Christian Köhler

Tailoring terahertz radiation by controlling tunnel photoionization events in gases

Various applications ranging from nonlinear terahertz (THz) spectroscopy to remote sensing require broadband and intense THz radiation, which can be generated by focusing two-color laser pulses into a gas. In this setup, THz radiation originates from the buildup of electron density in sharp steps of attosecond duration due to tunnel ionization, and the subsequent acceleration of free electrons in the laser field. We show that the spectral shape of the THz pulses generated by this mechanism is determined by the superposition of contributions from individual ionization events. This provides a straightforward analogy to linear diffraction theory, where the ionization events play the role of slits in a grating. This analogy offers simple explanations for recent experimental observations and opens new avenues for THz pulse shaping based on temporal control of the ionization events. We illustrate this novel technique by tailoring the spectral width and position of the resulting radiation using multi-color pump pulses.

Saturation of the nonlinear refractive index in atomic gases

Motivated by the ongoing controversy on the origin of the nonlinear index saturation and subsequent intensity clamping in femtosecond filaments, we study the atomic nonlinear polarization induced by a high-intensity and ultrashort laser pulse in hydrogen by numerically solving the time dependent Schrodinger equation. Special emphasis is given to the efficient modeling of the nonlinear polarization at central laser frequency corresponding to 800 nm wavelength. Here, the recently proposed model of the Higher-Order Kerr Effect (HOKE) and two versions of the Standard model for femtosecond filamentation, including either a multi-photon or tunnel ionization rate, are compared. We find that around the clamping intensity the instantaneous HOKE model does not reproduce the temporal structure of the nonlinear response obtained from the quantum mechanical results. In contrast, the non-instantaneous charge contributions included in the Standard models ensure a reasonable quantitative agreement. Therefore, the physical origin for the observed saturation of the overall electron response is confirmed to mainly result from contributions of free or nearly free electrons.

Boosting terahertz generation in laser-field ionized gases using a sawtooth wave shape

Broadband ultrashort terahertz (THz) pulses can be produced using plasma generation in a noble gas ionized by femtosecond two-color pulses. Here we demonstrate that, by using multiple-frequency laser pulses, one can obtain a waveform which optimizes the free electron trajectories in such a way that they acquire the largest drift velocity. This allows us to increase the THz conversion efficiency to 2%, an unprecedented performance for THz generation in gases. In addition to the analytical study of THz generation using a local current model, we perform comprehensive 3D simulations accounting for propagation effects which confirm this prediction. Our results show that THz conversion via tunnel ionization can be greatly improved with well-designed multicolor pulses.

Directionality of terahertz emission from photoinduced gas plasmas

Forward and backward terahertz emission by ionizing two-color laser pulses in gas is investigated by means of a simple semianalytical model based on Jefimenkos equations and rigorous Maxwell simulations in one and two dimensions. We find the emission in the backward direction has a much smaller spectral bandwidth than in the forward direction and explain this by interference effects. Forward terahertz radiation is generated predominantly at the ionization front and is thus almost not affected by the opacity of the plasma, in excellent agreement with results obtained from a unidirectional pulse propagation model.

Effects of multiple ionization in atomic gases irradiated by one- and two-color ultrashort pulses

The dynamics of femtosecond light pulses ionizing noble gases from single or multiple ionization schemes are numerically compared, with the emphasis on two-color pulses. We discuss the influence of multiply-charged ions on the excitation of harmonics in focused propagation and on the supercontinuum and clamping intensity of laser filaments. Depending on the atom’s first binding energy, multiple ionization based on Ammosov–Delone–Krainov (ADK) tunneling rates can increase the peak intensities, the number of harmonics or the spectral blueshifts, compared with quasistatic hydrogen-like rates. With two-color pulses, noticeable differences occur in the frequency domain corresponding to broadband terahertz pulses.

THz generation by ionizing two-color laser pulses in gases

We present a combined theoretical and experimental study of THz generation in gases using two-color ionizing laser pulses. Results obtained from (3+1)-dimensional simulations are in good agreement with experimental findings and clarify the mechanisms responsible for THz emission as well as the observed dependencies on the gas pressure.

