Photonic molecule state transition by collision.

We investigate the impact of collisions with two-frequency photonic molecules aiming to observe internal dynamic behavior and challenge their strong robustness. Versatile interaction scenarios show intriguing state changes expressed through modifications of the resulting state such as temporal compression and unknown collision-induced spectral tunneling. These processes show potential for efficient coherent supercontinuum generation and all-optical manipulation.

Single-cycle pulse compression in dense resonant media.

We propose here a new approach for compression and frequency up-conversion of short optical pulses in the regime of extreme nonlinear optics in optically dense absorbing media, providing an alternative route to attosecond-scale pulses at high frequencies. This method is based on dynamics of self-induced transparency (SIT) pulses of nearly single cycle duration, leading to single-cycle-scale Rabi oscillations in the medium. The sub-cycle components of an incident pulse behave as separate SIT-pulses, approaching each other and self-compressing, resulting in the threefold compression in time and frequency up-conversion by the same factor. As we show, the scheme can be cascaded, staying at the subsequent stage with nearly the same compression and up-conversion ratio. In this way, as our simulations show, after only few micrometers of propagation, a 700 nm wavelength single cycle pulse can be compressed to a pulse of 200 attoseconds duration located in XUV frequency range.

Role of frequency dependence of the nonlinearity on a soliton's evolution in photonic crystal fibers.

We reveal the crucial role played by the frequency dependence of the nonlinear parameter on the evolution of femtosecond solitons inside photonic crystal fibers (PCFs). We show that the conventional approach based on the self-steepening effect is not appropriate when such fibers have two zero-dispersion wavelengths, and several higher-order nonlinear terms must be included for realistic modeling of the nonlinear phenomena in PCFs. These terms affect not only the Raman-induced wavelength shift of a soliton but also impact its shedding of dispersive radiation.

Selective ultrafast control of multi-level quantum systems by subcycle and unipolar pulses.

The most typical way to optically control population of atomic and molecular systems is to illuminate them with radiation, resonant to the relevant transitions. Here we consider a possibility to control populations with the subcycle and even unipolar pulses, containing less than one oscillation of electric field. Despite the spectrum of such pulses covers several levels at once, we show that it is possible to selectively excite the levels of our choice by varying the driving pulse shape, duration or time delay between consecutive pulses. The pulses which are not unipolar, but have a peak of electric field of one polarity much higher (and shorter) than of the opposite one, are also capable for such control.

Higher-order dispersion and the spectral behavior in a doubly resonant optical parametric oscillator.

In doubly resonant optical parametric oscillators (DROPOs), it is possible to generate, enhance, and phase lock two frequencies at once. Following intracavity phase conditions, a complex tuning behavior of the signal and idler spectra takes place in DROPOs, cumulating into degeneracy with phase self-locking and coherent wavelength doubling. In this work, we identify group delay matching as the important parameter determining the global tuning behavior and demonstrate the key role of higher-order dispersion in the spectral dependencies. Applicationwise, we suggest a simple way to control the phase self-locking region by varying the intracavity third-order dispersion.

Manipulation of infrared dispersive waves in customized microstructured optical fibers for 1.7 and 2.0 µm light sources.

We demonstrate the controllable generation of infrared dispersive waves (DWs) from customized, in-house fabricated silica microstructured optical fibers (MOFs) by manipulating the location of zero dispersion wavelength (ZDW) through the structure of the fibers. The highly enriched shaping mechanism of arrested soliton in the MOFs with two ZDWs provides a technique for efficient energy transfer into the targeted eye-safe wavelengths at 1.7 and 2.0 µm by the virtue of DW formation.

Soliton Molecules with Two Frequencies.

We demonstrate a peculiar mechanism for the formation of bound states of light pulses of substantially different optical frequencies, in which pulses are strongly bound across a vast frequency gap. This is enabled by a propagation constant with two separate regions of anomalous dispersion. The resulting soliton compound exhibits moleculelike binding energy, vibration, and radiation and can be understood as a mutual trapping providing a striking analogy to quantum mechanics. The phenomenon constitutes an intriguing case of two light waves mutually affecting and controlling each other.

Low-loss curved waveguides in polymers written with a femtosecond laser.

We present straight and s-curve waveguides in polymers fabricated by femtosecond laser writing. A number of parallel tracks are written inside the bulk material with a well-defined gap in the middle that forms the waveguide core. This approach offers the flexibility to tailor the mode-field diameter of the waveguide by adjusting the size of the gap. The waveguides exhibit very low propagation losses of 0.3 dB/cm and no significant bend losses for curve radii of R ≥ 20 mm. This fabrication process will allow for the realization of complex waveguide networks in a compact footprint chip.

