WEBVTT Kind: captions Language: en 00:00:02.580 --> 00:00:07.020 Hello 00:00:31.320 --> 00:00:37.800 students, welcome to lecture 28 of the online course on Nanophotonics, Plasmonics 00:00:37.800 --> 00:00:43.740 and Metamaterials. Today's lecture will be on Metasurfaces and Frequency Selective Surfaces. 00:00:44.400 --> 00:00:49.320 So here is the lecture outline, we will look into the basics of metasurfaces, 00:00:50.400 --> 00:00:57.060 their application towards phase modulation and some other applications and then we will move on 00:00:57.060 --> 00:01:03.240 to frequency selective surfaces. We will see their definition, we will look into the fundamentals 00:01:03.240 --> 00:01:10.500 and also discuss their applications. So metasurfaces when it comes to mind, 00:01:11.220 --> 00:01:17.160 it is basically a two dimensional metamaterial with sub wavelength periodicity 00:01:18.180 --> 00:01:25.320 and this metasurfaces are able to demonstrate unusual electromagnetic properties and it can 00:01:25.320 --> 00:01:32.520 vary over a frequency range from microwave to terahertz to optical. There are resonating 00:01:32.520 --> 00:01:40.020 metamaterials which can be tailored by tuning the geometry of its unit cells or meta atoms. 00:01:41.460 --> 00:01:50.280 So conventionally they are used for phase change and focusing of electromagnetic waves at optical 00:01:50.280 --> 00:01:57.600 frequency in the far field region. So here is an illustration of a typical metasurface. So 00:01:57.600 --> 00:02:03.780 you see it is a very thin, it is a basically 2D material with all these unit cells which 00:02:03.780 --> 00:02:11.820 are basically working on the phase of this incident terahertz wave. It can be terahertz, 00:02:11.820 --> 00:02:16.620 microwave or optical depending on the frequency range you are looking at. 00:02:16.620 --> 00:02:23.280 But what it can do, it can modulate the phase or the amplitude or the polarization. So that 00:02:23.280 --> 00:02:29.640 way you can actually get polarization, modulation, spatial beams, active control, focusing, hologram. 00:02:30.480 --> 00:02:37.200 All these different things can be generated by using metasurfaces. So a formal definition 00:02:37.200 --> 00:02:45.360 for metasurface is basically an ultra thin array of sub wavelength scale metallic elements which 00:02:45.360 --> 00:02:51.840 are deposited in periodic, aperiodic or random patterns on the surface of a dielectric substrate. 00:02:51.840 --> 00:02:57.720 And the shapes of the individual elements and their geometry of the layout on the surface, 00:02:58.680 --> 00:03:04.260 they endow the metasurfaces with distinctive optical properties. 00:03:04.920 --> 00:03:10.020 And if you think of the origin of these spatial effects that comes from the metasurfaces, 00:03:10.020 --> 00:03:14.580 they are basically a consequence of coupling of light and the surface plus 00:03:14.580 --> 00:03:19.920 bond propagation waves that generate at the metal dielectric boundary. 00:03:20.700 --> 00:03:27.060 So today we will look at a comparison of metasurface with metamaterials. 00:03:27.060 --> 00:03:32.160 So if you remember metamaterials, they are basically 3D materials which are able to 00:03:32.160 --> 00:03:39.480 provide artificial permeability and permittivity. So if you remember the split tree resonator array 00:03:40.440 --> 00:03:48.480 positioned on a metallic wire, that was able to give you negative permittivity as well as negative 00:03:48.480 --> 00:03:55.560 permeability. So what we do, we can actually model the system as an effective permeability, 00:03:55.560 --> 00:04:03.000 mu effective or epsilon effective. So this is typically a 3D version, that is the 00:04:03.000 --> 00:04:10.680 periodic cells, sorry the unit cells are repeated in periodic fashion in all three dimensions. 00:04:13.320 --> 00:04:19.500 On the other hand, you can think of metasurface which is basically a 2D version. So here the 00:04:19.500 --> 00:04:27.120 periodic arrangement of unit cell happens in two lateral dimensions, the thickness is very little. 00:04:28.020 --> 00:04:33.600 So how it can help? So it can actually change the amplitude, frequency, 00:04:33.600 --> 00:04:39.960 polarization or phase of the incident wave. So here is an example, say if right circularly 00:04:39.960 --> 00:04:45.780 polarized light falls on the metasurface, it may give you a left circularly polarized light. 00:04:47.340 --> 00:04:52.860 You can also think of left circularly polarized light falling and some part 00:04:52.860 --> 00:04:58.440 of it getting reflected. So it is blocking the left circularly 00:04:58.440 --> 00:05:04.260 polarized light to go through. So this kind of applications may be possible. 00:05:04.260 --> 00:05:12.660 So let us look into the basics of how phase modulation can be obtained through metasurfaces. 00:05:13.560 --> 00:05:18.780 So let us assume a wave that is traveling along the z direction as shown in the figure. 00:05:20.640 --> 00:05:26.940 And on the transmission through a dielectric plate of fixed thickness that is d 00:05:29.700 --> 00:05:36.000 and graded refractive index, so the refractive index is given as n xy, 00:05:36.660 --> 00:05:45.180 so it is in the xy plane. So this is z direction, so the xy plane is basically the vertical plane. 00:05:46.620 --> 00:05:53.040 And in that case the wave will undergo a spatially varying phase shift 00:05:54.180 --> 00:05:58.920 which modified its wavefront. So you can write the phase shift phi 00:05:59.520 --> 00:06:07.380 xy as n xy k naught d. So here you can see this is the free space wavelength. 00:06:07.380 --> 00:06:17.640 As soon as it enters the medium with a refractive index n xy, so the wavelengths get shorter. So you 00:06:17.640 --> 00:06:24.240 can see the wave looks compressed. When it comes out it again retains the same kind of wavelength 00:06:24.240 --> 00:06:32.280 in vacuum. So here the variation is in xy plane. You are seeing this, this is the z direction. 