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Resources for the manipulation and measurements of high-dimensional photonicsignals are crucial for implementing qu$d$it-based applications. Here wepropose potentially high-performance, chip-compatible devices for such purposesby exploiting quantum-frequency conversion in nonlinear optical media.Specifically, by using sum-frequency generation in a $\chi^{(2)}$ waveguide weshow how mode-resolved photon counting can be accomplished for telecom-bandphotonic signals subtending multiple temporal modes. Our method is generallyapplicable to any nonlinear medium with arbitrary dispersion property.

Mode-resolved Photon Counting via Cascaded Quantum Frequency Conversion