Few Cycle Optical Pulse Propagation: a detailed calculation
P. Kinsler
备注：
Please read arXiv:0707.0982 instead; the approach in this paper is out-dated. 16 pages, two figures; (v2) improved discussion in Sec.IV (Approximations); (v3) updated references
This document contains my detailed calculation of the Generalised Few-cycle Envelope Approximation (GFEA) propagation equation reported and used in Phys. Rev. A (submitted) and its associated longer version at arXiv.org. This GFEA propagation equation is intended to be applicable to optical pulses only a few cycles long, a regime where the standard Slowly Varying Envelope Approximation (SVEA) fails.
We present a significantly different reflection process from an optically thin flat metallic or dielectric layer and propose a strikingly simple method to form approximately unipolar half-cycle optical pulses via reflection of a single-cycle optical pulse. Unipolar pulses in reflection arise due to specifics of effectively one-dimensional pulse propagation. Namely, we show that in considered system the field emitted by a flat medium layer is proportional to the velocity of oscillating medium charges instead of their acceleration as it is usually the case. When the single-cycle pulse interacts …
We show that propagation of ultrashort (few-cycle) pulses in nonlinear Drude metamaterials with both electric and magnetic Kerr nonlinearities is described by coupled generalized Short Pulse Equations. The resulting system of equations generalizes to the case of metamaterials both the Short Pulse Equation and its vector generalizations which describe the few-cycle pulses in dielectric optical fibers beyond the slowly varying envelope approximation leading to the nonlinear Schroedinger equation.
The generation of single-cycle attosecond pulses based on Thomson scattering of terahertz (THz) pulses is proposed. In the scheme, a high-quality relativistic electron beam produced by a laser-plasma wakefield accelerator (LPWA), is sent through suitable magnetic devices to produce ultrathin electron layers for coherent Thomson backscattering of intense THz pulses. According to numerical simulations, single-cycle attosecond pulse generation is possible with up to 1 nJ energy. The waveform of the attosecond pulses closely resembles that of the THz pulses. This allows for a flexible waveform con…
An intuitive physical mechanism for single attosecond pulse generation in multi-cycle pulse regime is proposed. We suggest that the continuum spectra of HHG can be controlled through the modulation of carrier wave, while keeping the multi-cycle envelope unchanged approximately. By increasing the time interval between the adjacent maximum return kinetic energy peaks, the kinetic energy of the side peaks will be apparently suppressed by the multi-cycle envelope. The photons with energies near the cutoff burst only at the pulse center with high coherence, which contribute to the generation of sin…
The possibility of soliton self-compression of ultrashort laser pulses down to the few-cycle regime in photonic crystal fibers is numerically investigated. We show that efficient sub-two-cycle temporal compression of nanojoule-level 800 nm pulses can be achieved by employing short (typically 5-mm-long) commercially available photonic crystal fibers and pulse durations of around 100 fs, regardless of initial linear chirp, and without the need of additional dispersion compensation techniques. We envisage applications in a new generation of compact and efficient sub-two cycle laser pulse sources.
We study theoretically a new possibility of unipolar pulses generation in Raman-active medium excited by a series of few-cycle optical pulses. We consider the case when the Raman-active particles are uniformly distributed along the circle, and demonstrate a possibility to obtain a unipolar rectangular video pulses with an arbitrarily long duration, ranging from a minimum value equal to the natural period of the low frequency vibrations in the Raman-active medium.
We report on the characterization of space-time couplings in high energy sub-2-cycle 770nm laser pulses using a self-referencing single-shot method. Using spatially-encoded arrangement filter-based spectral phase interferometry for direct electric field reconstruction (SEA-F-SPIDER) we characterize few-cycle pulses with a wave-front rotation of 2.8x?10^11 rev/sec (1.38 mrad per half-cycle) and pulses with pulse front tilts ranging from to -0.33 fs/um to -3.03 fs/um.