00:06:33.540 --> 00:06:41.340 So this is how it changes. Now achieving a phase shift of 2 pi requires a local 00:06:41.340 --> 00:06:46.200 thickness which is equivalent to the wavelength of the light in that medium. 00:06:46.200 --> 00:06:53.100 So that is how you can actually get a phase shift of 2 pi. So d has to be equal to lambda in that 00:06:53.100 --> 00:06:59.580 particular medium. Now a planar metasurface has the merit that it can introduce a phase shift of 00:06:59.580 --> 00:07:04.800 similar magnitude with far less thickness and this is where things become interesting. 00:07:05.340 --> 00:07:09.840 There the same amount of phase shift can now be achieved using metasurface instead 00:07:09.840 --> 00:07:16.140 of using this dielectric plate. You can use a very very thin metasurface which is only 00:07:16.140 --> 00:07:24.960 couple of nanometers thin and still you can get a similar kind of effect. Normally lambda 00:07:24.960 --> 00:07:32.640 in optics it is like in micrometers, orders of micrometers you can think of. So if you think of 00:07:32.640 --> 00:07:36.840 telecommunication wavelength it is 1. 55 micron. So in that case to achieve 00:07:36.840 --> 00:07:41.820 2 pi phase shift you will require lambda thickness of this material. 00:07:43.140 --> 00:07:51.780 So that is typically 1.55 divided by n that will be the lambda in this particular case but that is 00:07:51.780 --> 00:08:00.360 also in micrometer range. But metasurface can help you achieve that with a nanometer scale thickness. 00:08:01.020 --> 00:08:07.740 Now what is the magic in this metasurface? So the metallic elements that you see in the metasurface 00:08:07.740 --> 00:08:13.980 that function much like optical antennas which can modify the optical wavefronts. 00:08:15.060 --> 00:08:22.740 So when you think of resonant antennas they act as scatterers and they can introduce a frequency 00:08:22.740 --> 00:08:29.040 dependent phase shift which can range from minus pi to pi for the frequencies below and 00:08:29.040 --> 00:08:37.740 above resonance. So a spatially varying phase shift like phi xy may be implemented by making 00:08:37.740 --> 00:08:46.020 use of a metasurface which comprises elements of spatially graded size because along x and y there 00:08:46.020 --> 00:08:54.000 is a variation in the phase shift. So the elements need not be same along x and y you have to change 00:08:54.000 --> 00:09:00.660 their size and geometry so that you are able to get spatially varying resonance frequencies. 00:09:00.660 --> 00:09:10.260 I will explain this with example very soon. So an incoming wave of fixed frequency is then subjected 00:09:10.260 --> 00:09:16.260 to this spatially varying phase shift so that the metasurface can now act as a phase modulator. 00:09:18.000 --> 00:09:23.520 So let us take this particular example where the metasurface 00:09:24.960 --> 00:09:29.820 is basically an array of metallic elements. So these elements that you see these are metallic 00:09:29.820 --> 00:09:37.680 elements. So the metallic elements the element size and geometry are same along the y direction 00:09:37.680 --> 00:09:44.700 but along z direction they are different. So that way the phase will be changing 00:09:45.420 --> 00:09:52.560 along the x direction. So the phases so this is just an example of how you can 00:09:52.560 --> 00:09:58.440 change phase along one particular direction. So here you can see the shapes of the elements 00:09:59.040 --> 00:10:06.180 are engineered such that the phase shift they introduce becomes a linear function like phi 00:10:06.180 --> 00:10:13.320 equals qx for one of the polarization components. So here it becomes a linear function along x. 00:10:14.880 --> 00:10:21.900 Now since these metasurfaces are ultra thin they can be modeled as optical components that 00:10:21.900 --> 00:10:29.880 introduces a spatially varying phase shift or you can say phase discontinuity because a phase shift 00:10:30.780 --> 00:10:35.340 that takes place over a distance d equals 0 can be thought of as a 00:10:35.340 --> 00:10:40.620 discontinuity and the thickness of this metasurface is like almost 0. 00:10:40.620 --> 00:10:46.980 So you can say that they introduce spatially varying phase discontinuities. 00:10:47.820 --> 00:10:54.540 Now what is the benefit by doing phase modulation from these metasurfaces you can actually 00:10:54.540 --> 00:11:07.500 modify the incoming optical phase front. So like this you have seen you can use in the 00:11:07.500 --> 00:11:13.740 same manner like plane transfer and plates they may allow the light to simply go through without 00:11:13.740 --> 00:11:20.040 modulating the phase front but when you take prism you can actually send it at a particular 00:11:20.040 --> 00:11:26.700 angle depending on the prism angle alpha. So all these functionalities can be achieved 00:11:26.700 --> 00:11:33.000 not only these two the work of a lens which does the focusing at a particular focal point at a 00:11:33.000 --> 00:11:39.300 distance f or diffraction grating or graded index plate which also does focusing kind of application 00:11:39.300 --> 00:11:48.060 all these components can be literally replaced by metasurfaces. So the design of the constituent 00:11:48.720 --> 00:11:56.340 elements need to be changed depending on the application. So this is what a solitary feature 00:11:56.340 --> 00:12:03.780 of this approach of using metasurface is that the wave will undergo minimal spatial spread 00:12:03.780 --> 00:12:12.420 or diffraction as it crosses the infinitesimal small metasurface. So this is a very good benefit 00:12:12.420 --> 00:12:18.900 of using metasurface because the thickness is almost 0 so it will have very minimal diffraction 00:12:18.900 --> 00:12:27.120 or you can say minimal spatial spreading. So that is why people are trying to replace 00:12:27.120 --> 00:12:35.580 all these bulky optical components using this ultra-thin metasurfaces. Now let us look into how 00:12:35.580 --> 00:12:44.520 this phase modulation works. So let us consider a phase which is phi xy that can vary linearly 00:12:45.900 --> 00:12:52.080 along this metasurface at a rate q. So q is nothing but the rate of phase change. 