Nonlinear propagation analysis of few-optical-cycle pulses for subfemtosecond compression and carrier envelope phase effect

Abstract

A numerical approach called Fourier direct method ͑FDM͒ is applied to nonlinear propagation of optical pulses with the central wavelength 800 nm, the width 2.67-12.00 fs, and the peak power 25-6870 kW in a fused-silica fiber. Bidirectional propagation, delayed Raman response, nonlinear dispersion ͑self-steepening, core dispersion͒, as well as correct linear dispersion are incorporated into "bidirectional propagation equations" which are derived directly from Maxwell's equations. These equations are solved for forward and backward waves, instead of the electric-field envelope as in the nonlinear Schrödinger equation ͑NLSE͒. They are integrated as multidimensional simultaneous evolution equations evolved in space. We investigate, both theoretically and numerically, the validity and the limitation of assumptions and approximations used for deriving the NLSE. Also, the accuracy and the efficiency of the FDM are compared quantitatively with those of the finite-difference time-domain numerical approach. The time-domain size 500 fs and the number of grid points in time 2048 are chosen to investigate numerically intensity spectra, spectral phases, and temporal electric-field profiles up to the propagation distance 1.0 mm. On the intensity spectrum of a few-optical-cycle pulses, the self-steepening, core dispersion, and the delayed Raman response appear as dominant, middle, and slight effects, respectively. The delayed Raman response and the core dispersion reduce the effective nonlinearity. Correct linear dispersion is important since it affects the intensity spectrum sensitively. For the compression of femtosecond optical pulses by the complete phase compensation, the shortness and the pulse quality of compressed pulses are remarkably improved by the intense initial peak power rather than by the short initial pulse width or by the propagation distance longer than 0.1 mm. They will be compressed as short as 0.3 fs below the damage threshold of fused-silica fiber 6 MW. It is demonstrated that the carrier envelope phase ͑CEP͒ causes the difference on the temporal electric-field profile and the intensity spectrum for the initial peak power of the order of megawatts. At the propagation distance longer than the coherence length for third-order harmonics, the difference grows in the spectral components around the third-order and higher-order harmonics. The CEP can be a sensitive marker to monitor the evolution of nonlinear optical process by a few-optical-cycle electric-field wave-packet source.

Four Poynting theorems

“…We can now show how these residual terms affect a propagating wave, by deriving propagation equations for the Poynting vectors themselves. To do this we use the concept of directional electromagnetic fields [31][32][33], and as a result do not need to resort to restrictive approximations, such as e.g. assuming plane wave or harmonic fields.…”

“…First we note that each of our electromagnetic continuity eqns. (22), (29), (33), (38), has the general form…”

Pulse propagation methods in nonlinear optics

“…[8][9][10]). Practical versions of directional Maxwell's equations have appeared only recently, such as that of Kolesik et al [11,12]; other approaches followed [13][14][15], the most general being [16]. However the first proposal dates back to Fleck in 1970 [17], although only as something of a remark in passing, rather than a full investigation.…”

Zero-velocity solitons in high-index photonic crystal fibers

“…In recent years, substantial efforts have been put into developing such schemes to deal with the challenges of modern fiber technology, including fullvectorial effects [6][7][8], strong mode profile dispersion [9][10][11][12], and ultrashort pulses [10]. However, any such method will naturally run into problems when it encounters a zero-velocity state, and one indeed finds that both the nonlinear coefficient and the dispersion parameter derived in the z-propagation schemes diverge at β ¼ 0.…”