Energy-Velocity Scaling of Wavelet-Like Optical Solitons

We study localized solutions (LSs) in nonlinear waveguides, enabled by alternate domains of anomalous and normal dispersion [1], [2]. Such systems allow for the interaction of quasi group-velocity matched optical pulses across a vast frequency gap. Suitable dispersion profiles can, e.g., be realized in photonic crystal fibers. They provide conditions for novel effects such as spectral tunneling [3], direct optical analogs of quantum mechanical bound-states [1], and generalized solitons [1], [2], [4]. In this context we demonstrate carrier-envelop-phase (CEP) stabilized solitary waves with spectra that can extend over extremely wide frequency-ranges [2]. They are robust against nonlinear perturbations and independent of fine details of the dispersion profile [2]. At small wavenumbers, their shape coincides with the modified Morlet wavelet [2]. We show that the energy scaling of such wavelet-like solitons is markedly different from solitons of the usual nonlinear Schrödinger equation (NSE).