00:12:52.080 --> 00:12:58.620 So you can write phi equals qx because in this case it is only changing along x direction. 00:12:58.620 --> 00:13:04.860 So this is the same metasurface that you have seen before. So it is changing only along x 00:13:04.860 --> 00:13:12.480 along y it is same. Now the complex amplitude of any incoming wave can then be modulated by a 00:13:12.480 --> 00:13:20.340 factor exponential minus jqx. So this is the phase that will be modulate coming into the picture. 00:13:21.360 --> 00:13:28.260 So which is basically a periodic function of the spatial frequency vx that is q over 2 pi. 00:13:28.260 --> 00:13:33.960 So this is the spatial frequency of those elements that introduces this phase. 00:13:34.500 --> 00:13:40.800 So now look into this figure. So this figure basically shows a negative reflection and 00:13:40.800 --> 00:13:49.560 negative refraction at the boundary between the two media of refractive index n1 and n2 when the 00:13:49.560 --> 00:14:00.360 metasurface is basically present at the interface. So here an incoming plane wave of wave vector k1 00:14:01.080 --> 00:14:10.440 which has got an incident angle of theta 1 and it will generate a refracted wave with wave vector 00:14:10.440 --> 00:14:16.800 k2 but it is basically a negative refraction. So instead of going that side it is basically coming 00:14:16.800 --> 00:14:21.900 towards on the other side of the normal. So the angle here is theta 2. 00:14:22.680 --> 00:14:28.440 Similarly some part of the incoming wave will be reflected back but here also we are considering 00:14:28.440 --> 00:14:36.960 negative reflection. So k3 is the reflected wave vector and the angle of reflection is theta 3. 00:14:38.460 --> 00:14:46.560 So what has to be done for this wave to exist or this condition to exist you have to go through 00:14:46.560 --> 00:14:53.340 the phase matching condition for the incident and refracted waves as well as for the incident and 00:14:53.340 --> 00:14:59.280 the reflected waves at the metasurface boundary. So this is the metasurface boundary and you can 00:14:59.280 --> 00:15:08.160 see that all the wave vectors are drawn here. So this is k3 the reflected one this is k2 the 00:15:08.160 --> 00:15:16.200 refracted one k1 is the incident one and this is the vector of the phase change. 00:15:17.880 --> 00:15:28.620 And this is n1 k0 that is n2 k0. So now to ensure the phase matching at both sides of the surface 00:15:28.620 --> 00:15:35.700 as we have seen in this figure what we have to do we have to look for the component of the vector k2 00:15:35.700 --> 00:15:42.360 parallel to the surface. So that will be basically the sine theta component and that should match 00:15:42.360 --> 00:15:49.800 the same component of k1 the surface parallel component of k1 that will be again the sine theta 00:15:49.800 --> 00:15:59.700 component plus that q vector. And q is basically the vector of magnitude small q that points in 00:15:59.700 --> 00:16:06.120 positive x direction or in the x direction because it is changing in x. So you can take it like that. 00:16:06.840 --> 00:16:14.880 So if you do that you can actually put that for the reflected wave you can do the similar kind of 00:16:14.880 --> 00:16:22.080 exercise which is basically you have to look for the parallel component to the surface that will 00:16:22.080 --> 00:16:32.340 be the sine theta component here theta will be theta 3 and that should match your k1 plus q. 00:16:34.080 --> 00:16:41.280 So this way you can actually obtain the conditions and find out the phase matching conditions. 00:16:41.880 --> 00:16:48.240 So hence if the metasurface lies at the boundary between the two ordinary medium 00:16:48.240 --> 00:16:55.020 of refractive indices n1 and n2 its presence can cause the conventional 00:16:55.020 --> 00:17:01.440 Snell's law of refraction and reflection to assume this particular modified form. 00:17:01.980 --> 00:17:07.680 So as I was talking about the phase matching so here you can see what is happening. So n2 00:17:09.780 --> 00:17:19.020 k0 that is basically your k2 the sine component that is sine theta 2 so that is the component 00:17:19.020 --> 00:17:25.680 of the refracted wave parallel to the surface that is same as n1 k0 that is nothing but k1 00:17:26.400 --> 00:17:32.160 and its parallel component to the surface that is sine theta 1 plus q. 00:17:32.940 --> 00:17:42.300 Similarly for the refracted wave you can write n1 k0 that is basically k3 sine theta 3 equals 00:17:42.300 --> 00:17:49.800 n1 k0 that is k1 sine theta 1 plus q. So this is how you are actually adding 00:17:49.800 --> 00:17:57.660 this particular factor q in your reflection and reflection equations. So these are the 00:17:57.660 --> 00:18:03.540 metasurface refraction and reflection equations. So these are basically modified Snell's law 00:18:03.540 --> 00:18:11.880 where you have introduced your particular design parameter into this law. So here we have already 00:18:11.880 --> 00:18:19.380 discussed theta 1 theta 2 theta 3 are basically the incidence refraction and reflection angles and 00:18:20.100 --> 00:18:29.640 by appropriate choice of the magnitude and sine of q you can actually make this work like a negative 00:18:29.640 --> 00:18:36.480 refractive or negative reflection as well as negative refraction kind of surface as we have 00:18:37.080 --> 00:18:44.460 considered till now. So this is how a metasurface is able to get into the 00:18:44.460 --> 00:18:52.320 Snell's law and allow you that modification of the refraction and reflection characteristics. 