Keywords

1 Motivation

Confining laser light to a few cycles of its oscillating electromagnetic field and controlling the underlying electric-field waveform gave access to a variety of novel applications. They include the generation of isolated attosecond pulses [1] as well as sub-femtosecond optical control of solid-state electronic processes [2, 3]. Due to tremendous progress in the field of precision dispersion management, waveform control and synthesis of few-cycle pulses could be demonstrated in the near-infrared and visible spectral ranges [4, 5]. Extending waveform control to the mid-infrared region will enable a plethora of new applications, ranging from advances in electric-field-resolved vibrational spectroscopy of biological samples [6] to novel optoelectronic devices based on low-bandgap heavily-doped semiconductors [7]. To date, however, common approaches [8,9,10,11] for generating and controlling coherent mid-infrared radiation typically suffer from system complexity and limited reproducibility of the output waveforms. In addition, full phase control over bandwidths spanning an octave or more is lacking thus far.

In this work, we demonstrate a novel approach for generating coherent multi-octave mid-infrared radiation with the intrinsic capability of shaping the emerging waveforms. The concept is based on intrapulse difference-frequency generation (IPDFG) [12] in a single nonlinear crystal and demonstrated using the 7-fs single-cycle pulses from a diode-pumped, Kerr-lens-mode-locked, carrier-envelope-phase (CEP)-stabilized Cr:ZnS laser system. Specifically, we created infrared continua spanning 3.7 optical octaves in several spectral bands via cascaded IPDFG and manipulated their spectral phases by exploiting their different dependence on the CEP of the driving laser. This allows to manipulate the electric field of the single-cycle mid-infrared waveforms in the time domain, using the CEP of the driving laser as a control parameter. Our approach yields the first multi-octave control of single-cycle mid-infrared waveforms, with a continuous and highly reproducible adjustment of the electric-field evolution.

2 Overview of the Experimental Setup

Major components of this work have been demonstrated in a recent publication [13] and are illustrated in Fig. 1. While this section serves to provide a general overview of the experimental layout, further details on specific parts of the setup are discussed in subsequent sections, namely the generation of CEP-stable single-cycle pulses (Sect. 3) and their use for single-cycle infrared waveform generation and control (Sect. 4).

Fig. 1
A schematic of an experimental set-up features the following blocks. C r Z n S laser oscillator, delay, I P D F G, out-of-loop C E P stabilizer with spectrometer, E O S, C E P locking with feedback loop etcetera.

Schematic of the experimental setup. The output pulses of the Cr:ZnS laser oscillator are spectrally broadened in a 0.5-mm-thick TiO2 plate and subsequently split into three individual channels by using a wedged beam splitter (BS1): the transmitted beam is used for intrapulse difference-frequency generation (IPDFG), the primary wedge reflection (blue line) acts as a gate pulse for electro-optic sampling (EOS) and the secondary wedge reflection (red line) is used for carrier-envelope-phase (CEP) locking. DC dispersion compensation unit, λ/2 half-wave plate, λ/4 quarter-wave plate, MC mechanical chopper, BC beam combiner, SF1–5 spectral bandpass filters, BPD1–3 balanced photodetectors, WP Wollaston prism, BS1–2 beam splitters, PPLN1–2 periodically poled lithium niobate crystals, VA variable attenuator, CaF2 Calcium Fluoride, FM flip mirror

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Briefly, the core of the system constitutes a carrier-envelope-phase-stabilized, Kerr-lens-mode-locked, diode-pumped Cr:ZnS laser system, generating trains of 28-fs-long pulses with pulse energies of 24 nJ. In a first step, the direct output of the oscillator is sent into a highly nonlinear bulk dielectric medium (rutile TiO2) to spectrally broaden the laser output and generate an octave-spanning spectrum. The broadened pulses span a spectral range of 1.1 to 3.2 μm (at −20 dB) and are compressed with a combination of custom-made dispersive mirrors and bulk material (dispersion control units DC) to durations of 7 fs, corresponding to a single cycle of the electric field at the spectral centroid of 2.24 μm. For our experiment, we split the broadened pulses first into three beams with a wedged ZnS beam splitter (BS1) and compressed each of the beams individually.

A coherent near- to mid-infrared continuum is generated via cascaded IPDFG by focusing the beam traversing BS1 into a zinc germanium phosphide (ZGP) crystal. The reflection off the beam splitter’s front surface (blue line) is used as a gate pulse for characterizing the mid-infrared electric-field waveforms with electro-optic sampling (EOS). For that, a thin ZnS wedge (BC) combines the gate and infrared continuum beams, followed by EOS in GaSe and ellipsometric detection. The influence of water absorption on mid-infrared generation and detection was minimized by purging this part of the experimental setup with nitrogen.

