Terahertz pulse propagation in the near field and the far field

We present a detailed investigation of the propagation properties of beams of ultrashort terahertz (THz) pulses emitted from large-aperture (LA) antennas. The large area of the emitter is demonstrated to have substantial influence on the temporal pulse profile in both the near field and the far field. We perform a numerical analysis based on scalar and vectorial broadband diffraction theory and are able to distinguish between near-field and far-field contributions to the total THz signal. We find that the THz beam from a LA antenna propagates like a Gaussian beam and that the temporal profile of the THz pulse, measured in the near field, contains information about the temporal and spatial field distribution on the emitter surface, which is intrinsically connected to the carrier dynamics of the antenna substrate. As a result of pulse reshaping, focusing of the THz beam leads to a reduced relative pulse momentum, with implications in THz field-ionization experiments.     

Spatial chirp in the focusing of few-optical-cycle pulses by a mirror

We calculate the electric field of few-optical-cycle pulses at the focus of a perfectly conducting mirror by adding coherently the Airy diffraction patterns for each pulse frequency. We will show that the pulse suffers temporal spreading generated by a change in the spectrum of the pulse as a function of position in the focal plane, which introduces spatial chirp to the pulse. A double pulse appears near to the diffraction minima of the carrier frequency due to the variations in the spectra.     

Wave optical modelling of focusing of an ultra short pulse

The spatial–temporal evolution of an ultrashort pulse at different planes on propagation through a spherical lens is modelled using an efficient numerical algorithm. With this model it is possible to observe the on- and off-axis pulse evolution at any arbitrary plane. This model is applicable to pulses of arbitrary spatial and temporal shapes and can be used beyond paraxial approximation. We can obtain the exact amplitude information at any plane fairly easily. The asymmetry of the pulse shape at the focus is reported for the first time. The focusing of a pulse with TEM₀₁ spatial profile has been considered as an example and its evolution is analysed at different planes of propagation.     

Channel modeling of light signals propagating through a battlefield environment: analysis of channel spatial, angular, and temporal dispersion

Free-space optical communication (FSOC) is used to transmit a modulated beam of light through the atmosphere for broadband applications. Fundamental limitations of FSOC arise from the environment through which light propagates. We address transmitted light signal dispersion (spatial, angular, and temporal dispersion) in FSOC that operates in the battlefield environment. Light signals (photons) transmitted through the battlefield environment will interact with particles of man-made smoke such as fog oil, along the propagation path. Photon-particle interaction causes dispersion of light signals, which has significant effects on signal attenuation and pulse spread. We show that physical properties of battlefield particles play important roles in determining dispersion of received light signals. The correlation between spatial and angular dispersion is investigated as well, which has significant effects on receiver design issues. Moreover, our research indicates that temporal dispersion (delay spread) and the received power strongly depend on the receiver aperture size, field of view (FOV), and the position of the receiver relative to the optical axis of the transmitter. The results describe only specific scenarios for given types of battlefield particles. Generalization of the results requires additional work. Based on properties of the correlation, a sensitive receiver with a small FOV is needed that can find the line-of-sight photons and work with them.     

Spatial and temporal properties of ultrashort pulses propagating in free space

Abstract

By means of the Rayleigh diffraction integral and analytic signal complex representation, the propagation equation of ultrashort pulses in free space is derived, which permits us to study spatial and temporal properties of ultrashort pulses during propagation in free space. It is shown that the pulse deformation and broadening, spectrum redshifting, narrowing and distortion can take place with increasing diffraction angle, and the pulse form changes with propagation distance in the near field, but is preserved in the far field. A comparison with previous work is also made.     

Propagation of terahertz pulses in random media

We describe measurements of single-cycle terahertz pulse propagation in a random medium. The unique capabilities of terahertz time-domain spectroscopy permit the characterization of a multiply scattered field with unprecedented spatial and temporal resolution. With these results, we can develop a framework for understanding the statistics of broadband laser speckle. Also, the ability to extract information on the phase of the field opens up new possibilities for characterizing multiply scattered waves. We illustrate this with a simple example, which involves computing a time-windowed temporal correlation between fields measured at different spatial locations. This enables the identification of individual scattering events, and could lead to a new method for imaging in random media.     

Femtosecond single-shot correlation system: a time-domain approach

We introduce, analyze, and experimentally demonstrate what to the best of our knowledge is a new pulse correlation technique that is capable of real-time conversion of a femtosecond pulse sequence into its spatial image. Our technique uses a grating at the entrance of the system, thus introducing a transverse time delay (TTD) into the transform-limited reference pulse. The shaped signal pulses and the TTD reference pulse are mixed in a nonlinear optical crystal (LiB(3)O(5)), thus producing a second-harmonic field that carries the spatial image of the temporal shaped signal pulse. We show that the time scaling of the system is set by the magnification of the anamorphic imaging system as well as by the grating frequency and that the time window of the system is set by the size of the grating aperture. Our experimental results show a time window of ~20 ps. We also show that the chirp information of the shaped pulse can be recovered by measurement of the spectrum of the resulting second-harmonic field.     