We demonstrate that the resonant medium with essentially nonlinear field coupling can exhibit specific response when excited by the few-cycle optical pulse. We provide an effective theoretical background that allows relating the type of the field coupling function with the medium oscillators output on the few-cycle pulse-driven excitation. Possible applications of such the optical response are discussed for the controllable generation and shaping of the unipolar video pulses.
We report on the nonlinear temporal compression of mJ energy pulses from a Ti:Sa chirped pulse amplifier system in a multipass cell filled with argon. The pulses are compressed from 30 fs down to 5.3 fs, corresponding to two optical cycles. The post-compressed beam exhibits excellent spatial quality and homogeneity. These results pave the way to robust and energy-scalable compression of Ti:Sa pulses down to the few-cycle regime.
While the performance of mode-locked fiber lasers has been improved significantly, the limited gain bandwidth restricts them to generate ultrashort pulses approaching a few cycles or even shorter. Here we present a novel method to achieve few cycle pulses (~5 cycles) with ultra-broad spectrum (~400 nm). To our best knowledge, this is the shortest pulse width and broadest spectrum directly generated from fiber lasers. It is noteworthy that a dramatic ultrashort pulse evolution can be stabilized in a laser oscillator by the unique nonlinear processes of a self-similar evolution as a nonlinear at…
Ultrashort laser pulses that last only a few optical cycles have been transformative tools for studying and manipulating light--matter interactions. Few-cycle pulses are typically produced from high-peak-power lasers, either directly from a laser oscillator, or through nonlinear effects in bulk or fiber materials. Now, an opportunity exists to explore the few-cycle regime with the emergence of fully integrated nonlinear photonics. Here, we experimentally and numerically demonstrate how lithographically patterned waveguides can be used to generate few-cycle laser pulses from an input seed pulse…
We propose a novel scheme to generate single-cycle terahertz (THz) pulses via reflection of an optical femtosecond pulse train from a thin layer of nonlinear resonant medium. Our method is based on a coherent control of low-frequency oscillations and free induction decay in the medium. The specific single-cycle shape of generated THz pulses requires a plane wavefront and detection in the near field. Our theoretical results pave the way to a new, simple and high-efficiency way to generate single-cycle waveshape-tunable terahertz pulses.
Unidirectional pulse propagation equations [UPPE, Phys. Rev. E 70, 036604 (2004)] have provided a theoretical underpinning for computer-aided investigations into dynamics of high-power ultrashort laser pulses and have been successfully utilized for almost a decade. Unfortunately, they are restricted to applications in bulk media or, with additional approximations, to simple waveguide geometries in which only a few guided modes can approximate the propagating waveform. The purpose of this work is to generalize the directional pulse propagation equations to structures characterized by strong ref…
In contrast to the case of quasi-monochromatic waves, a focused optical pulse in the few-cycle limit may exhibit two independent curved wavefronts, associated with phase and group retardations, respectively. Focusing optical elements will generally affect these two wavefronts differently, thus leading to very different behavior of the pulse near focus. As limiting cases, we consider an ideal diffractive lens introducing only phase retardations and a perfect non-dispersive refractive lens (or a curved mirror) introducing equal phase and group retardations. We study the resulting diffraction eff…
The propagation of an electromagnetic pulse in a plasma is studied for pulse durations that are comparable to the plasma period. When the carrier frequency of the incident pulse is much higher than the plasma frequency, the pulse propagates without distortion at its group speed. When the carrier frequency is comparable to the plasma frequency, the pulse is distorted and leaves behind it an electromagnetic wake.
Using the tilted-pulse-intensity-front scheme, we generate single-cycle terahertz (THz) pulses by optical rectification of femtosecond laser pulses in LiNbO3. In the THz generation setup, the condition that the image of the grating coincides with the tilted-optical-pulse front is fulfilled to obtain optimal THz beam characteristics and pump-to-THz conversion efficiency. The designed focusing geometry enables tight focus of the collimated THz beam with a spot size close to the diffraction limit, and the maximum THz electric field of 1.2 MV/cm is obtained.
