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What does refractive index mean?
The refractive index is calculated according to the angle of light before and after entering the object, and the formula is [sin(i)]/[sin(r)], where i= incident angle and r= refraction angle.

In recent two years, an artificial composite metamaterial called "left-handed medium" has become more and more popular in the fields of solid state physics, material science, optics and applied electromagnetism. This fictional substance was first considered by Russian Fislag in 1967. It has many strange properties, such as its refractive index is negative, and the energy propagation direction of electromagnetic waves in it is opposite to its wave vector (phase propagation direction). This material has negative refractive index because its dielectric constant and permeability are negative. We know from Maxwell's electromagnetic field equation that the electric field, magnetic field and wave vector (phase propagation direction) of the incident electromagnetic wave constitute a right-handed orthogonal system in the usual medium that we used to be familiar with (its dielectric constant and permeability are positive, and its refractive index is also positive, and now we can call it "right-handed chiral material"). But in this negative refractive index "left-handed material", the electric field, magnetic field and wave vector of electromagnetic wave constitute the left-handed system, which is why this material is named "left-handed material".

Because the remarkable feature of left-handed chiral materials is that their dielectric constant and permeability are negative, some people call them "double negative media (materials)". Usually we call it "negative refractive index material" or "negative material" for short; Some people call it "Fislag material" because it was first studied by Fislag after all, although it was still an imaginary material at that time.

In fact, the discovery of this negative refractive index left-handed material is equivalent to opening the other half of the world of matter (matter), and some people even compare it with Dirac's work of predicting "antimatter" (mirror matter) in 1928. Antimatter is such a substance, and its world laws are exactly the same as those in the mirror of our material world. For example, what they call left is what we call right. The mirror world is a left-handed world. Because once the positive and negative matter contact, they instantly annihilate into energy (photons), so if an "alien" reaches out his left hand to shake your hand, you should run away quickly to avoid mutual destruction. Comparing left-handed matter with antimatter does have some truth and similarity. Telling Dirac's story is very interesting and will give us some inspiration. 1928, Dirac got a set of positive energy solutions and a set of negative energy solutions when solving the relativistic wave equation of electrons he discovered. According to the habit of old physicists, the negative energy solution has no physical meaning (because according to experience, there is no substance with negative mass in nature), so it can be abandoned artificially. However, in the eyes of mathematicians, this practice of physicists seems lame and reckless, because "completeness of solutions" is a basic property and requirement of wave equations, which makes it possible to linearly expand arbitrary wave functions with a set of complete eigensolutions. Dirac gave up the negative energy solution, which caused his equation solution to be incomplete, which was absolutely not allowed in mathematics, so mathematicians advised Dirac not to give up that group of negative energy solutions. Physicists soon discovered that Dirac's negative energy solution was actually a solution describing "antimatter" (positively charged electrons), which was a great discovery. In order to maintain the beauty of mathematics, we would rather sacrifice some physical knowledge, or even break with it, or we may usher in a vast sky. We know that in the classical Maxwell equation, the square of the refractive index of a medium is equal to the product of dielectric coefficient and permeability, so the refractive index is equal to the square root of the product of dielectric coefficient and permeability (so there are positive roots and negative roots). Previously, researchers chose positive roots (positive refractive index) and habitually discarded negative roots (negative refractive index). Of course, negative refractive index media have never been encountered in ordinary materials, which makes it very "natural" to abandon negative roots. In this case, in 100 before the 1960s, did we also make the mistake that mathematicians accused "old physicists"? It seems that no one has consciously considered this problem, and it was not until Fislag first took the initiative to study the possible optical and electromagnetic properties of this medium more than 30 years ago that the situation changed slightly.

Fislag's brilliant and rich paper was first published in Russian in a Soviet academic journal in 1967. Farley of Britain translated it into English and republished it in another academic journal of Soviet physics the following year (1968). Unfortunately, Farley falsely claimed that Fislag's original paper was published in 1964. This led some researchers who did not consult the original literature to claim that Fislag put forward the concept of "left-handed substance" in 1964, and then said it was in 1968. Actually, it's not. Fislag put forward the concept of "left-handed substance" in 1967.