Sinusoidal Phase Modulation Research Articles

Optimization of smoothing by spectral dispersion with a sinusoidal phase modulation

In order to improve the propagation of a laser in a plasma, the intensity profile should be as uniform as possible. For this purpose, smoothing techniques are used. The most commonly used, smoothing by spectral dispersion (SSD), induces temporal fluctuations of the effective amplification length of Stimulated Brillouin scattering (SBS) or Stimulated Raman scattering (SRS). These fluctuations are random from shot to shot and may thus induce unpredictable levels of the efficient laser power used in laser-plasma experiments. Increasing the modulation frequency fm while maintaining the modulation bandwidth strongly reduces these fluctuations and even reduces the average SBS level. However, increasing fm has also an impact on laser propagation within the laser optical components. We show that, as long as chromatic dispersion is precompensated in the front-end, FM-to-AM conversion, a detrimental propagation effect, may remain sufficiently low and that anormal FM-to-AM conversion is not sensitive to the modulation frequency. Hence, there is no important bottleneck to an increase of the modulation frequency.

A Mach–Zehnder Fabry–Perot Hybrid Fibre-Optic Interferometer for a Large Measurement Range Based on the Kalman Filter

To solve the short working distance and small measurement range of an all-fibre interferometer, we proposed a Mach–Zehnder Fabry–Perot hybrid fibre-optic interferometry system based on sinusoidal phase modulation. In this paper, a low-finesse fibre interferometer with a larger linear operating range for displacement measurement is realised using a self-collimating probe and incorporating a Kalman filter-based phase demodulation algorithm. Through experimental comparisons, it is demonstrated that the interferometer proposed in this paper can effectively reduce the phase delay, compensate for the depth of modulation drift, and correct the error due to parasitic interference introduced by the optical path structure through the algorithm. A linear large measurement working range of 20 cm is realised.

A PGC demodulation scheme based on the Lissajous ellipse fitting for homodyne interferometer without using second harmonic carrier signal

This paper proposes a phase generated carrier (PGC) demodulation scheme for sinusoidal phase modulation interferometer (SPMI) that does not require a second harmonic carrier signal. In this scheme, an in-phase interference signal component with direct current (DC) bias is obtained by low-pass filtering the original interference signal, and a quadrature interference signal component is obtained by conventional means. The Lissajous figure formed by these two quadrature interference signal components is an ellipse whose center deviates from the origin of the I-Q coordinates. By fitting this ellipse, the major and minor axes and the center coordinates can be obtained. These elliptic parameters are then used to eliminate DC bias and normalize the amplitude of the quadrature signal components. Finally, the phase demodulation of the interference signal can be realized by using arctangent algorithm or differential cross multiplication (DCM) algorithm. The results of simulation and experiment have verified the validity and accuracy of the proposed PGC demodulation scheme, and show that it is insensitive to the phase modulation depth C. Compared with conventional PGC demodulation, this scheme requires lower depth of carrier phase modulation. The vibration measurement results indicate that the average signal-to-noise and distortion Ratio (SINAD) and total harmonic distortion (THD) values of demodulation results in the frequency range of 130 Hz to 250 Hz are 34 dB and -33 dB respectively. The proposed PGC demodulation scheme shows good performance in displacement measurement using SPMI.

Detection of Water Surface Acoustic Waves Using Sinusoidal Phase Modulation Interferometer and Prenormalized PGC-Arctan Algorithm