We describe the coupling between orbital angular momentum (OAM) and temporal degrees of freedom in pulsed Laguerre-Gauss beams. The effects of this coupling are to increase significantly the duration of few-cycle pulses when the OAM carried by the pulse is large, and to enhance spatiotemporal couplings. Contrary to other detrimental but retrievable effects such as spatial, group velocity and topological charge dispersions in these pulses, OAM-temporal coupling effects are unavoidable, and have therefore an impact in applications such as OAM-based optical communications, or in the generation of…
Octave-spanning, 12.5 fs, (1.9 cycle) pulses with 115 μJ energy in the short-wavelength mid-infrared spectral range (1-2.5 μm) have been generated via phase-mismatched cascaded nonlinear frequency conversion using organic DAST crystal. Such ultra-fast cascading effect is ensured by the interaction of a pump pulse with the exceptionally large effective nonlinearity of the DAST crystal and experiencing non-resonant, strongly phase mismatched, Kerr-like negative nonlinearity.
High-energy, carrier-envelope phase (CEP)-stable, sub-cycle, mid-infrared (mid-IR) pulses can provide unique opportunities of exploring phase-sensitive strong-field light-matter interactions in atoms, molecules, and solids. In the mid-IR wavelength, the ponderomotive energy of laser pulses is dramatically increased (versus the visible/near-infrared) and, therefore, the Keldysh parameter is much smaller than unity even at relatively modest laser intensities. This enables to study the sub-cycle electron dynamics in solids via high-harmonic generation (HHG) without damage. One can also control th…
A parallel 2D+1 split-step Fourier method with Crank-Nicholson scheme running on multi-core shared memory architectures is developed to study the propagation of ultra-short high-intensity laser pulses in air. The parallel method achieves a near linear speed-up with results for the efficiency of more than 95% on a 24-core machine. This method is of great potential application in studying the long-distance propagation of the ultra-short high intensity laser pulses.
The evolution of THz waveform generated in air plasma provides a sensitive probe to the variation of the carrier envelope phase (CEP) of propagating intense few-cycle pulses. Our experimental observation and calculation reveal that the number and positions of the inversion of THz waveform are dependent on the initial CEP, which is near 0.5π constantly under varied input pulse energies when two inversions of THz waveform in air plasma become one. This provides a method of measuring the initial CEP in an accuracy that is only limited by the stability of the driving few-cycle pulses.
In this work, we perform a detailed review about the theoretical modeling of the optical propagation of ultra-short pulses in different scenarios of nonlinear optics. In particular, we focus our efforts on optical fibers and uniform media, with special attention on the white light continuum generation by using gases.
We report a 21-W mid-IR OPCPA that generates 131-μJ and 97 fs (sub-9-cycle) pulses at 160 kHz repetition rate and at a centre wavelength of 3.25 μm. Pulse-to-pulse stability of the CEP-stable output is excellent with 0.33% rms over 288 million pulses (30 min) and compression close to a single optical cycle was achieved through soliton self- compression inside a gas-filled mid-IR anti-resonant-guiding photonic crystal fibre. Without any additional compression device, stable generation of 14.5 fs (1.35-optical-cycle) pulses was achieved at an average power of 9.6 W. The resulting peak power of 3…
We report on the generation of 6.1 mJ, 3.8 fs pulses by the compression of a kHz Ti:sapphire laser in a large-aperture long hollow fiber. In order to find optimal conditions for spectral broadening at high pulse energies, we explore different parameter ranges where ionization or the Kerr effect dominates. After identifying the optimum parameter settings, large spectral broadening at high waveguide transmission is obtained. The intense 1.5-cycle pulses are used for high-harmonic generation in argon and neon.
