Theoretical analysis of the optical rotational Doppler effect under atmospheric turbulence by mode decomposition

The optical rotational Doppler effect associated with orbital angular momentum provides a new means for rotational velocity detection.In this paper,we investigate the influence of atmospheric turbulence on the rotational Doppler effect.First,we deduce the generalized formula of the rotational Doppler shift in atmospheric turbulence by mode decomposition.It is found that the rotational Doppler signal frequency spectrum will be broadened,and the bandwidth is related to the turbulence intensity.In addition,as the propagation distance increases,the bandwidth also increases.And when C_(n)^(2)≤5×10^(-15)m^(-2/3)and 2z≤2 km,the rotational Doppler signal frequency spectrum width d and the spiral spectrum width d_(0)satisfy the relationship d=2d_(0-1).Finally,we analyze the influence of mode crosstalk on the rotational Doppler effect,and the results show that it destroys the symmetrical distribution of the rotational Doppler spectrum about 2l·Ω/2π.This theoretical model enables us to better understand the generation of the rotational Doppler frequency and may help us better analyze the influence of the complex atmospheric environment on the rotational Doppler frequency.

TRANSVERSE VELOCITY ESTIMATION BASED ON HIGH-ORDER DOPPLER EFFECT OF MOVING OBJECT

The one-order phase of the echo changes if there is relative radial moving between the object and the radar, i.e. , the Doppler effect. The Doppler effect is widely used in radar signal processing. The transverse motion of the object cannot change the one-order phase of the echo, but the high-order phase. The high-order Doppler effect of the transverse moving target is presented and a new algorithm for obtaining the transverse velocity is given. The scalar velocity of a target moving steadily in any direction can be calculated with one-order and two-order items of the echo phase. The calculating method and simulating results are given. As the transverse speed is 900 km/h, the speed calculation error is less than 0. 06% if SNR of echo signal is higher than 0 dB.

Doppler effect of the rupture process of the great M_W7.9 Wenchuan earthquake

In this study we performed a classical spectrum analysis of seismic waveforms recorded at far field stations of the great MW7.9 Wenchuan earthquake to observe the shifts of the corner frequency with azimuth due to the Doppler effect.Our results show that this damaging great earthquake had a dominating rupture propagation direction of 64.0°.The equivalent radius of the fault rupture surface was estimated to be 33 km,yielding the rupture area of about 3 500 km2.Thus the length of the rupture fault surface is about 230 km if the depth（or width） extent is 15 km.The computer program developed in this study can quickly provide the information about the source of a future large（damaging） earthquake,which could be very useful for predicting aftershocks and planning the rescue operations.

Noticeable positive Doppler effect on optical bistability in an N-type active Raman gain atomic system

We theoretically investigate the Doppler effect on optical bistability in an N-type active Raman gain atomic system inside an optical ring cavity. It is shown that the Doppler effect can greatly enhance the dispersion and thus create the bistable behaviour or greatly increase the bistable region, which has been known as the positive Doppler effect on optical bistability. In addition, we find that a positive Doppler effect can change optical bistability from the hybrid dispersion-gain type to a dispersive type.

DETECTION ON MICRO-DOPPLER EFFECT BASED ON LASER COHERENT RADAR

A laser coherent detection system of 1550 nm wavelength was presented, and experimen- tal research on detecting micro-Doppler effect in a dynamic target was developed. In the study, the return signal in the time domain is decomposed into a set of components in different wavelet scales by multi-resolution wavelet analysis, and the components are associated with the vibrational motions in a target. Then micro-Doppler signatures are extracted by applying the reconstruction. During the course of the final data processing frequency analysis and time-frequency analysis are applied to analyze the vibrationM signals and estimate the motion parameters successfully. The experimental results indicate that the system can effectively detect micro-Doppler information in a moving target, and the tiny vibrational signatures also can be acquired effectively by wavelet multi-resolution analy- sis and time-frequency analysis.

The Modulation of Ionospheric Alfvén Resonator on Heating HF Waves and the Doppler Effect

The propagation of HF waves in IAR can produce many nonlinear effects, including the modulation effect of IAR on HF waves and the Doppler effect. To start with the dependence of the ionospheric electron temperature variations on the Alfvén resonant field, We discuss the mechanism of the modulation effect and lucubrate possible reasons for the Doppler effect. The results show that the Alfvén resonant field can have an observable modulation effect on HF waves while its mechanism is quite different from that of Schumann resonant field on HF waves. The depth of modulation of IAR on HF waves has a quasi\|quadratic relation with the Alfvén field, which directly inspires the formation of cross\|spectrum between ULF waves and HF waves and results in spectral peaks at some gyro\|frequencies of IAR. With respect to the Doppler effect during the propagation of HF waves in IAR, it is mainly caused by the motion of the high\|speed flyer and the drifting electrons and the frequency shift from the phase variation of the reflected waves can be neglected when the frequency of HF incident wave is high enough.

Experimental Studies of the Doppler Effect

Recent experimental results of the Doppler effect formula verification are reported. The moving emitters are hydrogen atoms in the excited state. The results of the work corroborate the classical not the relativistic,formula for the Doppler effect.

