Laser Line Shape Research Articles

Design of a three-frequency Rayleigh lidar for simultaneous temperature and wind measurements.

This study proposes what we believe to be a novel high-spectral-resolution three-frequency Rayleigh lidar for simultaneously measuring middle atmosphere temperature and wind. The temperature and wind could be retrieved without assuming an external reference temperature, as typical for a traditional Rayleigh Doppler lidar. Adopting a similar idea used in sodium temperature/wind lidar, this system alternatively emits laser pulses at three frequencies. It receives the corresponding Rayleigh backscattered signals filtered by an iodine cell as a frequency discriminator. The three frequencies are optimized based on the spectral characteristics resulting from the convolution of the pulse laser lineshape convolved Rayleigh scattering signal with iodine molecular absorption spectrum. A two-dimensional calibration curve for temperature and wind ratio is then generated from the theoretical calculation of the final convoluted spectra and used to retrieve temperature and wind simultaneously. Simulated with the return signals collected by a current broadband Rayleigh lidar (30-inch telescope and 15 W output laser power), the temperature and wind uncertainties with resolutions of 1 km and 1 hr are estimated to be 0.4 K and 0.35 m/s, respectively, at 30 km and increase to 16.3 K and 8.1 m/s at 70 km.

Evaluation of LIF thermometry technique using Krypton as a tracer: Impact of laser lineshape and collisional bandwidth

In recent years, two-photon laser-induced fluorescence (TPLIF) of inert gas krypton (Kr) has received much attention as a potential non-intrusive flow diagnostic, thermometry, and velocimetry technique. However, the interaction between the laser bandwidth and the atomic excitation transition at varying pressures, and the variation of the fluorescence quantum yield due to spatially varying collisional quenching of Kr are not fully understood. The resulting lineshape and quenching corrections become especially important when the temporal scales of excitation laser pulses vary from nanosecond (ns) to femtosecond (fs) timescales. In this study, we report a comprehensive investigation of Kr line broadening and quenching effects, in particular, with respect to TPLIF-based temperature (T) measurements in flames. Experiments were conducted in both low-pressure and atmospheric-pressure flames and in two different burner configurations, using conventional ns and ultrafast fs duration laser sources. When using ns pulses, the results suggest no lineshape corrections are necessary at low pressure; however, a T-dependent empirical model was needed for atmospheric-pressure flames. In contrast, broadband fs pulses have linewidths in excess of 400 cm−1, which are significantly larger than sub-cm−1 spectral transitions, hence requiring no lineshape corrections at any pressure. Quenching measurements in low-pressure flames were found to be scaled by T−0.5 using previous low-pressure thermometry data and 1D flame model predictions. The Kr TPLIF temperature profiles measured using ns pulses (low and atmospheric pressures) and fs pulses (atmospheric pressures) agreed well with model predictions. In the absence of the necessity for lineshape corrections, fs Kr-TPLIF provides an easy way to extract T simply by taking the inverse square of the fluorescence signal. T-line imaging using fs-pulses are presented for several flame heights. The present study establishes a simplified approach for Kr TPLIF-based thermometry in flames.

Line shape of a delayed self-heterodyne varied with noise types and delays.

The delayed self-heterodyne and self-homodyne (DSH) method is widely used for measuring the line shapes of high coherent lasers. This method results in an autocorrelation of a laser line under the condition of a delay that is much larger than its coherent time. In practice, the delay is often not so long, especially for very narrow linewidth lasers, resulting in errors in rebuilding the laser's line shape from the DSH line. Many papers were devoted to the topic, but most of them are based on the formula for white noise. Analytical formulas of phase variance for 1/f noises are presented in this paper; the DSH line shapes for different noise types and different delay lengths are simulated based on the formulas. Some experimental data of the DSH line, combined with the power spectral density of frequency noise, are processed, showing good agreement with the theoretical analysis. It is indicated that the DSH line shape shows complicated behaviors varied with the delay, with noise types, and with the measurement duration. Such effects are to be compensated for in retrieving the laser's linewidth from the DSH data.

Gain-dependent Purcell enhancement, breakdown of Einstein's relations, and superradiance in nanolasers

Light emitters in a single-mode nanolaser interact with the same cavity field, that gives rise to polarization correlations which transform the cavity mode. Usually these correlations are ignored, however, collective phenomena can lead to the distinct sub- and superradiance, whose fully quantum description is challenging. Here, we develop a simple yet rigorous picture of radiative transitions in single-mode nanolasers that accounts for polarization correlations. We show that the collective behavior of emitters modifies the photonic density of states leading to gain-dependent Purcell enhancement of spontaneous emission. Moreover, the stimulated emission rate is dependent on both the photon number and the laser lineshape. As the laser line narrows, stimulated emission becomes stronger than predicted by Einstein's relations and the nanolaser reaches the threshold earlier. Finally, we provide concise, ready-to-use expressions for spontaneous and stimulated emission rates seamlessly describing both conventional and superradiant nanolasers.

