Laser Frequency Fluctuations Research Articles

Subfemtowatt Laser Phase Tracking.

Low power optical phase tracking is an enabling capability for intersatellite laser interferometry, as minimum trackable power places significant constraints on mission design. Through the combination of laser stabilization and control-loop parameter optimization, we have demonstrated continuous tracking of a subfemtowatt optical field with a mean time between slips of more than 1000s. Comparison with analytical models and numerical simulations verified that the observed experimental performance was limited by photon shot noise and unsuppressed laser frequency fluctuations. Furthermore, with two stabilized lasers, we have demonstrated 100min of continuous phase tracking of Gravity Recovery and Climate Experiment (GRACE)-like signal dynamics with an optical carrier ranging in power between 1-7fW with zero cycle slips. These results indicate the feasibility of future interspacecraft laser links operating with significantly reduced received optical power.

Characterization of Laser Frequency Stability by Using Phase-Sensitive Optical Time-Domain Reflectometry

A new method to measure laser phase noise and frequency stability based on the phase-sensitive optical time-domain reflectometry is proposed. In this method, the laser under test is utilized in a phase-sensitive optical time-domain reflectometer, which employs phase-modulated dual pulses and acts as an optical frequency discriminator: laser frequency fluctuations are deduced from the analysis of the reflectometer data corresponded to phase fluctuations along the vibration-damped and thermally insulated fiber spool. The measurement results were validated by comparison with direct optical heterodyning of the tested and more coherent reference lasers. The use of dual pulses generated by an acousto-optic modulator makes it easy to adjust the time delay during measurements, which distinguishes favorably the proposed method from standard optical frequency discriminators. The method is suitable for testing highly coherent lasers and qualifying their parameters such as linear drift rate, random frequency walk rate, white frequency noise (which is directly related to laser instantaneous linewidth), and flicker noise level.

Temperature-insensitive FDL-stabilized laser using a PMF-based dual interferometer.

We demonstrate a temperature-insensitive fiber-delay-line-stabilized (FDL-stabilized) laser based on a dual Mach-Zehnder interferometer (MZI) by using polarization maintaining fibers (PMFs). Two orthogonal polarization components of a beam are simultaneously transmitted in the interferometer. Each polarization component exhibits a unique phase shift in response to the changes in temperature, forming a dual MZI. One of the heterodyne signals is used to lock the laser frequency, while the other one is used to compensate the frequency change induced by the temperature fluctuation. The experiment shows that the laser frequency fluctuation has been suppressed at least 25 times. This is an effective method to reduce the laser frequency noise induced by the temperature fluctuation of the FDL. In this way, a compact system with less thermal shields can be realized, and the thermal equilibrium time could be decreased dramatically.

Frequency Noise Characterization of Diode Lasers for Vapor-Cell Clock Applications

The knowledge of the frequency noise spectrum of a diode laser is of interest in several high-resolution experiments. Specifically, in laser-pumped vapor cell clocks, it is well established that the laser frequency noise plays a role in affecting clock performances. It is then relevant to characterize the frequency noise of a diode laser since such measurements are rarely found in the literature and hardly ever provided by vendors. In this paper, we describe a technique based on a frequency-to-voltage converter that transforms the laser frequency fluctuations into voltage fluctuations. In this way, it is possible to characterize the laser frequency noise power spectral density in a wide range of Fourier frequencies, as required in cell clock applications.

Theoretical and Experimental Investigation of the Effect of Pump Laser Frequency Fluctuations on Signal-to-Noise Ratio of Brillouin Dynamic Grating Measurement with Coherent FMCW Reflectometry.

Signal-dependent speckle-like noise has constituted a serious factor in Brillouin-grating based frequency-modulated continuous-wave (FMCW) reflectometry and it has been indispensable for improving the signal-to-noise ratio (S/N) of the Brillouin dynamic grating measurement to clarify the noise generation mechanism. In this paper we show theoretically and experimentally that the noise is generated by the frequency fluctuations of the pump light from a laser diode (LD). We could increase the S/N from 36 to 190 merely by driving the LD using a current source with reduced technical noise. On the basis of our experimental result, we derived the theoretical formula for S/N as a function of distance, which contained the second and fourth-order moments of the frequency fluctuations, by assuming that the pump light frequency was modulated by the technical noise. We calculated S/N along the 1.35 m long optical fiber numerically using the measured power spectral density of the frequency fluctuations, and the resulting distributions agreed with the measured values in the 10 to 190 range. Since higher performance levels are required if the pump light source is to maintain the S/N as the fiber length increases, we can use the formula to calculate the light source specifications including the spectral width and rms value of the frequency fluctuations to achieve a high S/N while testing a fiber of a given length.