Regularizing Aperiodic Cycles of Resonant Radiation in Filament Light Bullets.

We demonstrate an up to now unrecognized and very effective mechanism which prevents filament collapse and allows persistent self-guiding propagation retaining a large portion of the optical energy on axis over unexpected long distances. The key ingredient is the possibility of continuously leaking energy into the normal dispersion regime via the emission of resonant radiation. The frequency of the radiation is determined by the dispersion dynamically modified by photogenerated plasma, thus allowing us to excite new frequencies in spectral ranges which are otherwise difficult to access.

Role of Intrapulse Coherence in Carrier-Envelope Phase Stabilization.

The concept of coherence is of fundamental importance for describing the physical characteristics of light and for evaluating the suitability for experimental application. In the case of pulsed laser sources, the pulse-to-pulse coherence is usually considered for a judgment of the compressibility of the pulse train. This type of coherence is often lost during propagation through a highly nonlinear medium, and pulses prove incompressible despite multioctave spectral coverage. Notwithstanding the apparent loss of interpulse coherence, however, supercontinua enable applications in precision frequency metrology that rely on coherence between different spectral components within a laser pulse. To judge the suitability of a light source for the latter application, we define an alternative criterion, which we term intrapulse coherence. This definition plays a limiting role in the carrier-envelope phase measurement and stabilization of ultrashort pulses. It is shown by numerical simulation and further corroborated by experimental data that filamentation-based supercontinuum generation may lead to a loss of intrapulse coherence despite near-perfect compressibility of the pulse train. This loss of coherence may severely limit active and passive carrier-envelope phase stabilization schemes and applications in optical high-field physics.

Cascaded-focus laser writing of low-loss waveguides in polymers.

Waveguide writing in poly (methyl methacrylate) (PMMA) with femtosecond laser radiation is presented. An adequate refractive index change is induced in the border area below the irradiated focal volume. It supports an almost symmetric fundamental mode with propagation losses down to 0.5 dB/cm, the lowest losses observed so far in this class of materials. The writing process with a cascaded focus is demonstrated to be highly reliable over a large parameter range.

Controlling formation and suppression of fiber-optical rogue waves.

Fiber-optical rogue waves appear as rare but extreme events during optical supercontinuum generation in photonic crystal fibers. This process is typically initiated by the decay of a high-order fundamental soliton into fundamental solitons. Collisions between these solitons as well as with dispersive radiation affect the soliton trajectory in frequency and time upon further propagation. Launching an additional dispersive wave at carefully chosen delay and wavelength enables statistical manipulation of the soliton trajectory in such a way that the probability of rogue wave formation is either enhanced or reduced. To enable efficient control, parameters of the dispersive wave have to be chosen to allow trapping of dispersive radiation in the nonlinear index depression created by the soliton. Under certain conditions, direct manipulation of soliton properties is possible by the dispersive wave. In other more complex scenarios, control is possible via increasing or decreasing the number of intersoliton collisions. The control mechanism reaches a remarkable efficiency, enabling control of relatively large soliton energies. This scenario appears promising for highly dynamic all-optical control of supercontinua.

Predictability of rogue events.

Using experimental data from three different rogue wave supporting systems, determinism, and predictability of the underlying dynamics are evaluated with methods of nonlinear time series analysis. We included original records from the Draupner platform in the North Sea as well as time series from two optical systems in our analysis. One of the latter was measured in the infrared tail of optical fiber supercontinua, the other in the fluence profiles of multifilaments. All three data sets exhibit extreme-value statistics and exceed the significant wave height in the respective system by a factor larger than 2. Nonlinear time series analysis indicates a different degree of determinism in the systems. The optical fiber scenario is found to be driven by quantum noise whereas rogue waves emerge as a consequence of turbulence in the others. With the large number of rogue events observed in the multifilament system, we can systematically explore the predictability of such events in a turbulent system. We observe that rogue events do not necessarily appear without a warning, but are often preceded by a short phase of relative order. This surprising finding sheds some new light on the fascinating phenomenon of rogue waves.

Supercontinuum generation by multiple scatterings at a group velocity horizon.

