Generation and propagation of a resonant CARS signal from biomolecules: Application to dipicolinic acid

Abstract

We develop a theoretical approach and perform simulations of coherent anti-Stokes Raman scattering (CARS) with ultrashort laser pulses. The signal is generated by biomolecules having subpicosecond dephasing times, from femtosecond pulses on exact resonance with the molecular transitions. All propagation effects are explicitly accounted for, including pump depletion, Raman amplification, parametric generation and pulse reshaping. Our model predicts that a measurable CARS signal can be generated by the dipicolinic acid biomolecule under realistic conditions.     

Spatially induced spatiotemporally nonspreading Airy-Bessel wave packets

By studying the effect of spatially induced group velocity dispersion (SIGVD) during the propagation of ultrashort pulsed Bessel beams in free space, we numerically prove that third-order SIGVD can temporally cause Gaussian distribution of pulsed Bessel beams to gradually evolve as unsymmetrical trailing oscillatory structures. The pulse shape is confirmed to be temporal Airy distributions on the basis of the cross-correlation function. Therefore, it is demonstrated that the scheme of generating spatiotemporally nonspreading Airy-Bessel wave packets in free space is possible by using a precompensating second-order SIGVD. The results of numerical simulation show that the quasi-Airy pulses induced by third-order SIGVD are temporally nonspreading during propagation in dispersive media. The reasons for nonspreading of such Airy distribution pulses are phenomenologically analyzed by a time-frequency Wigner distribution function of the pulse.     

Diffraction characteristics of 10 fs laser pulses passing through an aperture

Results are presented on experimental and theoretical work performed to compare diffraction phenomena for ultrashort 10 fs pulses and continuous-wave propagation modes illuminating different-sized pinholes and slits. Results demonstrate that 10 fs pulses do not produce high-frequency diffraction like that produced with continuous-wave illumination. The diffraction through a 1 mm pinhole of temporally stretched pulses obtained by using fused silica plates whose frequency spectrum remains the same is compared with those of 10 fs pulses. The overall diffraction intensity profiles are, however, nearly identical in this case. The simulations of diffraction patterns for 100 fs, 10 fs, and 1 fs incident pulse were compared theoretically for different aperture sizes and frequencies. Calculations indicate that the lack of high-frequency diffraction for the mode-locked case is due to the broadband nature of the ultrashort laser pulses; i.e., the distribution of the frequency contained in the pulse ends up washing out when objects are illuminated with pulses of broad frequency content. The results of this work have important application in biomedical imaging and remote imaging applications, to name only a few.     

An intuitive model for on-axis pulse evolution of ultrashort pulsed Gaussian beams diffracted from a circular aperture

The diffraction of ultrashort pulsed Gaussian beams from a circular aperture is studied by means of Fresnel diffraction integral and Fourier transform method. A uniform analytical expression is derived for temporal pulse form of ultrashort pulsed Gaussian beams in two cases, i.e. with constant beam waist and with constant diffraction length. It is shown that the on-axis pulse can be formulated as a superposition of an unapertured pulse and an aperture-induced pulse. The superposition of these two pulses leads to an enhanced pulse intensity for small truncation parameters at certain distances in the near field. Our results may find applications in high-intensity laser waveform control.     

Propagation of Bessel-X pulses in a hybrid photonic crystal

We report the propagation of Bessel-X pulses in a two-dimensional hybrid photonic crystal, investigated by the finite-difference time-domain method, in which broadband super-collimation and the propagation of self-collimated ultrashort pulses were reported. We first show the propagation of Bessel-X pulses in two-dimensional free space, whose transverse branches diverge rapidly with propagation. We then show that Bessel-X pulses propagate with their transverse and longitudinal shapes almost unchanged in the hybrid photonic crystal.     

Bessel pulse beams and focus wave modes

Free-space propagation of ultrashort pulses is investigated. Space-time couplings are reduced for a particular form of beams that is termed a pulse beam, or a type 3 pulsed beam. General conditions for the formation of pulse beams in the paraxial approximation are presented. The free-space propagation of spatially localized ultrashort laser pulses is investigated. This treatment is based on a particular pulsed form of the well-known Bessel beam, which is termed a Bessel pulse beam. The connections with focus wave modes and X waves are discussed.     

Dynamics of ultrashort light pulses in a semiconductor superlattice in the presence of a magnetic field

A system of equations that describes the propagation of ultrashort light pulses (optical solitons) in a semiconductor superlattice in the presence of a magnetic field is obtained using coupled Maxwell equations for the electromagnetic field and the Boltzmann equation written in the relaxation time approximation for the one-electron distribution function. It is shown that an initial linearly polarized light pulse induces a field with the orthogonal polarization in the sample. The dynamics of joint propagation of the initial and induced pulses in the sample is studied.     