We review and extend the analogies between Gaussian pulse propagation and Gaussian beam diffraction. In addition to the well-known parallels between pulse dispersion in optical fiber and CW beam diffraction in free space, we review temporal lenses as a way to describe nonlinearities in the propagation equations, and then introduce further concepts that permit the description of pulse evolution in more complicated systems. These include the temporal equivalent of a spherical dielectric interface, which is used by way of example to derive design parameters used in a recent dispersion-mapped soli…
We report an asymmetric behavior of optical pulses during their propagation through a time-varying linear optical medium. The refractive index of the medium is considered to be varying with time and complex such that a sufficient amount of gain and loss is present to realize their effect on pulse propagation. We have exploited the universal formula for optical fields in time-varying media. Numerically simulated results reveal that pulses undergo opposite temporal shifts around their initial center position during their bi-directional propagation through the medium along with corresponding spec…
Soliton self-compression is demonstrated during the propagation of high spatial modes in hollow core fibers in the near-infrared spectral region, taking advantage of their negative dispersion response. We have found that there is always an optimum spatial mode to observe this phenomenon, compressing the pulses down to the single-cycle regime without needing any external compression device and with a consequent increase in the output peak power. Our result is relevant for any ultrashort laser application in which few- or single-cycle pulses are crucial.
Intense few cycle terahertz pulses exhibit complex non-linear behavior under interaction with heavily n-doped Si. Fast increase in the transmission of a 700 fs pulse (central frequency 1.5 THz) through the Si sample (low field transmission of 0:02 %) saturates at 8 % for the external field of 5 MV/cm and then drops twofold at 20 MV/cm. An electro-optical sampling measurements revealed formation of a single cycle terahertz pulse at this field due to formation of a thin ionized layer by the first intense oscillation of the terahertz field.
I apply the method of characteristics to both bi-directional and uni-directional pulse propagation in dispersionless media containing nonlinearity of arbitrary order. The differing analytic predictions for the shocking distance quantify the effects of the uni-directional approximation used in many pulse propagation models. Results from numerical simulations support the theoretical predictions, and reveal the nature of the coupling between forward and backward waves.
In this work we study the impact of chromatic focusing of few-cycle laser pulses on high-order harmonic generation (HHG) through analysis of the emitted extreme ultraviolet (XUV) radiation. Chromatic focusing is usually avoided in the few-cycle regime, as the pulse spatio-temporal structure may be highly distorted by the spatiotemporal aberrations. Here, however, we demonstrate it as an additional control parameter to modify the generated XUV radiation. We present experiments where few-cycle pulses are focused by a singlet lens in a Kr gas jet. The chromatic distribution of focal lengths allow…
An effort was conducted to study temporal soliton pulse propagation in silicon nano-waveguides. These nonlinear phenomenas were studied both numerically and experimentally with phase-resolved Frequency Resolved Optical Gating. Soliton pulse broadening, as well as pulse splitting from two-photon absorption, was observed experimentally, and the simulations matched all of the experimental results. Further simulations with the validated model have demonstrated that compression can be observed in centimeter-length waveguides. This study has demonstrated the feasibility of self-sustaining soliton pu…
A tilted-pulse-front pumped terahertz pulse source is proposed for the generation of extremely high field single-cycle terahertz pulses. The very simple and compact source consists of a single crystal slab having a blazed reflection grating grooved in its back surface. Its further important advantages are the energy scalability and the symmetric THz beam profile. Generation of 50 MV/cm focused field with 5.6 mJ terahertz pulse energy is predicted for a 5 cm diameter LiNbO$_3$ crystal, if the pump pulse is of 450 mJ energy, 1030 nm central wavelength and 1 ps pulse duration. Such sources can ba…
The generation of few-cycle pulses with controlled waveforms in the mid-infrared spectral region is a long-standing challenge but is expected to enable a new generation of high-field physics experiments, uncovering intricate physical phenomena. Successful generation of such optical pulses is limited by the tremendous spectral width required to withstand few-cycle pulses in the mid-IR correlated with the need to tightly control the spectral phase over such a broad bandwidth. Here, we present the first demonstration of sub-three cycle optical pulses at 3.1 μm central wavelength using for the fir…
BGGSe is a newly developed nonlinear material that is attractive for ultrabroad frequency mixing and ultrashort pulse generation due to its comparably low dispersion and high damage threshold.In a first experiment, we show that a long crystal length of 2.6 mm yields a pulse energy of 21 pJ at 100 MHz with a spectral bandwidth covering 5.8 to 8.5 microns. The electric field of the carrier-envelope-phase stable pulse is directly measured with electro-optical sampling and reveals a pulse duration of 91 fs, which corresponds to sub-four optical cycles, thus confirming some of the prospects of the …
In this paper, the unidirectional pulse propagation equation generalized to structured media is derived. A fast modal transform linking the spatio-temporal representation of the field and its modal distribution is presented. This transform is used for solving the propagation equation by using a split-step algorithm. As an example, we present, to the best of our knowledge, the first numerical evidence of the generation of conical waves in highly multimodes waveguides.