声场计算模型的环境宽容性分析

浅海水声环境容易受到各种因素的影响,导致其环境参数具有很强的不确定性,依据环境宽容性选择快速、精确的声场计算模型是保证后续研究分析正确性的重要前提。以海水声速为例,简述了基于传播损失和声场互相关系数的计算模型环境宽容性分析方法。为定量描述环境和声场计算模型的失配情况,在研究浅海不确定环境对于声场空间相关性影响的基础上,结合水声环境不确定性推理模型,得到声场空间相关半径和传播损失概率分布可信区间,提出利用声场空间相关半径相对值来度量声场计算模型的环境宽容性,同时利用非嵌入式随机多项式展开(NON-Polynomial Chaos Expansion, NPCE)法,结合差值评定方法对得到的环境宽容区间进行验证,结果表明,利用声场相关半径相对值可以定量分析不确定性环境下声场计算模型的宽容性。     

Principles of calculating the dynamical response of misaligned complex resonant optical interferometers

In the long-baseline laser interferometers for measuring gravitational waves that are now under construction, understanding the dynamical response to small distortions such as angular alignment fluctuations presents a unique challenge. These interferometers comprise multiple coupled optical resonators with light storage times approaching 100 m. We present a basic formalism to calculate the frequency dependence of periodic variations in angular alignment and longitudinal displacement of the resonator mirrors. The electromagnetic field is decomposed into a superposition of higher-order spatial modes, Fourier frequency components, and polarization states. Alignment fluctuations and length variations of free-space propagation are represented by matrix operators that act on the multicomponent state vectors of the field.     

Adiabatic description of superfocusing of femtosecond plasmon polaritons

A surface plasmon polariton is a collective oscillation of free electrons at a metal–dielectric interface. As wave phenomena, surface plasmon polaritons can be focused with the use of an appropriate excitation geometry of metal structures. In the adiabatic approximation, we demonstrate a possibility to control nanoscale short pulse superfocusing based on generation of a radially polarized surface plasmon polariton mode of a conical metal needle in view of wave reflection. The results of numerical simulations of femtosecond pulse propagation along a nanoneedle are discussed. The space–time evolution of a pulse for the near field strongly depends on a linear chirp of an initial laser pulse, which can partially compensate wave dispersion. The field distribution is calculated for different metals, chirp parameters, cone opening angles and propagation distances. The electric field near a sharp tip is described as a field of a fictitious time-dependent electric dipole located at the tip apex.     

Synthesis of three-dimensional light fields with binary spatial light modulators

Computation of a binary spatial light modulator (SLM) pattern that generates a desired light field is a challenging quantization problem for which several algorithms have been proposed, mainly for far-field or Fourier plane reconstructions. We study this problem assuming that the desired light field is synthesized within a volumetric region in the non-far-field range after free space propagation from the SLM plane. We use Fresnel and Rayleigh-Sommerfeld scalar diffraction theories for propagation of light. We show that, when the desired field is confined to a sufficiently narrow region of space, the ideal gray-level complex-valued SLM pattern generating it becomes sufficiently low pass (oversampled) so it can be successfully halftoned into a binary SLM pattern by solving two decoupled real-valued constrained halftoning problems. Our simulation results indicate that, when the synthesis region is considered, the binary SLM is indistinguishable from a lower resolution full complex gray-level SLM. In our approach, free space propagation related computations are done only once at the beginning, and the rest of the computation time is spent on carrying out standard image halftoning.     

Universal space-time properties of X waves

Exact results concerning spatiotemporal universal features of three-dimensional propagation-invariant solutions of the wave equation (X waves) are derived. In particular, relations connecting the pulse transverse extension to the longitudinal coordinate and the propagation velocity to the spatial field distribution are obtained for the whole class of X waves.     

Polarization properties of a nematic liquid-crystal spatial light modulator for phase modulation

The polarization properties of a nematic zero-twist liquid-crystal (NLC) spatial light modulator (SLM) were studied. A large ratio between the liquid-crystal (LC) layer thickness and the pixel pitch combined with spatial variations in the applied electric field causes fringing fields between pixels. Depending on the LC alignment, the electric field components within the LC layer can result in a twist deformation. The produced inhomogeneous optical anisotropy affects the polarization of light propagating through the device. We experimentally examined polarization effects in different diffraction orders for both binary and blazed phase gratings. Simulations of the LC deformation together with finite-difference time-domain simulations for the optical propagation were used to calculate the corresponding far-field intensities. It was demonstrated how rigorous simulations of the NLC SLM properties can be used to understand the polarization features of different diffraction orders.     