Intensity pattern types in broadband Fourier domain mode-locked (FDML) lasers operating beyond the ultra-stable regime

We report on the formation of various intensity pattern types in detuned Fourier domain mode-locked (FDML) lasers and identify the corresponding operating conditions. Such patterns are a result of the complex laser dynamics and serve as an ideal tool for the study of the underlying physical processes as well as for model verification. By numerical simulation we deduce that the formation of patterns is related to the spectral position of the instantaneous laser lineshape with respect to the transmission window of the swept bandpass filter. The spectral properties of the lineshape are determined by a long-term accumulation of phase-offsets, resulting in rapid high-amplitude intensity fluctuations in the time domain due to the narrow intra-cavity bandpass filter and the fast response time of the semiconductor optical amplifier gain medium. Furthermore, we present the distribution of the duration of dips in the intensity trace by running the laser in the regime in which dominantly dips form, and give insight into their evolution over a large number of roundtrips.

Determination and Analysis of Line-Shape Induced Enhancement of Stimulated Brillouin Scattering in Noise Broadened, Narrow Linewidth, High Power Fiber Lasers

We investigate the origin of line-shape induced enhancement of stimulated Brillouin scattering (SBS) in narrow linewidth, noise broadened, high-power fiber lasers. A polarization-maintaining seed laser with continuously tunable linewidth (single frequency to >10 GHz), based on white noise modulation was developed for this study. With increasing linewidths, a substantial difference in SBS thresholds was observed depending on the end termination utilized. This observation can be explained by the line-broadened source, having significant power in the Stokes frequency at larger linewidths, seeding the SBS process. Here, SBS threshold for the system terminated with an anti-reflection coated delivery cable is compared with a simple angle cleaved end termination. The influence of end termination on SBS threshold becomes significant with increased linewidths, showing >20% difference in output power between the two cases at ~10 GHz linewidth. The experiments are complemented by simulations, analyzing relative contributions of Rayleigh scattering and fiber end-facet reflections to SBS. At larger linewidths, due to substantial overlap between laser line-shape and SBS Stokes, with low end-facet reflectivity, Rayleigh is the dominant mechanism, which gives way to end-facet reflections with increasing reflectivity. The Rayleigh contribution is negligible at smaller linewidths, and end-facet reflectivity has a weaker influence than with larger linewidths.

Hardware-Oriented Algorithm for High-Speed Laser Centerline Extraction Based on Hessian Matrix

Centerline extraction is the basic and key procedure in line-structured laser 3-D scanners. In this article, we propose a hardware-oriented algorithm for fast and accurate extraction of a laser centerline based on the Hessian matrix. The algorithm is divided into three low-coupling modules that can be processed in parallel—coarse positioning, linewidth estimation, and precise positioning module. In the coarse positioning module, a window slider is used to traverse all image pixels in the raster-scan mode for collecting local image features, based on which the potential region of interest (ROI) containing laser lines is detected. In the linewidth estimation module, the second-order moment features in the detected ROI are calculated to estimate the linewidth according to the local rectangular similarity characteristics of the laser line. In the precise positioning module, the optimal Gaussian template estimated by the linewidth is convolved with the ROI to obtain the Hessian matrix. Based on the Hessian matrix, the normal direction of the laser line is obtained, and the second-order Taylor expansion is performed in that direction to determine the subpixel position of the center point. Finally, non-maximum suppression is used to remove noise points and obtain the most reliable single-pixel centerline. The proposed algorithm is evaluated using thousands of sample images with different materials, exposure times, and laser line shapes, and it presents high robustness for subpixel precision extraction. By implementing the proposed algorithm on a field-programmable gate array (FPGA), a high-speed, high-precision laser centerline extraction system is achieved, which operates at 1350 frames/s for a 1-million-pixel video stream.

Effect of laser linewidth on the tunable diode laser absorption spectroscopy system

In this paper, a theoretical investigation of the influence of laser linewidth on the tunable diode laser absorption spectroscopy system is presented. The theoretical analysis and formula discussion of laser line shape are carried out by frequency noise spectrum density. Taking Lorentz line shape of laser line width as an example, the interaction principle of laser line width and gas absorption spectral line is analyzed. The relation curve of laser linewidth and maximum amplitude is simulated by MATLAB platform with self-defined simulation parameters. These results can provide theoretical basis for guiding the selection of laser and gas absorption spectral line and improving the detection accuracy of gas concentration.

