Analysis of frequency offset in the frequency stabilization of semiconductor laser based on frequency dithering technique

Scientists throughout the world are seeking to enhance the capabilities of satellite-to-satellite tracking laser interferometer-based optical systems used to measure the alterations in earth's gravitational field that indicate critical changes in the environment. These systems must be able to measure infinitesimal fluctuations in the relative velocities of two satellites, using a light source that oscillates at a level of frequency stability rated better than 10-13 in the square root of the Allan variance. In our experiments, semiconductor laser frequency stabilization that typically requires a brief direct modulation of the laser injection current to obtain an error signal, was accomplished using the Faraday effect of Rb absorption lines. This effectively modulates the reference frequency of the stabilization system, i.e., the Rb absorption line, by modulating the magnetic field applied to the Rb absorption cell, instead of the oscillation frequency of the laser diode. Most recently, we used the Faraday method, in conjunction with a precision temperature controller. For present purposes, we also use the PEAK method, to obtain the most accurate signal possible, comparing it with saturated absorption spectroscopic readings, to determine the noise-source.

Narrow linewidth and high stability of frequency are extremely necessary in modern precision experiments. The frequency of a free running semiconductor laser will drift several GHz per day, far too much to fulfill the demands in atomic and laser physics. In order to overcome this disadvantage, a variety of technologies for frequency stabilization are researched. The experimental realizations of frequency stabilization based on 780nm semiconductor laser are described in detail. Meanwhile, the performance and capabilities of the various frequency stabilization technologies are analyzed.

The differential absorption lidar (DIAL) can help us to obtain the vertical distribution of the atmospheric CO2 concentration, which is important to the study of carbon sources and carbon sinks. We design a seeder injected pulsed laser system, working as the laser source of the CO2 DIAL. Unlike the other CO2 DIALs, our laser source is the result of difference frequency of two lasers at the wavelengths of 1064 nm and 634 nm, respectively. It should be pointed out that the high frequency (wavelength) accuracy and stability of the emission laser, especially the on-line one, are greatly required in the CO2 DIAL system. However, the mechanical properties of the dye laser (634 nm) and the application of laser difference frequency technique make the wavelength drift constantly; besides, the extremely unstable energy of the pulsed laser increases the difficulty in identifying and stabilizing the on-line wavelength. Hence, a fast and efficient frequency (wavelength) stabilization method is needed to achieve a stable emission wavelength. Aiming at the research gap of the high precision requirements of on-line laser for this kind of pulsed DIAL, we propose a frequency stabilization method based on matching algorithm. The basic idea is to utilize the saturable absorption of CO2 molecule, by measuring the differential residual-intensity after the laser passing through dual absorption cells to calculate the optical depth (OD) and obtain the so-called pseudo CO2 absorption spectrum, which can be used to identify the on-line laser accurately. Finally, based on the matching algorithm of one-dimensional image, treating the OD as the gray value in the image, we implement the OD matching as a most important part in the process of frequency stabilization, and determine the exact position of the real-time output laser in the measured pseudo absorption spectrum. Thus, when some errors happen to the monitored ODs, by continuously adjusting the wavelength of the laser, the proposed method can fulfill the wavelength adjustment and accomplish the continuous frequency stabilization for on-line laser. Experimental results show that the frequency stabilization algorithm based on OD matching can satisfy the requirements for pulsed on-line laser frequency stabilization, and the sum of squares of deviation method is the optimal one in this application, with a stabilization accuracy of 0.3 pm. Besides, the proposed method can also be introduced in other laser frequency stabilization.

Frequency tuning and stability of Nd:YVO 4 in a dual coupled cavity

An electromagnetically induced transparency (EIT) signal is observed in a V-type energy level scheme in a cesium vapor cell at room temperature. The effects of frequency detuning and the intensity of the pump laser on the EIT signal have been investigated. The performance of the probe-diode laser system, which is frequency stabilized on the EIT signal by using electrical feedback, is explored. The first derivative of the EIT signal offers a steeper slope and better S/N ratio for laser frequency stabilization than that of the Doppler-free hyperfine and crossover resonances. A comparative study of the frequency stability of an external-cavity diode laser stabilized at EIT and at the crossover resonance is presented. The square root of the Allan variance (σ) vs. integration time (τ) plot shows about a tenfold improvement in the frequency stability of the EIT-locked laser (σ ∼ 2.043 × 10−13τ−1/2) over that of the crossover-locked laser under a short integration time (1–10 ms), whereas a twofold improvement is found under a long integration time (∼1 s).

The method of intracavity polarization spectroscopy was employed to measure the Doppler-free saturated dispersion spectrum in CH4 (the E component of the P(7) line in the ν3 band). A He-22Ne laser at 3.39 µm was used as a light source. The experimental results agreed well with the results of numerical calculations. This spectrum was used to stabilize the laser frequency without frequency modulation, and a stability of 1.1×10-12 was obtained for an integration time of 200 s. The second derivative signal of the spectrum was also used for the stabilization by modulating the laser frequency. The stability obtained was 2.5×10-13 for an integration time of 300 s. Furthermore, an alternative method using a Faraday rotator is proposed to get higher frequency stability.

