Theory of self-focusing in a hollow waveguide

We present a theoretical investigation of self-focusing in a hollow waveguide filled with noble gas. Our analysis was performed for a laser pulse that was predominantly in the fundamental mode and revealed the physical processes involved in self-focusing in a hollow waveguide. A critical power for self-focusing was obtained that was found to be substantially higher than the critical power for self-focusing in a bulk medium. Useful design criteria for pulse-compression systems are presented. We identify the parameter range for which the transverse variation of the pulse phase introduced by the Kerr nonlinearity is small.     

Spatiotemporal propagation dynamics of intense optical pulses in loosely confined gas-filled hollow-core fibers

We numerically study the propagation dynamics of intense optical pulses in gas-filled hollow-core fibers(HCFs). The spatiotemporal dynamics of the pulses show a transition from tightly confined to loosely confined characteristics as the fiber core is increased, which manifests as a deterioration in the spatiotemporal uniformity of the beam. It is found that using the gas pressure gradient does not enhance the beam quality in large-core HCFs, while inducing a positive chirp in the pulse to lower the peak power can improve the beam quality. This indicates that the self-focusing effect in the HCFs is the main driving force for the propagation dynamics. It also suggests that pulses at longer wavelengths are more suitable for HCFs with large cores because of the lower critical power of self-focusing, which is justified by the numerical simulations. These results will benefit the generation of energetic few-cycle pulses in large-core HCFs.     

Breakdown of the slowly varying envelope approximation in the self-focusing of ultrashort pulses

We show theoretically and experimentally that with ultrashort pulses much longer than a single optical cycle, the effects of self-steepening and space-time focusing are important for describing the nonlinear dynamics of self-focusing. Asymmetric temporal splitting of the pulse envelope is observed in which the relative magnitudes of the peaks are reversed as the input power is increased.     

All-optical limiting using nonlinear directional couplers composed of a self-focusing and a self-defocusing waveguide

We numerically demonstrate the all-optical limiting features in a mismatched nonlinear directional coupler (NLDC) composed of a self-focusing and a self-defocusing waveguide for both continuous wave and pulse cases. The working conditions required are analyzed. To obtain the limiting feature, the propagation constant of the self-focusing waveguide should not be larger than that of the self-defocusing waveguide. Cascaded asymmetric NLDCs are investigated to improve the limiting characteristics. The limiting threshold and the limiting output power can be adjusted by varying the coupler length or the ratio of the nonlinearity coefficients of the self-defocusing and self-focusing waveguides. Analytical solutions are presented in the case of a continuous wave. For the pulse case, numerical solutions show that the top part of the output pulse, if it exceeds the limiting threshold, will be tailored, while the rising and falling edges of the output pulse are almost the same as the input pulse. There is almost no pulse breakup. The influence of the second order dispersion and the intermodal dispersion on the limiting characteristics are analyzed. PACS 42.79.Gn; 42.79.Ta     

Self-focusing and defocusing of self-similar π pulses in an amplifying two-level medium

The effect of transverse perturbations on the propagation of electromagnetic π pulses in an amplifying two-level medium is studied. The cases of quasi-monochromatic and extremely short pulses are considered. The equations describing the behavior of the transverse size of the pulse during its propagation in the medium are derived. It is shown that, if the ratios of the diffraction length to the length of dispersion spreading are smaller than certain critical values, self-focusing regimes are realized for both types of pulses. Otherwise, at a finite distance, blowup of defocusing occurs, after which the amplified pulse propagates as if it is a one-dimensional pulse, with the velocity equal to the velocity of light in vacuum. Similarities and distinctions in the dynamics of propagation of extremely short and quasi-monochromatic pulses are indicated.     

大芯径石英光纤中皮秒脉冲激光的自聚焦

本文报道了对大芯径石英光纤中皮秒脉冲激光自聚焦现象的实验研究和理论分析.文中测量了自聚焦先场的近场光强轮廓,研究了自聚焦光场的时域和频域性质,并对环形自聚焦光场的成因进行了解释.     

Multicore, tapered optical fiber for nonlinear pulse reshaping and saturable absorption

We present a new method to create a coupled waveguide array via tapering a seven-core telecommunications fiber. The fiber based waveguide array is demonstrated to exhibit the novel physics associated with coupled waveguide arrays, such as discrete diffraction and discrete self-focusing. The saturable absorber characteristics of the device are characterized and an autocorrelation measurement reveals significant single-pass pulse reshaping.     

Nonlinear femtosecond pulse reshaping in waveguide arrays

We observe nonlinear pulse reshaping of femtosecond pulses in a waveguide array owing to coupling between waveguides. Amplified pulses from a mode-locked fiber laser are coupled to an AlGaAs core waveguide array structure. The observed power-dependent pulse reshaping agrees with theory, including shortening of the pulse in the central waveguide.     

