Sulzer, Philipp
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Few-femtosecond phase-sensitive detection of infrared electric fields with a third-order nonlinearity
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.
Ultrabroadband suppression of mid-infrared reflection losses of a layered semiconductor by nanopatterning with a focused ion beam
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
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.
Deterministic Nonlinear Transformations of Phase Noise in Quantum-Limited Frequency Combs
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.
Passively phase-locked Er:fiber source of single-cycle pulses in the near infrared with electro-optic timing modulation for field-resolved electron control
A single-cycle light source in the near infrared is demonstrated enabling sensitive applications of ultrafast optical field control of electronic transport. The compact Er:fiber system generates passively phase-locked pulses with broadband spectra covering 150 THz to 350 THz at a duration of 4.2 fs and 40 MHz repetition rate. A second output arm is equipped with an electro-optic modulator that switches the arrival time of the pulses by 700 ps at arbitrary frequencies up to 20 MHz, enabling timing modulation of the pump pulse without changing the average intensity. As a benchmark demonstration, we investigate the carrier relaxation dynamics in low-temperature-grown InGaAs using quantum interference currents.
Ultrabroadband Moth-Eye Antireflection Structures on GaSe Produced by Focused-Ion Beam Milling
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 [1] . 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 [2] .
Determination of the electric field and its Hilbert transform in femtosecond electro-optic sampling
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.
Analysis of Subcycle Electro-Optic Sampling Without Background
We explore background-free options to detect mid-infrared (MIR) electric transients. The MIR field and a near-infrared probe interact via sum- (SFG) and difference-frequency generation (DFG) in an electro-optic crystal. An intuitive picture based on a phasor representation and rigorous numerical calculations are used for analysis. It turns out that separating photons generated either by SFG or DFG from the local oscillator via spectral filtering leads to a signal purely proportional the MIR intensity envelope. Background-free phase information may be extracted in a spectral window containing both SFG and DFG components and blocking the local oscillator background based on its orthogonal polarization. This variant leads to signal proportional to the square of the MIR field amplitude. It is limited by the finite efficiency of polarization filtering. The Hilbert transform as a conjugate variable to the electric field in the time domain turns out to play a fundamental role for the context discussed in this paper.
Passive elimination of correlated amplitude fluctuations in ultrabroadband supercontinua from highly nonlinear fibers by three-wave mixing
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.
Up to 70 THz bandwidth from an implanted Ge photoconductive antenna excited by a femtosecond Er:fibre laser
Phase-stable electromagnetic pulses in the THz frequency range offer several unique capabilities in time-resolved spectroscopy. However, the diversity of their application is limited by the covered spectral bandwidth. In particular, the upper frequency limit of photoconductive emitters - the most widespread technique in THz spectroscopy – reaches only up to 7 THz in the regular transmission mode due to absorption by infrared-active optical phonons. Here, we present ultrabroadband (extending up to 70 THz) THz emission from an Au-implanted Ge emitter that is compatible with mode-locked fibre lasers operating at wavelengths of 1.1 and 1.55 μm with pulse repetition rates of 10 and 20 MHz, respectively. This result opens up the possibility for the development of compact THz photonic devices operating up to multi-THz frequencies that are compatible with Si CMOS technology.