Two-photon absorption of ultrashort electromagnetic pulses by negative halogen ions

Abstract

Within the framework of the perturbation theory, two-photon absorption of ultrashort electromagnetic pulses of a corrected Gaussian shape by negative halogen ions during the action of a pulse is calculated and analysed. Photoabsorption with excitation of an electron to a state with a specified energy is also considered. Particular attention is given to the dependence of the probability of these processes on the pulse duration. The features of two-photon absorption that are characteristic of sufficiently short pulses and do not take place in the monochromatic limit are revealed.     

Shift and shape of grating diffracted beams

Abstract

The grating diffraction of beams is theoretically investigated by applying an electromagnetic method (the Integral Equation System Method with Parametrization of the grating profile = IESMP) to their plane wave components. For the first time, explicit values for the displacement of grating diffracted Gaussian beams are calculated with this method. For total reflection this displacement of beams is known as the Goos-Hänchen shift. A maximum shift of 36 μm has been found for the investigated sinusoidal grating near an anomaly which is much greater than the known Goos–Hänchen shift of about 1 μm for the total reflection case. The replacement of the angular spectrum of plane waves with constant wavelength by a wavelength spectrum of plane waves of constant direction allows an analogous treatment of short-time pulses. Surprisingly, the above anomaly causes a maximum temporal shift of 80 fs for the pulse diffraction. These temporal shifts and additional effects like pulse deformations can influence ultra short-time pulse experiments. Furthermore, the behaviour of temporally and spatially Gaussian shaped light pulses (TSG pulses) by grating diffraction are studied considering the diffraction of an angular and wavelength dependent spectrum of plane waves. The diffraction of a short TSG pulse at the above grating deforms the pulse and creates an additional smaller satellite pulse. All described effects occur only at positions of the space–time complex filtering function in the angular-wavelength frequency space with high gradient of the phase.     

Effect of material dispersion on the focusing of isodiffracting ultrashort pulses by a lens

Abstract

Based on the Fourier transform, the focusing of isodiffracting ultrashort pulses by a lens is studied, where the material dispersion of first, second and higher order is taken into account, respectively. Numerical calculation results for spatial and temporal intensity distributions, photon flux and energy density of focused isodiffracting ultrashort pulses are given and illustrated. It is shown, compared to the dispersion-free case, that the first-order dispersion leads to a broadening of the pulse form, photon flux and energy density, and a decrease of their peak values. The second-order dispersion results in a further broadening of the pulse form and photon flux, and a further decrease of their peak values, whereas the higher-order dispersion plays a relatively minor role.     

Rapid two-dimensional optical spectroscopy through acousto-optic pulse shaping

Abstract

Phase-matching techniques are widely used to retrieve nonlinear optical signals of electronic and vibrational transitions. Here, collinear, phase cycled pulses are used to collect the same nonlinear signals in direct analogy to nuclear magnetic resonance studies. An acousto-optic pulse shaper is used to create suitable sequences of ultrashort pulses with arbitrary relative delays and phases. The rapid update rate of the acousto-optic modulator allows for impressive data rates.     

Generalized Bessel pulse beams

A generalization of type 3 ultrashort pulses (also known as pulse beams or isodiffracting pulses) is introduced. The Bessel beam form of this generalized beam consists of pulses that propagate in free space, without spreading, with a velocity that can be less than that of light. A model spectral distribution that is zero outside a finite range is investigated.     

Caustics of a Light Beam Passing Through a Time-varying Dielectric Wedge

Abstract

A caustic of cusp type in space-time is found to arise in a laser beam deflected by a wedge with time-varying refractive index. Asymptotic formulae describing the wave field under the assumption that the refractive index varies slowly compared with the oscillations of the light wave are given. The intensity of the wave field at the cusp point can be, say, 10³ times greater than the initial one. The temporal variation of the field at the cusp gives rise to an ultrashort pulse. The lengths of these pulses can be 10⁵ times less than the characteristic time of modulation of the refractive index, i.e., of subpicosecond range.     

Terahertz pulse propagation in the near field and the far field

We present a detailed investigation of the propagation properties of beams of ultrashort terahertz (THz) pulses emitted from large-aperture (LA) antennas. The large area of the emitter is demonstrated to have substantial influence on the temporal pulse profile in both the near field and the far field. We perform a numerical analysis based on scalar and vectorial broadband diffraction theory and are able to distinguish between near-field and far-field contributions to the total THz signal. We find that the THz beam from a LA antenna propagates like a Gaussian beam and that the temporal profile of the THz pulse, measured in the near field, contains information about the temporal and spatial field distribution on the emitter surface, which is intrinsically connected to the carrier dynamics of the antenna substrate. As a result of pulse reshaping, focusing of the THz beam leads to a reduced relative pulse momentum, with implications in THz field-ionization experiments.     