Spectral filtering of dual lasers with a high-finesse length-tunable cavity for rubidium atom Rydberg excitation* *Project supported by National Key Research and Development Program of China (Grant No. 2016YFA0302800), the National Natural Science Foundation of China (Grant Nos. U20A2074 and 12074391), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB 21010100), the Youth Innovation Promotion Association

We propose and demonstrate an alternative method for spectral filtering and frequency stabilization of both 780-nm and 960-nm lasers using a high-finesse length-tunable cavity (HFLTC). Firstly, the length of HFLTC is stabilized to a commercial frequency reference. Then, the two lasers are locked to this HFLTC using the Pound–Drever–Hall (PDH) method which can narrow the linewidths and stabilize the frequencies of both lasers simultaneously. Finally, the transmitted lasers of HFLTC with each power up to about 100 μW, which act as seed lasers, are amplified using the injection locking method for single-atom Rydberg excitation. The linewidths of obtained lasers are narrowed to be less than 1 kHz, meanwhile the obtained lasers’ phase noise around 750 kHz are suppressed about 30 dB. With the spectrally filtered lasers, we demonstrate a Rabi oscillation between the ground state and Rydberg state of single-atoms in an optical trap tweezer with a decay time of (67 ± 37) μs, which is almost not affected by laser phase noise. We found that the maximum short-term laser frequency fluctuation of a single excitation lasers is at ∼3.3 kHz and the maximum long-term laser frequency drift of a single laser is ∼46 kHz during one month. Our work develops a stable and repeatable method to provide multiple laser sources of ultra-low phase noise, narrow linewidth, and excellent frequency stability, which is essential for high precision atomic experiments, such as neutral atom quantum computing, quantum simulation, quantum metrology, and so on.

Research on frequency stability of narrow linewidth laser in resonant optical gyro

In this study, to measure the frequency drift characteristics of the narrow-linewidth laser, we provide a method with high accuracy and adjustable measuring range that can be applied in a resonant optical gyro (ROG) system. In an ROG system, the laser frequency drift characteristics, such as fluctuation range and frequency, influence the performance of the closed-loop frequency-locked module. To measure the above performance of the laser, we proposed a novel measurement system based on the Fabry–Pérot cavity. We proved the feasibility of the scheme through theory and simulation. Then, the calibration of the experimental device and the measurement of the tested laser were completed. The measurement accuracy of this method is 1.2 kHz, and the measurement range reaches ±60 MHz, which can be adjusted by the modulation index. The results show that the laser has a frequency fluctuation of 30 MHz in the stabilization stage, and there is mainly a low-frequency component under 5 Hz in the frequency domain of the laser frequency fluctuation. Furthermore, this measurement scheme can be applied in other fiber sensor systems to evaluate the effect of laser frequency fluctuation on system output performance.

A General Relation Between Frequency Noise and Lineshape of Laser Light

Lasers and especially semiconductor lasers (SCLs) are playing a major role in advanced technological and scientific tasks ranging from sensing, fundamental investigations in quantum optics and communications. The demand for ever-increasing accuracy and communication rates has driven these applications to employ phase modulation and coherent detection. The main laser attribute that comes into play is its coherence which is usually quantified by either the Schawlow-Townes (S-T) linewidth, the spectral width of the laser field, or the power spectral density (PSD) function of the laser frequency fluctuation. In this paper, we present a derivation of a general and direct relationship between these two coherence measures. We refer to the result as the Central Relation. The relation applies independently of the physical origin of the noise. Experiments are described which demonstrate the validity of the Central Relation and at the same time suggest new methods of controlling frequency noise at base band by optical filtering.