Direct phase and amplitude characterization of femtosecond laser pulses undergoing filamentation in air

Measurement of the temporal (spectral) phase and amplitude of a 50 fs laser pulse approaching and exceeding the critical power for self-focusing (P(crit)) in air reveals the formation of an isolated 17 fs pulse at 3P(crit). The dynamics of self-shortening are measured directly in the filament using transient-grating cross-correlation frequency-resolved optical gating with a noble gas serving as the nonlinear medium. Our results support recent filamentary propagation simulations, suggesting that a Kerr-dominated temporal reshaping process toward the end of the filament is largely responsible for the generation of short pulses.     

Nonlinear regimes of ultrashort pulse propagation in an array of anisotropic tunneling states

Dynamics of an ultrashort electromagnetic pulse in a system with an array of anisotropic tunneling states spanned by the pulse spectrum are analyzed. A system of nonlinear wave equations is derived for the ordinary and extraordinary components of the pulse propagating at an arbitrary angle to the anisotropy axis. Different regimes of ultrashort pulse propagation parallel and perpendicular to the anisotropy axis are examined. Ultrashort-pulse propagation regimes analogous to self-induced transparency and extraordinary transparency are identified. The properties of rational soliton-like pulses having no quasi-monochromatic analogs are analyzed. A longitudinal electric field component is generated in each regime, whereas off-resonance quasi-monochromatic pulses propagating under similar conditions (parallel and perpendicular to the anisotropy axis) have no longitudinal components. Stability of the solutions obtained and the effect of diffraction on ultrashort pulse dynamics are analyzed. The values of pulse parameters for which defocusing dominates over self-focusing are calculated.     

Effects of waveguide behavior during femtosecond-laser drilling of metals

We investigate the dynamics of femtosecond-laser drilling of metals, both theoretically and experimentally, by taking into account waveguide-like behavior of ablated cavities. In particular, we show that cylindrical holes generated during laser ablation of metals act like hollow optical waveguides. Since the drilling is generally achieved by a large number of consecutive pulses, each pulse is first guided through the channel formed by the previous pulses, and at the end of the channel, it is absorbed by the metal, making its own contribution to ablation. The ablation stops at maximum depth when attenuation in the cavity reduces the pulse fluence to the ablation threshold. We use waveguide theory to calculate attenuation constants, and perform an iterative calculation to model pulse-by-pulse ablation. We also performed detailed experiments and compare the results with the theoretical findings. When only absorption losses are included, the waveguide model predicts significantly deeper structures. On the other hand, when we include scattering losses caused by nanostructures formed on the cavity walls, quantitative agreement with experiments is achieved. The waveguide model is particularly effective at fluences close to ablation threshold, and it can explain several behaviors such as evolution of the depth per pulse and effect of the incoming pulse energy in different focusing configurations.     

Effect of pulse slippage on density transition-based resonant third-harmonic generation of short-pulse laser in plasma

The resonant third-harmonic generation of a self-focusing laser in plasma with a density transition was investigated. Because of self-focusing of the fundamental laser pulse, a transverse intensity gradient was created, which generated a plasma wave at the fundamental wave frequency. Phase matching was satisfied by using a Wiggler magnetic field, which provided additional angular momentum to the third-harmonic photon to make the process resonant. An enhancement was observed in the resonant third-harmonic generation of an intense short-pulse laser in plasma embedded with a magnetic Wiggler with a density transition. A plasma density ramp played an important role in the self-focusing, enhancing the third-harmonic generation in plasma. We also examined the effect of the Wiggler magnetic field on the pulse slippage of the third-harmonic pulse in plasma. The pulse slippage was due to the group-velocity mismatch between the fundamental and third-harmonic pulses.     

Self-focusing of laser radiation in cluster plasma

The self-focusing of laser radiation in plasma with ionized gaseous clusters is studied both analytically and numerically. An electrodynamic model is proposed for cluster plasma in a field of ultrashort laser pulse. The radiation self-action dynamics are studied using the equation for wave-field envelope with allowance for the electronic nonlinearity of the expanded plasma bunches and the group-velocity dispersion in a nanodispersive medium. It is shown that, for a laser power exceeding the self-focusing critical power, the wave-field self-compression occurs in a medium with dispersion of any type (normal, anomalous, or combined). Due to the strong dependence of the characteristic nonlinear field on the size of ionized cluster, the corresponding processes develop faster than in a homogeneous medium and give rise to the ultrashort pulses.     