THz generation by filamentation of two-color femtosecond laser pulses

Summary form only given. Terahertz (THz) sources have attracted an increasing interest for applications in time-domain spectroscopy and security screening for many years [1]. Recently, two-color laser filaments were reported to be efficient tools for the remote generation of THz radiation over long distances in gases [2]. Despite numerous experimental results, there is, however, no clear understanding of the dominant physical mechanism driving THz generation in filamentation regime, i.e., either rectification by four-wave mixing (FWM) or plasma currents generated by tunnel ionization. Here, we examine THz generation by two-color filamentation in argon by means of fully three-dimensional (3D) numerical simulations for different pump pulse energies, durations and central wavelengths. Evaluating the THz spectra from either Kerr or plasma sources reveals that photocurrents are dominant in THz generation during filamentation at clamping intensity. Our numerical results reproduce several experimental features, such as the growth of the THz yield with the pump pulse energy or with the pulse duration.Using the unidirectional pulse propagation equation (UPPE) model [3] with a tunnel ionization rate, we simulate the Ilamentation of various pump pulses with 12 % of their energy converted to the second harmonic (SH). Figure 1(a,b) shows the evolution of a 800-nm Gaussian pump pulse (red curves), a perturbed Supergaussian one (green curves), both with 20 fs duration and ~ 7 mJ energy, and a Gaussian pump pulse with doubled duration and energy (blue curves). Using a noisy Supergaussian proIle favors the emergence of multiple Ilaments, which spread out the pulse energy and lower the plasma response. The THz Ield amplitude reaches 2 GV/m [see Fig. 1(b)s inset] and the THz yield attains ~ 1.5 μJ for the 20-fs pulses, which corresponds to 25 times the THz energy of a small Ilament created with a 270 μJ, 20-fs pump (not shown). This conIrms the quasi-linear growth of THz energy with the pump-pulse power reported in [2]. In addition, the 40-fs Gaussian pulse develops several temporal peaks and thus triggers more ionization events associated with higher peak density. These features lead to an almost fourfold increase of the THz signal compatible with [2]. To understand the origin of the THz signal, we plug the on-axis temporal proIles of the propagated pulses into either the Kerr term or the plasma term of the UPPE model, which are potential sources for THz generation. The resulting spectra, shown in Fig. 1(c), evidence that, for the Gaussian pulses, plasma currents prevail over FWM contributions at clamping intensity.In conclusion, 3D numerical simulations conIrm the efIcient generation of THz radiation over long distances by two-color laser Ilaments for various pump parameters. Local THz spectra computed from Kerr and plasma sources show that the photocurrent mechanism prevails in producing THz emission at clamping intensity. Experimental features are reproduced and we identify typical spectral signatures of Kerr-driven and plasma-driven THz generation, which could be used as diagnostics in further experiments [4].

Modeling the nonlinear refractive index in atomic gases

Accurate modeling of optical nonlinearities is crucial to describe macroscopic laser propagation in a medium, including sum frequency generation, spectral broadening due to self-phase modulation, various ionization processes and soliton formation. For incident laser light the response of the medium is given by the induced polarization of the microscopic system. The polarization is usually expanded in a Taylor series for the electric field amplitude, which is truncated after the first non-linear term being of third order for isotropic media. A third-order nonlinearity leads to the well-known optical Kerr effect, where the refractive index of the medium becomes intensity dependent via n = n0 + n2I. This leads to an inherent problem when modeling laser propagation in two or more spatial dimensions, linked to the formal divergence (n2 > 0) of the refractive index for increasing intensity.

Direction of THz emission by ionizing two-color pulses

Radiation in the THz range has a broad spectrum of applications, reaching from nonlinear THz spectroscopy to biological and medical imaging, but the design of efficient THz sources is a challenging task. Recently, a method using ionizing two color laser fields has attracted much interest, since the generated THz amplitudes are comparably high and exhibit a broad spectrum at the same time [1, 2]. In such a setup, electrons generated by tunnel ionization are accelerated in the two-color laser field and thus build up a current, which partly radiates in the THz range. On the basis of this model, very good agreement between forward emitted THz radiation in experiment and simulation was obtained [3].

Carrier-envelope phase in pulse compression mediated by filamentation

Modern laser sources deliver intense, ultrashort pulses containing a few optical cycles only. This progress paved the way to the quickly-developing field of “extreme nonlinear optics”, for which the position of the carrier wave with respect to the envelope, the so-called carrier-envelope phase (CEP), matters. The CEP is expected to modify the pulse dynamics when the pulse duration becomes comparable to the oscillation cycle of the carrier wave [1]. Here we report on changes induced over remote distances by an initial phase offset along the self-compression of infrared and near-infrared femtosecond pulses mediated by filamentation. Few-cycle pulses can indeed be obtained by filamentary compression [2] and they have interesting properties, e.g., the self-guiding process acts as a spatial filter producing an excellent mode quality. In Ref. [3], energy variations at the percent level were observed to keep the filament CEP rather stable, as measured by ƒ – 2ƒ spectral interferometry. In Ref. [4], simulated ultrashort filaments were even proposed to maintain a nearly constant CEP upon meter-range distances.