Diffraction of electromagnetic waves

Yeh, C., 1964. Perturbation approach to the diffraction of electromagnetic waves by arbitrarily shaped dielectric obstacles, Phys. Rev., 135, A1193-A1201. 

Optical memory density is ultimately limited by the diffraction of electromagnetic waves. Present techniques have almost reached this limitation in those optical memories that are commercially available as CDs or DVDs. Even with an infinitely large objective lens with high numerical-aperture (NA) value, the bit data resolution distance for recording and reading cannot be reduced to less than half of the beam wavelength. 

Figure 12.46 Diffraction of electromagnetic waves by a crystal. The detector counts photons being diffracted at an angle 6, i.e., photons having wavelength A satisfying Eq. 12.18.

Fig. 4(a) presents the reflection spectra from the (111) composite surface at normal light incidence. The spectra were measured at two temperature values below the phase transition temperature (the semiconductor phase) and above it (the metallic phase). The observable peaks are due to the Bragg diffraction of electromagnetic waves by the periodic stmeture of the samples, characterizing the stop band in the [111] direction. 

In the intermediate case Ei < Eq and y T], we observe a photon energy (or frequency) bands either allowed or forbidden for the wave propagation. Therefore, there are some selection rules for the Bragg diffraction of electromagnetic waves on the periodical structure. Here, we see a deep analogy with the Bloch -de Broglie waves in crystals. For this reason we speak of photonic crystals. 

The problem consists in finding as precisely as possible the discontinuity position and in estimating its sub-surface depth. For this reason, a method has been developed based on the general theory of electromagnetic wave diffraction on the discontinuity [6], [7]. 

The next field of applications of elementary catastrophe theory are optical and quantum diffraction phenomena. In the description of short wave phenomena, such as propagation of electromagnetic waves, water waves, collisions of atoms and molecules or molecular photodissociation, a number of physical quantities occurring in a theoretical formulation of the phenomenon may be represented, using the principle of superposition, by the integral... 

The interpretation of electromagnetic waves as probability waves often leaves one with some feelings of unreality. If the wave only tells us relative probabilities for finding a photon at one point or another, one is entitled to ask whether the wave has physical reality, or if it is merely a mathematical device which allows us to analyze photon distribution, the photons being the physical reality. We will defer discussion of this question until a later section on electron diffraction. 

The Index of Refraction n describes the property of a media to change the direction of electromagnetic waves while passing through it. A measure of the diffraction is given by the quantity n = c / V, where c is the speed of the electromagnetic wave in free space and v the propagation velocity in the media. 

Bragg W L 1913 The diffraction of short electromagnetic waves by a crystal Proo. Camb. Phil. Soo. 17 43-58... 

Diffraction is based on wave interference, whether the wave is an electromagnetic wave (optical, x-ray, etc), or a quantum mechanical wave associated with a particle (electron, neutron, atom, etc), or any other kind of wave. To obtain infonnation about atomic positions, one exploits the interference between different scattering trajectories among atoms in a solid or at a surface, since this interference is very sensitive to differences in patii lengths and hence to relative atomic positions (see chapter B1.9). 

It has been shown by Herr Lane and his colleagues that the diffraction patterns which they obtain with x-rays and crystals are naturally explained by assuming the existence of very short electromagnetic waves. The spots of the pattern represent interference maxima of waves diffracted by... 

You can appreciate why scientists were puzzled The results of some experiments (the photoelectric effect) compelled them to the view that electromagnetic radiation is particlelike. The results of other experiments (diffraction) compelled them equally firmly to the view that electromagnetic radiation is wavelike. Thus we are brought to the heart of modern physics. Experiments oblige us to accept the wave-particle duality of electromagnetic radiation, in which the concepts of waves and particles blend together. In the wave model, the intensity of the radiation is proportional to the square of the amplitude of the wave. In the particle model, intensity is proportional to the number of photons present at each instant. 

Diffraction grating The most common gratings are made of reflecting or transparent sheets marked with fine parallel and equally spaced grooves or rulings. The grating separates polychromatic electromagnetic waves into their components. Similar results can be produced with a prism, but the mechanism is quite different. Fraunhofer used very fine parallel wires in his experiments. 

X-ray diffraction. The mechanism by which atoms diffract or scatter electromagnetic radiation via the coupling of the electron cloud of the atom to the incident oscillating electric field was discussed in the section on SERS. The X-rays scattered by an atom are the resultant of the waves... 

De Broglie s hypothesis of matter waves received experimental support in 1927. Researchers observed that streams of moving electrons produced diffraction patterns similar to those that are produced hy waves of electromagnetic radiation. Since diffraction involves the transmission of waves through a material, the observation seemed to support the idea that electrons had wave-like properties. 

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