Generation of intense ultrabroadband optical pulses by induced phase modulation in an argon-filled single-mode hollow waveguide

We experimentally demonstrate the generation of intense ultrabroadband optical pulses whose spectrum ranges from 300 to 1000 nm (700-THz bandwidth) with a well-behaved spectral phase and 23-muJ pulse energy by a novel, simple setup utilizing induced phase modulation (IPM) in an argon-filled single-mode hollow waveguide. Fundamental as well as second-harmonic pulses produced by one common femtosecond pulse from a Ti:sapphire laser-amplifier system are copropagated in the hollow waveguide. The effect of the delay time between the two input pulses on the IPM spectral broadening is clarified and confirmed to agree with the theoretical result. It is found that the compressed pulse duration from this pulse is 1.51 fs if its phase is completely compensated for.     

Picosecond all-optical switching using nonlinear Mach–Zehnder with silicon subwavelength grating and photonic wire arms

We investigate the picosecond switching capabilities of a planar waveguide interferometric photonic device when used for all-optical wavelength conversion of one picosecond pulses. Our device comprises a subwavelength grating waveguide arm and a photonic wire waveguide arm in a Mach–Zehnder configuration, fabricated on the silicon-on-insulator material platform. No detrimental effects of pulse broadening for transient pulses were observed.     

THz generation via optical rectification with ultrashort laser pulse focused to a line

We report on efficient THz pulse generation via optical rectification with femtosecond laser pulses focused to a line by a cylindrical lens. This configuration provides phase-matched conditions in the superluminal regime. 35 pJ THz pulses have been generated with this technique in a stoichiometric LiNbO₃ crystal pumped by 2 μJ femtosecond laser pulses at room temperature. An unusual superquadratic rise of the THz pulse energy with the laser pulse energy has been observed at high laser energies. This extraordinary energy dependence of the THz generation efficiency is explained by self-focusing of the laser beam in the crystal. Z-scan measurements and comparison of the THz pulse spectra created with laser pulses having different energies confirm this interpretation.     

Sub-10-fs supercontinuum radiation generated by filamentation of few-cycle 800 nm pulses in argon

Focusing 12 fs pulses of 800 nm with moderate energy (0.35 mJ) into atmospheric-pressure argon (Ar) gives rise to filamentation (self-focusing) and a supercontinuum with a very broad pedestal, extending to 250 nm. According to the present understanding, the short wavelengths are produced by self-phase modulation in the self-steepened trailing edge of the pulse. Pulses in this spectral range might thus be intrinsically short. Indeed we demonstrate this by extracting the light near the end of the filament, terminating self-focusing by a pressure gradient at a pinhole, beyond which the Ar is pumped away. We obtain pulses of 9.7 fs in the region of 290 nm without the necessity of compression.     

The influence of transverse perturbations on the propagation of picosecond acoustic pulses in a paramagnetic crystal

The influence of transverse perturbations on the dynamics of a picosecond soliton-like acoustic pulse in a paramagnetic crystal in an external magnetic field is investigated. The nonlinear and dispersion effects are governed by the intrinsic properties of the crystal and the spin-phonon interaction. The effect of different nonlinear mechanisms and an external magnetic field on the stability against transverse perturbations is analyzed. It is shown that, in the absence of paramagnetic impurities, there can exist only a compression pulse that propagates in a defocusing regime. In the presence of paramagnetic ions in the crystal, there can arise rarefaction pulses that, under specific conditions, can propagate in self-focusing and self-channeling regimes.     

An improved nonlinear optical pulse propagation equation

A new equation for self-focusing of extremely focused short-duration intense pulses is derived using a method that treats diffraction and dispersion to all orders with nonlinearity present, and self-consistently determines the nonlinear derivative terms present in the propagation equation. It generalizes both the previous formulation of linear optical pulse propagation to the nonlinear regime, and the cw nonlinear regime propagation to the pulsed regime by including temporal characteristics of the pulse. We apply the new equation and propagate a tightly focused picosecond pulse in silica and explicitly show the effects of spatial-derivative nonlinear coupling terms.     

Mode improvement of a femtosecond laser beam by the spatially self-focusing effect in solid material

The self-focusing effect of femtosecond pulses in a thin piece of BK7 glass is researched through experiment and calculation. The spatial-mode improvement of the femtosecond laser beam is observed. Against the incident pulse with spatial wings, a Gauss-like spatial mode is obtained due to the spatially self-focusing effect in a solid material. The femtosecond pulse propagation in the thin glass plate is analyzed by the amended propagation equation, and the theoretical result shows a qualitative agreement with the experimental result. According to the analysis, the mode improvement of the femtosecond laser beam is resulted from the combination with the self-focusing and dispersion effects in the solid material.