Laser frequency locking with subnatural linewidth spectroscopy

We demonstrate a simple technique to lock the frequency of a laser to an atomic transition with a new technique of subnatural linewidth spectroscopy. The coupled rubidium system exhibits an enhanced absorption spectrum of the probe beam with a subnatural linewidth. Compared with other techniques with an additional laser, our scheme only utilizes a single laser, which will be locked. The observed spectroscopic linewidth is down to about 3.5 MHz. The laser frequency fluctuation is about 226 kHz after locking on. The demonstrated scheme offers a convenient and low-cost technique for laser frequency stabilization and related precision measurements.

Effect of laser-frequency fluctuation on the decay rate of Rydberg coherence

The effect of electromagnetically induced transparency (EIT) combined with Rydberg-state atoms provides high optical nonlinearity to efficiently mediate the photon-photon interaction. However, the decay rate of Rydberg coherence, i.e., the decoherence rate, plays an important role in optical nonlinear efficiency, and can be largely influenced by laser frequency fluctuation. In this work, we carried out a systematic study of the effect of laser frequency fluctuation on the decoherence rate. We derived an analytical formula that quantitatively describes the relationship between the decoherence rate and laser frequency fluctuation. The formula was experimentally verified by using the $\Lambda$-type EIT system of laser-cooled $^{87}$Rb atoms, in which one can either completely eliminate or controllably introduce the effect of laser frequency fluctuation. We also included the effect of Doppler shift caused by the atomic thermal motion in the formula, which can be negligible in the $\Lambda$-type EIT experiment but significant in the Rydberg-EIT experiment. Utilizing the atoms of 350 $\mu$K, we studied the decoherence rate in the Rydberg-EIT system involving with the state of $|32D_{5/2}\rangle$. The experimental data are consistent with the predictions from the formula. We were able to achieve a rather low decoherence rate of $2\pi\times$48 kHz at a moderate coupling Rabi frequency of $2\pi\times$4.3 MHz.

Frequency locking of semiconductor lasers to RF oscillators using hybrid-integrated opto-electronic oscillators with dispersive delay lines.

Direct frequency locking of lasers to RF oscillators has many applications such as high resolution optical frequency synthesis, coherent optical communication, spectroscopy, sensing, and imaging. Here we present a hybrid-integrated opto-electronic loop that directly frequency locks a semiconductor laser to an RF synthesized source using an opto-electronic oscillator with a dispersive optical delay line. Cascaded ring filters, operating near the resonance frequency, provide an enhanced chromatic dispersion with a compact footprint. The electronic chip is integrated in the GlobalFoundries 180 nm CMOS SOI technology and the photonic chip is integrated in the IME 180 nm SOI technology. A tracking range of 0.5 GHz is achieved while consuming 33 mW power. The proposed scheme is used to frequency lock a commercially available DFB laser, reducing the laser frequency fluctuations by an order of magnitude compared to the free-running case.

Effect of laser noise on the propagation of laser radiation in dispersive and nonlinear media

The effect of laser noise on the atmospheric propagation of high-power CW lasers and high-intensity short pulse lasers in dispersive and nonlinear media is studied. We consider the coupling of laser intensity noise and phase noise to the spatial and temporal evolution of laser radiation. High-power CW laser systems have relatively large fractional levels of intensity noise and frequency noise. We show that laser noise can have important effects on the propagation of high-power as well as high-intensity lasers in a dispersive and nonlinear medium such as air. A paraxial wave equation, containing dispersion and nonlinear effects, is expanded in terms of fluctuations in the intensity and phase. Longitudinal and transverse intensity noise and frequency noise are considered. The laser propagation model includes group velocity dispersion, Kerr, delayed Raman response, and optical self-steepening effects. A set of coupled linearized equations are derived for the evolution of the laser intensity and frequency fluctuations. In certain limits, these equations can be solved analytically. For example, we find that, in a dispersive medium, frequency noise can couple to and induce intensity noise (fluctuations) and vice versa. At high intensities, the Kerr effect can reduce this intensity noise. In addition, significant spectral modification can occur if the initial intensity noise level is sufficiently high. Finally, our model is used to study the transverse and longitudinal modulational instabilities. We present atmospheric propagation examples of the spatial and temporal evolution of intensity and frequency fluctuations due to noise for laser wavelengths of 0.85 μm, 1 μm, and 10.6 μm.

