Femtosecond snapshot imaging of propagating light itself

An ultrafast imaging technique has been developed to visualize directly a light pulse that is propagating in a medium. The method, called femtosecond time-resolved optical polarigraphy (FTOP), senses instantaneous changes in the birefringence within the medium that are induced by the propagation of an intense light. A snapshot sequence composed of each femtosecond probing the pulse delay enables ultrafast propagation dynamics of the intense femtosecond laser pulse in the medium, such as gases and liquids, to be visualized directly. Other examples include the filamentation dynamics in CS2 liquid and the propagation dynamics in air related to the interaction with laser breakdown plasma. FTOP can also be used to extract information on the optical Kerr constant and its decay time in media. This method is useful in the monitoring of the intensity distribution in the nonlinear propagation of intense light pulses, which is a frequently studied subject in the field of physics regarding nonlinear optics and laser processing.     

Gauss-Legendre quadrature method used to evaluate the spatio-temporal intensity of ultrashort pulses in the focal region of lenses

We analyze the spatio-temporal intensity of sub-20 femtosecond pulses with a carrier wavelength of 810 nm along the optical axis of low numerical aperture achromatic and apochromatic doublets designed in the IR region by using the scalar diffraction theory. The diffraction integral is solved by expanding the wave number around the carrier frequency of the pulse in a Taylor series up to third order, and then the integral over the frequencies is solved by using the Gauss-Legendre quadrature method. The numerical errors in this method are negligible by taking 96 nodes and the computational time is reduced by 95% compared to the integration method by rectangles. We will show that the third-order group velocity dispersion (GVD) is not negligible for 10 fs pulses at 810 nm propagating through the low numerical aperture doublets, and its effect is more important than the propagation time difference (PTD). This last effect, however, is also significant. For sub-20 femtosecond pulses, these two effects make the use of a pulse shaper necessary to correct for second and higher-order GVD terms and also the use of apochromatic optics to correct the PTD effect. The design of an apochromatic doublet is presented in this paper and the spatio-temporal intensity of the pulse at the focal region of this doublet is compared to that given by the achromatic doublet.     

Soliton propagation in nonlinear optics with higher-order effects

Abstract

We consider the nonlinear wave propagation in a single-mode dielectric waveguide. Considering the envelope equation by Kodama and Hasegawa, which consists of the higher-order terms in the form of higher-order dispersion and dissipation, we investigate the conditions for which the system admits soliton-type pulse propagation through Painlevé analysis. We also present N-soliton solutions.     

Intensity limitation for a self-focusing femtosecond laser pulse propagating in a medium with cubic nonlinearity

The self-focusing of an axisymmetric beam propagating in a cubically nonlinear medium has been studied by computer simulation with allowance for the temporal dispersion of the nonlinear response, which is manifested for femtosecond laser pulses. It shown that, depending on the ratio of the medium length and the diffraction length, the dispersion of the nonlinear response can lead either to limitation of the intensity growth rate in the nonlinear focus or its absence (for weakly diffracting beams), to an increase in the range of the nonlinear focus formation (for beams with a diffraction length 2.5–25 times the medium length), or to a decrease in this range (for beams with a diffraction length approximately equal to or shorter than the medium length). These phenomena are related to the dependence of the group velocity of pulse propagation on its intensity.     

Propagation properties and dispersion characteristics of the tapered gap plasmonic waveguides

Abstract

In this study, we numerically analyse the propagation properties and dispersion characteristics of the tapered gap plasmonic waveguides (TGPWs). Using the finite element method, the waveguide parameters such as modal field distribution and complex propagation constant are calculated for different geometrical parameters over a wide spectral range. Moreover, using a kind of active medium with appropriate gain, the required gains for lossless propagation are obtained. Results show that the propagation properties and dispersion characteristics of the waveguide along with the value of required gain for achieving lossless propagation can be well controlled by adjusting the geometrical parameters of the waveguide. The simulation results indicate that the calculated gain values are obtainable using the existing semiconductor technology such as InGaAsP–InGaAlAs multi-quantum well and InAs/GaAs quantum dot active medium at the wavelength of 1550 nm. The strong mode confinement of the TGPWs can be used for achieving strong nonlinear effects. Furthermore, due to optical energy confinement in nanoscale, optical nanofocusing devices based on TGPWs are attainable. TGPWs can be utilized in the field of nanotechnology to fulfil the photonic devices integration.     

Measurements and numerical analysis for femtosecond pulse deformations after propagation of hundreds of meters in air with water-vapor absorption lines

We have clarified the influences of water-vapor absorption lines in air on femtosecond pulse propagations from experimental and theoretical points of view. Precise measurements for the femtosecond pulse shapes after propagation of as much as 300 m through air have been made in a semiunderground optical testing tunnel. We observed the pulse splitting and the enhancement of the pulse broadening due to the 100-m propagation in air. The experimental results are in good agreement with the theoretical analysis by use of the HITRAN database at the edge and the center of the water-vapor absorption regions in air. Measured autocorrelation traces are mostly reproduced by those calculated with only the real part (dispersion) of the refractive index modulated by water-vapor absorption lines in air. This fact enables us to conclude that the pulse deformations due to water absorption lines in air are caused mainly by the real part (dispersion), not by the imaginary part (absorption), of the refractive index of air.     