A method for measuring the frequency stability of tunable laser is proposed by using confocal Fabry-Perot (F-P) interferometer. The F-P interferometer is used to get the output frequency of the laser as a reference, and the method eliminates the need of an independent optical source as a frequency reference. Using this technique, the frequency stability of the tunable external-cavity diode laser (ECDL) is measured to be 2.26×10−9 with an integration time of 20 ms.

We report on frequency stabilization of multiple wavelength lasers operating at 1389 and 1695 nm simultaneously on a broadband spectrum. These lasers are implemented in ytterbium optical lattice clock experiments, which need to have a narrow enough linewidth and maintain high long-term frequency stability. A 1560 nm femtosecond mode-locked laser with a narrow mode spacing of 250 MHz is used as a master laser, which is referenced to a local ultrastable optical cavity with the instability better than 1 × 10−15 at 1 s averaging time. Through the combination of erbium-doped fiber amplifier and high nonlinear fiber, the spectral width of the maser laser is broadened from 10 nm to more than 300 nm. The range of the broadened spectrum can cover 1389 and 1695 nm. Meanwhile, the spectral intensity at the corresponding wavelength can ensure that the signal-to-noise ratio of the beat signals between the two lasers and the broadened spectrum is about 30 dB at a resolution bandwidth (RBW) of 100 kHz. After phase locking the 1389 and 1695 nm lasers on the broadband spectrum, the residual linewidths are obtained to be about 0.8 Hz at 1 Hz RBW, and the stabilities are 3.5 × 10−16 and 4.7 × 10−16 at 1 s averaging time respectively, improving about six orders of magnitude. Our result can be conducive to obtaining the stabilized laser sources for the atomic optical clock, and will be of great significance for simplifying and miniaturizing the optical clock system.

We demonstrate frequency stabilization of DFB laser via modulation transfer spectroscopy, which avoids the interference of Doppler absorption spectrum. By modulating the frequency of laser beam(pump laser beam), the other laser beam(probe laser beam) overlap pump laser beam is modulated as the same frequency by nonlinear interaction. By demodulating the signal from detection beam, an error signal is generated through the low pass filter. The frequency is stabilized at the 0 point position of the MTS frequency discrimination curve by PID loop which shows frequency fluctuation is less than 149 kHz, and the relative frequency stability is improved by nearly two orders of magnitude.

We present a new method for accurate mid-infrared frequency measurements and stabilization to a near-infrared ultra-stable frequency reference, transmitted with a long-distance fibre link and continuously monitored against state-of-the-art atomic fountain clocks. We demonstrate the frequency stabilization of a mid-infrared laser with fractional stability better than 4×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-14</sup> at 1 s averaging. This new stabilization scheme gives us the ability to transfer frequency stability in the range of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-15</sup> or even better, currently accessible in the near-infrared or in the visible, to mid-infrared lasers in a wide frequency range.

A parametric loudspeaker has been used for audio guidance to a specific area because it has a sharper directivity compared with the conventional electrodynamic loudspeakers. The parametric loudspeaker emits an ultrasound as a carrier wave, which is modulated with an audio signal and has large-amplitude. An audible sound is reproduced by the modulated ultrasound with large-amplitude distorted by the nonlinearity on the air. The conventional modulations have been proposed as the amplitude modulation and the frequency modulation. In the sound quality, the amplitude modulation is superior to the frequency modulation. However, in the sound pressure level, the frequency modulation is superior to the amplitude modulation. In the present paper, we especially focus on that the parametric loudspeaker will emit the speech signals for the audio guidance. Therefore, we propose new modulation method based on the combination of amplitude and frequency modulations, which are specialized for speech signals. More specifically, we apply the amplitude and frequency modulations to the divided frequency bands of speech signals, respectively. In order to confirm the effectiveness of the proposed method, we carried out evaluation experiments. As a result of evaluation experiments, we confirmed the effectiveness of the proposed method compared with conventional methods.

The advancement of cold atom gravimeters (CAG) is based on the precise control and stabilization of lasers used for the atom interferometry.The 5S 5P transition in rubidium (Rb) at 780.241 nm is crucial for such quantum technology applications.In this study, the hyperfine structure of 5 2 S1/2 5 2 P3/2, D2 transition line of 87 Rb atoms obtained through saturation absorption spectroscopy, are used as a reference for the frequency stabilization of an external cavity diode laser (ECDL) operating at 780 nm.The ECDL is locked to the hyperfine saturated absorption peak of 87 Rb (F = 2 3').This laser beam is combined with another 780 nm ECDL laser to obtain the beat frequency spectrum, generating a beat note signal of ~ 6.8 GHz, which is needed for phase stabilization between lasers.These are critical for the Raman beam generation in the CAG, as the 87 Rb atoms ground hyperfine states (F = 1 and F = 2) have separation of ~ 6.834 GHz, and two Raman beams with an 6.8 GHz offset can drive transitions between these hyperfine states of 87 Rb to realize the CAG interferometry scheme.

