Stéphane Schilt

Wavelength modulation spectroscopy: combined frequency and intensity laser modulation

A theoretical model of wavelength modulation spectroscopy that uses a laser diode on a Lorentzian absorption line is presented. This theory describes the general case of a current-modulated semiconductor laser, for which a combined intensity and frequency modulation with an arbitrary phase shift occurs. On the basis of this model, the effect of several modulation parameters on the detected signals is evaluated. Experimental signals measured on an absorption line of CO2 by use of a 2-microm distributed-feedback laser are also presented and validate this analysis. These experimental results agree with the calculated signals, confirming the relevance of the model.

Simple approach to the relation between laser frequency noise and laser line shape

Frequency fluctuations of lasers cause a broadening of their line shapes. Although the relation between the frequency noise spectrum and the laser line shape has been studied extensively, no simple expression exists to evaluate the laser linewidth for frequency noise spectra that does not follow a power law. We present a simple approach to this relation with an approximate formula for evaluation of the laser linewidth that can be applied to arbitrary noise spectral densities.

Fully stabilized optical frequency comb with sub-radian CEO phase noise from a SESAM-modelocked 1.5-µm solid-state laser

We report the first full stabilization of an optical frequency comb generated from a femtosecond diode-pumped solid-state laser (DPSSL) operating in the 1.5-μm spectral region. The stability of the comb is characterized in free-running and in phase-locked operation by measuring the noise properties of the carrier-envelope offset (CEO) beat, of the repetition rate, and of a comb line at 1558 nm. The high Q-factor of the semiconductor saturable absorber mirror (SESAM)-modelocked 1.5-µm DPSSL results in a low-noise CEO-beat, for which a tight phase lock can be much more easily realized than for a fiber comb. Using a moderate feedback bandwidth of only 5.5 kHz, we achieved a residual integrated phase noise of 0.72 rad rms for the locked CEO, which is one of the smallest values reported for a frequency comb system operating in this spectral region. The fractional frequency stability of the CEO-beat is 20‑fold better than measured in a standard self-referenced commercial fiber comb system and contributes only 10(-15) to the optical carrier frequency instability at 1 s averaging time.

CEO stabilization of a femtosecond laser using a SESAM as fast opto-optical modulator

We present a new method for intra-cavity control of the carrier-envelope offset (CEO) frequency of ultrafast lasers that combines high feedback bandwidth with low loss, low nonlinearity, and low dispersion. A semiconductor saturable-absorber mirror (SESAM) inside a modelocked laser is optically pumped with a continuous-wave (cw) laser. In this way, the SESAM acts as intra-cavity opto-optical modulator (OOM): the optical power of the cw-laser corresponds to a high-bandwidth modulation channel for CEO frequency control. We experimentally verified this method for a femtosecond Er:Yb:glass oscillator (ERGO), in which one SESAM is in parallel used for modelocking and as intra-cavity OOM for achieving a tight CEO lock. This laser can also be CEO-stabilized in the usual scheme, in which the laser pump current is modulated, i.e., the gain element acts as intra-cavity OOM. We compare the performance with gain and SESAM OOM measuring CEO transfer function, frequency noise power spectral density (PSD), and Allan deviation for integration times up to 1000 s. In the case of the gain OOM, the millisecond upper-state lifetime of the Er:Yb:glass limits the achievable CEO-control bandwidth to <10 kHz. The feedback bandwidth of the SESAM OOM was more than a factor of 10 higher than the gain OOM bandwidth and was mainly limited by the used current driver. The residual integrated phase noise (1 Hz - 100 kHz) of the ~20-MHz CEO beat was improved by more than an order of magnitude (from 720 mrad to less than 65 mrad), and the fractional frequency stability by a factor of 4 (from 1∙10

Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb.

