Coherent control of high harmonic generation via dual-gas multijet arrays

High harmonic generation (HHG) is a central driver of the rapidly growing field of ultrafast science. We present a novel quasiphase-matching (QPM) concept with a dual-gas multijet target leading, for the first time, to remarkable phase control between multiple HHG sources (>2) within the Rayleigh range. The alternating jet structure with driving and matching zones shows perfect coherent buildup for up to six QPM periods. Although not in the focus of the proof-of-principle studies presented here, we achieved competitive conversion efficiencies already in this early stage of development.     

Coherent optical harmonic generation in rat-tail tendon

Measurements of the angular divergence of optical second harmonic generation in rat-tail tendon reveal a very narrow forward peak. This implies the existence of coherent order and, together with the demonstration of nonlinear susceptibility components d₃₃ and d₃₂, confirms prior indications that the tendon is polar. Some biological consequences of this polarity are considered.     

Second harmonic generation in generalized Thue-Morse ferroelectric superlattices

In this paper the second harmonic generation (SHG) in generalized Thue-Morse (GTM(m, n)) ferroelectric superlattices is studied. Under the small-signal approximation, the SHG spectra in both real and reciprocal spaces are investigated. It is found that: (1) only when the structure parameters l, l_A, and l_B are all chosen to be proper, can SHG in GTM(m, n) ferroelectric superlattices be generated; (2) for Family A of generalized Thue-Morse, GTM(m, 1) ferroelectric systems, with the increase of parameter m, the intense peaks of SHG concentrate on the long wavelength (the fundamental beam (FB) wavelength is within ), but for Family B of generalized Thue-Morse, GTM(1, n) ferroelectric superlattices, with the increase of parameter n, the intense peaks of SHG concentrate on the middle wavelength ; and (3) for GTM(m, 1) ferroelectric superlattices, the bigger the m, the stronger the relative integral intensity (RII) of SHG would be, but for GTM(1, n) ferroelectric systems, the bigger the n, the weaker the RII of SHG would be.     

Coherent ultrashort XUV emission by harmonic generation

By focusing an intense short-pulse laser into a rare gas jet, high-order harmonics of the laser frequency are generated. Considerable progress have been made in the last few years, with the observation of harmonic orders higher than 200, extending the emission down to 3 nm. Besides its fundamental interest, this XUV emission represents a new source with unique properties of coherence and ultrashort (femtosecond) duration. A growing number of applications are reported, ranging from atomic and molecular spectroscopy to solid-state and plasma physics.     

Coherent harmonic generation on UVSOR-II storage ring

Among the attractive coherent light sources resulting from the interaction between femtosecond lasers and relativistic electron beams, simultaneous Coherent Synchrotron Radiation (CSR) in the THz region, slicing and UV-VUV Coherent Harmonic Generation (CHG) can be achieved on synchrotron radiation facilities. Recently, a Ti:Sa laser at high repetition rate (1 kHz) has been seeded in the optical klystron of the Free Electron Laser at UVSOR-II (Okazaki, Japan). In this paper, the experimental set-up allowing delivery of sub picosecond UV pulses from CHG, and TeraHertz radiation from CSR is described. We further focus on the third coherent harmonic (266 nm) generated. The expected typical characteristics of this radiation, predicted by both numerical and analytical models recalled here, are experimentally verified and several studies of the influence of the seed laser on the output CHG intensity are reported. Such experiment enables UVSOR-II facility to produce in parallel short pulses at two different colors, synchronized at high repetition rate with one single infrared laser: a unique set-up of great interest for the facility users.     

Coherent and incoherent second harmonic generation in planar G-shaped nanostructures

Azimuthal anisotropy of Stokes parameters of the second harmonic generation (SHG) generated and observed in reflection from a periodic planar area of G-shaped gold nanostructures is studied. A strong anisotropy of both coherent and incoherent SHG components is observed. Finite-difference time-domain calculations prove that the observed effects are due to the anisotropic enhancement of the fundamental radiation within the G-shaped structures.     

