Pump Power and Length for Efficient Single-Photon Frequency Conversion in a Periodically Poled Waveguide

Converting a single photon from one wavelength to another in a periodically poled waveguide is governed by a sinusoidal exchange with the pump field. The first maximum of that exchange sets the pump power and length a design should aim for; overshooting it converts the photon back. This study computes the quantities that follow from stated assumptions for a periodically poled lithium niobate waveguide converting 780 nm to 1550 nm, normalised efficiency 100 percent per watt per square centimetre in the stated convention, using the relations set out in the Methods. The headline results are pump full at 3cm W = 0.2742, pump full at 1cm W = 2.467, pump full at 5cm W = 0.0987, conversion detuned dkL 2 = 0.7081, conversion on phase match = 1. The central question is stated as follows: For a stated normalised efficiency, what pump power reaches full conversion in waveguides of 1 to 5 cm, and how much conversion remains when the phase matching is detuned by a stated amount? The answer obtained here is conditional on the assumptions listed in the paper and in the deposited calculation; changing an assumption changes the numbers in the way the sensitivity discussion describes. Waveguide converters report internal conversion from tens of percent to near unity, with external values reduced by coupling and filtering losses. The work is a computation, not a laboratory measurement, and it is labelled accordingly. Where the computed result is unfavourable to the device or effect under study, that outcome is reported in the same terms as a favourable one, because a bound that only appears when it is welcome is not a bound at all. All numerical statements in this abstract are reproduced by the deposited script from the stated inputs.