Pulse propagation and windowed wave functions

Abstract

We apply quasi-distribution methods developed for quantum mechanics to the propagation of pulses in dispersive media with attenuation. We show that a Schrödinger type equation follows for propagation of the pulse for each mode. One then transforms the equation to obtain an equation of evolution in the phase space of position and wavenumber. In this paper we emphasize windowed wave functions and their corresponding phase space quasi-distributions. We obtain the time evolution equation, discuss possible approximations, and compare to the Wigner distribution approximation previously derived by Loughlin and Cohen by different methods.     

Wave optical modelling of focusing of an ultra short pulse

The spatial–temporal evolution of an ultrashort pulse at different planes on propagation through a spherical lens is modelled using an efficient numerical algorithm. With this model it is possible to observe the on- and off-axis pulse evolution at any arbitrary plane. This model is applicable to pulses of arbitrary spatial and temporal shapes and can be used beyond paraxial approximation. We can obtain the exact amplitude information at any plane fairly easily. The asymmetry of the pulse shape at the focus is reported for the first time. The focusing of a pulse with TEM₀₁ spatial profile has been considered as an example and its evolution is analysed at different planes of propagation.     

Dynamics and interference of fine-structure wave packets created by strong ultrashort pulses

This work presents a theoretical study of two coherent schemes which allow the manipulation of wave packets created in atomic systems by strong ultrashort pulses. Our three-state system is composed of a ground state and two excited states simultaneously excited by the laser pulses. The corresponding dynamics are described in the bright state-dark state formalism where spectacular effects appear. (1) The wave packet created initially by a first pulse can be completely frozen through the action of a second strong pulse. (2) For pulses with a generalized pulse area equal to (2 p +1)2π (p integer), the population is preferentially transferred from the ground state to the dark state whatever the pulse duration. This is in complete disagreement with the physical interpretation valid in the weak field regime where the wave packet created by an ultrashort pulse is localized in the bright state at the end of the pulse. This effect can be revealed with wave packet interference induced by a second identical pulse. A simple analytical model using squared pulses is used to highlight the physical insight. This model is ‘reinforced’ by numerical simulations on the (4s–4p ² P 1/2,1/3) transitions in potassium atoms excited with Gaussian pulses.     

Reproduction in free space of fields confined by 3-dimensional optical waveguides

Abstract

It is shown by using the Fresnel-Kirchhoff diffraction theory and the method of images that a scalar field confined by a 3-dimensional optical waveguide can be generated in free space by a suitable light source. In the method the boundaries of a waveguide are replaced by virtual sources. This allows one to present the wave guiding as the interference and diffraction of multiple light beams produced in free space by the guide equivalent source (Fresnel waveguide). Thus, the scalar optics of a 3-dimensional waveguide is presented as the free-space beam optics. The method is illustrated by construction of the Fresnel sources for the triangular, rectangular and hexagonal waveguides. The numerical examples demonstrate the diffraction-free and self-imaging propagation in the free-space of the eigenmodes of the Fresnel rectangular-waveguide.     

Two-photon excitation of atoms by ultrashort electromagnetic pulses in a discrete spectrum

Abstract

The paper is devoted to the theoretical investigation of two-photon excitation of atom in a discrete energy spectrum by ultrashort electromagnetic pulses of femto- and subfemtosecond ranges of durations. An analytical expression for the total probability of the process is derived. Numerical simulations are made for hydrogen and sodium atoms. It is shown that the total probability of the process is nonlinear function of pulse duration and character of this function depends strongly on the frequency detuning of pulse carrier frequency from two-photon resonance.     

Physical significance of the group velocity in dispersive,ultrashort gaussian pulse dynamics

The properties of ultrashort gaussian pulse propagation in a dispersive, attenuative medium are reviewed with emphasis on the pulse velocity. Of particular interest is the group velocity whose physical interpretation loses meaning in causally dispersive materials as the temporal pulse width decreases into the ultrashort pulse regime. A generalized definition of the group velocity that applies to ultrashort pulses in causally dispersive materials is provided by the centroid velocity of the pulse Poynting vector whose properties are described here. In particular, it is shown that this physical velocity measure approaches the group velocity for any value of the initial pulse carrier frequency and at any fixed value of the propagation distance in the limit as the initial pulse width increases indefinitely. This then provides a convenient measure for determining when the group velocity approximation is valid.