Erratum: Nonlinear dynamics of a self-mixing thin-slice solid-state laser subjected to Doppler-shifted optical feedback [Phys. Rev. E 104, 044203 (2021)].

This corrects the article DOI: 10.1103/PhysRevE.104.044203.

Nonlinear dynamics of a self-mixing thin-slice solid-state laser subjected to Doppler-shifted optical feedback.

Chaotic oscillations of a linearly polarized single longitudinal-mode thin-slice Nd:GdVO_{4} laser placed in a self-mixing laser Doppler velocity scheme were dynamically characterized in terms of the intensity probability distribution, joint time-frequency analysis, and short-term Fourier transformation of temporal evolutions, and the degree of disorder in the amplitude and phase of the long-term temporal evolutions. The transition from chaotic relaxation oscillations (ROs) to chaotic spiking oscillations (SOs) was explored via the chaotic itinerancy (CI) regime by increasing the feedback ratio toward the laser from a rotating scattering object. The intensity probability distribution was found to change from an exponential decay in the RO regime to an inverse power law in the SO regime, which manifests itself in self-organized critical behavior, while stochastic subharmonic frequency locking among the two periodicities of RO and SO takes place in the CI regime featuring quantum-noise (spontaneous-emission)-induced order in the amplitude and phase of the spiking oscillations. All of the experimental results were reproduced by numerical simulations of a model equation of a single-mode self-mixing solid-state laser subjected to Doppler-shifted optical feedback from a rotating scattering object.

Erratum: Nonlinear dynamics of a self-mixing thin-slice solid-state laser subjected to Doppler-shifted optical feedback [Phys. Rev. E 104, 044203 (2021)].

This corrects the article DOI: 10.1103/PhysRevE.104.044203.

High degree of chaos synchronization in pairs of transverse modes with parity-symmetric polarizations in a thin-slice solid-state vector laser and application to polarimetric secure self-mixing metrology: erratum.

In my previous Letter [Opt. Lett.45, 4907 (2020)OPLEDP0146-959210.1364/OL.401474], oscillation wavelengths corresponding to σ1-transition line, 4F3/2(1)→4I11/2(1), and σ2-transition line, 4F3/2(2)→4I11/2(2) were described in inverse. Here, the corrected correspondence between transition lines and oscillation wavelengths is addressed. The correction has no influence on the conclusions of the original Letter.

High degree of chaos synchronization in pairs of transverse modes with parity-symmetric polarizations in a thin-slice solid-state vector laser and application to polarimetric secure self-mixing metrology.

A high degree of chaos synchronization among transverse mode pairs with parity-symmetric polarizations was demonstrated in a laser-diode pumped thin-slice c-cut Nd:GdVO4 laser. The amplitude correlation coefficient greater than R>0.994 resulted from a non-reversing mirror symmetric-polarization-dependent structural change in the modal patterns, where chaotic dynamics of the whole system consisting of qualitatively different dynamics, which depend on the polarization crossing angle, resembled that of a chaotic single mode laser. A self-organized sender-receiver type of chaos synchronization of a single pair of modes among an infinite number of parity-symmetric polarizations, the associated chaotic camouflaging, and the extracting experiment of a self-mixing solid-state laser Doppler velocimetry signal were demonstrated.

Evaluation of resonance phenomena of mechanical oscillator by self-mixing solid-state laser Doppler vibrometry.

We performed self-mixing laser Doppler vibrometry on a vibrating oscillator consisting of a rigid-body laser-light-scattering object attached to a piezoelectric element driven by low-frequency AC voltage to evaluate its motion. The sideband spectrum reflecting the motion of the oscillator is observed in the power spectrum of the modulated wave. The time dependence of the intensity of the sideband spectrum is explained by Newton's second law assuming that the oscillator has a mechanical resonance frequency and undergoes simple vibration under the driving force, which depends on the deformation velocity of the piezoelectric element. Our results indicate that the motion of a slowly moving target with sub-nanometer displacement, which is difficult to measure by general laser Doppler vibrometry, can be evaluated with high spatial and frequency resolutions by detecting the sideband signal, which changes periodically at the driving frequency of the piezoelectric element.

Detection and counting of a submicrometer particle in liquid flow by self-mixing microchip Yb:YAG laser velocimetry.