00:18:52.320 --> 00:18:59.220 And as you can see in this equations when you put q equals 0 that means along the x 00:18:59.220 --> 00:19:07.200 axis there is no change in the phase that means it's become a normal dielectric material q is 0 00:19:07.920 --> 00:19:16.920 this goes back to normal Snell's law. Now you can also write so if you take this k naught on 00:19:16.920 --> 00:19:23.760 the other side and n 2 you can write as n t that is the transmitted one and one you 00:19:23.760 --> 00:19:31.860 write as n i that is the incident one and theta 2 is basically theta 3 is basically the can see 00:19:31.860 --> 00:19:38.520 here theta 3 is basically the reflected angle so you can write a different notation something like 00:19:39.120 --> 00:19:46.200 theta r and theta i for the incident angle if you use this kind of notation. So here you are 00:19:46.740 --> 00:19:53.820 dividing so you are taking this term on the left side and taking k naught common and send it on 00:19:53.820 --> 00:19:57.960 the right side. So what you have k naught can be written as lambda naught over 2 pi 00:19:57.960 --> 00:20:04.620 and q that is the rate of phase change can be written as d phi x over d x because only along 00:20:04.620 --> 00:20:11.460 x your phase is changing. So this is also another form of this modified equations. 00:20:13.560 --> 00:20:20.280 So here you can see the generalized Snell's law of refraction so this is one medium this is another 00:20:20.280 --> 00:20:27.840 medium and there is a metal surface that you can see here at the boundary. So, depending on how 00:20:27.840 --> 00:20:36.060 you are designing q you can actually make it work like ordinary surface where you will have ordinary 00:20:36.060 --> 00:20:43.620 reflection and ordinary refraction or you can choose the amplitude and phase of q in such a 00:20:43.620 --> 00:20:50.940 way that it can give you anomalous reflection the red line or anomalous refraction this is the red 00:20:50.940 --> 00:20:57.120 line again. So it depends on the design of the metal surface whether you can get a ordinary 00:20:58.080 --> 00:21:03.120 reflection refraction characteristic or some extraordinary thing anomalous means which is not 00:21:03.120 --> 00:21:11.040 the normal one something opposite to the normal one. So here q as I told you this is basically 00:21:11.040 --> 00:21:16.620 the gradient of the phase discontinuity along the interface and this is where 00:21:17.220 --> 00:21:24.900 the meta-atom design comes into picture. So this is given by the meta-atoms of the meta-surface. 00:21:25.680 --> 00:21:35.580 So, this equations also tell you that if there is no change this part becomes 0 it is a typical 00:21:35.580 --> 00:21:43.200 Snell's law. So you can actually make them go in any particular direction depending on whatever 00:21:43.200 --> 00:21:50.520 is the value here. So if you choose a suitable constant gradient for the phase discontinuity 00:21:50.520 --> 00:21:57.600 along the interface that is whatever you will choose your d phi over dx to be you can make 00:21:57.600 --> 00:22:07.500 the refracted or the transmitted and the reflected wave to go in any direction. So you get a complete 00:22:07.500 --> 00:22:14.400 control on the direction of reflection as well as refraction by introducing this 00:22:15.000 --> 00:22:22.140 d phi over dx that is the q and that is how meta-surface is gaining so much of attention. 00:22:24.120 --> 00:22:28.440 So for a phase discontinuity phi x that varies slowly with the position 00:22:28.440 --> 00:22:34.260 x you can say that the derivative may be regarded as a local spatial frequency. 00:22:34.980 --> 00:22:44.580 So this quantity also determines the local tilt imparted on a incoming wave and thus the angle of 00:22:44.580 --> 00:22:53.880 reflection and refraction also becomes a function of x. So this approach can be clearly seen to be 00:22:53.880 --> 00:23:01.020 generalized to meta-surfaces that introduces a two-dimensional phase discontinuity. So right now 00:23:01.020 --> 00:23:09.600 we just saw one example of one-dimensional phase discontinuity you can actually make it 2d and that 00:23:09.600 --> 00:23:17.340 that gives you that phi xy. So in that case the q vector will be basically the gradient grad of phi 00:23:18.000 --> 00:23:25.380 and this vector represents the magnitude and the direction of the local spatial frequency of the 00:23:25.380 --> 00:23:32.520 phase modulation. So that will determine which way the reflected and transmitted wave can travel. 00:23:33.240 --> 00:23:38.940 So here is the summary of the meta-surfaces. So we understood that the meta-surface can be designed 00:23:38.940 --> 00:23:48.960 to introduce desired local tilts in the wave front of the incoming wave in both xz and yz planes 00:23:49.680 --> 00:23:57.060 much like the antenna array or an optical phase plate ok. So the meta-surface can be engineered 00:23:57.060 --> 00:24:03.900 to introduce position dependent amplitude modulation which can be imparted by the 00:24:03.900 --> 00:24:11.580 shape of the local elements or the meta-atoms. The combination of phase and amplitude modulation can 00:24:11.580 --> 00:24:18.900 serve as a hologram with complex transmittance that is designed to simulate the wave front of 00:24:18.900 --> 00:24:26.820 light generated by an object. So here are the main understandings of this meta-surface. So 00:24:27.480 --> 00:24:32.580 we understood light propagation with phase discontinuities which 00:24:32.580 --> 00:24:39.480 are basically introduced by meta-surfaces. Now by engineering a phase discontinuity along 00:24:39.480 --> 00:24:48.960 an interface you are able to fully steer the light wave front and accomplish some unparalleled 00:24:48.960 --> 00:24:56.160 control of anomalous reflection and refraction which is described by generalized Snell's law 00:24:56.700 --> 00:25:03.540 ok. So we will take some example here. So as shown in the figure so you have got a V-shape resonator. 