Towards space-deployable laser stabilization systems based on vibration-insensitive cubic cavities with crystalline coatings.

We present the development of a transportable laser frequency stabilization system with application to both optical clocks and a next-generation gravity mission (NGGM) in space. This effort leverages a 5-cm long cubic cavity with crystalline coatings operating at room temperature and with a center wavelength of 1064 nm. The cavity is integrated in a custom vacuum chamber with dedicated low-noise locking electronics. Our vacuum-mounted cavity and control system are well suited for space applications, exhibiting state-of-the-art noise performance while being resilient to radiation exposure, vibration, shock, and temperature variations. Furthermore, we demonstrate a robust means of automatically (re)locking the laser to the cavity when resonance is lost. We show that the mounted cavity is capable of reaching technology readiness level (TRL) 6, paving the way for high-performance ultrastable laser systems and eventually optical atomic clocks amenable to future satellite platforms.

Simultaneous Monitoring of Atmospheric CH4, N2O, and H2O Using a Single Gas Sensor Based on Mid-IR Quartz-Enhanced Photoacoustic Spectroscopy.

An optical sensor based on external-cavity quantum cascade laser (EC-QCL) was developed for simultaneous triple-species monitoring of CH4, N2O, and H2O vapor using off-beam quartz-enhanced photoacoustic spectroscopy (OB-QEPAS). The EC-QCL wavelength was scanned over three neighboring absorption lines of CH4 (1260.81 cm-1), N2O (1261.06 cm-1), and H2O vapor (1261.58 cm-1) by tuning the grating of the EC-QCL with a piezoelectric actuator. Molecular relaxation effects impacting the generation of the QEPAS signals resulting from light absorption by CH4 and N2O molecules were investigated in the mid-infrared region near 8 µm. A theoretical model was introduced for the mid-infrared region, including the beneficial influence of water vapor. An enhancement of the QEPAS signals by a factor of 3 for CH4 in air and of 20% for N2O in air was observed in humidified samples compared to that in dry samples. The QEPAS measurement was scaled by the calibrated reference spectrometers; detection limits of 98 ppbv for CH4, 12 ppbv for N2O, and 750 ppmv for H2O vapor were obtained with a 1σ signal-to-noise ratio (SNR = 1) in humidified gas mixtures. Real-time Kalman filtering was applied to improve the measurement precision by a factor of approximately 4 while keeping the same temporal resolution, leading to measurement precisions of 60 ppbv for CH4, 10 ppbv for N2O, and 0.07% for H2O in the measurements of 1.99 ppmv CH4 and 312 ppbv N2O humidified with 2.8% H2O vapor, with a 1 s lock-in amplifier time constant and an equivalent bandwidth of 0.1 Hz.

High-power dual-comb thin-disk laser oscillator for fast high-resolution spectroscopy.

Free-running dual-comb systems based on a single laser cavity are an attractive next generation technology for a wide variety of applications. The high average power achievable by dual-comb thin-disk laser (TDL) oscillators make this technology especially attractive for spectroscopy and sensing applications in the molecular fingerprint region enabled by nonlinear frequency conversion. However, the high noise levels of TDL oscillators, e.g., induced by the turbulent water-cooling of the disk, are a severe challenge for spectroscopic applications. In this contribution, we confirm for the first time the suitability of dual-comb TDLs for high-resolution spectroscopy. Based on the novel concept of polarization splitting inside a TDL, our oscillator generates two asynchronous pulse trains of 240-fs pulse duration at 6-W and 8-W average power per pulse train and ∼97-MHz repetition rate at a central wavelength of 1030 nm. In the first detailed noise investigation of such a system, we identify the repetition frequency as the dominant noise term and show that ∼85% of the frequency noise of the comb lines of both pulse trains is correlated (integrated from 200 Hz to 20 kHz). We detect the absorption spectrum of acetylene in free-running operation within a measurement time of 1 millisecond. Being highly suitable for nonlinear frequency conversion, we believe the here presented result is an important step towards simple yet powerful mid-infrared dual-comb systems for high-resolution spectroscopy.

Frequency noise correlation between the offset frequency and the mode spacing in a mid-infrared quantum cascade laser frequency comb.