A sinusoidal phase modulation laser interferometer is proposed to detect water surface acoustic waves excited by underwater acoustic radiation, and an improved PGC-Arctan demodulation algorithm that combines prenormalization and Lissajous ellipse fitting is proposed to demodulate detection signals. In this paper, the effects of phase modulation depth, carrier phase delay, and interference signal visibility on the Lissajous figure formed by quadrature interference components are analyzed. The demodulation algorithm first uses the amplitudes of multiple Fourier spectral components of an interference signal to calculate the phase modulation depth C, and calculation of the carrier phase delay Vc is achieved through the introduction of a quadrature carrier signal. Then, certain coefficients regarding C and Vc are constructed for prenormalization of the two quadrature interference signal components to eliminate the local nonuniform widening phenomenon of Lissajous ellipse. Next, the outer and the inner contours are extracted from a uniformly widened Lissajous ellipse resulting from light intensity disturbance, and the axial ratio of the ellipse is obtained, which is used to correct the ratio of the quadrature interference signal to eliminate the effect of filter gain coefficients. At last, through the combination of an Arctan algorithm and a phase-unwrapping algorithm, high-precision demodulation of the interference signal is realized. A sinusoidal phase modulation interferometer was set up to detect water surface acoustic waves, and a series of detection experiments were carried out. The experiment results show that the detection method and demodulation algorithm described in this paper can accurately realize the measurement of weak water surface acoustic waves. The proposed algorithm shows less distortion in demodulation results, and its signal-to-noise distortion ratio is less than 20 dB at 500 Hz, which is significantly better than traditional algorithms. The experimental results demonstrate the effectiveness and accuracy of water surface acoustic wave detection using sinusoidal phase modulation interferometer.

SBS mitigation by sinusoidal phase modulation of a 1572 nm all-fiber amplifier for lidar CO2 sensing.

Lidar C O 2 sensing can be performed by 1572nm pulsed laser sources. This work presents the development of a fiber amplifier at this wavelength emitting 1µs FWHM Gaussian pulses at a repetition rate of 7.5kHz. We obtain the mitigation of stimulated Brillouin scattering (SBS) by shaping the seed laser spectrum into a frequency comb with sinusoidal phase modulation. This frequency comb is compatible with a coherent dual-comb spectroscopy (DCS) method for a targeted lidar C O 2 sensing application. The effect of the harmonics spacing and relative intensity on the SBS threshold is studied. Laser pulses are amplified up to 182µJ (182W peak power) from a single-mode erbium (Er) and ytterbium (Yb) co-doped fiber. Those results hold promise for seeding large mode area Er-Yb co-doped fiber power amplifiers.

Development of Band-Limitless Demodulation Method for Sinusoidal Phase Modulation Interferometry (Evaluation of Noise Floors, Maximum Measurement Speeds and Resolutions)

Development of Band-Limitless Demodulation Method for Sinusoidal Phase Modulation Interferometry (Evaluation of Noise Floors, Maximum Measurement Speeds and Resolutions)

On the improvement of smoothing by spectral dispersion efficiency for laser–plasma interaction

Large energetic laser facilities provide an amazing tool for bringing matter into high energy density states but achieving a good energy conversion requires to optically smooth the high-power laser beams. Optical smoothing reduces the laser spatial and temporal coherences, allowing to mitigate the development of unwanted laser–plasma instabilities (LPI). Two schemes have been mainly developed: polarization smoothing and smoothing by spectral dispersion. Here, we focus on the latter. Smoothing by spectral dispersion consists in broadening the spectrum usually through a sinusoidal phase modulation and dispersing it with an optical grating. It is usually considered that the modulation frequency should be equal to the inverse of the time delay of the grating, because it maximizes the number of uncorrelated speckles patterns at a given bandwidth. However, current optical smoothing designs are still not sufficient for mitigating LPI. Because the optical smoothing system possesses degrees of freedom, we propose to improve the optical smoothing efficiency by a better tuning of those parameters. Considering the Laser Mégajoule optical system framework, we show that an increase in the modulation frequency allows a better efficiency of the smoothing while keeping the same bandwidth. We assess the efficiency by looking at a better mitigation of the stimulated Brillouin scattering that, due to its dangerousness in hohlraums developed for inertial confinement fusion applications in the indirect drive scheme, serves as a witness instability.

Spectral broadening scheme for high stimulated Brillouin scattering thresholds on multi-harmonic linear frequency modulation

This paper proposes a spectral-broadening scheme for suppressing the stimulated Brillouin scattering (SBS) in fibers using multi-harmonic linear frequency modulation (LFM). The frequency tuning range of the LFM lasers is further expanded by incorporating sinusoidal phase modulation (PM) to achieve more effective spectrum spreading. Furthermore, the ability of multi-harmonic-LFM light sources to suppress SBS is investigated using the effective Brillouin gain spectra (BGS). Meanwhile, the experimental results reveal that at a 3 dB bandwidth of ∼480 MHz, the SBS thresholds of multi-harmonic-LFM light sources were improved by 8.36 times compared to a single-frequency laser, and by appropriately 69% compared to the LFM light sources. Because the spectra of the multi-harmonic-LFM light sources and the multifrequency-sinusoidal-PM light sources have a near-rectangular shape, the capacity of the two schemes to suppress SBS is comparable, which verifies the advantages of the multi-harmonic-LFM light sources in suppressing SBS. Our study also investigated the effects of frequency intervals between each chirp harmonic and the chirp period of multi-harmonic-LFM light sources on the suppression of SBS, which provides guidance for optimizing multi-harmonic-LFM light sources.