00:25:04.200 --> 00:25:11.760 So there are two ways light can fall one is this S that is this particular direction we 00:25:11.760 --> 00:25:17.880 can call it as a symmetric direction or A that is asymmetric direction. So when light 00:25:17.880 --> 00:25:26.040 falls or the electric field is along this S vector you can excite symmetric mode on 00:25:26.040 --> 00:25:35.700 the two branches of this V-shape resonator. The angle is 45 degree ok and what you see here 00:25:35.700 --> 00:25:42.900 is basically the current distribution which is represented by the colors ok. So the blue line 00:25:42.900 --> 00:25:48.360 shows current distribution for the symmetric case the red one shows for the asymmetric case and the 00:25:48.360 --> 00:25:56.220 brighter the color larger is the current. And the current flow direction is also shown here ok 00:25:57.480 --> 00:26:05.700 through this arrows. Now in this case what happens you can also take mirror image of 00:26:05.700 --> 00:26:14.160 this particular antennas and they also do similar kind of properties and you can get 00:26:14.160 --> 00:26:21.420 the components of the scattered electric fields just that they will be pi phase difference from 00:26:22.020 --> 00:26:29.460 this one. So just by rotating the antenna you can create a pi phase difference ok. 00:26:30.120 --> 00:26:35.220 So in the symmetric mode if you look into the current distribution in each arm 00:26:35.820 --> 00:26:44.820 ok it approximates that of an individual straight antenna of length h. So this is length h ok 00:26:45.540 --> 00:26:53.940 and therefore the first order antenna resonance can occur at h equals lambda effective by 2. 00:26:54.540 --> 00:26:59.220 So what is lambda effective that is the effective wavelength. So in symmetric mode 00:26:59.220 --> 00:27:05.220 h equals lambda effective by 2 whereas when you go for anti symmetric mode ok. 00:27:05.940 --> 00:27:11.580 So anti symmetric mode this is the direction of the electric field ok it is along this a axis. 00:27:11.580 --> 00:27:18.360 So you can see the current distribution is actually in the entire arm ok. 00:27:19.140 --> 00:27:29.820 So in that case the total length is 2h and that is equal to lambda effective by 2 ok. So 00:27:29.820 --> 00:27:37.500 you can also say that the current distribution in each arm approximates that one half of the 00:27:38.160 --> 00:27:44.400 straight antenna of length 2h that you can see here. So here the overall length 00:27:44.400 --> 00:27:50.100 antenna length is 2h and the condition is basically 2h equals lambda by 2 ok. 00:27:51.180 --> 00:27:58.320 So this is how the symmetric and anti symmetric modes will operate differently ok. 00:27:59.700 --> 00:28:05.460 So you can also see the analytically calculated amplitude so this is basically the amplitude 00:28:05.460 --> 00:28:14.520 shift and this is the phase shift. So this is different length or you can say height h of 00:28:14.520 --> 00:28:21.060 the antenna and these are the different delta angle that is basically the opening between 00:28:21.060 --> 00:28:29.040 the two arms or you can say the angle between the two arms ok. So what we are seeing here 00:28:29.580 --> 00:28:34.980 so analytically it has been calculated what happens to the amplitude and phase shift of 00:28:34.980 --> 00:28:41.820 this cross polarized scattered light by this V antenna. Now if they are made of gold rods so 00:28:41.820 --> 00:28:48.840 gold rods they are basically having cylindrical or circular cross section. So if you see take the 00:28:48.840 --> 00:28:56.340 cross section they are basically circle so these are rods ok and their height or length h is varied 00:28:56.340 --> 00:29:02.700 and the angle is also varied and the wavelength is kept fixed lambda naught equals 8 mm. 00:29:04.920 --> 00:29:12.120 So what happens in this case so you see the four circles ok so these four circles 00:29:12.120 --> 00:29:19.380 basically show that you are basically changing the angle ok between them. 00:29:19.920 --> 00:29:26.160 So the optical property of the rod of the same length so here you are keeping the length same, 00:29:26.160 --> 00:29:34.800 but you are changing the angle between them and you are comparing it with a flat antenna of the 00:29:34.800 --> 00:29:44.640 same length. So you can see how the amplitude as well as the phase changes ok in this two case. 00:29:45.360 --> 00:29:53.880 So here the blue and dashed curves they correspond to the resonance peaks of the symmetric and anti 00:29:53.880 --> 00:30:00.180 symmetric mode. So symmetric mode is this one sorry this one anti symmetric mode is this one. 00:30:00.720 --> 00:30:07.620 So we are only talking about like this particular case so you can only think of the top case not 00:30:07.620 --> 00:30:13.920 the bottom one. But then if you look at these four antennas what is happening here you also 00:30:13.920 --> 00:30:20.880 correspondingly see the phase pattern. So when they are detuned from the resonance peaks ok 00:30:21.600 --> 00:30:28.980 as indicated by the circles in (c) here you can see the circles ok. You can see that there is a 00:30:28.980 --> 00:30:36.180 incremental phase shift this guy is having you know 90 degree then you have 45 degree 00:30:36.180 --> 00:30:45.180 then you have 0 degree and then you have minus 45 degree. So this is how the phase of the cross 00:30:45.180 --> 00:30:53.340 polarized scattered light is changing you by changing only the design of the elements. 00:30:54.000 --> 00:31:01.020 So if you start opening up this antennas so this is a V type of antenna and then you start 00:31:01.740 --> 00:31:07.860 opening them up you will actually get incremental phase of pi by 4 00:31:08.760 --> 00:31:17.220 getting changed from this design to this design. Now if you do the mirror symmetry mirror structure 00:31:17.220 --> 00:31:25.440 that is this one and this one ok you can actually get additional pi phase shift introduced. So you 00:31:25.440 --> 00:31:33.120 actually got many many elements which can give you your desired phase shifts. So, this is evident by 00:31:33.120 --> 00:31:40.620 observing the currents so because they do have completely different current pattern obviously 00:31:40.620 --> 00:31:48.060 they are 180 degree out of phase or you can say pi is the phase different between this one and this 00:31:48.060 --> 00:31:58.080 one ok. So they if this is giving you 45 degree this will give you 45 plus pi ok like that. 00:31:58.800 --> 00:32:05.700 So with that people have done some experiments with the matter surface. So this is a set of 8 00:32:05.700 --> 00:32:13.620 antennas that has been taken but you see there are basically 4 antennas and then they are repeated. 