(* ***2016**)

**Strong-field interactions and nano-optics experiments.** — Probing nanooptical near-fields is a major challenge in plasmonics. We demonstrated an experimental method based on utilizing ultrafast photoemission from plasmonic nanostructures that is capable of probing the maximum nanoplasmonic field enhancement in any metallic surface environment. Directly measured maximum field enhancement values for various samples are in good agreement with detailed finite-difference time-domain simulations. These results establish ultrafast plasmonic photoelectrons as versatile probes for nanoplasmonic near-fields. Figure 1 shows test samples and spectral cutoffs according to which maximum field enhancement values are determined.

**Figure 1. (a-c)** Atomic force microscope scans of plasmonic surfaces with controlled, different rms roughnesses of 0.8 nm, 1.6 nm and 4.5 nm, after applying a tip shape deconvolution procedure. (d-f) Plasmonic photoelectron spectra (logarithmic scale) from the three surfaces by generating plasmons with a 38-fs laser pulse with different focused intensities. Black symbols correspond to electron spectral cutoffs. Cutoff error bars are determined according to fit uncertainty.

**Surface plasmon experiments**. — We studied electron emission induced by intense, femtosecond plasmon field on a periodically structured gold film. Results on previous, disordered samples agreed well qualitatively (see electron pairing at an intensity of around 80 GW/cm^{2}), however, new phenomena were discovered as well. Most interestingly, we found narrow resonances in time-of-flight electron spectra that can be interpreted as a quantum interference effect. Emission related to electron pairs produce different narrow resonances of this kind.

**Femtosecond photonics.** — Improving the laser-induced damage threshold of optical components is a basic endeavor in femtosecond technology. By testing more than 30 different femtosecond mirrors with 42 fs laser pulses at 1 kHz repetition rate, we found that a combination of high-bandgap dielectric materials and improved design and coating techniques enable femtosecond multilayer damage thresholds exceeding 2 J/cm^{2} in some cases. We also studied damage threshold dependence as a function of the number of interacting pulses and other relevant parameters. A significant x2.5 improvement in damage resistance can also be achieved for hybrid Ag-multilayer mirrors exhibiting more than 1 J/cm^{2} threshold with a clear anticorrelation between damage resistance and peak field strength in the stack.

**Theoretical research.** — In studying the quantum phase properties of electromagnetic radiation fields, we have recently derived the regular-phase coherent states, which are in fact SU(1,1) coherent states, introduced earlier in a more general context. In the one-mode representation, these states are generated by a perturbed electromagnetic oscillator Hamiltonian containing an intensity-dependent coupling term. By applying this abstract formalism for a completely different system, we have discussed a new physical realization of these regular-phase coherent states, which may be relevant in the non-perturbative theory of some strong-field processes. We have shown that the motion of a charged particle in a Coulomb field can naturally be described by using SU(1,1) generators and a fictious time parameter, the so-called eccentric anomaly. By analysing the interaction of a Rydberg atom with a strong microwave field at the main resonance, we have described squeezing and stretching in real space as a result of the generation of SU(1,1) coherent states for the Coulomb problem. If the microwave field is linearly polarized along the *z*-direction, the Bargmann index of the sub-space of these states is (|*m*|+1)/2, where *m* is the (conserved) z-component of the angular momentum. In Figs. 2 and 3, we illustrate the resulting spatial distorsions of the wave functions, for two initial set of parabolic quantum numbers.

**Figure 2.** The left figure (a) shows the initial wave function (with parabolic quantum numbers: m=0, n_{1}=0, n_{2}=60) as a function of the x and z coordinates. The microwave field is assumed to be linearly polarized along the z-direction. The central (b) and the right (c) figures display the the distorted wave functions (stretching along the polarization, after the microwave field has been switched on) at two instants: after one and two cycles of the scaled time parameter, respectively.

**Figure 3. **The same as in Figure 2, but now with different intitial parabolic quantum numbers: m=1, n_{1}=60, n_{2}=0.

**Strong-field interactions and nano-optics experiments.** — Probing nanooptical near-fields is a major challenge in plasmonics. Here, we demonstrate an experimental method based on utilizing ultrafast photoemission from plasmonic nanostructures that is capable of probing the maximum nanoplasmonic field enhancement in any metallic surface environment. Directly measured maximum field enhancement values for various samples are in good agreement with detailed finite-difference time-domain simulations. These results establish ultrafast plasmonic photoelectrons as versatile probes for nanoplasmonic near-fields. Fig. 1 shows the measurement scheme and spectral cutoffs according to which maximum field enhancement values are determined.

