Pulsed beam reflection and transmission at a planar interface: exact solutions and local models

Pulsed beams (PB) are collimated space-time wavepackets that propagate along ray trajectories. Because they are localized in spacetime, they are useful in modeling applications addressing highly focused energy transfer, local (high resolution) probing of the propagation environment, etc. An important class of PB are the complex source PB (CSPB) which are modeled mathematically by a pulsed source located at a complex coordinate point. Their properties, physical realization and application have been explored extensively in recent years. A whole new class of wavepacket scattering problems can therefore be modeled by substituting complex source coordinates into the time-dependent Green's function of the environment. The response to the PB input can be evaluated exactly via the previously introduced spectral theory of transients (STT). This procedure is applied here for the canonical problem of a PB scattering at a planar interface separating two homogeneous half spaces. Exact field solutions are derived in closed form via the STT while extension to more general interface configurations is addressed by deriving approximate scattering models that depend on the local properties of the interrogation wavepacket and of the interface. Depending on the PB angle, these models involve PB reflection and refraction, evanescent wavepackets and local excitation of a head-wavepacket. Via numerical examples and parametrical studies, we emphasize both the physical phenomena and the new mathematical procedures of the full 3D solution.     

Physical source realization of complex source pulsed beams

Complex source pulsed beams (CSPB) are exact wave-packet solutions of the time-dependent wave equation that are modeled mathematically in terms of radiation from a pulsed point source located at a complex space-time coordinate. In the present paper, the physical source realization of the CSPB is explored. This is done in the framework of the acoustic field, as a concrete physical example, but a similar analysis can be applied for electromagnetic CSPB. The physical realization of the CSPB is addressed by deriving exact expressions for the acoustic source distribution in the real coordinate space that generates the CSPB, and by exploring the power and energy flux near these sources. The exact source distribution is of finite support. Special emphasis is placed on deriving simplified source functions and parametrization for the special case where the CSPB are well collimated.     

Non-dispersive closed form approximations for transient propagation and scattering of ray fields

Wave types employed for mathematical modeling of propagation and scattering in fairly general environments usually exhibit frequency dispersion, which may arise either from the material properties of the media or from boundary shapes and inhomogeneities even when bulk media are nondispersive. This feature creates difficulties for recovering transient fields from the harmonic constituents. At high frequencies, effects of dispersion are minimal and may be neglected in an asymptotic sense. For local plane wave spectral integrals representing ray-type fields, it is then possible to effect the inversion into the time domain explicitly, in closed form. Two principal methods, by Cagniard-DeHoop and by Chapman, have been employed in this context. The former has limited scope. The latter, while more broadly applicable, requires real values for the wavenumbers in the local plane wave spectra; this restriction forces results for certain ray fields into an inconvenient form, dissimilar from that for Cagniard-DeHoop inversion. The two methods are examined here from the perspective of a unified Spectral Theory of Transients that allows spectral wavenumbers to be real or complex and is shown to accommodate both formulations within the same spectral framework. The theory is described and illustrated on examples for which the Cagniard-DeHoop method is inapplicable and the Chapman method less convinient.     

Multi‐use high/low‐temperature and pressure compatible portable chamber for in situ grazing‐incidence X‐ray scattering studies

The multipurpose portable ultra‐high‐vacuum‐compatible chamber described in detail in this article has been designed to carry out grazing‐incidence X‐ray scattering techniques on the BM25‐SpLine CRG beamline at the ESRF. The chamber has a cylindrical form, built on a 360° beryllium double‐ended conflate flange (CF) nipple. The main advantage of this chamber design is the wide sample temperature range, which may be varied between 60 and 1000 K. Other advantages of using a cylinder are that the wall thickness is reduced to a minimum value, keeping maximal solid angle accessibility and keeping wall absorption of the incoming X‐ray beam constant. The heat exchanger is a customized compact liquid‐nitrogen (LN2) continuous‐flow cryostat. LN2 is transferred from a storage Dewar through a vacuum‐isolated transfer line to the heat exchanger. The sample is mounted on a molybdenum support on the heat exchanger, which is equipped with a BORALECTRIC heater element. The chamber versatility extends to the operating pressure, ranging from ultra‐high vacuum (<10^?10 mbar) to high pressure (up to 3 × 10³ mbar). In addition, it is equipped with several CF ports to allocate auxiliary components such as capillary gas‐inlet, viewports, leak valves, ion gun, turbo pump, etc., responding to a large variety of experiment requirements. A movable slits set‐up has been foreseen to reduce the background and diffuse scattering produced at the beryllium wall. Diffraction data can be recorded either with a point detector or with a bi‐dimensional CCD detector, or both detectors simultaneously. The system has been designed to carry out a multitude of experiments in a large variety of environments. The system feasibility is demonstrated by showing temperature‐dependence grazing‐incidence X‐ray diffraction and conductivity measurements on a 20 nm‐thick La_0.7Ca_0.3MnO₃ thin film grown on a SrTiO₃(001) substrate.