Programmable unitary spatial modes manipulation (1005.3366v1)

Abstract: Free space propagation and conventional optical systems such as lenses and mirrors all perform spatial unitary transforms. However, the subset of transforms available through these conventional systems is limited in scope. We present here a unitary programmable mode converter (UPMC) capable of performing any spatial unitary transform of the light field. It is based on a succession of reflections on programmable deformable mirrors and free space propagation. We first show theoretically that a UPMC without limitations on resources can perform perfectly any transform. We then build an experimental implementation of the UPMC and show that, even when limited to three reflections on an array of 12 pixels, the UPMC is capable of performing single mode tranforms with an efficiency greater than 80% for the first 4 modes of the TEM basis.

Unitary Programmable Mode Converter: Capabilities and Implementation

The research on the development of a Unitary Programmable Mode Converter (UPMC) represents a cohesive advancement in the domain of optical systems. This paper presents a detailed exploration into the UPMC's capabilities to perform any spatial unitary transformation of a light field, highlighting its potential applications in areas including quantum information processing and advanced optical communications.

Theoretical Framework

The authors develop a theoretical foundation demonstrating that a sequence of reflections on programmable deformable mirrors, interspersed with free-space propagation, can achieve any desired spatial unitary transformation. This concept extends beyond conventional optical systems, which are typically limited by the physics of Gaussian optics, to offer comprehensive control over the spatial profile of light. Such capability is realized through a strategic combination of phase manipulation via deformable mirrors and Fourier transforms, executed through lenses.

The crux of the theoretical proposition is rooted in linear algebra and group theory, with the UPMC capable of performing a succession of unitary transformations represented mathematically. These transformations allow for arbitrary modifications of spatial light modes without destructive interference, a significant departure from traditional methods reliant on intensity attenuation.

Experimental Implementation

The experimental realization of the UPMC features a multi-pass configuration over a single deformable mirror, allowing for three distinct reflections. The mirror is equipped with 12 computer-controlled actuators, providing a practical albeit limited realization of the theoretically limitless transformations. Despite these constraints, the experimental UPMC achieves a mode conversion efficiency exceeding 80% for the first four modes of the Transverse Electromagnetic (TEM) basis, underscoring the feasibility of the theoretical capabilities discussed.

Results and Comparative Analysis

The results demonstrate strong alignment between experimental and theoretical expectations, notably in the single-mode transformations such as $TEM_{00}$ to $TEM_{10}$. The experimental setup, while subject to optical losses from the mirror surface and coatings, supports the claim that technical advancements in these areas could further minimize losses, maintaining fidelity with the original input beam's intensity profile.

Multimode Transformations

In a computational extension, the paper explores the UPMC's performance in multimode transformations. Simulations assess various two-mode and multimode scenarios, indicating that even with a constrained number of reflections, the UPMC can approach desired transformation efficiencies effectively. This suggests the UPMC's potential utility in complex optical systems where simultaneous mode manipulation is essential, such as in multimode optical fibers.

Implications and Future Directions

The development of a UPMC capable of executing any unitary transformation presents significant implications for fields requiring precise optical control. Its applications could extend into quantum optics, where precise control over photon states is paramount, and in high-dimensional optical communications, enhancing capacity and signal integrity.

Future advancements may focus on increasing the number of reflections and pixel density on deformable mirrors, improving the scope and fidelity of possible transformations. Additionally, addressing technical optical losses could further refine the UPMC's effectiveness, broadening its applicability and enhancing its integration potential in contemporary optical systems.

In summary, the UPMC embodies a versatile optical tool with profound implications for both theoretical physics and practical optical engineering. Its ability to perform arbitrary unitary transformations advances the frontier of optical manipulation, opening avenues for innovation in both classical and quantum regimes.