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Electro-optical modulation of a continuous wave laser is a highly stable way to generate frequency combs, gaining popularity in telecommunication and spectroscopic applications. These combs are generated by modulating non-linear electro-optic crystals with radio frequencies, creating equally spaced side-bands centered around the single-frequency seed laser. Electro-optic frequency comb architectures often choose between optical bandwidth (cascaded GHz combs) or higher mode density (chirped RF generation). This work demonstrates an electro-optic frequency comb with > 120 GHz of bandwidth and an 80 MHz repetition rate. The comb has three cascaded electro-optic modulators driven at sequentially lower harmonics, the last megahertz modulation dictating the repetition rate. This architecture can modulate at any individual harmonic and repetition rate without changes to the components. This comb can be used in any applications where a stable and tunable repetition rate is needed. 

The generation of shaped laser beams, or structured light, is of interest in a wide range of fields, from microscopy to fundamental physics. There are several ways to make shaped beams, most commonly using spatial light modulators comprised of pixels of liquid crystals. These methods have limitations on the wavelength, pulse duration, and average power that can be used. Here we present a method to generate shaped light that can be used at any wavelength from the UV to IR, on ultrafast pulses, and a large range of optical powers. By exploiting the frequency difference between higher-order modes, a result of the Gouy phase, and cavity mode matching, we can selectively couple into a variety of pure and composite higher-order modes. Optical cavities are used as a spatial filter and then combined with sum-frequency generation in a nonlinear crystal as the output coupler to the cavity to create ultrafast, frequency comb structured light.