**Figure 1.** (a) Experimental scheme for measuring photoemission spectra induced by localized plasmon fields at gold nanoparticle arrays. The sample is in vacuum and the substrate is illuminated from the back side through the transparent substrate, so that photoelectrons emitted from the nanoparticles can directly enter a time-of-flight electron spectrometer. (b) Experimental scheme for measurement of plasmonic photoelectrons from silver layers of some 50 nm thickness exhibiting different surface roughnesses. (c) Typical plasmonic photoelectron spectra. Intersection of the red line fitted to the decaying section of the spectrum and that fitted to the baseline define the maximum electron kinetic energy (cutoff) based on which we determine maximum field enhancement factors between 17 and 52.

We also developed an efficient, tailored optimization method for attopulse generation using a light-field-synthesizer which was demonstrated by M. Hassan et al. at the Max Planck Institute of Quantum Optics (Nature 530, 66 (2016)). We adapted genetic optimization of single-cycle and sub-cycle waveforms to attosecond pulse generation and achieved significantly improved convergence to several targeted attosecond pulse shapes. Importantly, we show that the single-atom approach based on strong-field approximation gives similar results to the more complex and numerically intensive 3D model of the attopulse generation process and that spectrally tunable attosecond pulses can be produced with a light-field synthesizer.

**Femtosecond photonics.** — Improving the laser-induced damage threshold of optical components is a basic endeavor in femtosecond technology. By testing more than 30 different femtosecond mirrors with 42 fs laser pulses at 1 kHz repetition rate, we found that a combination of high-bandgap dielectric materials and improved design and coating techniques enable femtosecond multilayer damage thresholds exceeding 2 J/cm^{2} in some cases. A significant improvement by a factor of 2.5 in damage resistance can also be achieved for hybrid Ag-multilayer mirrors exhibiting more than 1 J/cm^{2} threshold with a clear anticorrelation between damage resistance and peak field strength in the stack. Slight dependence on femtosecond pulse length and substantial decrease for high (MHz) repetition rates are also observed.

**Surface plasmon studies**. — In 2016, like in earlier years, we studied the properties of surface plasmon polaron (SPP)-assisted electron and photon emission in gold films. The surface plasmons were excited by femtosecond pulses of a Ti:sapphire laser in the 10 – 200 GW/cm^{2} intensity range. We have found oscillatory electromagnetic field dependence of the SPP dispersion curve and concluded, that the effect is due to the dynamical screening of electrons by the plasmonic/photonic field. A simple theoretical model agrees well with the experimental data if we suppose that the effective mass of the screened electrons is smaller, than the free electron mass and decreases with increasing laser intensity. We have also found strong evidence that in a laser intensity range around 80 GW/cm^{2}, the gold film turns into ideal diamagnetism.

In some further experiments, the 45 nm thick gold film was evaporated on an ordered surface of 100 nm glass spheres. The qualitative results of SPP-assisted electron and photon emission agree quite well with those of irregular surfaces, but with some modifications, indicating some interference of the emitted electrons and photons. To explain these experimental findings, further experiments are needed.

**Theoretical quantum optics.** — Recently, we have introduced a new regular phase operator, coherent-phase states (a special type of SU(1,1) coherent states), and the associated quantum phase probability distributions of electromagnetic radiation modes. This general formalism is expected to apply in quantifying the quantum phase uncertainties of extreme optical fields like high harmonics of strong laser fields, which we have been studying in various cases. In the meantime, by analyzing the time evolution of the regular phase operator, we have proved that in addition to the deterministic (linear) phase variation, there exists a second quantum term, which is in fact an invariant Haar integral of a positive operator-valued measure on the Blaschke group (which is another parametrization of the SU(1,1) group). In Figure 2 we illustrate this result by plotting the time-evolution of the expectation value of these two term and their sum. The above result may be considered as a proof of the periodicity of the complete physical phase. We also note that the matrix elements between photon number eigenstates of a certain unitary representation of the Blaschke group, appearing in our formalism, are directly expressed by the Zernike polynomials, which play an important role in optical wavefront analysis.

**Figure 2.** Time evolution of the expectation value in a regular coherent phase state (with a mean photon number of 200) of the components of the regular phase operator. The straight line with tangent -1 is the usual classical time dependence of a harmonic oscillator in phase space (clock-wise rotation in the q-p complex amplitude plane), which has a sharp value, also for all quantum states of the oscillator. The step-like curve (with 2p jumps) illustrates the increase of the quantum angle, which we call the Blaschke contribution. The 2p accumulations come from the invariant Haar integral of the positive operator-valued measure on the Blaschke group. The sum of these two contributions (i.e., the complete physical phase) appears as a periodic saw-tooth-like function. For increasing excitation amplitudes this curve gets sharper, and approaches the ideal saw-tooth function.