A new scheme for supercontinuum generation covering more than one octave and exhibiting extraordinary high coherence properties has recently been proposed [Phys. Rev. Lett. 110, 233901 (2013)]. The scheme is based on two-pulse collision at a group velocity horizon between a dispersive wave and a soliton. Here we demonstrate that the same scheme can be exploited for the generation of supercontinua encompassing the entire transparency region of fused silica, ranging from 300 to 2300nm. At this bandwidth extension, the Raman effect becomes detrimental, yet may be compensated by using a cascaded collision process. Consequently, the high degree of coherence does not degrade even in this extreme scenario.

Direct observation of pulse dynamics and self-compression along a femtosecond filament.

We report on the direct experimental observation of pulse-splitting dynamics along a femtosecond filament. The fundamental pulse experiences a significant self-shortening during the propagation leading to pulse durations of 5.3 fs, corresponding to sub-3 cycles, which is measured without external pulse compression. A compression factor of eight could be achieved in a single filamentary stage. Theoretical modeling of the fundamental pulse propagation confirms our observed pulse structures and durations and gives further insight into the nonlinear dynamics during filamentation.

Adjustable pulse compression scheme for generation of few-cycle pulses in the midinfrared.

A novel adjustable adiabatic soliton compression scheme is presented, enabling a coherent pulse source with pedestal-free, few-cycle pulses in the infrared or midinfrared regime. This scheme relies on interaction of a dispersive wave and a soliton copropagating at nearly identical group velocities in a fiber with enhanced infrared transmission. The compression is achieved directly in one stage, without the necessity of an external compensation scheme. Numerical simulations are employed to demonstrate this scheme for silica and fluoride fibers, indicating ultimate limitations as well as the possibility of compression down to the single-cycle regime. Such output pulses appear to be ideally suited as seed sources for parametric amplification schemes in the midinfrared.

Compressible octave spanning supercontinuum generation by two-pulse collisions.

We demonstrate a novel method for supercontinuum generation in an optical fiber based on two-color pumping with a delay and a group velocity matching. The scheme relies on the enhanced cross-phase-modulation at an intensity induced refractive index barrier between a dispersive wave and a soliton. The generation mechanism neither incorporates soliton fission nor a modulation instability and therefore exhibits extraordinary coherence properties, enabling the temporal compression of octave bandwidth into a short pulse. Moreover, the properties of the supercontinuum are adjustable over a wide range in the frequency domain by suitable choice of the dispersive wave.

Spatiotemporal rogue events in optical multiple filamentation.

The transient appearance of bright spots in the beam profile of optical filaments formed in xenon is experimentally investigated. Fluence profiles are recorded with high-speed optical cameras at the kilohertz repetition rate of the laser source. A statistical analysis reveals a thresholdlike appearance of heavy-tailed fluence distributions together with the transition from single to multiple filamentation. The multifilament scenario exhibits near-exponential probability density functions, with extreme events exceeding the significant wave height by more than a factor of 10. The extreme events are isolated in space and in time. The macroscopic origin of these experimentally observed heavy-tail statistics is shown to be local refractive index variations inside the nonlinear medium, induced by multiphoton absorption and subsequent plasma thermalization. Microscopically, mergers between filament strings appear to play a decisive role in the observed rogue wave statistics.

Saturation of the all-optical Kerr effect in solids.

We discuss the influence of the higher-order Kerr effect (HOKE) in wide bandgap solids at extreme intensities below the onset of optically induced damage. Using different theoretical models, we employ multiphoton absorption rates to compute the nonlinear refractive index by a Kramers-Kronig transform. Within this theoretical framework we provide an estimate for the appearance of significant deviations from the standard optical Kerr effect predicting a linear index change with intensity. We discuss the role of the observed saturation behavior in practically relevant situations, including Kerr lens mode-locking and supercontinuum generation in photonic crystal fibers. Furthermore, we present experimental data from a multiwave mixing experiment in BaF2, which can be explained by the appearance of the HOKE.

Saturation of the all-optical Kerr effect.

Saturation of the intensity dependence of the refractive index is directly computed from ionization rates via a Kramers-Kronig transform. The linear intensity dependence and its dispersion are found to be in excellent agreement with complete quantum mechanical orbital computations. Higher-order terms concur with solutions of the time-dependent Schrödinger equation. Expanding the formalism to all orders up to the ionization potential of the atom, we derive a model for saturation of the Kerr effect. This model widely confirms recently published and controversially discussed experimental data and corroborates the importance of higher-order Kerr terms for filamentation.