Identifying the Contribution of Carrier Shot Noise and Random Carrier Recombination to Excess Frequency Noise in Tunable Lasers

Tunable lasers are necessary devices for modern-day telecommunications and sensing systems. Tunable lasers based on altering the refractive index of the tuning sections of distributed Bragg reflectors (DBR) by varying the injected electrical current show significantly more instantaneous random changes in the instantaneous lasing frequency (or excess FM-noise) compared to non-tunable distributed feedback lasers. We identifies shot noise and random carrier recombination as being the culprits of the excess FM-noise of DBR lasers, and demonstrated this by invoking detailed analytical and numerical analyses of the stochastic carrier fluctuations in the tuning sections, as well as a simplified quasi-static laser tuning model to convert the carrier fluctuations into random instantaneous fluctuations. We found that the spectral density of the FM-noise was mostly in the range 0.5 MHz–10 MHz, and this is in agreement with many independently published results. Our analytical treatment allowed us to conclude that it would be advantageous to reduce the refractive index dependence on the carriers in order to reduce the excess FM-noise while still maintaining the tuning functionality. The simplified numerical model allowed us to create a system simulator to help further develop signal processing techniques to counteract against these instantaneous laser frequency fluctuations.

Performance estimation of dual-comb spectroscopy in different frequency-control schemes

Dual-comb spectroscopy (DCS) has shown unparalleled advantages but at the cost of highly mutual coherence between comb lasers. Here, we investigate spectral degradation induced by laser frequency instabilities and improvement benefited from active laser stabilization. Mathematical models of DCS in the cases of direct radio-frequency (RF) locking and optical phase stabilization were separately established first. Numerical simulations are utilized to study the impact of laser intrinsic stability and the improvement by different locking strategies on spectral performance in the following. Finally, both simulations are proven by corresponding experiments. It shows that an optically phase-stabilized system owns a better immunity of laser frequency fluctuations than a direct RF-stabilized one. Furthermore, the performance improvement by the feedback servos is also more effective in the optically phase-stabilized system. In addition, the simulations could instruct optimal design and system improvement.

Laser frequency locking based on Rydberg electromagnetically induced transparency**Project supported by the National Basic Research Program of China (Grant No. 2012CB921603), the National Natural Science Foundation of China (Grants Nos. 11274209, 61475090, 61378039, and 61378013), and the Research Project Supported by Shanxi Scholarship Council of China (Grant No. 2014-009).

We present a laser frequency locking to Rydberg transition with electromagnetically induced transparency (EIT) spectra in a room-temperature cesium vapor cell. Cesium levels 6S1/2, 6P3/2, and the nD5/2 state, compose a cascade three-level system, where a coupling laser drives Rydberg transition, and probe laser detects the EIT signal. The error signal, obtained by demodulating the EIT signal, is used to lock the coupling laser frequency to Rydberg transition. The laser frequency fluctuation, ∼0.7 MHz, is obtained after locking on, with the minimum Allan variance to be 8.9 × 10−11. This kind of locking method can be used to stabilize the laser frequency to the excited transition.

On the performance of joint iterative detection and decoding in coherent optical channels with laser frequency fluctuations

The joint iterative detection and decoding (JIDD) technique has been proposed by Barbieri et al. (2007) with the objective of compensating the time-varying phase noise and constant frequency offset experienced in satellite communication systems. The application of JIDD to optical coherent receivers in the presence of laser frequency fluctuations has not been reported in prior literature. Laser frequency fluctuations are caused by mechanical vibrations, power supply noise, and other mechanisms. They significantly degrade the performance of the carrier phase estimator in high-speed intradyne coherent optical receivers.This work investigates the performance of the JIDD algorithm in multi-gigabit optical coherent receivers. We present simulation results of bit error rate (BER) for non-differential polarization division multiplexing (PDM)-16QAM modulation in a 200Gb/s coherent optical system that includes an LDPC code with 20% overhead and net coding gain of 11.3dB at BER=10−15. Our study shows that JIDD with a pilot rate ⩽5% compensates for both laser phase noise and laser frequency fluctuation. Furthermore, since JIDD is used with non-differential modulation formats, we find that gains in excess of 1dB can be achieved over existing solutions based on an explicit carrier phase estimator with differential modulation. The impact of the fiber nonlinearities in dense wavelength division multiplexing (DWDM) systems is also investigated. Our results demonstrate that JIDD is an excellent candidate for application in next generation high-speed optical coherent receivers.

