Optical Solitary Wavelets

We investigate wavelet-like localized solutions in nonlinear waveguides, enabled by complementary propagation constants embedded in domains of anomalous dispersion. They are carrier-envelope-phase stable and independent of fine details of the dispersion profile. Their spectra extend over vast ranges and they are also robust against nonlinear perturbations, providing properties highly demanded in ultrafast science. In the limits of low and high energies, approximate representations are given by modified Morlet wavelets and Gaussian pulses, respectively. We demonstrate their special features by exploiting general principles of quantum scattering theory and solid-state physics, realizing interlocked chains of wavelets analog to photonic time crystals.