Bloch Wave Analysis of Dispersion and Pulse Propagation in Pure Distributed Feedback Structures

Abstract

The excitation and behaviour of monochromatic and pulsed optical Bloch waves in pure distributed feed-back structures are discussed and analysed. The Bloch wave approach, based on a detailed knowledge of the natural optical modes of the periodic structure, is complementary to the more commonly used coupled-wave approach. The inter-relationship between dispersion, field micro-structure and group velocity is discussed, and the effects of group-velocity and higher-order dispersion on pulse propagation treated. Questions about the usefulness of DFB structures for dispersion correction and soliton formation are addressed.     

Femtosecond laser pulse propagation in a uniaxial crystal

Abstract

The wave equation describing the vector propagation of a femtosecond laser pulse of a few optical cycles in a uniaxial crystal is solved numerically by the method of unidirectional waves. Propagation of the pulse in the direction normal to the optical axis is studied, taking into account both second- and third-order nonlinearities of the crystal. Conversion efficiency as a function of crystal length, pump intensity and pulse duration is studied. As an example, the propagation of femtosecond laser pulse of τ = 10 fs duration at λ = 810 nm in a LiNbO₃ crystal 12 μm thick is studied numerically.     

Transmission properties in waveguides: an optical streamline analysis

We present a novel approach to study transmission through waveguides in terms of optical streamlines. This theoretical framework combines the computational performance of beam propagation methods with the possibility to monitor the passage of light through the guiding medium by means of these sampler paths. In this way, not only can the optical flow along the waveguide be followed in detail, but also a fair estimate of the transmitted light (intensity) can be accounted for by counting streamline arrivals with starting points statistically distributed according to the input pulse. Furthermore, this approach allows elucidation of the mechanism leading to energy losses, namely, a vortical dynamics, which can be advantageously exploited in optimal waveguide design.     

Tailoring of group velocity dispersion in dual-core chiral nihility waveguide

The article focuses on an approach to overcome the dispersion present in optical communication systems. The group velocity dispersion (GVD) remains an important issue in this context. The approach presented in this paper is based on the use of chiral nihility mediums with different chirality parameters in dual-core planar optical waveguide. It is found that the two cores can be resonantly coupled in the guide, and also, the waveguide would yield high GVD by choosing suitable design parameters. For the analytical investigation, transfer matrix method is used and the dispersion relation is derived by implementing appropriate boundary conditions. Excitation of supermodes in the guide may be achieved through the coupling of two particular core modes, which would ultimately result in giant GVD. This essentially demonstrates that the structure may find applications in dispersion compensating systems.     

Realization of wavelength conversion with hyperbolic secant femtosecond pulse in normal dispersion regime

Realization of wavelength conversion based on second-order femtosecond dark solitons with hyperbolic secant pulse is presented. This is achieved by introducing localized dispersion perturbation along the optical fiber. We demonstrate that an initial 30 fs second-order pulse decays to similar sub-pulses by applying perturbation using a step increment of β₂ from 6.3 to 15.75 ps² km^?1. This shows that the realization of a 1 × 2 channel wavelength converter for femtosecond pulses is possible. Recent research shows the possibility of realizing wavelength conversion generated from picosecond solitons neglecting nonlinear effects. However, employing the same method for femtosecond pulses fails due to the manifestation of nonlinear effects. In this paper, pulse deformation under different levels of perturbation was tested, and appropriate perturbation leading to similar sub-pulses is achieved.     

High-intensive femtosecond singular pulses in Kerr dielectrics

The nonlinear dynamics of a high-power femtosecond singular pulse in Kerr media are analyzed numerically upon optically induced ionization. We examine the plasma inertia impact to stable propagation of optical vortices. Multifoci behavior of vortices in medium are revealed. Next we numerically demonstrate that inertial character of plasma formation provides a quasi-soliton regime of vortex propagation resistant to symmetry-breaking perturbation.     

Suppression of parabolic pulse-pair interaction using dispersion-managed fiber links with non-zero dispersion

We report on the suppression of the parabolic pulse-pair interaction by using the dispersion-managed optical fiber links with non-zero dispersion maps. The numerical results show that both the interaction and pulse splitting can be efficiently suppressed when the integrated dispersion is non-zero, and the pulse-pair can maintain their parabolic characteristics through the whole distance and turn to its original shape at the end of each map. Moreover, we numerically investigate the influence of the initial pulse width and chirp on the parabolic pulse pair propagation, which shows that the higher chirp is not conducive to pulse transmission.     

