In-phase sub-Nyquist lenslet arrays encoded onto spatial light modulators.

When encoding diffractive lenses onto a spatial light modulator (SLM), there is a Nyquist limit to the smallest focal length that can be formed. When this limit is surpassed, a two-dimensional array of lenslets is formed. There have been very few discussions on the performance of these lenslets. In this work, we focus on the phase distribution of these lenses in the array. We show that, for certain values of the focal length, the lenslets are all in perfect phase. We show that this situation happens for a total number of N/4 different discrete equidistant sub-Nyquist focal lengths, where N×N is the number of pixels in the SLM. We find other distances in between where the array is composed of two sets of lenslets with a relative π phase among them. Finally, we illustrate these phase distributions in the application to generate an array of vortex producing lenses. We expect that these results might be useful for high-accuracy interferometric or multiple imaging where this phase must be exactly the same for each replica.

Encoding lenses with focal lengths lower than the Nyquist limit using high phase-modulation displays.

Liquid crystal displays allow the easy implementation of diffractive optical elements. However, the shortest focal lengths for lenses are limited by Nyquist conditions. In this work, we show that focal lengths much lower than this Nyquist limit can be encoded onto devices having a large phase-dynamic range. Experimental results are included with a display showing 10π phase modulation reducing the Nyquist limit by a factor of about 1/10.

Ultrafast mode-locked laser in nanophotonic lithium niobate.

Mode-locked lasers (MLLs) generate ultrashort pulses with peak powers substantially exceeding their average powers. However, integrated MLLs that drive ultrafast nanophotonic circuits have remained elusive because of their typically low peak powers, lack of controllability, and challenges when integrating with nanophotonic platforms. In this work, we demonstrate an electrically pumped actively MLL in nanophotonic lithium niobate based on its hybrid integration with a III-V semiconductor optical amplifier. Our MLL generates [Formula: see text]4.8-ps optical pulses around 1065 nm at a repetition rate of ∼10 GHz, with energies exceeding 2.6 pJ and peak powers beyond 0.5 W. The repetition rate and the carrier-envelope offset frequency of the output can be controlled in a wide range by using the driving frequency and the pump current, providing a route for fully stabilized on-chip frequency combs.