Asymptotic theory of mode coupling in a space-time periodic medium—Part I: Stable interactions

Abstract

Abrtmet-Asingdm pertprb.tion adysis of the coupling of plane electromrgnetic waves in m unbounded medium having ita permittRity m a t e d by 8 progressive sinusoidal wave h a d d out for the waves progressins p d M to the modulational direction. The phase velocity of the wave modulation h less than that of the electromagnetic w e s in the u n m m medium. The mtemctions of the fundamental w r v e p~m t h e d i r e c t i o n o f t h e m o d~~w a v e w i t h t h e d r s t four h.tmorucs prqreshg in the r e vdirection ne investigated. The periodic inhomogeaeity introduced dfeffect md m u d effect. Theselfeffect,mgenerrl,producesrphaseshiltmd~themuturl effect to occm for different frequencies md wrrrenumbeas from those predicted by the Bnsg conditiona The mutual effect introda complex chmge in the wavenumber d t h g in the evmeacence of the mtencting wavea. Adyticd expressions for the shifts in the frequency and the wavenumber UL well UL the other charactdtiat of the waves in the interrrtion region pe deduced. The aaymptotic remlta ne compued with the numedctl d t a enlprted from the mode theory.w

Uniform-velocity spacetime crystals

“…The other bandgap centers are found by a similar procedure. This relation reduces to the coupled-mode result in [57,58] under the approximation v + av = v − av . For the superluminal regime, we first calculate the ωintercepts of the forward and backward curve of each mode.…”

“…The fourth row provides the indices for the purely temporal limit, found by setting v m = ∞ in (57). The average indices for forward and backward waves are again equal.…”

Propagation of a femtosecond laser pulse through a dispersion‐free spatially‐chirped medium

“…where c 0 is the speed of light in a vacuum, n 0 is the medium reflection index, K ϭ 2/⌳, ⌳/ 2 is the grating's spatial quasiperiod, is the depth of modulation of the medium refraction index, and ␣ is the coefficient that describes the rate of change of the lattice's spatial period (chirp). For a chosen x polarization of the incoming electric field, we can write the wave equation that describes the propagation of a femtosecond laser pulse in a dispersion-free medium along the z axis as follows [6]:…”

“…However, because of the small nonlinearity coefficient in the fiber, long fiber is required to produce adequate nonlinearity, which is detrimental to the system's stability. Although using the SOA can remove the requirement for long lengths of fiber within the lasing cavity, it must take measures to overcome the pattern effect due to the slow carrier recombination rate of the SOA [6].…”