The Doppler effect induced by earthquakes:A case study of the Wenchuan MS8.0 earthquake

Seismologists have found that the first arrival frequencies of P waves at different seismic stations have different widths,that is,different periods or frequencies,and they think that this phenomenon can be used to identify whether a Doppler effect is induced by earthquakes.However,the fault rupture process of a real earthquake is so complex that it is difficult to identify a frequency shift similar to the Doppler effect.A method to identify whether a Doppler effect is induced by an earthquake is proposed here.If a seismic station is in the direction of fault rupture propagation,this station could observe a Doppler effect induced by the earthquake.The Doppler effect causes the frequency of the seismic wave to shift from low frequency to high frequency,and the high frequency amplitudes become mutually superimposed.Under the combined influences of the absorption effect,geometric spreading effect and Doppler effect,the high frequency amplitude of the seismic wave will gradually become higher than the low frequency amplitude with increasing epicentral distance.If we find that the high frequency amplitude is higher than the low frequency amplitude with increasing epicentral distance in the direction of fault rupture propagation,then there is a Doppler effect.The fault that generated the Wenchuan earthquake is a reverse fault,and its horizontal rupture propagation velocity was low.To link fault rupture propagation velocity with the Doppler effect and identify the Doppler effect more easily,we decompose three-component records into two directions:the direction of fault rupture propagation and the direction perpendicular to the fault rupture propagation along the fault plane.The initial components of the two directions are processed by wavelet transform.Several seismic stations in the direction of fault rupture propagation of the Wenchuan earthquake were selected,and it was found that with increasing epicentral distance,the high frequency amplitudes of the wavelet spectra become obviously higher than the low frequency amplitudes.It can be concluded that due to the existence of the Doppler effect,high frequency amplitudes can overcome the influences of the absorption and geometric spreading effects on seismic waves in the fault rupture propagation process.

Experimental Verification of Doppler Effect with the Refraction Method

The traditional method of measuring Doppler Effect is either reflection or dispersiion. This article clarifies that it can also verify the Doppler Effect with the refraction method. We have designed the experimental system with the method of optical heterodyne, using the refraction light beam from a prism, and made the experiment. The experimental results are in accordance with the theoretical calculation. It is very useful in some particular case, such as in Negative- Index Materials（NIM）, to verify the Doppler Effect with this method.

Exact Equations for the Light Doppler Effect

The influence of light source on the receiver as electromagnetic interaction is considered. The mechanical influence of the moving charged body on a motionless one is defined in the experimental laws of electrodynamics. These laws determine the changes of parameters of the light source that moves relatively the receiver. The laws of change of light frequency and its direction of the moving source are derived from the laws of electromagnetism. At small velocity of source movement they coincide with classical results: the Doppler effect and phenomenon of aberration. The interaction of the source and receiver depends only on their velocity of movement relatively each other. There is no world medium, the relative movement to which would influence the characteristics of light source.

Dual-point noncoaxial rotational Doppler effect towards synthetic OAM light fields for real-time rotating axis detection

Probing the axis of a rotator is important in astrophysics,aerospace,manufacturing,machinery,automation,and virtual reality,etc.Existing optical solutions commonly require multiple sequential measurements via symmetry-broken light fields,which make them time-consuming,inefficient,and prone to accumulated errors.Herein,we propose the concept of a dual-point noncoaxial rotational Doppler effect(DNRDE)and demonstrate a one-shot detection technique to solve this problem.An on-demand synthetic orbital angular momentum(OAM)light beam impinges on a rotating scatterer surface,supporting dual-point rotational Doppler shifts,in which the information of the rotating axis is acquired by comparing these two frequency shifts with a prescribed threshold.The existence of arbitrary dual-point Doppler shifts enables the one-time direct identification of rotating axis orientations,which is fundamentally inaccessible in single-point detection.This robust detection technique is compatible with generalised synthetic OAM light fields by utilising optical modal filters.Compared with traditional approaches,our DNRDE-driven detection approach exhibits a four-fold enhancement in measurement speed,higher energy efficiency,and superior accuracy with a maximal absolute measurement error of 2.23°.The proposed dual-point detection method holds great promise for detecting rotating bodies in various applications,such as astronomical surveys and industrial manufacturing.

Effect Due to the Particle Nature of the Doppler Shifted Radiation on the Dynamics of the Spherical Light Emitting Source

The Doppler effect is a phenomenon of intrinsic kinematic character. This paper analyzes the kinematic Doppler effect for the case where the source is moving and the observer is at rest in the classical limit. The particle nature properties of radiation are considered and how it affects the dynamics of the Source has been studied. The dynamical and kinematical equations have been derived by considering this effect. It has been conclusively shown that a moving light-emitting source experiences a finite recoil momentum in the direction opposite to the direction of motion and come to rest in finite time.