Propagation of optical pulses with spatial and temporal dependence

A convenient approximate formula is proposed for the study of free-space propagation of spatial and temporal pulses with an identifiable carrier frequency. It does not contain a time derivative operation on the pulse's temporal envelope explicitly. It is shown that once a short (for example, picosecond or subpicosecond) pulse is created with a spatial and a temporal structure, it does not last forever. The approximation discussed is valid over a certain distance as dictated by the wave equation. Beyond this distance, the spatial and temporal characteristics begin to influence each other significantly. Two examples are presented. The first example is that of a pulse with a factored form of a spatial envelope times a temporal envelope. The second example is that of a clear aperture with a grating, by which pulse stretching or temporal distortion is examined and the result is in agreement with that found in the literature.     

Numerical simulation of a dual frequency all-optical flip-flop based on a nonlinear semiconductor distributed feedback laser structure

A new all-optical flip-flop generating light at two different wavelengths λ1 (state "a"), or λ2 (state "b") was suggested. It consists of an active layer and a nonlinear wave-guiding layer. Two parallel nonlinear gratings having different periods and periodic negative nonlinearities exist along the propagation direction in the wave-guiding layer. In state "a," the first grating provides the optical feedback for lasing, and the second grating is weak. In state "b," due to optical nonlinearity, the first grating weakens, and the second one provides the optical feedback for lasing. The refractive index nonlinearity is due to the direct absorption of photons at the Urbach tail. The device is triggered from state "a" to state "b" and vise versa by input optical pulses of wavelengths λ2 and λ1, respectively. The time domain simulations show switching dynamics in nanosecond time scale.     

Causality in propagation of a pulse in a nonlinear dispersive medium

We investigate the causal propagation of the pulse through dispersive media by very precise numerical solution of the coupled Maxwell–Bloch equations without any approximations about the strength of the input field. We study full nonlinear behaviour of the pulse propagation through solid state media like ruby and alexandrite. We have demonstrated that the information carried by the discontinuity, i.e. front of the pulse, moves inside the media with velocity c even though the peak of the pulse can travel either with sub-luminal or with super-luminal velocity. Our numerical demonstration is subject to the condition that the background refractive index of the medium is unity. We extend the argument of Levi-Civita to prove that the discontinuity would travel with velocity c even in a nonlinear medium.     

Dynamics of ultrashort light pulses in a semiconductor superlattice in the presence of a magnetic field

A system of equations that describes the propagation of ultrashort light pulses (optical solitons) in a semiconductor superlattice in the presence of a magnetic field is obtained using coupled Maxwell equations for the electromagnetic field and the Boltzmann equation written in the relaxation time approximation for the one-electron distribution function. It is shown that an initial linearly polarized light pulse induces a field with the orthogonal polarization in the sample. The dynamics of joint propagation of the initial and induced pulses in the sample is studied.     

Knob of the group velocity by the external field coupling two upper levels

We investigate how the external field coupling the two upper levels produces a variety of effects on the propagation of a weak electromagnetic pulse in a V-type atomic system. Due to the upper level (UL) coupling field, the dispersion of the system has been influenced by the relative phase. Then, subluminal and superluminal phenomena can be unified. Thus, the external field and the relative phase can be regarded as switches to manipulate light propagation between subluminal and superluminal.     

Elastic Gaussian wave packets in isotropic media

Summary The theory of Gaussian wave packet (GWP) propagation in elastic materials is developed. The GWP solutions are in the form of localized disturbances with Gaussian spatial envelopes at any instant in time. The method is explicitly time dependent, but is conceptually no more difficult than time harmonic ray theory. The equations of propagation and evolution are very similar to those of standard, elastodynamic ray theory, but include an extra degree of freedom not considered previously: the temporal width of the pulse. The theory is valid if the carrier wavelength is short in comparison with typical length scales in the medium. Interfaces of discontinuity in material properties give rise to reflected and transmitted GWPs. Explicit expressions are presented that relate the incident GWP to the reflected and transmitted GWPs. These results are illustrated by numerical simulations of a pulse incident upon a spherical interface.With 5 Figures     

脉冲激光成像探测系统回波信号仿真

研究激光脉冲回波信号特性并建立其数学模型,是应用回波信号处理技术处理回波,生成目标三维激光仿真图像的基础.首先建立了激光器发射脉冲信号能量在时间和空间上的分布模型,然后依据成像目标的激光图像仿真模板,采用累加激光脚印各采样区发射脉冲信号与对应目标散射面单位冲激响应卷积值的方法,生成了探测器接收回波仿真信号,最后分析了影响回波信号仿真精度的因素.通过对激光脚印采样区个数的合理设置实现了激光脉冲回波波形的精确仿真.