Asymmetrical Fault Detection in Induction Motors Through Elimination of Load Torque Oscillations Effects in the Slight Speed Variations and Steady-State Conditions

Recently, motor current signature analysis (MCSA) has been widely considered for fault detections due to its simplicity, availability, and cost-effectiveness. The rotor asymmetry fault (RAF) is the most common fault that occurs in induction machines. It is extremely challenging to detect RAF indices occurred at the vicinity of the supply frequency. Moreover, load torque oscillations (LTOs) <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">which</b> appear as a sinusoidal phase modulation of the supply frequency, exhibit similar indications as the RAF, especially in gearbox-based electromechanical systems. Since LTOs lead to false alarm of RAF, separation of LTOs indices from RAF characteristic components is inevitable. In this paper, normalized frequency domain energy operator (NFDEO) is evaluated for demodulation and separation of RAF and LTOs in steady-state and transient conditions. Moreover, the proposed method is tested in both with-and-without speed control strategies. In this regard, the effects of RAF in the presence of LTOs investigated through both synthetic signals and experimental data in steady-state and transient conditions with slight variation in rotor speed. The obtained results show that NFDEO along with Winger-Ville can effectively detect RAF in the presence of LTOs even with speed control strategy.

Manipulating dispersive wave emission via temporal sinusoidal phase modulation.

We report the dispersive wave (DW) emission from the Gaussian pulse with temporal sinusoidal phase (TSP) modulation. The TSP-induced chirp can enhance or cancel the chirp generated by self-phase modulation by properly selecting the modulation parameters of TSP, which can influence the nonlinear propagation of the TSP-modulated pulse. It is shown that the TSP can effectively control the resonant frequency and energy conversion efficiency of the DW emission. We give a modified phase-matching condition to predict the resonant frequencies, which agree with the simulation results obtained by numerically solving the nonlinear Schrödinger equation. The enhanced conversion efficiency of the DWs can be increased up to 28% with only TSP modulation. Our results can extend the application of temporal phase modulation technology for wavelength conversion, and broadband supercontinuum generation.

Pair production in inhomogeneous electric fields with phase modulation

Electron-positron pair production in spatial inhomogeneous electric fields with sinusoidal phase modulation is studied within the Dirac-Heisenberg-Wigner formalism. The focus is on discussing the effects of the modulation parameters on the momentum spectrum and the reduced particle number at various spatial scales. For the momentum spectrum, the interference effect becomes more and more remarkable with the increase of modulated amplitude or frequency, while the symmetry is severely destroyed with modulated amplitude. For the reduced particle number, it is greatly enhanced by about a few times and evenly one order of magnitude when modulation parameters are applied. Moreover, the effect of spatial scales on the reduced particle number is carefully examined, and it is found that it increases rapidly at small spatial scales, while it tends to be a constant at large spatial scales. We also obtain the optimal pair production that can be achieved through different modulations. These results can provide a possibility for realizing the optimal pair production by combining the advantages of field spatial inhomogeneity with different choices of phase modulation.

Measurements of phase distributions of optical vortices based on the sinusoidal phase modulation method

Vortex beams (VBs), a type of light beam with a spiral wavefront, have unique properties, such as the orbit angular momentum (OAM), and diverse applications in optical communications and optical trapping and tweezers. Therefore, accurate measurements and estimations of the phase distribution and topological charge are essential for their applications to ensure VB quality. In this paper, we employed a sinusoidal phase modulation (SPM) interferometry to measure the phase distributions of VBs and the topological charge of VBs were estimated by mean of a method of the process of unwrapped phase. The phase measurement of optical vortices generated by a spatial light modulator (SLM) demonstrated that the SPM interferometry-based technique had a high measurement accuracy with a simplified configuration. The estimation errors of the topological charges for various orders of VBs were within approximately 4%. The fluctuation in the surface of the SLM leading to the flatness of the wavefront was estimated to be 0.06 rad by 10 consecutive measurements

Absolute distance measurement using sinusoidal phase modulating frequency sweeping interferometry with a reference interferometer.