Coherent hard x rays from attosecond pulse train-assisted harmonic generation

High-order harmonic generation from atomic systems is considered in the crossed fields of a relativistically strong infrared laser and a weak attosecond pulse train of soft x rays. Due to one-photon ionization by the x-ray pulse, the ionized electron obtains a starting momentum that compensates the relativistic drift, which is induced by the laser magnetic field, and allows the electron to efficiently emit harmonic radiation upon recombination with the atomic core in the relativistic regime. This way, short pulses of coherent hard x rays of up to 40 keV energy can be generated.     

Coherent control of THz wave generation in ambient air

Our study of THz wave generation in the pulsed laser induced air plasma with individually controlled phase, polarization, and amplitude of the optical fundamental wave (omega) and its second harmonic (2omega) indicates that the third-order nonlinear optical process mixing the omega and 2omega beams in the ionized plasma is the main mechanism of the efficient THz wave generation. The polarity and the strength of the emitted THz field are completely controlled by the relative phase between the omega and 2omega waves. The measured THz field amplitude is proportional to the pulse energy of the fundamental beam and to the square root of the pulse energy of the second-harmonic beam once the total optical pulse energy exceeds the plasma formation threshold. The optimal THz field is achieved when all waves (omega, 2omega, and THz waves) are at the same polarization in the four-wave-mixing process.     

Coherent spectral enhancement of carrier-envelope-phase stable continua with dual-gas high harmonic generation

Attosecond science is enabled by the ability to convert femtosecond near-infrared laser light into coherent harmonics in the extreme ultraviolet spectral range. While attosecond sources have been utilized in experiments that have not demanded high intensities, substantially higher photon flux would provide a natural link to the next significant experimental breakthrough. Numerical simulations of dual-gas high harmonic generation indicate that the output in the cutoff spectral region can be selectively enhanced without disturbing the single-atom gating mechanism. Here, we summarize the results of these simulations and present first experimental findings to support these predictions.     

Spectral phase distribution retrieval through coherent control of harmonic generation

The temporal intensity distribution of the third harmonic of a Ti:sapphire laser generated in Xe gas is fully reconstructed from its spectral phase and amplitude distributions. The spectral phases are retrieved by cross correlating the fundamental laser frequency field with that of the third harmonic, in a three laser versus one harmonic photon coupling scheme. The third harmonic spectral amplitude distribution is extracted from its field autocorrelation. The measured pulse duration is found to be in agreement with that expected from lowest order perturbation theory both for unstretched and chirped pulses.     

Coherent phonon dynamics in short-period InAs/GaSb superlattices

We have performed ultrafast pump-probe spectroscopy studies on a series of InAs/GaSb-based short-period superlattice (SL) samples with periods ranging from 46 Å to 71 Å. We observe two types of oscillations in the differential reflectivity with fast (∼$\sim$1–2 ps) and slow (∼$\sim$24 ps) periods. The period of the fast oscillations changes with the SL period and can be explained as coherent acoustic phonons generated from carriers photoexcited within the SL. This mode provides an alternative method for determining the SL period. The period of the slow mode depends on the wavelength of the probe pulse and can be understood as a propagating coherent phonon wavepacket modulating the reflectivity of the probe pulse as it travels from the surface into the sample.     

Coherent states of a damped harmonic oscillator

We construct here the coherent states (annihilation operator eigenstates) of a damped harmonic oscillator. These coherent states, which are normalizable, have the desired behaviour in the classical limit (ℏ→0).     

Coherent states of general time-dependent harmonic oscillator

By introducing an invariant operator, we obtain exact wave functions for a general time-dependent quadratic harmonic oscillator. The coherent states, both inx- andp-spaces, are calculated. We confirm that the uncertainty product in coherent state is always larger thankh/2 and is equal to the minimum of the uncertainty product of the number states. The displaced wave packet for Caldirola-Kanai oscillator in coherent state oscillates back and forth with time about the center as for a classical oscillator. The amplitude of oscillation with no driving force decreases due to the dissipation in the system. However, the oscillation with resonant frequency oscillates with a large amplitude, even after a sufficient time elapse.     