00:32:13.620 --> 00:32:20.820 So this is how the antennas are taken and then you take this as a unit cell and then you repeat 00:32:20.820 --> 00:32:28.200 it. So this is an SEM image of the antenna array which is fabricated on a silicon wafer. 00:32:28.200 --> 00:32:33.120 The unit cell is basically this ones which are highlighted in yellow these are all gold 00:32:33.120 --> 00:32:40.500 V shaped antenna the width is 220 nanometer and the thickness is 50 nanometer and the 00:32:40.500 --> 00:32:47.880 repeat period with a periodicity of 11 mm ok. So that is the periodicity in x direction. So this 00:32:47.880 --> 00:32:56.460 is x direction horizontal one so the periodicity is 11 mm ok the whole thing repeats like that and 00:32:56.460 --> 00:33:02.340 along this direction along the y direction you have 1.5 micrometer as the periodicity. 00:33:02.940 --> 00:33:09.300 So these antennas are designed in such a way that they have equal scattering amplitude so 00:33:09.300 --> 00:33:16.380 each of them will scatter the same amplitude but they will have a constant phase difference of pi 00:33:16.380 --> 00:33:20.880 by 4 between the neighbors from this one to this one pi by 4 difference from this one to this one 00:33:20.880 --> 00:33:26.880 pi by 4 difference and so on. So let us see what is the purpose of doing this so if you look into 00:33:26.880 --> 00:33:34.380 the simulation study so this is the 8 antennas that you have seen ok so they are basically 00:33:35.220 --> 00:33:41.220 created from this 4 antennas repeated again. So you can also see that their 00:33:41.220 --> 00:33:49.680 amplitude is pretty much same just that they have a phase that increments as pi by 4. 00:33:49.680 --> 00:33:56.520 So this is the silicon substrate on which the antennas are kept so this is the point where the 00:33:56.520 --> 00:34:07.140 antennas are placed and you can actually see that when ok this particular plot shows the scattered 00:34:07.140 --> 00:34:13.200 electric field which is polarized in the x direction for a y-polarized plane wave excitation 00:34:13.200 --> 00:34:19.440 at the normal incidence from the silicon substrate. So this is the silicon substrate 00:34:19.440 --> 00:34:26.820 part and it is located below this z equals 0 line and another important thing to notice here is that 00:34:26.820 --> 00:34:34.020 the antennas are equally spaced at sub wavelength separation of gamma by 8 where gamma is basically 00:34:34.020 --> 00:34:41.100 the length of the unit cell. So, total length is gamma so you have equally spaced them ok and 00:34:41.880 --> 00:34:50.700 this is how the spacing is 0 gamma by 8 gamma by 4, 3 gamma by 8 and so on ok. Now what happens if 00:34:50.700 --> 00:35:00.840 you draw the phase front ok you will see that this particular tilted red straight line shows you the 00:35:00.840 --> 00:35:07.380 envelope of the projection of the spherical waves that are scattered by these antennas onto the 00:35:07.380 --> 00:35:13.980 x-ray plane ok. So that way you are able to see that you are actually able to steer the beam. 00:35:13.980 --> 00:35:19.500 The beam normally it would have been this black dashed line but because they are incrementally 00:35:19.500 --> 00:35:27.360 adding pi by 4 phase ok you are able to tilt the beam or steer the beam. So that way a very very 00:35:27.360 --> 00:35:35.580 thin surface can do beam steering ok. So that is only one particular application which has caught 00:35:35.580 --> 00:35:42.540 the attention initial attention of the metasurface or all the scientific community at large. There 00:35:42.540 --> 00:35:47.940 are other applications also like metasurface holography, metasurface polarizer, metasurface 00:35:47.940 --> 00:35:54.660 lens, sensing, cloaking, beam steering, absorber, hyperspectral imaging. I believe 00:35:54.660 --> 00:36:00.060 in the initial lectures when we are talking about the applications of metasurfaces I have 00:36:00.060 --> 00:36:05.220 discussed all these applications in details. Now you can go back and revisit that lecture and 00:36:05.220 --> 00:36:11.640 now you will be able to make more sense that how metasurface is allowing you to achieve all this. 00:36:11.640 --> 00:36:18.120 Now let us look into another important topic which is frequency selected surfaces. 00:36:19.140 --> 00:36:25.080 So when we talk about frequency selective surfaces it is basically a periodic structure with two 00:36:25.080 --> 00:36:31.500 dimensional arrays of identical elements which are arranged on a dielectric substrate. This kind of 00:36:32.760 --> 00:36:41.544 surfaces when incoming plane wave falls on them they can be either transmitted so that 00:36:41.544 --> 00:36:48.060 is a pass band or reflected so that gives you a stop band ok which can completely 00:36:48.060 --> 00:36:54.600 block or selectively pass or something like that depending on the nature of the element that you 00:36:54.600 --> 00:37:00.660 have put in that periodic array ok. So something like this. So what is the 00:37:01.440 --> 00:37:09.780 advantage of FSS? It can be broadband ok. You can have it can be robust to angle of incidence 00:37:10.440 --> 00:37:18.840 and most importantly the resonance frequency depends on unit cells shape and size. So here 00:37:18.840 --> 00:37:25.380 you can see this is a frequency selective surface so only the in band frequency is allowed to pass 00:37:25.380 --> 00:37:31.860 through all the outer out of band frequencies are basically getting reflected. So at microwave and 00:37:31.860 --> 00:37:38.580 optical frequency ranges spatial filtering is most desirable in all signal processing systems 00:37:38.580 --> 00:37:43.800 and there frequency selective surfaces come into picture because they are called the 00:37:43.800 --> 00:37:52.440 spatial filters as they are used to modify the EM wave incident on such surfaces and then they can 00:37:52.440 --> 00:38:01.560 provide dispersive, transmittive or reflected characteristics. Now how FSS are designed? FSS 00:38:01.560 --> 00:38:09.000 are typically designed by periodic metallic arrays of elements placed on a dielectric substrate. 