Riesz potential type operators are of interest within mathematical modelling in economics, mathematical physics, and other, both theoretical and applied, disciplines as they play a significant role for analysis on fractal sets. Approaches of operator theory are relevant to researching various equations, which are widespread in financial analysis. In this chapter, integral equations with potential type operators are considered for functions from generalized Hölder spaces, which provide content terminology for formalizing the concept of smoothness, briefly described in the presented chapter. Results on potentials defined on the unit sphere are described for convenience of the analysis. An inverse operator for the Riesz potential with a logarithmic kernel is carried out, and the isomorphisms between generalized Hölder spaces are proven.

Доказаны условия ограниченности сферического и пространственного операторов типа потенциала Рисса переменного порядка с суммируемой плотностью в пространствах переменной гельдеровости. Библиография: 20 названий.

Boundedness conditions for spherical and spatial variable-order Riesz potential-type operators with integrable density in variable-exponent Hölder spaces are proved.

The chapter provides an overview of the advanced researches on the multidimensional Riesz potential operator in the generalized Hölder spaces. While being of interest within mathematical modeling in economics, theoretical physics, and other areas of knowledge, the Riesz potential plays a significant role for analysis on fractal sets, and this aspect is briefly outlined. The generalized Hölder spaces provide convenient terminology for formalizing the smoothness concept, which is described here. There are constant and variable order potential type operators considered, including a two-pole spherical one. As a sphere is, in some sense, a convenient set for analysis, there are two results, proved in detail: the conditions for the spherical fractional integral of variable order to be bounded in the generalized Hölder spaces, whose local continuity modulus has a dominant, which may vary from point to point, and the ones for the constant-order two-pole spherical potential type operator.