# Infinite charm brought by transformation optics
The basic principle of transformation optics is based on the spatial invariance of Maxwell equation. Simply put, change our physical space and keep the space of electromagnetic waves unchanged.
For example, the invisibility cloak, from the perspective of electromagnetic waves, the space it is in has not changed, so it can't feel the difference before and after the transformation, so it can't tell whether there is an object in the invisibility cloak. But from the perspective of our space, the space before and after the transformation is completely different. There is a "hole" in the transformed space, and this "hole" can hide objects.
Mathematically, Maxwell's equation outside the invisibility cloak has the same explanation before and after the transformation. This does not violate the uniqueness theorem, because the uniqueness theorem describes the situation of isotropic media. The composition of the invisibility cloak happens to be an anisotropic medium.
Invisibility cloak should be regarded as the most interesting thing brought by transformation optics. The possibility of invisibility cloak was proved mathematically for the first time. Of course, there are other applications.
Invisible cloak
Note that electromagnetic waves will bypass an object as if it does not exist for it.
Electromagnetic wave concentrator
The electromagnetic waves in the circle with radius c are all concentrated in the circle with radius a, and the electromagnetic waves outside are not affected.
Electromagnetic wave steering gear
The magnetic field in a circle with radius a rotates 90. Note that the electromagnetic waves outside are not affected.
Super patterning
Cover the star with a "bagel" to make it look magnified several times. Note that there is no dead angle amplification in 360, which is different from a magnifying glass.
Invisible waveguide
Curved waveguide
Optical black hole
As the name implies, all light will go back when it meets this device.
Optical black holes actually use electromagnetic materials to control the path of electromagnetic waves to simulate the path change of light falling into black holes. It's quite interesting from this point of view.
There are many other applications, so I won't list them one by one. Electromagnetic waves can be operated freely by changing optics, which is different from people's previous ideas.
# Electromagnetic waves pass through a very small waveguide tunnel.
For example, when electromagnetic waves pass through small channels, most of the energy will be reflected back. However, after filling this narrow channel with a medium with zero dielectric constant, all electromagnetic waves actually tunnel. This involves materials with zero refractive index, and electromagnetic waves propagate in narrow waveguides with infinite phase velocity.
# Super lens
As we all know, optical microscope has diffraction limit, which is about half the wavelength.
However, the super lens can break through the diffraction limit and distinguish objects with wavelength less than half.
Physically speaking, optical microscope only collects propagating waves, so it will lose some information, which is contained in evanescent waves.
The so-called propagating wave is a wave that can propagate, while the evanescent wave is a wave that cannot propagate, and its wave decays exponentially in the propagation direction. Superlens can transform evanescent waves into propagation waves, so that we can get the information in evanescent waves.
# Negative refractive index material
Negative refractive index materials were thought not to exist in the last century, but now they all exist. Metamaterials are usually used to achieve negative refraction, but photonic crystals are also possible.
Negative refractive index materials have many counter-intuitive properties, such as inverse Cherenkov radiation.
What is Cherenkov radiation?
Cherenkov radiation generally means that the speed of an object is greater than the propagation speed of waves in a medium. The waves here can be electromagnetic waves, sound waves, water waves and so on.
Therefore, the waterline generated by motorboats sliding on the water surface is Cherenkov radiation. The sonic boom caused by supersonic flight of aircraft is also due to Cherenkov radiation.
In electromagnetic waves:
For a medium with refractive index of 2, the limit velocity of electromagnetic wave is 0.5c(c is the velocity of electromagnetic wave in vacuum). If a high-energy particle is injected into this medium at a speed of 0.6c, the so-called Cherenkov radiation will be generated. So it should be like this:
Note that the direction of energy propagation here is the same as that of wave propagation.
If you replace this material with a negative refractive index material, something amazing will happen:
It can be seen that the direction of energy propagation is just opposite to the direction of wave propagation.
There is also the inverse Doppler effect, that is, when the electromagnetic wave source is far away from you, you find that its frequency is increasing.
Using negative refractive index materials, perfect lenses can be made, and the information carried by electromagnetic waves can be recovered, and there is no diffraction limit problem, that is, superlenses.
# Photonic Crystal
Photonic crystals are obtained by simulating crystals in solid physics. This is amazing. It has a forbidden band like a crystal.
First, let's look at how photonic crystals are realized. Here's the thing:
Blue is a common medium, such as a material with a dielectric constant of 8, and the rest is air.