Frequency stabilization of a 1083 nm fiber laser to ⁴He transition lines with optical heterodyne saturation spectroscopies.

Two kinds of optical heterodyne saturation spectroscopies, namely, frequency modulation spectroscopy (FMS) and modulation transfer spectroscopy (MTS), are demonstrated for locking a fiber laser to the transition lines of metastable (4)He atoms around 1083 nm. The servo-loop error signals of FMS and MTS for stabilizing laser frequency are optimized by studying the dependence of the peak-to-peak amplitude and slope on the optical power of pump and probe beams. A comparison of the stabilization performances of FMS/MTS and polarization spectroscopy (PS) is presented, which shows that MTS exhibits relatively superior performance with the least laser frequency fluctuation due to its flat-background dispersive signal, originated from the four-wave mixing process. The Allan deviation of the stabilized laser frequency is 5.4 × 10(-12)@100 s with MTS for data acquired in 1000 s, which is sufficiently applicable for fields like laser cooling, optical pumping, and optical magnetometry.

Error reduction of the Doppler lidar signal using a re-normalization method

In this paper, we present a re-normalization method for a Doppler signal of a Doppler lidar system. For the Doppler lidar system, we used an injection-seeded pulsed Nd:YAG laser as a transmitter and an iodine cell as a Doppler frequency discriminator. A frequency locking system that uses the absorption feature of iodine gas is too sensitive to the external or internal noises (iodine cell temperature instability, laser frequency fluctuation, environmental noises, etc.) to maintain its locking point ideally, and this frequency locking error makes the Doppler lidar system acquire the noises as the Doppler frequency shifts. To reduce the Doppler signal error induced by a frequency locking error, we used a re-normalization method by an addition of a laser beam path separated from a transmitter to the Doppler frequency discriminator for re-normalization. In this method, fluctuations of the Doppler signal were reduced using the reference signal. The reduced amount of standard deviation between the Doppler signal and the re-normalization signal was 4.838×10 –3 and the Doppler signals showed a 53.3% fluctuation reduction of the averaged error value by this method.

An all-optical locking of a semiconductor laser to the atomic resonance line with 1 MHz accuracy

An all-optical locking technique without extra electrical feedback control system for a semiconductor laser has been used in stabilizing the laser frequency to a hyperfine crossover transition of 87Rb 5(2)S(1/2), F = 2 → 5(2)P(3/2), F' = 2, 3 with 1 MHz level accuracy. The optical feedback signal is generated from the narrow-band Faraday anomalous dispersion optical filter (FADOF) with nonlinear saturation effect. The peak transmission of the narrow-band FADOF corresponding to 5(2)S(1/2), F = 2 → 5(2)P(3/2), F' = 2, 3 crossover transition is 18.6 %. The bandwidth is as wide as 38.9 MHz as the laser frequency changes. After locking, the laser frequency fluctuation is reduced to 1.7 MHz. The all-optical laser locking technique can be improved to much higher accuracy with increased external cavity length. The laser we have realized can provide light exactly resonant with atomic transitions used for other atom-light interaction experiments.

Investigation of Short-term Amplitude and Frequency Fluctuations of Lasers for Interferometry

One of the limiting factors of accuracy and resolution in laser interferometry is represented by noise properties of the laser powering the interferometer. Amplitude and especially frequency fluctuations of the laser source are crucial in precision distance measurement. Sufficiently high long-term frequency stability of the laser source must be achieved especially in applications in fundamental metrology. Furthermore, the short-term frequency variations are also important primarily for measurements done at high acquisition speeds. This contribution presents practical results of measurements of short-term amplitude and frequency noises of a set of laser sources commonly used in laser interferometry. The influence of the interferometer design and electrical parameters of the detection system are also discussed.