We observed intermittent modulation by scattered light from a single submicrometer particle moving in the flow channel using a self-mixing microchip Yb:YAG laser Doppler velocimeter (LDV) under lateral beam access. The Doppler-shift frequency chirping (i.e., velocity change) was identified in accordance with a particle passage through the beam focus. Single particle counting, which obeys the Poisson distribution, was performed successfully over a long period of time. The experimental results have been reproduced by a numerical simulation. The LDV signal was increased over 20 dB for a 202-nm particle without chirping by collinear beam access with the laser beam axis aligned along the flow direction.

Laser-diode-pumped thin-slice c-cut Nd:GdVO4 multimode laser with coherent vector fields: erratum.

In a previous Letter [Opt. Lett.40, 1177 (2015), oscillation wavelengths corresponding to two σ-polarized transition lines 4F(3/2)(1)→ 4I(11/2)(1) and 4F(3/2)(2)→4I(11/2)(2) were described in inverse. Here, the corrected correspondence between transition lines and oscillation wavelengths is addressed.

Self-mixing thin-slice solid-state laser Doppler velocimetry with much less than one feedback photon per Doppler cycle.

The drastic shortening of a photon lifetime as compared with normal TEM00 operations has been shown to be associated with the formation of annular mode operations in a thin-slice Nd:GdVO4 laser with tilted laser diode end pumping. The 15 dB enhancement of the signal-to-noise ratio, owing to the shortened photon lifetime, has been demonstrated in the self-mixing laser Doppler velocimetry experiment in comparison with the TEM00 operations, where the minimum intensity feedback rate from a target to the laser for successful measurements was estimated to be -123 dB, which corresponds to 0.007 photon per Doppler cycle.

Laser-diode-pumped thin-slice c-cut Nd:GdVO(4) multimode laser with coherent vector fields.

Spontaneous formation of coherent vector fields, which results from synchronization of longitudinal modes of orthogonally polarized transverse modes, has been observed in a laser-diode (LD)-pumped thin-slice c-cut Nd:GdVO(4) laser with reflective end faces operating under the multi-longitudinal mode oscillation condition. The suppression of antiphase dynamics inherent to multimode solid-state lasers as well as the enhanced self-mixing interference effect as compared with a linearly polarized multimode laser have been identified.

Long-haul self-mixing interference and remote sensing of a distant moving target with a thin-slice solid-state laser.

An effective long-haul self-mixing interference effect has been observed in a thin-slice LiNdP4O12 (LNP) laser due to Doppler-shifted optical feedback from a distant target. The narrow spectral linewidth of the LNP laser, which was evaluated to be 16 kHz by heterodyne measurements, led to successful self-mixing laser Doppler velocimetry and vibrometry of targets placed 2.5 km away from the laser through single-mode optical fiber access.

Microchip solid-state cylindrical vector lasers with orthogonally polarized dual laser-diode end pumping.

We report a simple method for generating cylindrical vector beams directly from laser-diode (LD)-pumped microchip solid-state lasers by using dual end-pumping beams. Radially as well as azimuthally polarized vector field emissions have been generated from the common c-cut Nd:GdVO4 laser cavity merely by controlling the focus positions of orthogonally polarized LD off-axis pump beams. Hyperbolically polarized vector fields have also been observed, in which the cylindrical symmetry of vector fields is broken. Experimental results have been well reproduced by numerical simulations.

Polarization-dependent intensity noise in a microchip solid-state laser with spatially coherent polarization vector fields.

Polarization-resolved intensity noise has been investigated experimentally in a laser-diode-pumped isotropic microchip solid-state laser possessing spatially coherent polarization vector fields, which are formed by the coherent superposition of a pair of orthogonally polarized Ince-Gauss (IG) modes through the transverse mode locking. A large amount of noise reduction as compared with the total output, which is a coherent state, was observed for the stronger IG mode component by controlling the pump-beam focus.

Generation of high-order Hermite-Gaussian modes in end-pumped solid-state lasers for square vortex array laser beam generation.