Frequency sweeping interferometry with reference interferometer based on sinusoidal phase modulating technique is proposed in this paper for absolute distance measurement. With the frequency of the external cavity diode laser (ECDL) swept continuously in sinusoidal, a HeNe laser was employed to monitor the drifts of the target and the reference length, and influences caused by drifts during the measurement were compensated in real time. Sinusoidal phase modulation with non-overlapping frequencies were applied to the two laser lights individually by two electro-optic modulators (EOM), and the interference phases corresponding to the two laser lights were extracted simultaneously using the phase generated carrier (PGC) demodulation based on frequency-division multiplex technique. Performance of the phase detection method has been verified by nanometer displacement measurements. Experimental results show that the measurement uncertainty can be considerably reduced by compensating the influences of drifts and by applying linear regression to get the ratio of interference phase changes between the measurement interferometer and the reference interferometer. Comparison of the absolute distance measurement with an incremental interferometer yields a measurement uncertainty of 10-5, which is in good agreement with the estimation of the measurement uncertainty.

Simultaneous Phase Detection of Multi-Wavelength Interferometry Based on Frequency Division Multiplexing

Simultaneous phases detection in multi-wavelength interferometry (MWLI) is essential for high-accuracy dynamic absolute distance measurement in high-end equipment manufacturing. To address this problem, a simultaneous phase detection scheme based on frequency-division multiplexing (FDM) technique is proposed in this paper. High-frequency sinusoidal phase modulation with non-overlapping frequencies were applied to multiple lasers individually using electro-optic modulators (EOMs), and interference phases of multiple wavelengths were extracted in parallel using phase generated carrier (PGC) demodulation technique from the FDM interference signal. Principles of FDM multi-wavelength interferometry and simultaneous phase detection scheme were illustrated. A FDM dual-wavelength interferometer was constructed to verify the performance of the proposed phase detection scheme by simulation analysis and experiments. Results of simulations show that the resolution, accuracy and nonlinear error of the two demodulated phases are all better than 0.01°. Experiments of nanometer displacement measurement further verified the good performance of the phase detection scheme and its feasibility in dynamic measurement.

Generation of high performance optical chirped pulse for distributed strain sensing application with high strain accuracy and larger measurement range.

A photonic approach for generating low frequency drifting noise, arbitrary and large frequency chirping rate (FCR) optical pulses based on the Kerr effect in the nonlinear optical fiber is theoretically analyzed and experimentally demonstrated. Due to the Kerr effect-induced sinusoidal phase modulation in the nonlinear fiber, high order Kerr pulse with a large chirping rate is generated. In the concept-proof experiments, the FCR of the mth Kerr pulse has been significantly improved by a factor of 2m+1. In addition, dynamic strain measurement along with a random fiber grating array (RFGA) sensor by using different order Kerr pulse is carried out for demonstrating a large strain measurement range with lower uncertainty sensing capability. Benefiting from the use of a single laser source and large FCR Kerr pulse, the system exhibits a 3.9 µɛ static strain measurable range, 0.24 µɛ measurement uncertainty by using -4th order Kerr pulse that has an FCR up to 0.8 GHz/ns. Note that the FCR of the chirped pulse could be further enhanced by using larger FCR chirped pulse seed or choosing higher order Kerr pulses.

High precision even-power phase modulation method for a self-mixing displacement sensor under the weak feedback regime.

A novel method called even-power phase modulation is proposed in a self-mixing displacement sensor to improve measuring accuracy, to the best of our knowledge, which is realized by combining the even-power fast algorithm with the sinusoidal phase-modulation method. By performing the even-power fast algorithm in the self-mixing interference system, the spectrum of harmonic components is broadened. In this case, the extracted first and second harmonic components in the frequency domain contain rich information, and the displacement of the target can be accurately reconstructed. The principle and signal processing approach are introduced in detail, and the simulation results show that the reconstruction error can be effectively reduced compared with the electro-optic modulator phase modulation method. A series of experiments at different vibration amplitudes is conducted to confirm the feasibility and effectiveness of the method. An amplitude of 120 nm is proved to be measurable, and the absolute error is 10 nm, which shows great potential in the field of non-contact nanometer vibration measurement sensors.