The generation of frequency combs in the mid-infrared (MIR) spectral range by quantum cascade lasers (QCLs) has the potential for revolutionizing dual-comb multi-heterodyne spectroscopy in the molecular fingerprint region. However, in contrast to frequency combs based on passively mode-locked ultrafast lasers, their operation relies on a completely different mechanism resulting from a four-wave mixing process occurring in the semiconductor gain medium that locks the modes together. As a result, these lasers do not emit pulses and no direct self-referencing of a QCL comb spectrum has been achieved so far. Here, we present a detailed frequency noise characterization of a MIR QCL frequency comb operating at a wavelength of 8 µm with a mode spacing of ∼7.4 GHz. Using a beat measurement with a narrow-linewidth single-mode QCL in combination with a dedicated electrical scheme, we measured the frequency noise properties of an optical mode of the QCL comb, and indirectly of its offset frequency for the first time, without detecting it by the standard approach of nonlinear interferometry applied to ultrafast mode-locked lasers. In addition, we also separately measured the noise of the comb mode spacing extracted electrically from the QCL. We observed a strong anti-correlation between the frequency fluctuations of the offset frequency and mode spacing, leading to optical modes with a linewidth slightly below 1 MHz in the free-running QCL comb (at 1-s integration time), which is narrower than the individual contributions of the offset frequency and mode spacing that are at least 2 MHz each.

Ultralow-noise photonic microwave synthesis using a soliton microcomb-based transfer oscillator.

The synthesis of ultralow-noise microwaves is of both scientific and technological relevance for timing, metrology, communications and radio-astronomy. Today, the lowest reported phase noise signals are obtained via optical frequency-division using mode-locked laser frequency combs. Nonetheless, this technique ideally requires high repetition rates and tight comb stabilisation. Here, a microresonator-based Kerr frequency comb (soliton microcomb) with a 14 GHz repetition rate is generated with an ultra-stable pump laser and used to derive an ultralow-noise microwave reference signal, with an absolute phase noise level below  -60 dBc/Hz at 1 Hz offset frequency and  -135 dBc/Hz at 10 kHz. This is achieved using a transfer oscillator approach, where the free-running microcomb noise (which is carefully studied and minimised) is cancelled via a combination of electronic division and mixing. Although this proof-of-principle uses an auxiliary comb for detecting the microcomb's offset frequency, we highlight the prospects of this method with future self-referenced integrated microcombs and electro-optic combs, that would allow for ultralow-noise microwave and sub-terahertz signal generators.

10 kHz linewidth mid-infrared quantum cascade laser by stabilization to an optical delay line.

We present a mid-infrared quantum cascade laser (QCL) with a sub-10 kHz full width at half-maximum linewidth (at 1 s integration time) achieved by stabilization to a free-space optical delay line. The linear range in the center of a fringe detected at the output of an imbalanced Mach-Zehnder interferometer implemented with a short free-space pathlength difference of only 1 m is used as a frequency discriminator to detect the frequency fluctuations of the QCL. Feedback is applied to the QCL current to lock the laser frequency to the delay line. The application of this method in the mid-infrared is reported for the first time, to the best of our knowledge. By implementing it in a simple self-homodyne configuration, we have been able to reduce the frequency noise power spectral density of the QCL by almost 40 dB below 10 kHz Fourier frequency, leading to a linewidth reduction by a factor of almost 60 compared to the free-running laser. The present limits of the setup are assessed and discussed.

Carrier-envelope offset frequency stabilization of a thin-disk laser oscillator operating in the strongly self-phase modulation broadened regime.

We demonstrate the carrier-envelope offset (CEO) frequency stabilization of a Kerr lens mode-locked Yb:Lu2O3 thin-disk laser oscillator operating in the strongly self-phase modulation (SPM) broadened regime. This novel approach allows overcoming the intrinsic gain bandwidth limit and is suited to support frequency combs from sub-100-fs pulse trains with very high output power. In this work, strong intra-oscillator SPM in the Kerr medium enables the optical spectrum of the oscillating pulse to exceed the bandwidth of the gain material Yb:Lu2O3 by a factor of two. This results in the direct generation of 50-fs pulses without the need for external pulse compression. The oscillator delivers an average power of 4.4 W at a repetition rate of 61 MHz. We investigated the cavity dynamics in this regime by characterizing the transfer function of the laser output power for pump power modulation, both in continuous-wave and mode-locked operations. The cavity dynamics in mode-locked operation limit the CEO modulation bandwidth to ~10 kHz. This value is sufficient to achieve a tight phase-lock of the CEO beat via active feedback to the pump current and yields a residual in-loop integrated CEO phase noise of 197 mrad integrated from 1 Hz to 1 MHz.

Ultra-low noise microwave generation with a free-running optical frequency comb transfer oscillator.