The carrier-envelope offset frequency (fCEO) of the single-cycle pulses is detected by sending the reflection off the back surface of BS1 (red line) into a common-path f-2f interferometer. From the fCEO beating signal an electronic feedback is generated to control and stabilize the CEP of the laser by active pump-power modulation. We characterized the performance of our CEP stabilization with a separate out-of-loop phase-noise measurement, enabled by redirecting the gate pulses with a flip mirror (FM).

3 Single-Cycle CEP-Stable Laser Pulses

Spectral broadening of the laser output in rutile serves several purposes: (i) It generates sufficient spectral bandwidth for compressing the pulses to the single-cycle regime. (ii) The 1.5-octave-spanning spectrum supports f-2f interferometry for fCEO detection and CEP stabilization. (iii) The single-cycle pulses allow efficient, ultra-broadband mid-infrared generation in ZGP, creating a supercontinuum spanning from 0.9 to 12 μm. (iv) The detection bandwidth of EOS is limited towards the blue by the pulse duration of the gate pulses. With our merely 7-fs-long pulses we could measure EOS waveforms with spectral components down to 3 μm.

3.1 Spectral Broadening and Temporal Compression in TiO2

Strong nonlinear spectral broadening via self-phase modulation (SPM) was achieved by focusing the 28-fs-long pulses from the Cr:ZnS oscillator tightly (20 μm (1/e2) focal spot size) into a 0.5-mm-thick, bulk rutile plate (TiO2), anti-reflection-coated for the range between 1.2 and 3.2 μm. In order to suppress any birefringent effects, the TiO2 medium was cut in the (001) orientation and to be used under normal incidence. The corresponding output spectrum (Fig. 2a) spans from 1.1 to 3.2 μm, at the −20-dB-level, featuring a Fourier-transform-limited pulse duration of 6 fs. The choice of using a thin plate under strong focusing conditions minimizes the degradation of the beam profile; due to strong Kerr-lensing, a high spatial and temporal beam quality is retained. Thus, the far-field beam profile remains clean (inset of Fig. 2b) and we obtain excellent focusing properties, with a beam quality parameter M2 < 1.4—ideal for downstream nonlinear conversion stages.

Fig. 2
A. A multi-line graph of normalized intensity and phase in radians versus wavelength in microns features 3 trends. B. A multi-line graph of normalized intensity and phase in radians versus time delay femtoseconds features 3 trends with an inset.

(a) Nonlinearly broadened output spectrum (blue curve) in comparison to the spectrum (grey curve) and spectral phase (red curve) retrieved from an SHG-FROG measurement. (b) Retrieved temporal intensity profile (blue curve), temporal phase (red curve), and Fourier-transform limit (grey curve) of the laser pulse

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Compression of the super-octave-spanning spectra was achieved with a set of custom-designed chirped mirrors, combined with the material dispersion provided by a thin BaF2 plate, and was optimized for each arm after beam splitter BS1 individually. The duration of the compressed pulses was measured with a home-built, all-reflective second-harmonic-generation frequency-resolved optical gating instrument (SHG-FROG) using a 0.1-mm-thick LiIO3 crystal (type-I phase-matching, θ = 20.5°). The resulting retrieved pulse (blue in Fig. 2b) has a duration of only 7 fs (full width at half maximum). This is equivalent to a mere single optical cycle at the spectral centroid position of 2.24 μm and slightly shorter than what has been demonstrated previously [13].

3.2 CEP-Stabilization

The super-octave-spanning spectrum allows us to directly perform carrier-envelope offset frequency (fceo) detection of the Cr:ZnS laser in an f-2f interferometer. For this, a fraction (36 mW, red beam) of the broadened pulses after the rutile plate is pre-chirped with dispersive mirrors and focused into a 1-mm-thick periodically poled lithium niobate crystal (PPLN1). The latter is optimized for second harmonic generation (SHG) of the signal at 2460 nm. Subsequently, the beam is spectrally bandpass-filtered (SF1) at around 1230 nm to isolate the 2f and frequency-doubled f components. Their beating is detected with a balanced photodetector (BPD1). The light reflected from the optical bandpass filter enters the other port of the detector, allowing to control the power of the fundamental repetition rate (frep) radio-frequency signal. We achieved a remarkably high signal-to-noise ratio reaching 70 dB for the detected fceo beat note. For CEP-stabilization (i.e. locking fceo to 0) a self-referencing technique is implemented [14]. CaF2 wedges in front of the PPLN crystal allow to control the CEP without changing the spectral phase of the main beam used for the experiment.