Group-velocity dispersion emulator using a time lens.

We report a novel method to continuously track the temporal evolution of an arbitrary complex waveform as it propagates through a group-velocity dispersion medium by using a single-frequency-driven phase modulator. The proposed method exploits the fact that the frequency spectrum of a given (input) waveform, following a suitable sinusoidal temporal phase modulation, exhibits the same shape as that of a dispersed version of the same temporal waveform after propagation through a prescribed amount of dispersion. In experiments, we track the dispersion-induced temporal evolution of different optical picosecond pulsed waveforms by tuning the frequency and/or amplitude of the phase modulation signal and observing the resulting shapes in the optical frequency domain. A good agreement is obtained between the measured spectra and predicted temporal shapes of the propagating waveform for different amounts of dispersion. Moreover, the method is successfully applied on a chirped optical pulse to find the optimal pulse compression conditions.

Self-correction of air refractive index in distance measurement using two-color sinusoidal phase modulating interferometry

A two-color sinusoidal phase modulating (SPM) interferometer based on electro-optic modulator (EOM) is devised for self-correction of air refractive index in distance measurement. Two laser sources with high frequency stability and close wavelengths (633 nm and 782 nm) are used in this scheme. High-accuracy phase demodulation was realized using phase generated carrier (PGC) demodulation techniques with an FPGA-based signal processing board. Experimental results of nanometer displacement measurements show that the resolution and accuracy of PGC demodulation is better than 1°, and the nonlinear error is less than 0.2°. Performance tests of two-color SPM interferometer compared with one-color interferometers under dynamic environment were implemented with an arm length difference of 4 m. The results show that, the measured distance of one-color interferometer drifts 4.8 μm in 600 s, which is caused by the deviation between the measured value of air refractive index and the actual value along the laser propagation path, and this drift reduces to ±1.5 μm using two-color interferometer without environmental sensing.

Research on resonance splitting under sinusoidal modulation in resonant optic fiber gyro

In this study, the sinusoidal phase modulation and demodulation principle in resonant fiber optic gyro (RFOG) are introduced. The RFOG simulation system is established, through which the relationship between resonance splitting and modulation frequency of dual-frequency sawtooth and sinusoidal signal is obtained. The resonance splitting is then explained based on sideband spectrum theory. The experimental device is built and the results show that there are obvious resonance splitting and distortion in linear region of demodulation output, when the sinusoidal frequency is higher than FWHM/2. Finally, the feasibility of the sideband frequency locking technology is verified by resonance splitting based on sideband spectrum theory, providing theoretical support for this novel technology, which can suppress backscattering noise effectively.

Focusing characteristics of linearly polarized Lorentz-Gaussian vortex beams with sinusoidal phase modulation.

Based on the vector diffraction theory, this paper investigates the focusing properties of linearly polarized Lorentz-Gaussian vortex beams with sinusoidal phase modulation and discusses the focused light intensity under different parameters in detail. Results show that the focus pattern in the horizontal direction at the focal region can be compressed by increasing the relative Gaussian parameter wx. As the relative Lorentz parameter γy increases, the focus pattern will separate in the vertical direction of the optical field. With the topological charge number m increases, a special tunable optical dark trap focusing mode can be obtained. Through changing the sinusoidal modulation parameter n, the regular trilateral, quadrangle, pentagon, and hexagon shapes of the focusing mode can be correspondingly constructed. Besides, on increasing propagation distance z, the focusing mode in the near focusing region gradually extends outside and always exhibits hexagon-shaped patterns, which reflects that this special focusing mode has a good stability. In addition, the optical gradient force distributions and the field intensity distributions in the longitudinal plane are also investigated to illuminate the applications of these alterable focal patterns. Those novel, to the best of our knowledge, findings may be helpful in applications such as optical manipulation, optical focusing, and imaging.