Bridging Theory and Experiment in Virtually Imaged Phased Array (VIPA) Spectrometers
Virtually imaged phased array (VIPA) spectrometers provide high resolution and fast acquisition in a compact design, but their performance is sensitive to fabrication tolerances, component dimensions, and alignment. Here, leveraging numerical simulations validated by experimental data, we present a framework to identify the parameters that limit VIPA spectrometer resolution. This framework is applied to the construction of a new mid-infrared VIPA spectrometer, tested at wavelengths near $λ$ = 4.6 $μ$m with both continuous-wave and frequency-comb laser sources, with a resolving power predicted by analytical expressions to be as high as $RP$ = 830 000 (corresponding to a resolution of $δν$ = 78 MHz). Validated numerical simulations, however, provided a more realistic estimate that captures limits set by all the optical components. By minimizing aberrations and optimizing alignment, a resolving power of $RP$ = 440 000 ($δν$ = 150 MHz) was experimentally achieved, corresponding to 80 % of the value predicted by numerical simulation of the entire spectrometer. The results bridge the gap between analytical expressions and experimental results for compact, high-resolution VIPA spectrometers to enable more efficient fabrication and advanced design across critical areas like space optics, line-by-line pulse shaping, and broadband spectral sensors.