The CEP-noise of the stabilized laser was measured in a separate out-of-loop f-2f interferometer. By using a 0.5-mm-thick PPLN crystal (PPLN2) for SHG, a beating signal was generated and sent into two separate channels for noise characterization. Slow drifts and components below 12 Hz were measured by evaluating the evolution of the spectral interference fringes in the f-2f spectral overlap region recorded with a spectrometer (Ocean Optics). Faster CEP noise components up to the Nyquist frequency (11.43 MHz) were measured with a separate balanced detection scheme [15]: the beam was split by a 50:50 nonpolarizing beam splitter (BS2) and filtered by optical bandpass filters (SF4,5). The filters isolated spectral components on opposing slopes of the interference fringes, which were then sent onto the photodiodes of a balanced detector (BPD3), with the balanced detection signal being directly proportional to the CEP fluctuations. The results of slow and fast CEP noise measurements were combined to give the CEP noise spectral density (Fig. 3, black). We find an integrated CEP noise of only 8.6 mrad for the range between 0.2 Hz and 11.5 MHz (Nyquist limit, Fig. 3, blue), which represents an improvement of around 20% compared with our previous result [13]. Moreover, it is approaching the level of the lowest CEP-noise ever demonstrated for ultrafast oscillators [16,17,18].

Fig. 3
A multi-line graph of C E P noise in radians square per hertz and integrated phase jitter in milliradians versus frequency in hertz features a highly fluctuating and stepwise falling trend for C E P noise and another falling step for integrated phase jitter of 8.6 milliradians.

CEP noise power spectral density, and the corresponding integrated phase jitter for the phase-stabilized laser

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4 CEP-Controlled Mid-Infrared Waveform Synthesis

For frequency down-conversion of the single-cycle laser pulses, the process of cascaded intrapulse difference-frequency generation (IPDFG) [12, 19] is used. In this way, coherent mid-infrared radiation spanning 3.7 optical octaves is generated. By varying the carrier-envelope phase of the driving pulses, the relative phase of different spectral regions of the supercontinuum is changed—thereby shaping the emerging waveforms. To trace changes in the electric field, the mid-infrared waveforms are recorded with the method of electro-optic sampling (EOS) [20].

4.1 Cascaded Intrapulse Difference-Frequency Generation (IPDFG) and its CEP-Dependence

When laser pulses are focused into a nonlinear crystal with suitable phase-matching conditions, difference-frequency mixing between the various spectral components of the input laser generates a 0th-order IPDFG field (Fig. 4). Upon further propagation through the crystal, newly generated frequency components sequentially re-mix with driving laser components creating down-converted radiation of higher cascading orders (first, second, etc.). Each higher-order component arises from mixing of components of the preceding order with that of the driving laser. Depending on the cascading order, the CEP of the newly generated spectral components is either following the CEP of the driver (odd orders) (Fig. 4, blue), or will be invariant to it (even orders) (Fig. 4, green). If the CEP of the incident laser pulses was not stabilized, the combined electric-field waveforms of the multi-octave output would vary from pulse to pulse. For a fixed CEP of the driving laser, the spectral distribution of CEP dependence remains stable. This approach enables waveform adjustment across multiple octaves without the need for spatial separation of specific spectral bands. Moreover, the spectral region in which odd- and even-order components overlap will exhibit pronounced interference effects when tuning the CEP of the driving laser (Fig. 4, light-red-shaded area).

Fig. 4
A graph of normalized intensity versus wavelength plots 4 types of spectral spikes labeled driving laser, odd I P D F G orders, even I P D F G orders, and sum frequency signal. Spikes of driving laser are mapped to the fundamental I P D F G spike with a wavelength of 10 micrometers.