Orbital angular momentum complex spectrum analyzer for vortex light based on the rotational Doppler effect

The ability to measure the orbital angular momentum(OAM)distribution of vortex light is essential for OAM applications.Although there have been many studies on the measurement of OAM modes,it is difficult to quantitatively and instantaneously measure the power distribution among different OAM modes,let alone measure the phase distribution among them.In this work,we propose an OAM complex spectrum analyzer that enables simultaneous measurements of the power and phase distributions of OAM modes by employing the rotational Doppler effect.The original OAM mode distribution is mapped to an electrical spectrum of beat signals using a photodetector.The power and phase distributions of superimposed OAM beams are successfully retrieved by analyzing the electrical spectrum.We also extend the measurement technique to other spatial modes,such as linear polarization modes.These results represent a new landmark in spatial mode analysis and show great potential for applications in OAM-based systems and optical communication systems with mode-division multiplexing.

Design of new seismometer based on laser Doppler effect

In order to improve the resolution of seismic acquisition,a new seismic acquisition system based on tangential laser Doppler effect with an optimized differential optical configuration is proposed.The relative movement of the inertia object and the immobile frame is measured by laser Doppler effect,which can avoid the electromagnetic and thermometric interference,and the adoption of frequency-modulated (FM) transmission can improve the ability of anti-jamming.The frequency bandwidth is properly determined by analyzing the frequency of the Doppler signal.The velocity, displacement,acceleration, and frequency to be measured can be real-time acquired by frequency/velocity (F/V) converting the FM Doppler signal. A 100-dB dynamic range and the linear frequency range of 1.0 to 1000 Hz are realized.

Doppler effect in high-speed rail seismic wavefield and its application

We demonstrate by theoretical analysis that periodically distributed viaduct piers of high-speed rail result in the Doppler effect in the seismic wavefield of high-speed rail at specific frequencies and analyze the Doppler effect’s influence on the wavefield’s spectrum feature.We further verify our theoretical prediction by using observational data of the high-speed rail seismic wavefield in Rongcheng,Hebei Province,China.We find that the wavefield component with a noticeable Doppler effect vibrates in the propagation direction and only has a unique apparent wave speed,indicating that P-wave is dominant.Furthermore,we propose a speed measurement method based on the Doppler effect and measure the wave speed of the medium along the rail.Measurement results are highly stable and consistent.

Bichromatic laser frequency stabilization with Doppler effect and polarization spectroscopy

The interaction between polychromatic fields and atoms is an important subject in quantum optics.Frequency locking for small frequency interval multi-field is usually required in some experiments.In this letter,we experimentally demonstrate a holistic scheme for bichromatic laser frequency stabilization.Compared with traditional saturation absorption methods and complicated frequency shift schemes,offset locking for bichromatic fields is simply achieved using polarization spectroscopy and Doppler effect.Frequency locking with a wide-range asymmetry of the detuning is also shown.Our scheme makes laser spectroscopy experiments with polychromatic fields more convenient.

Symmetry detection of rotating patterns based on rotational Doppler effect of light

We propose a method for detecting the symmetry of rotating patterns based on the rotational Doppler effect(RDE)of light.The basic mechanisms of the RDE are introduced,and the spiral harmonic distribution of rotating patterns is analyzed.By irradiating the rotating pattern using a superimposed optical vortex and analyzing the amplitude of the RDE signal,the spiral harmonic distribution of the pattern can be measured,and then its symmetry can be detected.We demonstrate this method experimentally by using patterns with different symmetries and shapes.As the method does not need to receive the scattered light completely and accurately,it promises potential application in detecting symmetrical rotating objects at a long distance.

A Thermal Analogue of the Zel’Dovich Effect

We analyze in this work anisotropic heat conduction induced by a harmonically oscillating laser source incident on rotating conductors, exploiting an analogy with an effect discovered long ago, called the Zel’dovich effect. We re-covered the main results of a recently published paper that predicts the translational Doppler frequency shift of a thermal wave induced on a sample moving with uniform rectilinear motion. We extend then this framework to take into account the frequency shift of a thermal field propagating on a rotating platform. We show that it coincides with the rotational frequency shift which has been recently observed on surface acoustic waves and hydrodynamic surface waves, called rotational superradiance. Finally, we use an analogy with the Tolman effect to deduce a simple estimate of the average temperature gradient induced by rotation, showing the existence of a new cooling effect associated with heat torque transfer.

Phase modulation of propagation effect with Doppler broadening

This paper studies the propagation effect in a closed lambda-type three-level atomic system with Doppler broadening. It is shown that, Doppler broadening due to atomic motion and propagation effect associated with driving field depletion along the active medium decreases obviously the gain and output of the lasing without inversion （LWI）; the relative phase between the probe and driving fields has a remarkable modulation role to the propagation effect on LWI when Doppler broadening presents; by choosing suitable value of the relative phase, we can get the largest gain and output of LWI.

DETERMINATION OF THE DEBYE TEMPERATURE OF THE AMORPHOUS ALLOYS BY THE SECOND-ORDER DOPPLER EFFECT

I. INTRODUCTION The interaction of the atoms in a solid leads to the vibration of atoms around their equilibrium position and hence the lattice waves with various modes. Debye.analysed the energy of the lattice vibration basing on the consideration of the elastic waves in the