We describe a radio-frequency (RF) discriminator, or frequency-to-voltage converter, based on a voltage-controlled oscillator phase-locked to the signal under test, which has been developed to analyze the frequency noise properties of an RF signal, e.g., a heterodyne optical beat signal between two lasers or between a laser and an optical frequency comb. We present a detailed characterization of the properties of this discriminator and we compare it to three other commercially available discriminators. Owing to its large linear frequency range of 7 MHz, its bandwidth of 200 kHz and its noise floor below 0.01 Hz(2)/Hz in a significant part of the spectrum, our frequency discriminator is able to fully characterize the frequency noise of a beat signal with a linewidth ranging from a couple of megahertz down to a few hertz. As an example of application, we present measurements of the frequency noise of the carrier envelope offset beat in a low-noise optical frequency comb.

Experimental method based on wavelength-modulation spectroscopy for the characterization of semiconductor lasers under direct modulation.

An experimental method is presented for characterization of the combined intensity and frequency modulation produced when the injection current of a laser diode is modulated. The reported technique is based on the analysis of the harmonic signals produced when a modulated laser is used to probe a gas absorption line by the so-called wavelength-modulation spectroscopy method. Based on a theoretical model of this technique, we present two methods that facilitate the determination of (i) the deviation in laser frequency and (ii) the phase shift between intensity and frequency modulation. These methods are illustrated experimentally by measurement of the modulation parameters of a 2-microm distributed-feedback laser by use of a CO2 absorption line. The experimental results have been compared with those obtained with another traditional method and have shown full agreement in the frequency range (400 Hz-30 kHz) considered.

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.

Phase-stabilization of the carrier-envelope-offset frequency of a SESAM modelocked thin disk laser

We phase-stabilized the carrier-envelope-offset (CEO) frequency of a SESAM modelocked Yb:CaGdAlO₄ (CALGO) thin disk laser (TDL) generating 90-fs pulses at a center wavelength of 1051.6 nm and a repetition rate of 65 MHz. By launching only 2% of its output power into a photonic crystal fiber, we generated a coherent octave-spanning supercontinuum spectrum. Using a standard f-to-2f interferometer for CEO detection, we measured CEO beats with 33 dB signal-to-noise ratio in 100 kHz resolution bandwidth. We achieved a tight lock of the CEO frequency at 26.18 MHz by active feedback to the pump current. The residual in-loop integrated phase noise is 120 mrad (1 Hz-1 MHz). This is, to our knowledge, the first CEO-stabilized SESAM modelocked TDL. Our results show that a reliable lock of the CEO frequency can be achieved using standard techniques in spite of the strongly spatially multimode pumping scheme of TDLs. This opens the door towards fully-stabilized low-noise frequency combs with hundreds of watts of average power from table-top SESAM modelocked thin disk oscillators.

Temperature dependence of the frequency noise in a mid-IR DFB quantum cascade laser from cryogenic to room temperature

We report on the measurement of the frequency noise power spectral density in a distributed feedback quantum cascade laser over a wide temperature range, from 128 K to 303 K. As a function of the device temperature, we show that the frequency noise behavior is characterized by two different regimes separated by a steep transition at ≈200 K. While the frequency noise is nearly unchanged above 200 K, it drastically increases at lower temperature with an exponential dependence. We also show that this increase is entirely induced by current noise intrinsic to the device. In contrast to earlier publications, a single laser is used here in a wide temperature range allowing the direct assessment of the temperature dependence of the frequency noise.

Experimental validation of a simple approximation to determine the linewidth of a laser from its frequency noise spectrum

Laser frequency fluctuations can be characterized either comprehensively by the frequency noise spectrum or in a simple but incomplete manner by the laser linewidth. A formal relation exists to calculate the linewidth from the frequency noise spectrum, but it is laborious to apply in practice. We recently proposed a much simpler geometrical approximation applicable to any arbitrary frequency noise spectrum. Here we present an experimental validation of this approximation using laser sources of different spectral characteristics. For each of them, we measured both the frequency noise spectrum to calculate the approximate linewidth and the actual linewidth directly. We observe a very good agreement between the approximate and directly measured linewidths over a broad range of values (from kilohertz to megahertz) and for significantly different laser line shapes.