Echelle grisms: an old challenge to the electromagnetic theory of gratings now resolved

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...

The nature of light has been a subject of inquiry since antiquity. In the seventeenth century, Isaac Newton performed experiments with lenses and prisms and was able to demonstrate that white light consists of the individual colors of the rainbow combined together. Newton explained his optics findings in terms of a "corpuscular" view of light, in which light was composed of streams of extremely tiny particles traveling at high speeds according to Newton's laws of motion.

The wavelengths of visible light ultimately limit the maximum theoretical resolution of images created by light microscopes. Most light microscopes can only magnify 1000X, and a few can magnify up to 1500X. Electrons, like electromagnetic radiation, can behave like waves, but with wavelengths of 0.005 nm, they produce significantly greater resolution up to 0.05 nm as compared to 500 nm for visible light. An electron microscope (EM) can create a sharp image that is magnified up to 2,000,000X.

Maxwell's equations for electromagnetic fields are related to source charges, either static or moving. These fields act on a test charge, whose trajectory can thus be determined using suitable boundary conditions. The objective of electromagnetism is thus theoretically complete.
However, although electric and magnetic fields were first introduced as mathematical constructs to simplify the description of mutual forces between charges, a natural question emerges from Maxwell's equations: What...

Electromagnetic (EM) radiation can be considered an oscillating electric and magnetic field propagating through a medium that can interact with matter in its path. The electric field in the radiation can interact with electrical charges in the atoms or molecules in the matter. On the other hand, the magnetic field can interact with the magnetic field in the atomic nucleus. The study of the interaction between electromagnetic radiation and matter is termed spectroscopy. Spectroscopy is the study...