Recent studies on amplitude modulation (AM) detection for tones in noise reported that AM-detection thresholds improve when the AM stimulus is preceded by a noise precursor. The physiological mechanisms underlying this AM unmasking are unknown. One possibility is that adaptation to the level of the noise precursor facilitates AM encoding by causing a shift in neural rate-level functions to optimize level encoding around the precursor level. The aims of this study were to investigate whether such a dynamic-range adaptation is a plausible mechanism for the AM unmasking and whether frequency modulation (FM), thought to be encoded via AM, also exhibits the unmasking effect. Detection thresholds for AM and FM of tones in noise were measured with and without a fixed-level precursor. Listeners showing the unmasking effect were then tested with the precursor level roved over a wide range to modulate the effect of adaptation to the precursor level on the detection of the subsequent AM. It was found that FM detection benefits from a precursor and the magnitude of FM unmasking correlates with that of AM unmasking. Moreover, consistent with dynamic-range adaptation, the unmasking magnitude weakens as the level difference between the precursor and simultaneous masker of the tone increases.

The single-step Rydberg excitation of cesium atoms requires a 319 nm ultraviolet laser with a narrow laser linewidth, high frequency stability, and high output power. To meet these requirements, in this work, we construct a high-power, single-frequency UV laser system at this wavelength. In this system, the frequency stabilization of the 1560.492 nm seed laser is critical to the performance of the ultraviolet laser. We employ nonlinear frequency conversion technology, the 1560.492 nm laser is frequency-doubled to 780.246 nm via a single pass through a PPLN crystal, and function integration is realized based on the modular parameter adjustment interface provided by the PyRPL software. Subsequently, the 1560.492 nm laser is stabilized to the D2 hyperfine transition line of Rb-87 atoms using polarization spectroscopy (PS) and radio-frequency-modulated saturation absorption spectroscopy (RF-SAS). A comparative study of these two techniques shows that RF-SAS achieves superior stabilization performance, with the residual frequency fluctuation of the frequency-doubled laser being 1.07 MHz over 30 min. According to frequency doubling theory, the actual residual frequency fluctuation of the 1560.492 nm fundamental-frequency laser can be calculated as 0.535 MHz. Compared with our earlier scheme that utilized an ultra-low-expansion (ULE) optical cavity as a frequency reference, the present scheme eliminates the long-term drift induced by environmental factors. In contrast to frequency stabilization relying on discrete instruments, this integrated scheme significantly reduces the cost, simplifies the system architecture, saves space, and greatly enhances the flexibility and controllability of the system. It therefore provides a reliable and cost-effective solution to ensure the portability and practicability of high-performance UV laser sources. This high-precision frequency stabilization scheme directly guarantees the performance of the 319 nm UV laser, suppressing its linewidth below 10 kHz. Thus, it fully meets the stringent laser linewidth and frequency stability requirements for the single-step Rydberg excitation of cesium atoms and provides a reliable light source foundation for subsequent precision spectroscopic measurements.

We analyse 38-month of contiguous short-cadence data, concentrating on mode multiplets induced by the star rotation and on frequencies forming linear combinations that show intriguing behaviors during the course of the observations. We find clear signatures that point toward nonlinear effects predicted by resonant mode coupling mechanisms. These couplings can induce various mode behaviors for the components of multiplets and for frequencies related by linear relationships. We find that a triplet at 5760\,$\mu$Hz, a quintuplet at 5287\,$\mu$Hz and a ($\ell>2$) multiplet at 5412\,$\mu$Hz, all induced by rotation, show clear frequency and amplitude modulations which are typical of the so-called intermediate regime of a resonance between the components. One triplet at 316\,$\mu$Hz and a doublet at 394\,$\mu$Hz show modulated amplitude and constant frequency which can be associated with a narrow transitory regime of the resonance. Another triplet at 519\,$\mu$Hz appears to be in a frequency lock regime where both frequency and amplitude are constant. Additionally, three linear combination of frequencies near 6076\,$\mu$Hz also show amplitude and frequency modulations, which are likely related to a three-mode direct resonance. The identified frequency and amplitude modulations are the first clear-cut signatures of nonlinear resonant couplings occurring in pulsating hot B subdwarf stars. However, the observed behaviors suggest that the resonances occurring in these stars usually follow more complicated patterns than the simple predictions from current nonlinear theoretical frameworks. These results should therefore motivate further work to develop the theory of nonlinear stellar pulsations, considering that stars like KIC~10139564 now offer remarkable testbeds to do so.