We used the femtosecond direct-write technique for fabricating waveguides in borosilicate glass (35, 36). Our SPDC source generates photons close to the 808-nm wavelength, and we fabricated waveguides that are single mode at this wavelength. The waveguides were fabricated by focusing a femtosecond-pulsed laser with a repetition rate of 1 MHz and energy of 220 nJ per pulse in the bulk of a borosilicate substrate (Eagle2000, Corning) by means of a 50× microscope objective (numerical aperture, 0.6). Waveguides were patterned by translating the sample at the constant speed of 40 mm/s. The resulting waveguides exhibit relatively low propagation losses (0.5 dB/cm) and a slightly elliptical guided mode, with an average diameter of ~8 μm.

The separation between neighboring waveguides controls the rate of coupling. There is, inevitably, coupling between next-nearest-neighbor waveguides; however, the coupling decays exponentially with distance, and hence, we can approximate to a nearest-neighbor model.

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