We present ultra-low noise microwave synthesis by optical to radio-frequency (RF) division realized with a free-running or RF-locked optical frequency comb (OFC) acting as a transfer oscillator. The method does not require any optical lock of the OFC and circumvents the need for a high-bandwidth actuator. Instead, the OFC phase noise is electrically removed from a beat-note signal with an optical reference, leading to a broadband noise division. The phase noise of the ∼15 GHz RF signal generated in this proof-of-principle demonstration is limited by a shot-noise level below -150 dBc/Hz at high Fourier frequencies and by a measurement noise floor of -60 dBc/Hz at 1 Hz offset frequency when performing 1,100 cross-correlations. The method is attractive for high-repetition-rate OFCs that lead to a lower shot-noise, but are generally more difficult to tightly lock. It may also simplify the noise evaluation by enabling the generation of two or more distinct ultra-low noise RF signals from different optical references using a single OFC and their direct comparison to assess their individual noise.

Electrically-driven pure amplitude and frequency modulation in a quantum cascade laser.

We present pure amplitude modulation (AM) and frequency modulation (FM) achieved electrically in a quantum cascade laser (QCL) equipped with an integrated resistive heater (IH). The QCL output power scales linearly with the current applied to the active region (AR), but decreases with the IH current, while the emission frequency decreases with both currents. Hence, a simultaneous modulation applied to the current of the AR and IH sections with a proper relative amplitude and phase can suppress the AM, resulting in a pure FM, or vice-versa. The adequate modulation parameters depend on the applied modulation frequency. Therefore, they were first determined from the individual measurements of the AM and FM transfer functions obtained for a modulation applied to the current of the AR or IH section, respectively. By optimizing the parameters of the two modulations, we demonstrate a reduction of the spurious AM or FM by almost two orders of magnitude at characteristic frequencies of 1 and 10 kHz compared to the use of the AR current only.

Carrier-envelope offset stabilization of a GHz repetition rate femtosecond laser using opto-optical modulation of a SESAM.

We demonstrate, to the best of our knowledge, the first carrier-envelope offset (CEO) frequency stabilization of a GHz femtosecond laser based on opto-optical modulation (OOM) of a semiconductor saturable absorber mirror (SESAM). The 1.05-GHz laser is based on a Yb:CALGO gain crystal and emits sub-100-fs pulses with 2.1-W average power at a center wavelength of 1055 nm. The SESAM plays two key roles: it starts and stabilizes the mode-locking operation and is simultaneously used as an actuator to control the CEO frequency. This second functionality is implemented by pumping the SESAM with a continuous-wave 980-nm laser diode in order to slightly modify its nonlinear reflectivity. We use the standard f-to-2f method for detection of the CEO frequency, which is stabilized by applying a feedback signal to the current of the SESAM pump diode. We compare the SESAM-OOM stabilization with the traditional method of gain modulation via control of the pump power of the Yb:CALGO gain crystal. While the bandwidth for gain modulation is intrinsically limited to ∼250 kHz by the laser cavity dynamics, we show that the OOM provides a feedback bandwidth above 500 kHz. Hence, we were able to obtain a residual integrated phase noise of 430 mrad for the stabilized CEO beat, which represents an improvement of more than 30% compared to gain modulation stabilization.

Full stabilization and characterization of an optical frequency comb from a diode-pumped solid-state laser with GHz repetition rate.

We demonstrate the first self-referenced full stabilization of a diode-pumped solid-state laser (DPSSL) frequency comb with a GHz repetition rate. The Yb:CALGO DPSSL delivers an average output power of up to 2.1 W with a typical pulse duration of 96 fs and a center wavelength of 1055 nm. A carrier-envelope offset (CEO) beat with a signal-to-noise ratio of 40 dB (in 10-kHz resolution bandwidth) is detected after supercontinuum generation and f-to-2f interferometry directly from the output of the oscillator, without any external amplification or pulse compression. The repetition rate is stabilized to a reference synthesizer with a residual integrated timing jitter of 249 fs [10 Hz - 1 MHz] and a relative frequency stability of 10-12/s. The CEO frequency is phase-locked to an external reference via pump current feedback using home-built modulation electronics. It achieves a loop bandwidth of ~150 kHz, which results in a tight CEO lock with a residual integrated phase noise of 680 mrad [1 Hz - 1 MHz]. We present a detailed characterization of the GHz frequency comb that combines a noise analysis of the repetition rate frep, of the CEO frequency fCEO, and of an optical comb line at 1030 nm obtained from a virtual beat with a narrow-linewidth laser at 1557 nm using a transfer oscillator. An optical comb linewidth of about 800 kHz is assessed at 1-s observation time, for which the dominant noise sources of frep and fCEO are identified.

