Few-femtosecond phase-sensitive detection of infrared electric fields with a third-order nonlinearity
2023-06-20, Kempf, Hannes, Sulzer, Philipp, Liehl, Andreas, Leitenstorfer, Alfred, Tenne, Ron
Measuring an electric field waveform beyond radio frequencies is often accomplished via a second-order nonlinear interaction with a laser pulse shorter than half of the field’s oscillation period. However, synthesizing such a gate pulse is extremely challenging when sampling mid- (MIR) and near- (NIR) infrared transients. Here, we demonstrate an alternative approach: a third-order nonlinear interaction with a relatively long multi-cycle pulse directly retrieves an electric-field transient whose central frequency is 156 THz. A theoretical model, exploring the different nonlinear frequency mixing processes, accurately reproduces our results. Furthermore, we demonstrate a measurement of the real part of a sample’s dielectric function, information that is challenging to retrieve in time-resolved spectroscopy and is therefore often overlooked. Our method paves the way towards experimentally simple MIR-to-NIR time-resolved spectroscopy that simultaneously extracts the spectral amplitude and phase information, an important extension of optical pump-probe spectroscopy of, e.g., molecular vibrations and fundamental excitations in condensed-matter physics.
Passive elimination of correlated amplitude fluctuations in ultrabroadband supercontinua from highly nonlinear fibers by three-wave mixing
2020-09-01, Sulzer, Philipp, Beckh, Cornelius, Liehl, Andreas, Huster, Jeldrik, Keller, Kilian R., Cimander, Moritz, Henzler, Philipp, Traum, Christian, Riek, Claudius, Seletskiy, Denis V., Leitenstorfer, Alfred
The nonlinear transformation of fluctuations by frequency broadening is found to produce strong anti-correlations in the spectral output. This effect is investigated by dispersive Fourier transform measurements. We exploit the anti-correlations in order to cancel the intensity noise in a subsequent sum-frequency mixing step. This principle allows for the generation of tunable visible pulses by cascaded nonlinear mixing whilst maintaining the same intensity noise performance as the input pulses. In addition, we demonstrate that the power fluctuations occurring in the process of passive stabilization of the carrier-envelope phase locking via difference frequency generation may be cancelled by an analogous strategy.
Deterministic Nonlinear Transformations of Phase Noise in Quantum-Limited Frequency Combs
2019-05-24, Liehl, Andreas, Sulzer, Philipp, Fehrenbacher, David, Rybka, Tobias, Seletskiy, Denis V., Leitenstorfer, Alfred
Optical phase noise of femtosecond lasers is analyzed over various steps of broadband nonlinear frequency conversion. The intrinsic phase jitter of our system originates from quantum statistics in the mode-locked oscillator. Supercontinuum generation by four-wave-mixing processes preserves a noise minimum at the optical carrier frequency. From there, a quadratic increase of the comb linewidth results with mutually anticorrelated phase fluctuations of both spectral wings. Passive phase locking by difference frequency generation strongly enhances the optical phase noise to a level equaling the carrier-envelope phase jitter of the fundamental comb. The same value results from quadratic extrapolation of the optical phase noise to radio frequencies. Our findings are consistent with a fully deterministic transformation of phase noise according to the elastic tape model.
Ultrabroadband out-of-loop characterization of the carrier-envelope phase noise of an offset-free Er:fiber frequency comb
2017, Liehl, Andreas, Fehrenbacher, David, Sulzer, Philipp, Leitenstorfer, Alfred, Seletskiy, Denis V.
Recent demonstrations of passively phase-locked fiber-based combs motivate broadband characterization of the noise associated with the stabilized carrier-envelope offset frequency. In our study, we analyze the phase noise of a 100 MHz Er:fiber system in a wide range spanning from microhertz to the Nyquist frequency. An interferometric detection method enables analysis of the high-frequency output of an f-to-2f interferometer. The dominant contribution of a broadband white noise floor at high frequencies attests quantum-limited performance. An out-of-loop measurement of the carrier-envelope phase reveals its jitter to be as low as 250 mrad when integrated over 12 orders of magnitude of the radio-frequency spectrum.
Ultrabroadband suppression of mid-infrared reflection losses of a layered semiconductor by nanopatterning with a focused ion beam
2021, Hagner, Matthias, Sulzer, Philipp, Liehl, Andreas, Cimander, Moritz, Kempf, Hannes, Bitzer, Annika, Herter, Alexa, Leitenstorfer, Alfred
Moth-eye structures are patterned onto gallium selenide surfaces with sub-micrometer precision. In this way, Fresnel reflection losses are suppressed to below one percent within an ultrabroad optical bandwidth from 15 to 65 THz. We tune the geometry by rigorous coupled-wave analysis. Subsequently, ablation with a Ga+ ion beam serves to write optimized structures in areas covering 30 by 30 μm. The benefits are demonstrated via optical rectification of femtosecond laser pulses under tight focusing, resulting in emission of phase-stable transients in the mid-infrared. We analyze the performance of antireflection coating directly in the time domain by ultrabroadband electro-optic sampling.
