We introduce and implement an interferometric technique based on chirped femtosecond laser pulses and nonlinear optics. The interference manifests as a high-visibility (> 85%) phase-insensitive dip in the intensity of an optical beam when the two interferometer arms are equal to within the coherence length of the light. This signature is unique in classical interferometry, but is a direct analogue to Hong-Ou-Mandel quantum interference. Our technique exhibits all the metrological advantages of the quantum interferometer, but with signals at least 10^7 times greater. In particular we demonstrate enhanced resolution, robustness against loss, and automatic dispersion cancellation. Our interferometer offers significant advantages over previous technologies, both quantum and classical, in precision time delay measurements and biomedical imaging.
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