Mid-IR spectra arising from the difference-frequency mixing in a ZGP crystal, simulated by using commercial nonlinear pulse propagation software. The basic principle of cascaded IPDFG is illustrated through a simplified modelling of the mixing of two isolated spectral components of the driving laser (black), which share the same CEP. For a broadband driving laser (dashed black), the mixing products merge into a continuum. The light-red and light-grey curves depict the intensity distribution for the driving field’s CEP set to yield constructive (Δφ = 0) and destructive (Δφ = ±π) interference, respectively

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4.2 CEP-Controlled Multi-Octave Mid-Infrared Generation

Experimentally, we achieve cascaded IPDFG by focusing the super-octave-spanning single-cycle pulses into an anti-reflection-coated (1.5–12 μm) 1-mm-thick ZnGeP2 (ZGP) crystal. The beam diameter inside the crystal was measured to be 30 μm (1/e2), resulting in an estimated peak intensity of ca. 150 GW/cm2. In order to optimize the IPDFG process and compensate for the ZGP dispersion, we have pre-chirped the input beam with a single dispersive mirror and an achromatic half-waveplate. The latter also serves for rotating the driver polarization to 45° in order to achieve two orthogonal polarization components of equal magnitude for type-I birefringent phase-matching (φ = 0°; θ = 51°). The down-converted IPDFG output spectrally overlaps with the driver radiation resulting in an ultrabroadband supercontinuum covering 3.7 optical octaves from 0.9 to 12 μm (−30 dB level, Fig. 5a). As described in the previous section, the output spectral intensity and phase can be modified by adjusting the CEP of the driver. In the two extreme cases shown in Fig. 5a, this leads to fully constructive (blue curve in Fig. 5a) or destructive (green curve in Fig. 5a) interference between the even and odd cascaded IPDFG orders, correspondingly modulating the spectral intensity around 5 μm. The average power of the mid-IR part of the supercontinuum (λ > 3.6 μm) for the case of constructive interference is 31 mW, corresponding to an IPDFG power conversion efficiency of14%.

Fig. 5
2 multi-line graphs. A. Normalized intensity in decibels versus wavelength in microns features 2 falling trends with fluctuations. E O S detection limit is 3 microns. B. E O S signal in volts versus time in picoseconds features 2 wavelets with 15 and 20 femtoseconds with 0.7 and 0.9 cycles.

(a) Supercontinuum from cascaded IPDFG for the extreme cases of constructive (blue) and destructive (green) interference between the even and odd cascaded IPDFG orders. The measurements were taken with a monochromator. The dashed line indicates the detection limit of the EOS measurement technique when using a 7-fs gating pulse, which allows to measure spectral components with wavelengths longer than about 3 μm. (b) EOS time-domain data for relative phases Δφ of 0 (blue curve, constructive interference) and π (green curve, destructive interference). For better comparison, the two traces are offset by a constant factor (0.2 V). The pulse durations correspond to the full-width at half-maxima (FWHM) of the intensity envelopes. For calculating the number of optical cycles, the spectral centroids of the waveforms are considered

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4.3 Observing Waveform Control with Electro-Optic Sampling

Electro-optic sampling (EOS) was used to directly observe changes of the mid-infrared waveform induced by varying the CEP of the driving laser. For EOS detection, the gate and mid-infrared beams, combined by BC (Fig. 1), are focused into a 0.1-mm-thick GaSe crystal, optimized for type-I phase-matching (φ = 30°) at an external angle of θ = 35°. Under these conditions, our gate pulse duration of 7 fs allows us to capture spectral components up to a maximum frequency of about 100THz, corresponding to a wavelength of 3 μm with EOS (dashed black line in Fig. 5a). For a relative phase of Δφ = 0, corresponding to constructive interference (see previous section), the EOS trace, indicative of the actual electric waveform, exhibits a clean cosine-pulse-like temporal profile (Fig. 5b, blue curve). The pulse duration of 20 fs corresponds to 0.9 cycles of the waveform at the EOS spectral centroid. For Δφ = π the EOS trace changes to a sine-pulse-like waveform, as a result of the phase changes and destructive interference in the spectral domain (Fig. 5a, b, green curves). Thus, changing the CEP of the driving laser allows us to reproducibly modify both the phase and intensity of the mid-infrared waveforms.

5 Conclusion

In conclusion, a new approach for coherent multi-octave mid-infrared generation was presented, which offers an intrinsic capability to change the relative phase and amplitude of different spectral regions. Driven by cascaded intrapulse difference-frequency generation, the emerging single-cycle mid-infrared waveforms are shaped in time, with the CEP of the driving laser as the control parameter. Due to the unprecedented CEP and amplitude stability of the diode-pumped laser, multi-octave-spanning waveforms with high fidelity and reproducibility are generated. This concept is generalizable towards the synthesis of a broader variety of infrared waveforms by combining it with other techniques [4], and gives access to a variety of new applications exploiting long-wavelength electric-field control on the sub-cycle level.