Broadband analysis and self-control of spectral fluctuations in a passively phase-stable Er-doped fiber frequency comb
2020-02-03, Liehl, Andreas, Sulzer, Philipp, Fehrenbacher, David, Eggert, Stefan, Ludwig, Markus, Ritzkowsky, Felix, Seletskiy, Denis V., Leitenstorfer, Alfred
Carrier-envelope and optical phase noise of a femtosecond frequency comb based on Er-doped fiber technology is investigated and minimized without exploiting active external references. Ultrabroadband, coherent, and tailorable supercontinua are generated in a highly nonlinear germanosilicate fiber assembly. Difference frequency mixing between comb modes in their spectral extrema passively eliminates the carrier-envelope phase slip. This step generates an inherently offset-free comb with a relative frequency stability better than 10−21. In contrast, the phase fluctuations at the carrier frequency of 193 THz are increased as compared to the fundamental comb. Their level matches the value found by parabolic extrapolation of the phase noise of the fundamental comb to zero frequency. The latter is unambiguously accessible by means of any beat note centered at the carrier-envelope offset frequency. All these findings rely on strong correlations between the comb modes that are quantitatively described by an elastic tape model, underlining the deterministic character of the processes involved. The superior optical phase noise of the fundamental comb is transferred to the difference-frequency comb while not compromising the inherent cancellation of the carrier-envelope offset frequency. In this way, the optical linewidth of the passively phase-locked comb is reduced from 100 kHz to a measured value of 5 kHz, which is limited by the cw laser reference used for out-of-loop characterization.
Passive Elimination of Spectrally Correlated Intensity Noise in Ultrabroadband Supercontinua from Highly Nonlinear Fibers
2019, Sulzer, Philipp, Liehl, Andreas, Keller, Kilian R., Huster, Jeldrik, Beckh, Cornelius, Leitenstorfer, Alfred
Amplitude fluctuations of pump pulses for frequency broadening by third-order processes are found to result in strong anti-correlations of spectral output components. We exploit this information to minimize intensity noise in subsequent nonlinear conversion steps.
Ultrabroadband Moth-Eye Antireflection Structures on GaSe Produced by Focused-Ion Beam Milling
2021, Sulzer, Philipp, Hagner, Matthias, Liehl, Andreas, Cimander, Moritz, Kempf, Hannes, Bitzer, Annegret, Herter, Alexa, Leitenstorfer, Alfred
Minimizing losses and suppression of reflection-induced echos in thin nonlinear crystals is of critical importance to both classical time-domain spectroscopy and time-domain quantum electrodynamics  . GaSe represents an important material in this context. However, it is challenging to coat and manipulate using macroscopic methods due to its van-der-Waals-bonded structure of hexagonal monolayers and atomically flat surfaces. At least, some progress relying on femtosecond laser ablation was demonstrated recently  .
Determination of the electric field and its Hilbert transform in femtosecond electro-optic sampling
2020, Sulzer, Philipp, Oguchi, Kenichi, Huster, Jeldrik, Kizmann, Matthias, Guedes, Thiago L.M., Liehl, Andreas, Beckh, Cornelius, Moskalenko, Andrey S., Burkard, Guido, Seletskiy, Denis V., Leitenstorfer, Alfred
We demonstrate time-domain sampling of mid-infrared electric field transients and their conjugate counterparts exploiting the dynamical Pockels effect. To this end, the complete polarization change of few-femtosecond probe pulses is studied. An intuitive picture based on a phasor representation is established before gaining quantitative understanding in experiment and theory. In the standard version of electro-optic sampling, the electric field is determined by analyzing the change of ellipticity of the probe polarization. Beyond this, we find that a temporal gradient of the input electric field manifests itself in a rotation of the polarization ellipsoid of the probe. The relative contribution of sum- and difference-frequency mixing processes and their spectral distribution over the near-infrared probe bandwidth are identified as key aspects. If one of these processes dominates, detecting ellipticity changes and polarization rotation as a function of time delay results in two waveforms which are Hilbert transforms of each other. Such conditions may be achieved by angle phase matching in birefringent materials or spectral filtering of the probe after the nonlinear interaction. In this case, a static phase introduced by birefringence or reflection at metallic mirrors results in a specific phase shift of both time traces with respect to the input electric field. Contributions from sum- and difference-frequency generation are found to be equivalent when using electro-optic sensors with isotropic refractive index. Polarization rotations in the low- and high-frequency parts of the probe then tend to cancel out. In this limit, spurious additional phase shifts do not change the phase of the detected transients. This fact leads to a robust recovery of the carrier-envelope phase of the input waveform. Clarifying the role of imperfections of superachromatic phase retarders completes our survey on proper determination of the electric field and its conjugate variable.
Spectral Correlations of Phase Noise in Ultrabroadband Femtosecond Lasers
2019, Liehl, Andreas, Sulzer, Philipp, Fehrenbacher, David, Seletskiy, Denis V., Leitenstorfer, Alfred
Phase noise in mode-locked Er:fiber systems shows strong spectral correlations emerging from broadband nonlinear-optical processes. Our fundamental insights are key to maximize the quality of passively phase-stable frequency combs and single-cycle pulse trains.