00:38:10.140 --> 00:38:17.100 The change brought to the transmitted waves can be both in amplitude or phase when you 00:38:17.820 --> 00:38:23.880 compare it with the incident wave and in any case the selectivity may be introduced 00:38:23.880 --> 00:38:29.640 against the incident polarization to improve the irregularities in the emission pattern 00:38:29.640 --> 00:38:36.000 which is exhibited through a change of the phase or amplitude of the transmitted wave. 00:38:36.840 --> 00:38:42.420 Now there are different applications depending on the nature of modification that you have done 00:38:42.420 --> 00:38:50.340 to the transmitted wave. So some examples are you can think of metal grid array so here the 00:38:50.340 --> 00:38:57.840 dark line shows the metal ok. So these are metal grids here also the dark one 00:38:57.840 --> 00:39:05.160 shows the metal grids. So this is basically a inductive element so you will get a high 00:39:05.160 --> 00:39:09.600 pass filter kind of characteristics when you see the transmission coefficient. 00:39:10.440 --> 00:39:15.660 You can also make array of metallic patches so here the dark ones are the metallic patches. 00:39:15.660 --> 00:39:23.100 So metallic patches they behave like capacitive element so you can get low pass characteristics 00:39:23.100 --> 00:39:30.120 based on this. You can also make other shapes something like plus shape metallic plus shape 00:39:30.120 --> 00:39:35.820 so that actually gives you a bend stop characteristics and if you try to make a 00:39:35.820 --> 00:39:41.760 inverse structure of that that is a complementary structure. So you take a metallic sheet and then 00:39:41.760 --> 00:39:47.880 you make this plus shape holes punch through them you can get the inverse characteristic of this 00:39:47.880 --> 00:39:53.340 bend stop you can get a bend pass transmission characteristics. So this is what we have seen 00:39:54.180 --> 00:40:00.720 typically the FSS patches they have resistance because you are using metallic elements and they 00:40:00.720 --> 00:40:05.940 can have inductance or capacitance depending on whatever the elements you are using. 00:40:05.940 --> 00:40:13.380 So, when you are using metallic patches you can think of a capacitive element so it can 00:40:13.380 --> 00:40:21.900 give you low pass characteristics and when you use inductive sorry when you use metal grids you 00:40:21.900 --> 00:40:29.100 can think of this as inductive elements and they will give you high pass characteristics 00:40:30.540 --> 00:40:36.000 that is basically the inductive response. So using this high pass and low pass you can always think 00:40:36.000 --> 00:40:42.420 of and you can combine them in series or parallel to make bend pass or bend stop characteristics as 00:40:42.420 --> 00:40:51.960 you learned already in circuit theory. Here also something like that can be used to make FSS based 00:40:51.960 --> 00:41:00.900 filters using this concepts. So physically when a unit cell of FSS is illuminated by electromagnetic 00:41:00.900 --> 00:41:09.900 wave you can convert that into a effective equivalent resonance circuit. So in the case 00:41:09.900 --> 00:41:15.840 of metallic patch it is a capacitive element as I mentioned metallic grids is a inductive element 00:41:15.840 --> 00:41:24.300 but when you try to make a metal square loop array like this so the dark one is the metallic loop 00:41:24.300 --> 00:41:31.740 so it can be modeled as a L loop and C loop. So there is gap between the loops that will give 00:41:31.740 --> 00:41:39.900 you that capacitance effect and this loop will give you that inductance. Similarly you can also 00:41:39.900 --> 00:41:50.220 make metal square slots so you are actually making slots like this so that can give you L slot and 00:41:50.220 --> 00:42:00.300 C slot in series parallel with another inductance that is coming from this particular grids. So that 00:42:00.300 --> 00:42:08.760 way you can actually make resonating elements and the resonance frequency of this kind of loops can 00:42:08.760 --> 00:42:18.060 be obtained as 1 F equals 1 over 2 pi square root L C. So that will tell you where the resonance of 00:42:18.060 --> 00:42:24.900 your bend pass or bend stop filter will be placed. So by choosing appropriate array element you can 00:42:24.900 --> 00:42:30.720 choose the characteristics of your FSS. So different types of unit cell geometries 00:42:30.720 --> 00:42:35.100 have been implemented which are very common to the FSS community. 00:42:35.880 --> 00:42:44.640 So let us classify this you can classify them based on their resonant properties. So you can 00:42:44.640 --> 00:42:51.120 also see that there are some elements which are non resonant like patch and wire grid where you 00:42:51.120 --> 00:42:57.600 only have either capacitance or inductance or you can also have single resonator element something 00:42:57.600 --> 00:43:04.020 like a loop or a cross or a dipole kind of thing which can be modeled as a series combination of 00:43:04.020 --> 00:43:09.840 inductor and capacitor. So this will be resonating element and these are non resonating elements. 00:43:10.680 --> 00:43:16.620 So the classification can be done like this the group 1 is basically center connected as you 00:43:16.620 --> 00:43:22.260 can see this is a center connected the length is basically kept as lambda naught by 2. 