Power Spectrum Computation for an Arbitrary Phase Noise Using Middleton's Convolution Series: Implementation Guideline and Experimental Illustration.

In this paper, we revisit the convolution series initially introduced by Middleton several decades ago to determine the power spectrum (or spectral line shape) of a periodic signal from its phase noise power spectral density. This topic is of wide interest, as it has an important impact on many scientific areas that involve lasers and oscillators. We introduce a simple guideline that enables a fairly straightforward computation of the power spectrum corresponding to an arbitrary phase noise. We show the benefit of this approach on a computational point of view, and apply it to various types of experimental signals with different phase noise levels, showing a very good agreement with the experimental spectra. This approach also provides a qualitative and intuitive understanding of the power spectrum corresponding to different regimes of phase noise.

Frequency stability of a dual wavelength quantum cascade laser.

We characterized the dual wavelength operation of a distributed Bragg reflector (DBR) quantum cascade laser (QCL) operating at 4.5 µm using two independent optical frequency discriminators. The QCL emits up to 150 mW fairly evenly distributed between two adjacent Fabry-Perot modes separated by ≈11.6 GHz. We show a strong correlation between the instantaneous optical frequencies of the two lasing modes, characterized by a Pearson correlation coefficient of 0.96. As a result, we stabilized one laser mode of the QCL to a N2O transition using a side-of-fringe locking technique, reducing its linewidth by a factor 6.2, from 406 kHz in free-running operation down to 65 kHz (at 1-ms observation time), and observed a simultaneous reduction of the frequency fluctuations of the second mode by a similar amount, resulting in a linewidth narrowing by a factor 5.4, from 380 kHz to 70 kHz. This proof-of-principle demonstration was performed with a standard DBR QCL that was not deliberately designed for dual-mode operation. These promising results open the door to the fabrication of more flexible dual-mode QCLs with the use of specifically designed gratings in the future.

Carrier envelope offset frequency detection and stabilization of a diode-pumped mode-locked Ti:sapphire laser.

We demonstrate the first diode-pumped Ti:sapphire laser frequency comb. It is pumped by two green laser diodes with a total pump power of 3 W. The Ti:sapphire laser generates 250 mW of average output power in 61-fs pulses at a repetition rate of 216 MHz. We generated an octave-spanning supercontinuum spectrum in a photonic-crystal fiber and detected the carrier envelope offset (CEO) frequency in a standard f-to-2f interferometer setup. We stabilized the CEO-frequency through direct current modulation of one of the green pump diodes with a feedback bandwidth of 55 kHz limited by the pump diode driver used in this experiment. We achieved a reduction of the CEO phase noise power spectral density by 140 dB at 1 Hz offset frequency. An advantage of diode pumping is the ability for high-bandwidth modulation of the pump power via direct current modulation. After this experiment, we studied the modulation capabilities and noise properties of green pump laser diodes with improved driver electronics. The current-to-output-power modulation transfer function shows a bandwidth larger than 1 MHz, which should be sufficient to fully exploit the modulation bandwidth of the Ti:sapphire gain for CEO stabilization in future experiments.

First investigation of the noise and modulation properties of the carrier-envelope offset in a modelocked semiconductor laser.

We present the first characterization of the noise properties and modulation response of the carrier-envelope offset (CEO) frequency in a semiconductor modelocked laser. The CEO beat of an optically-pumped vertical external-cavity surface-emitting laser (VECSEL) at 1030 nm was characterized without standard f-to-2f interferometry. Instead, we used an appropriate combination of signals obtained from the modelocked oscillator and an auxiliary continuous-wave laser to extract information about the CEO signal. The estimated linewidth of the free-running CEO beat is approximately 1.5 MHz at 1-s observation time, and the feedback bandwidth to enable a tight CEO phase lock to be achieved in a future stabilization loop is in the order of 300 kHz. We also characterized the amplitude and phase of the pump current to CEO-frequency transfer function, which showed a 3-dB bandwidth of ∼300 kHz for the CEO frequency modulation. This fulfills the estimated required bandwidth and indicates that the first self-referenced phase-stabilization of a modelocked semiconductor laser should be feasible in the near future.

Characterizing the carrier-envelope offset in an optical frequency comb without traditional f-to-2f interferometry.

We present a new method to measure the frequency noise and modulation response of the carrier-envelope offset (CEO) beat of an optical frequency comb that does not make use of the traditional f-to-2f interferometry. Instead, we use an appropriate combination of different signals to extract the contribution of the CEO frequency without directly detecting it. We present a proof-of-principle validation realized with a commercial Er:fiber frequency comb and show an excellent agreement with the results obtained using a standard f-to-2f interferometer. This approach is attractive for the characterization of novel frequency comb technologies for which self-referencing is challenging, such as semiconductor mode-locked lasers, microresonator-based systems, or GHz repetition rate lasers.

