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Ultra-stable microwave generation with a diode-pumped solid-state laser in the 1.5-?m range
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.
Effect of the carrier-envelope-offset dynamics on the stabilization of a diode-pumped solid-state frequency comb
Noise properties of an optical frequency comb from a SESAM-modelocked 1.5 µm solid-state laser stabilized to the 10 -13 level
We present a detailed investigation of the noise properties of an optical frequency comb generated from a femtosecond diode-pumped solid-state laser operating in the 1.5-μm spectral region. The stabilization of the passively mode-locked Er:Yb:glass laser oscillator, referred to as ERGO, is achieved using pump power modulation for the control of the carrier envelope offset (CEO) frequency and by adjusting the laser cavity length for the control of the repetition rate. The stability and the noise of the ERGO comb are characterized in free-running and in phase-locked operation by measuring the noise properties of the CEO, of the repetition rate, and of a comb line at 1558 nm. The comb line is analyzed from the heterodyne beat signal with a cavity-stabilized ultra-narrow-linewidth laser using a frequency discriminator. Two different schemes to stabilize the comb to a radio-frequency (RF) reference are compared. The comb properties (phase noise, frequency stability) are limited in both cases by the RF oscillator used to stabilize the repetition rate, while the contribution of the CEO is negligible at all Fourier frequencies, as a consequence of the low-noise characteristics of the CEO-beat. A linewidth of ≈150 kHz and a fractional frequency instability of 4.2×10−13 at 1 s are obtained for an optical comb line at 1558 nm. Improved performance is obtained by stabilizing the comb to an optical reference, which is a cavitystabilized ultra-narrow linewidth laser at 1558 nm. The fractional frequency stability of 8 × 1014− at 1 s, measured in preliminary experiments, is limited by the reference oscillator used in the frequency comparison.
Cross-influence between the two servo-loops of a fully-stabilized Er:fiber optical frequency comb
We present a study of the impact of the cross-coupling between the two servo loops used to stabilize the repetition rate frep and the carrier-envelope offset (CEO) frequency fCEO in a commercial Er:fiber frequency comb, based on the combination of experimental measurements and a model of the coupled loops. The developed theoretical model enables us to quantify the influence of the servo-loop coupling on an optical comb line, by simulating the hypothetic case where no coupling would be present. Numerical values for the model were obtained from an extensive characterization of the comb, in terms of frequency noise and dynamic response to a modulation applied to each actuator, for both frep and fCEO. To validate the model, the frequency noise of an optical comb line at 1.56 μm was experimentally measured from the heterodyne beat between the comb and a cavity-stabilized ultranarrow-linewidth laser and showed good agreement with the calculated noise spectrum. The coupling between the two stabilization loops results in a more than 10-fold reduction of the comb mode frequency noise power spectral density in a wide Fourier frequency range.
Noise properties of an optical frequency comb from a SESAM-modelocked 1.5 µm solid-state laser stabilized to the 10E-13 level
We present a detailed investigation of the noise properties of an optical frequency comb generated from a femtosecond diode-pumped solid-state laser operating in the 1.5-μm spectral region. The stabilization of the passively mode-locked Er:Yb:glass laser oscillator, referred to as ERGO, is achieved using pump power modulation for the control of the carrier envelope offset (CEO) frequency and by adjusting the laser cavity length for the control of the repetition rate. The stability and the noise of the ERGO comb are characterized in free-running and in phase-locked operation by measuring the noise properties of the CEO, of the repetition rate, and of a comb line at 1558 nm. The comb line is analyzed from the heterodyne beat signal with a cavity-stabilized ultra-narrow-linewidth laser using a frequency discriminator. Two different schemes to stabilize the comb to a radio-frequency (RF) reference are compared. The comb properties (phase noise, frequency stability) are limited in both cases by the RF oscillator used to stabilize the repetition rate, while the contribution of the CEO is negligible at all Fourier frequencies, as a consequence of the low-noise characteristics of the CEO-beat. A linewidth of ≈150 kHz and a fractional frequency instability of 4.2×1E−13 at 1 s are obtained for an optical comb line at 1558 nm. Improved performance is obtained by stabilizing the comb to an optical reference, which is a cavity-stabilized ultra-narrow linewidth laser at 1558 nm. The fractional frequency stability of 8×1E−14 at 1 s, measured in preliminary experiments, is limited by the reference oscillator used in the frequency comparison.
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 Hz2/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.
New-generation cryogenic sapphire microwave oscillators for space, metrology and scientific applications
This article reports on the characterization of cryogenic sapphireoscillators (CSOs), and on the first test of a CSO in a real field installation, where ultimate frequency stability and continuous operation are critical issues, with no survey. Thanks to low-vibration liquid-He cryocooler design, Internet monitoring, and a significant effort of engineering, these oscillators could bridge the gap from an experiment to a fully reliable machine. The cryocooler needs scheduled maintenance every 2 years, which is usual for these devices. The direct comparison of two CSOs demonstrates a frequency stability of 5 × 10E−16 for 30 s < τ < 300 s integration time, and 4.5 × 10E−15 at 1 day (1 × 10E−14 typical). Two prototypes are fully operational, codenamed ELISA and ULISS. ELISA has been permanently installed the new deep space antenna station of the European Space Agency in Malargüe, Argentina, in May 2012. ULISS is a transportable version of ELISA, modified to fit in a small van (8.5 m2 footprint). Installation requires a few hours manpower and 1 day of operation to attain full stability. ULISS, intended for off-site experiments and as a technology demonstrator, and has successfully completed two long-distance travels.
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.
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.