Deformed harmonic oscillators: Coherent states and Bargmann representations

Generalizing the case of the usual harmonic oscillator, we look for Bargmann representations corresponding to deformed harmonic oscillators. Deformed harmonic oscillator algebras are generated by four operators a, a , N and the unity 1 such as [a, N] = a, [a , N] = –a , a a = (N) and aa = (N + 1). We discuss the conditions of existence of a scalar product expressed with a true integral on the space spanned by the e igenstates of a (or a ). We give various examples, in particular we consider functions that are linear combinations of q ^N, q ^–N and unity and that correspond to q-oscillators with Fock-representations or with non-Fock-representations.     

Enhancement of high-order harmonic generation at tuned wavelengths through adaptive control

An adaptive learning loop enhances the efficiency and tuning of high-order harmonic generation. In comparison with simple chirp tuning, we observe a broader tuning range and a twofold to threefold enhancement in integrated photon flux in the cutoff region. The driving pulse temporal phase varies significantly for different tunings and is more complicated than a simple chirp. We compare our experimental results with a one-dimensional, time-dependent model that incorporates the intrinsic atomic response, the experimental pulse temporal phase, ionization effects, and transverse coherence of the spatial mode of the laser. The model agrees with our experimental results and indicates that a specific quantum path coupled with ionization effects determines the optimized harmonic spectrum.     

Chirp control on molecular harmonic generation and distribution in H2+

Chirp control on the molecular harmonic emission and distribution in H₂⁺ has been theoretically investigated. The results show that (i) with the introduction of the up-chirped pulse, the intensities of the higher harmonics are decreased; while with the introduction of the down-chirped pulse, the intensities of the higher harmonics can be enhanced. When E(t) < 0.0, the harmonic emission events (HEEs) from the positive-H are higher than those from the negative-H; while when E(t) > 0.0, the HEEs from the negative-H are higher than those from the positive-H. As a result, when the higher harmonics are produced from E(t) < 0.0 or E(t) > 0.0, the positive-H or the negative-H plays the main role in the harmonic spectra. (ii) The distribution of the higher harmonics from the two-H nuclei can be controlled with the introduction of the chirps and the carrier-envelope-phases of the laser field. (iii) Some minima on the harmonic spectra can be obtained, which is attributed to the coupling of the two-center interference and the electron-nuclear dynamics. (iv) By properly superposing the harmonics from the down-chirped pulse, an isolated attosecond pulse (IAP) with the duration of 45 as can be obtained, which is nearly 1 order of magnitude enhancement in pulse intensity compared with the chirp- free case.     

Second harmonic generation in InSe

Experimental evaluation of non-linear susceptibility coefficient d₂₂ for InSe, which is responsible for second harmonic generation in this material at 1.06 and 10.6 μm, is reported and the value compared with GaSe. At the CO₂ laser frequency of oscillation, phase matching has been observed and a value of d₂₂ almost equal to d₁₅ for CdSe has been found. The InSe high transparency in the wavelength range 1.1–22 μm, the sizeable value of d₂₂ and the possibility of reaching phase matching condition in the IR range make InSe a potential device for far IR frequency conversion.     

High-frequency generation in two coupled semiconductor superlattices

We theoretically show that two semiconductor superlattices arranged on the same substrate and coupled with the same resistive load can be used for a generation of high-frequency periodic and quasiperiodic signals. Each superlattice involved is capable to generate current oscillations associated with drift of domains of high charge concentration. However, the coupling with the common load can eventually lead to synchronization of the current oscillations in the interacting superlattices. We reveal how synchronization depends on detuning between devices and the resistance of the common load, and discuss the effects of coupling and detuning on the high-frequency power output from the system.     

Second harmonic generation in graphene

Second harmonic generation in graphene has been theoretically studied. Phenomenological analysis based on symmetry arguments is carried out. It is demonstrated that second harmonic generation in ideal graphene samples is possible only if the radiation wave vector or its magnetic field is taken into account. Microscopic theory is developed for the classical regime of radiation interaction with electrons, where the photon energy is much lower than the characteristic energy of charge carriers. It is demonstrated that the emitted radiation can be strongly circularly polarized for the linearly polarized incident wave.