Frequency comb offset dynamics of SESAM modelocked thin disk lasers.

We present a detailed study of the carrier-envelope offset (CEO) frequency dynamics of SESAM modelocked thin disk lasers (TDLs) pumped by kW-class highly transverse multimode pump diodes with a typical M(2) value of 200-300, and give guidelines for future frequency stabilization of multi-100-W oscillators. We demonstrate CEO frequency detection with > 30 dB signal-to-noise ratio with a resolution bandwidth of 100 kHz from a SESAM modelocked Yb:YAG TDL delivering 140 W average output power with 748-fs pulses at 7-MHz pulse repetition rate. We compare with a low-power CEO frequency stabilized Yb:CALGO TDL delivering 2.1 W with 77-fs pulses at 65 MHz. For both lasers, we perform a complete noise characterization, measure the relevant transfer functions (TFs) and compare them to theoretical models. The measured TFs are used to determine the propagation of the pump noise step-by-step through the system components. From the noise propagation analysis, we identify the relative intensity noise (RIN) of the pump diode as the main contribution to the CEO frequency noise. The resulting noise levels are not excessive and do not prevent CEO frequency stabilization. More importantly, the laser cavity dynamics are shown to play an essential role in the CEO frequency dynamics. The cavity TFs of the two lasers are very different which explains why at this point a tight CEO frequency lock can be obtained with the Yb:CALGO TDL but not with the Yb:YAG TDL. For CEO stabilization laser cavities should exhibit high damping of the relaxation oscillations by nonlinear intra-cavity elements, for example by operating a SESAM in the roll-over regime. Therefore the optimum SESAM operation point is a trade-off between enough damping and avoiding multiple pulsing instabilities. Additional cavity components could be considered for supplementary damping independent of the SESAM operation point.

Compact rubidium-stabilized multi-frequency reference source in the 1.55-µm region.

Combining light modulation and frequency conversion techniques, a compact and simple frequency-stabilized optical frequency comb spanning over 45 nm in the 1.56-µm wavelength region is demonstrated. It benefits from the high-frequency stability achievable from rubidium atomic transitions at 780 nm probed in a saturation absorption scheme, which is transferred to the 1.56-µm spectral region via a second-harmonic generation process. The optical frequency comb is generated by an electro-optic modulator enclosed in a Fabry-Perot cavity that is injected by the fundamental frequency stabilized laser. Frequency stability better than 2 kHz has been demonstrated on time scales between 1000 s and 2 days both at 1560 nm, twice the rubidium wavelength, and for a comb line at 1557 nm.

All-electrical frequency noise reduction and linewidth narrowing in quantum cascade lasers.

A novel all-electrical method of frequency noise reduction in quantum cascade lasers (QCLs) is proposed. Electrical current through the laser was continuously adjusted to compensate for fluctuations of the laser internal resistance, which led to an active stabilization of the optical emission frequency. A reduction of the linewidth from 1.7 MHz in the standard constant current mode of operation down to 480 kHz is demonstrated at 10-ms observation time when applying this method to a QCL emitting at 7.9 µm.

Gigahertz frequency comb from a diode-pumped solid-state laser.

We present the first stabilization of the frequency comb offset from a diode-pumped gigahertz solid-state laser oscillator. No additional external amplification and/or compression of the output pulses is required. The laser is reliably modelocked using a SESAM and is based on a diode-pumped Yb:CALGO gain crystal. It generates 1.7-W average output power and pulse durations as short as 64 fs at a pulse repetition rate of 1 GHz. We generate an octave-spanning supercontinuum in a highly nonlinear fiber and use the standard f-to-2f carrier-envelope offset (CEO) frequency fCEO detection method. As a pump source, we use a reliable and cost-efficient commercial diode laser. Its multi-spatial-mode beam profile leads to a relatively broad frequency comb offset beat signal, which nevertheless can be phase-locked by feedback to its current. Using improved electronics, we reached a feedback-loop-bandwidth of up to 300 kHz. A combination of digital and analog electronics is used to achieve a tight phase-lock of fCEO to an external microwave reference with a low in-loop residual integrated phase-noise of 744 mrad in an integration bandwidth of [1 Hz, 5 MHz]. An analysis of the laser noise and response functions is presented which gives detailed insights into the CEO stabilization of this frequency comb.