I would put these into just two categories: (1) metamaterials/metasurfaces, and (2) photonic crystals.  HIS, RIS, and AMC are all variants of metamaterials and metasurfaces.  Metamaterials are essentially effective mu/eps media where the lattice spacing is too small to scatter waves.  HIS is a specific type of metasurface that exhibits a high permeability and low permittivity to give high impedance.  These are often used to flatten antennas because they do not phase shift a reflected wave and antennas can be placed immediately above them.  I do not know much about the reactive surfaces and artificial magnetic conductors, but they are in the metamaterial/metasurface family.

Photonic crystals can look similar to metamaterials, but their lattice spacing is large enough to scatter waves and it is a very complex arrangement of interference that gives rise to their strange properties.  An electromagnetic band gap (EBG) material is one that possesses a band of frequencies that are prohibited in any direction and any polarization.  The EBG acts like a mirror in this band.  There are other very use photonic crystals that do not possess a band gap so I don’t use EBG as the generic title for photonic crystals, but many still do.

Rumpf's answer is right!

BTW, people often confuse the FSS and metamaterials. if you want to distinguish metamaterials from FSS, I suggest you do it based on the design and application method. When people design or apply metamaterials they usually focus on how to realize specific constitutive parameters or how to apply the effective constitutive parameters of metamaterial to some novel devices. In contrast, the work about FSS just talks about the EM scattering of FSS.

Kang Ding

Let's confine the discussion within metasurface only.

Given a frequency, there can be a case, where mushroom ≠ EBG ≠ HIS ≠ AMC < RIS

HIS: Measured by the surface impedance specific to an excitation. I will say the surface impedance is an input impedance which is a complex number. A surface is called an HIS when it exhibits high "input impedance" at a certain frequency for a specific incidence, such as a plane wave of normal incidence. At this specific frequency, both the real part and the imaginary part are much higher than those at nearby frequencies. Therefore, HIS occurs at resonant POINT with high loss.

RIS: similar to HIS, it is the surface/input impedance measured by an incidence. However, the real part is zero instead of a peak like HIS. The imaginary part is non-zero but not a peak like HIS. On the bandwidth,, note that RIS happens over a VERY wide frequency band except for the resonant point. Oppositely, HIS occurs at a point only. On the loss, RIS is LOSSLESS but HIS is usually very LOSSY.

AMC: it is a surface that gives in-phase reflection.It can be an inductive impedance surface (a subclass of RIS ) without loss or an HIS with loss. In other words, this term does not represent a measurable quantity like HIS and RIS, but simply an effect concerning the reflection phase. Conceptually, it has nothing to do with EBG.

All the three cases above are frequently measured by the scattering coefficients due to illumination of space wave.

EBG: completely different, EBG describes a phenomena (not effect, not reflection, not impedance) specifically for wave that propagates along the surface. For EBG, there is a bandgap within which no propagating wave is allowed. EBG has nothing to do with plane wave.

All the four cases are source dependent, meaning that the results are generally different for wave mode in terms of different propagating direction, polarization, an d wave number.

Feng Han Lin

Thanks for your nice explanation. But, usullay we count the phase responce of unit cell -90 to 90 degree for HIS surface. What will be the phase response for RIS surface?

Which surface is a better choice to use as a reflector for dipole antenna? Is it true that HIS is mostly lossy material that is why it has very low radiation efficiency?

Is it possible to reduce the size of the Antenna by using HIS or RIS surface (not the thickness, i am concerned about the antenna size)

Hi Debraj Kar, thanks for your interest. Unfortunately, it is difficult to trace back the origin why plus/minus 90-degree becomes so popular. To my understanding, it is a condition for a certain context but somehow it is soon widely misused for all applications when there is no better argument.

1. What will be the phase response for RIS surface?

- For RIS surface, the phase response really depends what it is designed for. Please be noted that the properties observed in far-field scattering may not carry on to neaf-field problem, such as a dipole closely on top of an RIS.

2. Which surface is a better choice to use as a reflector for dipole antenna?

- Case by case. It would be more clear if the spec to be improved could define first. For example, if a highest gain is desired, nothing above suits but a parabolic PEC reflector. In case wideband low mutual-coupling is wanted, a surface designed below in the 2nd reference paper may be the best choice.

3. Is it true that HIS is mostly lossy material that is why it has very low radiation efficiency?

- Yes at the resonant frequency.

4. Is it possible to reduce the size of the Antenna by using HIS or RIS surface (not the thickness, i am concerned about the antenna size)

- Yes at the cost of reduced gain-bandwidth product.

- However, when you examine any comparison or argument, it is of vital importance to check first how the "antenna size" is defined. In my opinion, anything carrying currents is considered part of the antenna. If a surface is designed such that there is no induced currents on it at all, you may simply removing it without affecting anything. Therefore, one can never design a surface "bigger" than a “dipole” in order to "reduce" the size of “antenna”. Many people put a surface below a dipole so that the gain-bandwidth product can be significantly improved. However, when comparing the improvement, people somehow forget the size increase by the surface. In fact, the dipole becomes a primary exciter and the surface itself becomes the main radiator that carries a much larger portion of radiating currents, i.e., antenna = dipole + surface. To this point, you may find more detail in either of the following articles:

Article Low-Profile Wideband Metasurface Antennas Using Characterist...

Available online: https://ieeexplore.ieee.org/document/7858683

Article A Method of Suppressing Higher-Order Modes for Improving Rad...

Available online: https://ieeexplore.ieee.org/document/8292893

Article Truncated Impedance Sheet Model for Low-Profile Broadband No...

Available online: https://ieeexplore.ieee.org/document/8408836

- The three articles also provide solid evidence that the +/- 90° is absolutely not necessary for antenna applications, especially when the surface is coupled to its primary source in near-field region. A significant step forward is made to change the way one looks into a metasurface, from conventional far-field scattering properties (such as scattering coefficients and effective medium properties toward) to source-independent characteristic modes.

EBGs, HISs, AMCs are parts of Metamaterials technologies. Please see Anil Kumar Pandey. "Metamaterial-based Miniaturized Antenna Designs for Ultra-Wide Band Applications":https://on24static.akamaized.net/event/24/37/79/0/rt/1/documents/resourceList1600806762032/pandey2020102712301600806742695.pdf

This presentation thoroughly describes various uses of the AMC/EBG/RIS/HIS in antenna engineering,

https://fr.slideshare.net/ssuser947a58/amc-hisrisisomostructure-application-in-antenna-engineering

Metamaterial-based Miniaturized Antenna Designs for Ultra-Wide Band Applications

By: Anil Kumar Pandey

good question ...

can anyone tell the difference between EBG and FSS (frequency selective surface)?

can anyone give clear difference between metamaterials and EBG

FYI.