Pierre Brochard

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.

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.

Rb-stabilized laser at 1572 nm for CO2 monitoring

We have developed a compact rubidium-stabilized laser system to serve as optical frequency reference in the 1.55-μm wavelength region, in particular for CO2 monitoring at 1572 nm. The light of a fiber-pigtailed distributed feedback (DFB) laser emitting at 1560 nm is frequency-doubled and locked to a sub-Doppler rubidium transition at 780 nm using a 2-cm long vapor glass cell. Part of the DFB laser light is modulated with an electro-optical modulator enclosed in a Fabry-Perot cavity, generating an optical frequency comb with spectral coverage extending from 1540 nm to 1580 nm. A second slave DFB laser emitting at 1572 nm and offset-locked to one line of the frequency comb shows a relative frequency stability of 1.10-11 at 1 s averaging time and <4.10-12 from 1 hour up to 3 days.

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 comb metrology with an optical parametric oscillator

We report on the first demonstration of absolute frequency comb metrology with an optical parametric oscillator (OPO) frequency comb. The synchronously-pumped OPO operated in the 1.5-µm spectral region and was referenced to an H-maser atomic clock. Using different techniques, we thoroughly characterized the frequency noise power spectral density (PSD) of the repetition rate frep, of the carrier-envelope offset frequency fCEO, and of an optical comb line νN. The comb mode optical linewidth at 1557 nm was determined to be ~70 kHz for an observation time of 1 s from the measured frequency noise PSD, and was limited by the stability of the microwave frequency standard available for the stabilization of the comb repetition rate. We achieved a tight lock of the carrier envelope offset frequency with only ~300 mrad residual integrated phase noise, which makes its contribution to the optical linewidth negligible. The OPO comb was used to measure the absolute optical frequency of a near-infrared laser whose second-harmonic component was locked to the F = 2→3 transition of the 87Rb D2 line at 780 nm, leading to a measured transition frequency of νRb = 384,228,115,346 ± 16 kHz. We performed the same measurement with a commercial fiber-laser comb operating in the 1.5-µm region. Both the OPO comb and the commercial fiber comb achieved similar performance. The measurement accuracy was limited by interferometric noise in the fibered setup of the Rb-stabilized laser.

Compact GHz Frequency Comb from an Ultrafast Solid-State Laser with Cost-Efficient 3D-Printed Plastic Cavity Base

We present a GHz mode-locked laser with a 3D-printed cavity base resulting in substantial noise reduction from the previous use of traditional opto-mechanical mounts. Additionally, the repetition rate is stabilized to a low-noise optically-derived 15-GHz signal.

Carrier-envelope offset frequency stabilization of an ultrafast semiconductor laser

We present the self-referenced stabilization of the carrier-envelope offset (CEO) frequency of a semiconductor disk laser. The laser is a SESAM-modelocked VECSEL emitting at a wavelength of 1034 nm with a repetition frequency of 1.8 GHz. The 270-fs pulses are amplified to 3 W and compressed to 120 fs for the generation of a coherent octavespanning supercontinuum spectrum. A quasi-common-path f-to-2f interferometer enables the detection of the CEO beat with a signal-to-noise ratio of ~30 dB sufficient for its frequency stabilization. The CEO frequency is phase-locked to an external reference with a feedback signal applied to the pump current.

Optical frequency comb stabilization of a gigahertz semiconductor disk laser

Semiconductor lasers are a promising technology to make optical comb systems more accessible and cost-efficient. We stabilized the carrier-envelope offset (CEO) frequency of a semiconductor disk laser. The laser was modelocked by a SESAM and generates pulses at a wavelength of 1034 nm. It operates at a repetition frequency of 1.8 GHz. The 270-fs pulses are amplified to 3 W and compressed to 120 fs. A coherent octave-spanning supercontinuum spectrum is generated in a highly nonlinear fiber. Using a standard f-to-2f interferometer, we detect the CEO beat with a signal-to-noise ratio of ~30 dB. By applying a feedback signal to the pump current, the CEO frequency is phase-locked to an external reference.

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.