Clustered gases as a medium for efficient plasma waveguide generation

Clustered gas jets are shown to be an efficient means for plasma waveguide generation, for both femtosecond and picosecond generation pulses. These waveguides enable significantly lower on-axis plasma density (less than 10(18) cm(-3)) than in conventional hydrodynamic plasma waveguides generated in unclustered gases. Using femtosecond pump pulses, self-guided propagation and strong absorption (more than 70%) are used to produce long centimetre scale channels in an argon cluster jet, and a subsequent intense pulse is coupled into the guide with 50% efficiency and guided at above 10(17)W cm(-2) intensity over 40 Rayleigh lengths. We also demonstrate efficient generation of waveguides using 100 ps axicon-generated Bessel-beam pump pulses. Despite the expected sub-picosecond cluster disassembly time, we observe long pulse absorption efficiencies up to a maximum of 35%. Simulations show that in the far leading edge of the long laser pulse, the volume of heated clusters evolves to a locally uniform and cool plasma already near ionization saturation, which is then efficiently heated by the remainder of the pulse.     

Ultrasensitive nonlinear measurements of femtosecond pulses in the telecommunications band by aperiodically poled LiNbO3 waveguides

We have used aperiodically poled lithium niobate waveguides to perform intensity autocorrelation and frequency-resolved optical gating (FROG) measurements for ultraweak femtosecond pulses at 1.5 microm wavelength. The required pulse energies for intensity autocorrelation and FROG are as low as 52 aJ and 124 aJ, respectively. The corresponding sensitivities are 3.2 x 10(-7) mW(2) and 2.7 x 10(-6) mW(2), about 3-5 orders of magnitude better than the previous records. The high nonlinear conversion efficiency is attributed to the long waveguide structure, and the needed broad phase-matching bandwidth is realized by chirping the poling period. We discuss the theory of intensity autocorrelation and FROG measurements in the presence of different phase-matching bandwidths, and we show, for the first time to our knowledge, that the distorted intensity autocorrelation trace due to a delta-like phase-matching spectrum is described by a modified field autocorrelation function. We also report new experimental results comparing autocorrelation traces measured with chirped and unchirped waveguide samples and demonstrating high-quality FROG measurements for cubic phase waveforms generated in a programmable pulse shaper.     

The imaginary components of dispersion parameters and the Stokes mode dynamics in stimulated Raman scattering

The Stokes pulse dynamics during stimulated Raman scattering has been studied in the constant pumping approximation. The nonlinear problem of interaction between a pumping wave and the Stokes component is reduced to a linear equation describing propagation of an optical pulse in the amplifying medium with imaginary components of the first-and second-order dispersion parameters, the presence of which leads to the possibility of the pulse envelope propagation at a supraluminal velocity.     

Soliton self-frequency shift effects in photonic crystal fibre

Using a femtosecond Ti:sapphire laser operating at a wavelength of 810nm we have demonstrated infrared generation in photonic crystal fibre at distinct wavelengths which can be attributed to the soliton self-frequency shift effect. The maximum observed shift produced spectra centred at 1260nm and the frequency-shifted light accounted for up to 80% of the fibre output power. We show that the shifts can be explained by the dispersion properties of the fundamental and higher-order waveguide modes of the fibre.     

Terahertz polariton propagation in patterned materials

Generation and control of pulsed terahertz-frequency radiation have received extensive attention, with applications in terahertz spectroscopy, imaging and ultrahigh-bandwidth electro-optic signal processing. Terahertz 'polaritonics', in which terahertz lattice waves called phonon-polaritons are generated, manipulated and visualized with femtosecond optical pulses, offers prospects for an integrated solid-state platform for terahertz signal generation and guidance. Here, we extend terahertz polaritonics methods to patterned structures. We demonstrate femtosecond laser fabrication of polaritonic waveguide structures in lithium tantalate and lithium niobate crystals, and illustrate polariton focusing into, and propagation within, the fabricated waveguide structures. We also demonstrate a 90 degrees turn within a structure consisting of two waveguides and a reflecting face, as well as a structure consisting of splitting and recombining elements that can be used as a terahertz Mach-Zehnder interferometer. The structures permit integrated terahertz signal generation, propagation through waveguide-based devices, and readout within a single solid-state platform.     

Combined optical solitons with parabolic law nonlinearity and spatio-temporal dispersion

In this work, combined optical solitons are constructed in a weakly nonlocal nonlinear medium. The spatio-temporal dispersion (STD), parabolic law nonlinearity, detuning, nonlinear dispersion as well as inter-modal dispersion are taken into account. The integration tool that is applied is the complex envelope function ansatz. The influences of different parameters on dynamical behavior of combined optical solitons are discussed. The results are useful in describing the propagation of combined optical solitons with STD and parabolic law nonlinearity.     

Infinite guided modes in a planar waveguide with a biaxially anisotropic metamaterial

We investigate in detail the guided modes in a two-layered planar waveguide where one layer is filled with an ordinary right-handed material (RHM) and the other is filled with a biaxially anisotropic metamaterial. We show that the mode properties are closely dependent on the spatial dispersion relation of the anisotropic medium. When the dispersion equation for the anisotropic medium becomes a two-sheet or a one-sheet hyperbola type, an infinite number of guided modes can be supported simultaneously in the waveguide, which is completely different from the cases of RHM and isotropic metamaterial. We also investigate the mode distributions of the planar waveguide in the lossy case, where we discover that the dominant mode in the waveguide is a forward wave while the higher-order modes are backward waves under the two-sheet hyperbolic dispersion. Numerical results validate our theoretical analysis.