Generalized Miller Formulae

Abstract

We derive the spectral dependence of the non-linear susceptibility of any order, generalizing the common form of Sellmeier equations. This dependence is fully defined by the knowledge of the linear dispersion of the medium. This finding generalizes the Miller formula to any order of non-linearity. In the frequency-degenerate case, it yields the spectral dependence of non-linear refractive indices of arbitrary order.

12 pages, 1 figure (4 panels)

References in corpus (1)

• Ultrashort filaments of light in weakly-ionized, optically-transparent media

Cited by in corpus (15)

• Probing material absorption and optical nonlinearity of integrated photonic materials
• Optical nonlinearity in Ar and N${}_2$ near the ionization threshold
• Spectral dynamics of THz pulses generated by two-color laser filaments in air: The role of Kerr nonlinearities and pump wavelength
• The anisotropic Kerr nonlinear refractive index of the beta-barium borate (β-BaB2O4) nonlinear crystal
• Generating mid-IR octave-spanning supercontinua and few-cycle pulses with solitons in phase-mismatched quadratic nonlinear crystals
• On negative higher-order Kerr effect and filamentation
• Third and fifth harmonics generation by tightly focused femtosecond pulses at 2.2 μm wavelength in air
• Spectral dependence of purely-Kerr driven filamentation in air and argon
• Higher-order Kerr effect and harmonic cascading in gases
• Arbitrary-order non-linear contribution to self-steepening
• Ab-initio calculations of the linear and nonlinear susceptibilities of N${}_2$, O${}_2$, and air in the mid-infrared
• Energy conservation in self-phase modulation
• Ultrasolitons: multistability and subcritical power threshold from higher-order Kerr terms
• Intense sub-2 cycle infrared pulse generation via phase mismatched cascaded nonlinear interaction in DAST crystal
• A Normalized Descriptor for Unbiased Screening of Second-Order Nonlinear Optical Materials