The Impact of Local Oscillator Frequency Jitter and Laser Linewidth to Ultra High Baud Rate Coherent Systems

Through theoretical analysis and simulation, we investigate the system impact due to a sinusoidal jitter tone and the resultant local oscillator (LO) laser linewidth requirement in ultra-high baud rate and long distance coherent optical systems. We also carried out experiments in 64 Gbaud, dual-polarization (DP)-16 QAM systems to verify the theoretical analysis and simulation. We have also obtained a jitter interference tolerance mask to qualify LO lasers. A jitter tone with a frequency lower than ∼1 MHz has a higher tolerance since it generally causes constant frequency or phase shift, which can be tracked by a receiver DSP. For a jitter tone with a frequency higher than ∼1 MHz, the tolerance becomes much tighter since the tone will affect laser lineshape and induce equalizer-enhanced phase noise (EEPN). Consequently, a jitter tone in the higher frequency region could severely affect the system performance. Theoretical analysis and numerical result illustrate that EVM2 due to the effect of laser linewidth and a sinusoidal jitter tone is proportional to the weighted sum of $[ \Delta \nu \times B_{s}\times \text{L}] $ and $[ \Delta f_{pp}\times B_{s}\times \text{L}] ^{2}$ , where Δν is the laser linewidth, $B_{s}$ is the baud rate, $\Delta f_{pp}$ is the laser peak-to-peak frequency deviation due to a sinusoidal jitter tone, and L is the fiber transmission length. This result is applicable for all orders of QAM constellations. The implication to future 100 Gbaud and beyond systems is delineated.

Broadening the optical bandwidth of quantum cascade lasers using RF noise current perturbations.

We report on the broadening of the optical bandwidth of a distributed feedback quantum cascade laser (QCL) caused by the application of radio frequency (RF) noise to the injection current. The broadening is quantified both via Lamb-dip spectroscopy and the frequency noise power spectral density (PSD). The linewidth of the unperturbed QCL (emitting at ∼5.3 μm) determined by Lamb-dip spectroscopy is 680±170 kHz, and is in reasonable agreement with the linewidth of 460±40 kHz estimated by integrating the PSD measured under the same laser operating conditions. Measurements with both techniques reveal that by mixing the driving current with broadband RF noise the laser lineshape was reproducibly broadened up to ca 6MHz with an increasing Gaussian contribution. The effects of linewidth broadening are then demonstrated in the two-color coherent transient spectra of nitric oxide.

光腔衰荡光谱技术用于OH浓度测量的误差分析

Cavity ring down spectroscopy(CRDS) is an absorption spectroscopy technique with high sensitivity, which is a very important quantitative concentration measurement approach in combustion spectral diagnosis. The principle analysis of CRDS was presented to apply to absolute concentrations of intermediate species in flames, and then an experimental setup of pulsed CRDS was established based on this principle. The absolute OH concentration was measured by using absorption on the P1(2) rotational line in the A2+-X2(0,0) band of OH on a plat flame at atmospheric pressure. Influence of several major factors on the measurement uncertainty was analyzed, such as laser line shape and linewidth, frequency stability of the laser, flame temperature, and cavity parameters. This uncertainty analysis provides several guidelines to improve the measurement accuracy of CRDS.

光腔衰荡光谱技术用于OH浓度测量的误差分析

Cavity ring down spectroscopy(CRDS) is an absorption spectroscopy technique with high sensitivity, which is a very important quantitative concentration measurement approach in combustion spectral diagnosis. The principle analysis of CRDS was presented to apply to absolute concentrations of intermediate species in flames, and then an experimental setup of pulsed CRDS was established based on this principle. The absolute OH concentration was measured by using absorption on the P1(2) rotational line in the A2+-X2(0,0) band of OH on a plat flame at atmospheric pressure. Influence of several major factors on the measurement uncertainty was analyzed, such as laser line shape and linewidth, frequency stability of the laser, flame temperature, and cavity parameters. This uncertainty analysis provides several guidelines to improve the measurement accuracy of CRDS.