00:43:23.040 --> 00:43:27.900 So this is the overall length as you can see here. So here larger elements 00:43:28.680 --> 00:43:37.920 relative to wavelength. Now in this one the loop type the circumference is basically of the order 00:43:37.920 --> 00:43:43.260 of lambda naught and in the solid type or the plate type as you can see there are different 00:43:44.040 --> 00:43:49.740 structures designs possible for patch you can have square patch hexagonal patch circular 00:43:49.740 --> 00:44:03.900 patch and so on. So here the length of this is kept as lambda naught by 2. So again the larger 00:44:03.900 --> 00:44:12.780 elements relative to the wavelength and group 4 can be combination of any of these elements 00:44:12.780 --> 00:44:19.020 from the group 1, 2 and 3. Now what is the main application of FSS one important application 00:44:19.020 --> 00:44:25.020 is towards electromagnetic shielding. Now electromagnetic interference is a very 00:44:26.040 --> 00:44:32.520 important factor because it may cause malfunction of any electrical and electronic component in a 00:44:32.520 --> 00:44:39.420 sensitive environment. Now it is important to shield the source of interference but that may 00:44:39.420 --> 00:44:45.600 not be the optimum solution. So one of the most common approach is basically to shield 00:44:45.600 --> 00:44:54.000 the sensitive device. And typically what people do they apply a metal foil that can be employed as a 00:44:54.000 --> 00:45:01.980 electromagnetic shield to protect the RF circuitry from the radiated fields. Although this technology 00:45:01.980 --> 00:45:07.500 has some disadvantage because it blocks all kind of transmissions irrespective of the origin. 00:45:08.220 --> 00:45:18.660 Now that you may not like. So in that case FSS may actually help you from getting rid of this kind 00:45:18.660 --> 00:45:25.620 of problems. So if you design a 2D single layer FSS they will definitely have clear advantages 00:45:25.620 --> 00:45:33.300 because they will be easy to fabricate and they can only block or emit a selective frequency. 00:45:33.300 --> 00:45:40.380 They will not shield all the frequencies. So those are the different scenarios. So here is a 00:45:40.380 --> 00:45:45.360 design layout of an FSS as you can see these are the different structural parameters. 00:45:45.360 --> 00:45:53.700 This is the period that is periodic arrangement. This is the overall 3D view of the unit cell and 00:45:53.700 --> 00:46:00.540 this is the side view of the unit cell. So this is basically FSS made of copper on a dielectric 00:46:00.540 --> 00:46:09.120 substrate and it is Rogers 5880 unit which is called a thickness of 0.127 mm permittivity of 00:46:09.120 --> 00:46:15.240 2.2 and dielectric loss tangent is given here. And this is the overall dimension of the unit 00:46:15.240 --> 00:46:23.340 cell 6.8 by 6.8 millimeter square and dx is the parameter that gives you inter element 00:46:23.340 --> 00:46:29.640 spacing. So what I am showing here is a design of a FSS and how what will be the response for that. 00:46:30.420 --> 00:46:35.640 So we are putting this parameter p on the rectangular lattice that tells you about 00:46:35.640 --> 00:46:44.160 the periodicity in of the proposed unit cell in this fabricated FSS. Then you want a resonating 00:46:44.160 --> 00:46:49.860 frequency at 10 gigahertz so you actually optimized all these physical parameters L, g, 00:46:49.860 --> 00:46:56.040 w, r, Dx and P all are these physical parameters. These are the range over which they are optimized 00:46:56.040 --> 00:47:01.080 and these are the basically the optimized dimensions of the FSS that has been obtained. 00:47:01.080 --> 00:47:08.460 Once you optimized you have fabricated the FSS and this is how the fabricated 00:47:08.460 --> 00:47:14.640 FSS looks like. So this is how you can create a measurement setup. So you can put two horn 00:47:14.640 --> 00:47:20.700 antennas operating with operating bandwidth of say 8 to 12 gigahertz for measuring the 00:47:20.700 --> 00:47:26.580 transmission characteristics. Here the antennas are connected to a network analyzer and you can 00:47:26.580 --> 00:47:33.480 actually measure the transmission characteristics by placing a FSS between these two horn antennas. 00:47:34.920 --> 00:47:42.000 And what you will see you can measure the S11 and S21 parameter. So this is the plot of the direct 00:47:42.000 --> 00:47:46.560 line shows the transmission characteristics and the dotted line shows you the S11. 00:47:46.560 --> 00:47:57.000 So, here you can see for the 10 gigahertz it is giving a very effective shielding of almost 56 dB. 00:47:57.000 --> 00:48:05.640 It is minus 56 dB here you see. So it can block 10 gigahertz frequency up to 56 dB. So that is 00:48:05.640 --> 00:48:11.940 very very good shielding and it will not actually block other frequencies. So this is very very good 00:48:12.600 --> 00:48:21.960 electromagnetic shield this FSS at 10 gigahertz. So because of the design symmetry along x and y 00:48:21.960 --> 00:48:28.620 you can say that this FSS will give identical response in both TE and TM incidences. 00:48:28.620 --> 00:48:34.800 So that makes this a very very useful one. So here are the other potential applications. You 00:48:34.800 --> 00:48:41.160 can think of absorbers, you can think of filter plus antenna. So here you have receiver antenna 00:48:41.160 --> 00:48:46.380 you can have a band per structure made of FSS and then you have a transmitter antenna. You 00:48:46.380 --> 00:48:52.320 can also have absorber plus filter where you can have a resistive FSS here which 00:48:52.320 --> 00:48:59.640 can absorb. You can have a pass band metallic FSS here and in between there is a spacer. 00:48:59.640 --> 00:49:06.060 So these two combined can give you something between transmission or absorption. So you are 00:49:06.060 --> 00:49:12.480 switching between transmission and absorption and you are keeping the reflection more or less flat. 00:49:13.860 --> 00:49:21.540 You can also have tunable absorbers. So based on this FSS where you can also include some of 00:49:21.540 --> 00:49:26.580 the this one liquid crystals. So, I will not go into details of this but these are 00:49:26.580 --> 00:49:31.620 different different applications apart from shielding you can have absorber, 00:49:31.620 --> 00:49:36.240 filter plus antenna, absorber plus filter and all these things made out of FSS. 00:49:36.900 --> 00:49:43.680 So with that we will stop here today and in the next lecture we will consider guided mode 00:49:43.680 --> 00:49:48.540 resonance. So regarding this lecture if you have got any query you can always drop an 00:49:48.540 --> 00:49:52.920 email to me at this address mentioning MOOC on the subject line. Thank you.