The propagation of pulses through waveguides with subwavelength features, inhomogeneous transverse structure, and high index contrast cannot be described accurately using existing models in the presence of nonlinear effects. Here we report the development of a generalised full vectorial model of nonlinear pulse propagation and demonstrate that, unlike the standard pulse propagation formulation, the z-component of guided modes plays a key role for these new structures, and results in generalised definitions of the nonlinear coefficient $γ,$ $A_{eff}$, and mode orthognality. While new definition…
In this paper, the microwave pulse propagation transferred through a left-handed transmission line using Complementary Omega-Like Structures (COLS) loaded was studied. There was a stop band in transmission from 5.6GHz to 6.1GHz, and the anomalous dispersion was causes in this band. Negative group velocity corresponds to the case in which the peak of the pulse exited before the peak of the incident pulse had entered the sample. The negative group velocity reached (-0.27c~-1.85c).
We report supercontinuum generation and pulse compression in two stacked multipass cells based on dielectric mirrors. The 230 fs pulses at 1 MHz containing 12 $μ$J were compressed by factor 33 down to 7 fs, corresponding to 1.0 GW peak power and overall transmission of 84 %. The source is particularly interesting for such applications as time-resolved ARPES, photoemission electron microscopy, and nonlinear spectroscopy.
We derive an analytical expression that describes the complete three-dimensional carrier-envelope phase (CEP) distribution of in the focal volume of ultrashort pulsed Gaussian beams focused by spherical mirrors or lenses. The focal CEP map depends on the so-called factor $g$ specifying the frequency-dependence of the beam width of the source few-cycle pulse, on its chirp and on the small chromatic aberration introduced by a lens without appreciably distorting or broadening the few-cycle pulse. We show how to tailor the CEP map of mirror-focused and lens-focused few-cycle pulses in order to pro…
Over the past years, ultrafast lasers with average powers in the 100 W range have become a mature technology, with a multitude of applications in science and technology. Nonlinear temporal compression of these lasers to few- or even single-cycle duration is often essential, yet still hard to achieve, in particular at high repetition rates. Here we report a two-stage system for compressing pulses from a 1030 nm ytterbium fiber laser to single-cycle durations with 5 $μ$J output pulse energy at 9.6 MHz repetition rate. In the first stage, the laser pulses are compressed from 340 to 25 fs by spect…
In this paper, we describe analytically the propagation of Airy-type pulses truncated by a finite-time aperture when second and third order dispersion effects are considered. The mathematical method presented here, based on the superposition of exponentially truncated Airy pulses, is very effective, allowing us to avoid the use of time-consuming numerical simulations. We analyze the behavior of the time truncated Ideal-Airy pulse and also the interesting case of a time truncated Airy pulse with a "defect" in its initial profile, which reveals the self-healing property of this kind of pulse sol…
Optical soliton pulses offer many applications within optical communication systems, but by definition a soliton is only subjected to second-order anomalous group-velocity-dispersion; an understanding of higher-order dispersion is necessary for practical implementation of soliton pulses. A numerical model of a waveguide was developed using the Nonlinear Schrodinger Equation, with parameters set to ensure the input pulse energy would be equal to the fundamental soliton energy. Higher-order group-velocity-dispersion was gradually increased, for various temporal widths and waveguide dispersions. …