Theoretically, this material cannot completely block the propagation of electromagnetic waves, but if it is arranged in this periodic structure, it can prohibit the propagation of electromagnetic waves at certain frequencies. So it can be used to bind electromagnetic waves and make waveguides:
Someone asked what this thing is for. The waveguide can be metal. But in the optical channel, metals are no longer metals, they become ordinary media. Therefore, photonic crystals have the potential to become optical devices. It can also be made into three dimensions, and it becomes something like an optical fiber. Note that it is different from optical fiber. Photonic crystals modulate light waves on a sub-wavelength scale.
# Surface wave
In fact, when I first came into contact with surface waves, I felt quite counterintuitive. Because in our impression, electromagnetic waves are all in metal waveguides or optical fibers, that is, like water pipes, water is confined in water pipes through walls.
But in fact, electromagnetic waves can exist on the surface of an object or on the interface between an object and a vacuum. In fact, there are many surface waves in nature, such as water waves, which are one kind of surface waves. This wave exists between water and air.
For electromagnetic waves, a strange surface wave is surface plasmon. This kind of surface wave generally exists in a relatively high frequency band, such as optical frequency band. This frequency band is close to the resonance frequency of electrons in some metals (such as gold and silver), and light and electrons can exchange energy directly, forming a very strange mode. According to Maxwell's parameters, the dielectric constant of metal is negative at this time.
This thing is very interesting. It can be made into waveguides or other optical devices. It can be used in future optical circuits.
Of course, it is also possible in low frequency bands, such as microwave bands. Although there is no material with negative dielectric constant in the microwave section in nature, it can be manufactured artificially. It can be made like this:
This thing is like a wire ... is it amazing that electromagnetic waves walk along this "line"?
# Topological optics
Topological insulator, which is the latest fire, is as influential as graphene. Of course, this thing first appeared in condensed matter physics and expanded to electromagnetic waves in the last year or two. Surprisingly, electromagnetic waves can only propagate on its surface, but not in this material. Moreover, when propagating on the surface, its mode is protected by topology. Simply put, a pattern can only spread in a specific direction, even if there are some obstacles, it can be bypassed.
So obviously, it is very suitable to be a waveguide, and there is no need to worry about the reflection caused by the electromagnetic wave turning outside. Just like the previous driveway, some cars drive forward and some cars drive backward, which is easy to cause traffic congestion. Now that we have built a one-way street, or expressway (consisting of two one-way streets forward and backward), the congestion problem will be alleviated.
Above the picture first ↓
# Slow light
As the name implies, let the light go slowly. One of the principles is electromagnetic induction transparency. This is actually a concept introduced from quantum physics. We can construct a two-level system from various structures or materials, that is, two different modes. In this two-level system, different energy levels or modes interact with each other, and under certain circumstances, electromagnetic induction transparency will appear.
This phenomenon can be achieved by metamaterials. A dark element resonates at a certain frequency point, and the quality factor of resonance is very high; The other is that bright elements resonate at the same frequency point, and the quality factor of resonance is relatively small. Then the two are superimposed and electromagnetic waves can be transmitted. Put a picture:
(c) is the result of the interaction between (a) and (b). We can observe that in C, electromagnetic waves propagate.
In fact, this is not the point. At this point, the group velocity of electromagnetic waves will be very small, that is, the light will stop there. Of course, this actually comes from condensed matter physics. What's really interesting may not be in my familiar field. Last year, scientists were able to stop the light 1 minute.
# Casimir Force and Spontaneous Radiation
Vacuum is not empty (zero point energy), but there are all kinds of photons produced and annihilated. Although the total field is zero, their disturbance is not zero.
Consider the above model. There are two metal plates with some gaps in the middle. Because electromagnetic waves have specific modes between metal plates, and because of the action of two plates, there cannot be some low-frequency modes between plates, that is to say, the fluctuation of some photons is limited. This causes the force outside the plate to be greater than the force inside the plate, and then produces Casimir force.
In addition, van der Waals force is actually a kind of Casimir force. So van der Waals force can also be explained by the above physics.
In addition, the disturbance in vacuum is also the fundamental cause of spontaneous emission. It is precisely because of the disturbance in vacuum that the energy level of electrons in atoms changes, thus emitting photons.
Now scientists generally study counter-intuitive things. The more counterintuitive, the more valuable. Every major breakthrough is refreshing people's world outlook.
Source: global physics, super mathematical modeling