Numerical Study of the Dynamics of Laser Lineshape and Linewidth

give no information about the dynamics of lineshape and linewidth. Second, their way of calculating lineshape and linewidth leads through the implicit assumption that the laser field can be represented by a complex amplitude oscillating at the resonance frequency of the pure cavity, which is equivalent to requiring the solutions for the laser field to be self-consistent. In this context, the finite linewidth of the laser radiation is not related to the existence of solutions at frequencies other than the resonance frequency, it is just the fingerprint of the statistical fluctuations of the complex amplitude when transformed into the frequency domain. The Fokker‐Plank equation divides these statistical fluctuations into a drift term and a diusion term. The former is assigned the coherent

Retrieving mesopause temperature and line-of-sight wind from full-diurnal-cycle Na lidar observations.

Narrowband Na lidar measurement of mesopause region temperatures were pioneered by Fricke and von Zahn in 1985, in 1990 by She et al. at Colorado State University (CSU), with upgrades to measure both temperature and wind in 1994, and under sunlit conditions in 1996 with 24 h continuous observational capability in 2002. This paper details the assumptions and procedures for the retrieval of mesopause region temperatures, line-of-sight winds, and sodium densities from day and night signals from the CSU narrowband Na lidar. The Hanle effect and the effect of the pulsed laser line shape function on the accuracy of temperature and LOS wind retrieval are also discussed.

Simultaneously reducing the intensity and frequency noise of single-frequency phosphate fiber laser

We demonstrate an optoelectronic feedback method to simultaneously reduce the intensity and frequency noise of a single-frequency phosphate fiber laser for the first time. Based on the fact that the intensity and frequency noise in this laser mainly originate from the pump power fluctuations, we implement a simple and compact feedback loop and achieve a maximum noise reduction of over 20 dB for the intensity noise at frequencies of 0.3–3 kHz and 10 dB for the frequency noise at around 1 kHz. In addition, the laser instability is improved from ±1.7% to ±0.1%, and the laser line shape is observed to be compressed at the central part.

Impact of broadened laser line-shape on retrievals of atmospheric species from lidar sounding absorption spectra.

We examine the impact of broadened laser line-shape on retrievals of atmospheric species from lidar-sounding absorption spectra. The laser is assumed to be deterministically modulated into a stable, nearly top-hat frequency comb to suppress the stimulated Brillouin scattering, allowing over 10-fold pulse energy increase without adding measurement noise. Our model remains accurate by incorporating the laser line-shape factor into the effective optical depth. Retrieval errors arising from measurement noise and model bias are analyzed parametrically and numerically to provide deeper insight. The stable laser line-shape broadening minimally degrades the column-averaged retrieval, but can significantly degrade the multiple-layer retrievals.

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.

Line shapes of near-infrared DFB and VCSEL diode lasers under the influence of system back reflections

Laser diode line widths and line shapes are experimentally investigated in dependence on the diode current and on back reflections from an optical system. Four distributed-feedback (DFB)-type diode lasers and two vertical-cavity surface-emitting lasers (VCSELs) have been tested within the same optical setup and using the same fitting methods. System back reflection ratios of light reflected back to the laser have been varied between −1 dB and −45 dB and were below −60 dB when all reflections were blocked. The background of this investigation is the evaluation of different laser types with respect to their suitability for sensor applications in which optical back reflections may occur, for example tunable diode-laser spectroscopy (TDLS). While DFB-type lasers showed almost pure Lorentzian line shapes and line widths of a few MHz, the tested VCSELs had a strong Gaussian contribution to the line shape, indicating stronger 1/f noise, which was also observed in the relative intensity noise of these particular lasers. System reflection ratios above −25 dB had strong effects on the line width in both DFB diode lasers and VCSELs, while some influences have been observed at even lower reflection ratios for DFB diode lasers. As much smaller reflection ratios are typically required in TDLS systems to avoid etalon-like fringes and self-mixing interference effects, we conclude that the influence on the line width is not the most important reason to minimize back reflections in practical TDLS systems or to choose one type of diode laser over the other.

Limitation and improvement in the performance of recirculating delayed self-heterodyne method for high-resolution laser lineshape measurement

This paper presents a detailed analysis of the performance of a recirculating delayed self-heterodyne (R-DSH) method for high-resolution laser lineshape measurement. For increasing the delay time the R-DSH method utilizes circulation of light in a heterodyne ring interferometer (HRI) containing a frequency shifter, delay fiber, and fiber amplifier. It is shown both theoretically and experimentally that unwanted higher order frequency-shifted components induce distortion in the beat signal spectra, which significantly limits the maximum number of circulations. An effective technique is proposed and demonstrated for reducing the distortion by using optical filtering at the HRI output. Furthermore, a practical limit on the number of circulations is investigated by comparing the shape of observed beat signal spectra with theory. It is shown that the maximum delay is limited to about 180 km even with the use of the optical filtering technique.

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.