Few-cycle pulses present an essential tool to track ultrafast dynamics in matter and drive strong field effects. To address photon-hungry applications, high average power lasers are used which, however, cannot directly provide sub-100 fs pulse durations. Post-compression of laser pulses by spectral broadening and dispersion compensation is the most efficient method to overcome this limitation. Here, we demonstrate a notably compact setup which turns a 0.1 GW peak power, picosecond laser into a 2.9 GW peak power, 8.2 fs source. The 120-fold pulse duration shortening is accomplished in a two-sta…
We propose an efficient approach to improve few-cycle soliton compression with cascaded quadratic nonlinearities by using an engineered multi-section structure of the nonlinear crystal. By exploiting engineering of the cascaded quadratic nonlinearities, in each section soliton compression with a low effective order is realized, and high-quality few-cycle pulses with large compression factors are feasible. Each subsequent section is designed so that the compressed pulse exiting the previous section experiences an overall effective self-defocusing cubic nonlinearity corresponding to a modest sol…
In this work, we demonstrate a discrete dispersion scan scheme using a low number of flat windows to vary the dispersion of laser pulses in discrete steps. Monte Carlo simulations indicate that the pulse duration can be retrieved accurately with less than 10 dispersion steps, which we verify experimentally by measuring few-cycle pulses and material dispersion curves at 3 and 10 micrometer wavelength. This minimal measuring scheme using only five optical components without the need for high-precision positioners and interferometric alignment can be readily implemented in many wavelength ranges …
We present a numerical parametric study of single-cycle electromagnetic pulse generation in a DAST/SiO2 multilayer structure via collinear optical rectification of 800 nm femtosecond laser pulses. It is shown that modifications of the thicknesses of the DAST and SiO2 layers allow tuning of the average frequency of the generated THz pulses in the frequency range from 3 to 6 THz. The laser-to-THz energy conversion efficiency in the proposed structures is compared with that in a bulk DAST crystal and a quasi-phase-matching periodically poled DAST crystal and shows significant enhancement.
Propagation of few-cycle laser pulses in optical fiber is investigated beyond the unidirectional approximation. Considered medium parameters include dispersion, Kerr and Raman nonlinearities. High intensities of ~10^10 kW/cm^2 lead to generation of the octave-spanning continuum. The error of the unidirectional approximation is seen in simulations as two pulses propagating forwards and backwards, both remain weak under the considered conditions. Direct analytical estimate of the error is derived and verified numerically. It can be applied to a priory justification of the unidirectional approach…
We demonstrate efficient generation of coherent super-octave pulses via a single-stage spectral broadening of a Yb:KGW laser in a single, pressurized, Ne-filled, hollow-core fiber capillary. Emerging pulses spectrally spanning over more than $\sim$1 PHz (250 nm- 1600 nm) at a dynamic range of $\sim$60 dB, and an excellent beam quality open the door to combining Yb:KGW lasers with modern light field synthesis techniques. Compression of a fraction of the generated supercontinuum to intense (8 fs, $\sim$2.4 cycle, $\sim$650 $μ$J) pulses allows convenient use of these novel laser sources in strong…
We present a new technique to synthesize high-power single-cycle pulses in the visible and ultraviolet ranges by coherent superposition of a multiband octave-spanning spectrum obtained by highly-nondegenerate cascaded four-wave mixing of femtosecond pulses in bulk isotropic nonresonant media. The generation of coherent spectra spanning over two octaves in bandwidth is experimentally demonstrated using a thin fused silica slide. Full characterization of the intervening multicolored fields using frequency-resolved optical gating, where multiple cascaded orders have been measured simultaneously f…