This study reports the first systematic approach to the excitation of all high-order Hermite-Gaussian modes (HGMs) in end-pumped solid-state lasers. This study uses a metal-wire-inserted laser resonator accompanied with the "off axis pumping" approach. This study presents numerical analysis of the excitation of HGMs in end-pumped solid-state lasers and experimentally generated HGM patterns. This study also experimentally demonstrates the generation of an square vortex array laser beams by passing specific high-order HGMs (HGn,n + 1 or HGn + 1,n modes) through a Dove prism-embedded unbalanced Mach-Zehnder interferometer [Optics Express 16, 19934-19949]. The resulting square vortex array laser beams with embedded vortexes aligned in a square array can be applied to multi-spot dark optical traps in the future.

Analysis of molecular dynamics of colloidal particles in transported dilute samples by self-mixing laser Doppler velocimetry.

Colloidal particles in a liquid medium are transported with constant velocity, and dynamic light scattering experiments are performed on the samples by self-mixing laser Doppler velocimetry. The power spectrum of the modulated wave induced by the motion of the colloidal particles cannot be described by the well-known formula for flowing Brownian motion systems, i.e., a combination of Doppler shift, diffusion, and translation. Rather, the power spectrum was found to be described by the q-Gaussian distribution function. The molecular mechanism resulting in this anomalous line shape of the power spectrum is attributed to the anomalous molecular dynamics of colloidal particles in transported dilute samples, which satisfy a nonlinear Langevin equation.

Chaotic oscillations associated with the breakup of polarization entangled coherent states in a microchip solid-state laser.

We demonstrate the breakup of spatial-polarization entangled lasing patterns, which possess vector phase singularities, and the resultant dynamic instabilities featuring chaotic oscillations. The frequency splitting between a pair of Ince-Gauss (IG) lasing modes, originally forming a coherent entanglement state, and a self-excited additional nonorthogonal IG mode through a new class of transverse effect of self-injection pattern seeding, is shown to result in modal-interference-induced modulation at the beat frequency, leading to chaotic oscillations.

Self-mixing thin-slice solid-state laser metrology.

This paper reviews the dynamic effect of thin-slice solid-state lasers subjected to frequency-shifted optical feedback, which led to the discovery of the self-mixing modulation effect, and its applications to quantum-noise-limited versatile laser metrology systems with extreme optical sensitivity.

Determination of velocity of self-mobile phytoplankton using a self-mixing thin-slice solid-state laser.

We present an analysis of the shoulder-shaped power spectrum observed in the modulated laser output due to feedback light scattered from dynamic changes in self-mobile phytoplankton with flagella in seawater performed using a self-mixing laser Doppler vibrometry system. The power spectrum occasionally has shoulder-shaped broad frequency components superimposed on a Lorentz-type spectrum. This reflects the translational motion of phytoplankton moving across the beam-focus area. The velocity of phytoplankton in the focus area can be obtained by applying a curve fitting procedure to the power spectrum. Moreover, the average velocity and the velocity distribution of phytoplankton can be determined from curve fitting of the long-term power spectrum.

Three-channel three-dimensional self-mixing thin-slice solid-state laser-Doppler measurements.

We report successful real-time three-channel self-mixing laser-Doppler measurements with extreme optical sensitivity using a laser-diode-pumped thin-slice Nd:GdVO(4) laser in the carrier-frequency-division-multiplexing scheme with three pairs of acoustic optical modulators (i.e., frequency shifters) and a three-channel FM-wave demodulation circuit. We demonstrate (1) simultaneous independent measurement of three different nanometer-vibrating targets, (2) simultaneous measurements of small particles in Brownian motion from three directions, and (3) identification of the velocity vector of small particles moving in water flowing in a small-diameter glass pipe.

Generation of vortex array beams from a thin-slice solid-state laser with shaped wide-aperture laser-diode pumping.

We demonstrate vortex array-beam generations from a thin-slice, wide-aperture, solid-state laser with laser-diode end-pumping. Radial and rectangular vortex arrays were found to be formed in a controlled fashion with symmetric and asymmetric pump-beam profiles, respectively. Most of these vortices exhibited single-frequency oscillations arising from a spontaneous process of transverse mode locking of degenerate or nearly degenerate modes assisted by the laser nonlinearity. Single-frequency rectangular array beams consisting of a large number of vortices, e.g., closely packed 25, 36, or 46 vortex pixels, were generated, originating from Ince-Gaussian modes excited by the asymmetric pumping.