Analyzing and generating multimode optical fields using self-configuring networks
David A. B. Miller
Abstract
Working with finite numbers of modes to describe, generate, and detect optical fields can be both mathematically economical and physically useful. Such a modal basis can map directly to various applications in communications, sensing, and processing. But, we need a way to generate and analyze such fields, including measurement and control of both the relative amplitudes and phases of the modal components. Ideally such an analysis scheme would operate directly on the field, without needing a separate, mutually coherent reference beam. Here, we show first how to measure all those relative amplitudes and phases automatically and simultaneously. The method repurposes a self-configuring network of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mn>2</mml:mn></mml:mrow><mml:mo>×</mml:mo><mml:mrow class="MJX-TeXAtom-ORD"><mml:mn>2</mml:mn></mml:mrow></mml:math> blocks, such as integrated Mach–Zehnder interferometers, that can automatically align itself to the optical field by a sequence of simple one-parameter power minimizations when network elements, such as phase shifters, are adjusted. The optical field is then directly deduced from the resulting settings of those elements. We show how the entire network can be calibrated for such measurements, automatically and with just two light beams. Then, using the same calibration and running the mesh backwards, we can also controllably generate an arbitrary multimode field. Explicit algorithms and formulas are given for operating this system.