 Now, let us go to optical absorption of nano materials. So, to summarize before we do that let us summarize the brief concept. So, far we have various phenomena in materials and various like reflection, refraction and diffraction etcetera absorption. These phenomena give rise to colors and materials and they are also responsible for what you might call the overall optical response of the material. Then we notice that we have to differentiate the optical behavior of metals, wherein there are free electrons, which give rise to plasmones. When we talk about and we have to talk about the frequency regime that means the wave length of the incoming radiation determines the response of the metal to the incoming radiation. In other words the metal itself could actually becoming become somewhat transparent or it could be reflecting depending on the frequency of the incoming radiation. We also noted that in the case of semiconductors we have to worry about the band gap and excitons if you have to understand how the absorption of a semiconductor is going to be when I impose an electromagnetic radiation. Therefore, and of course the important question we are going to now ask is that when you go to nano materials how is the behavior as compared to a bulk metal going to change or a bulk semiconductor going to change when you have a material in the nano scale. So, when you are talking about size effect on optical properties bulk metal absorbs electromagnetic radiation say in the visible region thin films of metals may become partially transmitting and this is because of the insufficient material effect as we pointed out. So, gold films about 10 nanometer thick can become partially transparent and this is not something very what you might call unexpected. Apart from the insufficient material effects there are other important phenomena which come into play in nano materials and especially nano freestanding nano crystalline particles and these include the phenomena of surface plasmons and quantum confinement effects. So, we will take up these two important phenomena we already talked about what is called the bulk plasmon which is a longitudinal wave. Now, we will take up the concept of a surface plasmon because now we know in a nano structure nano crystalline material or a nano material freestanding nano particles you have a large surface to volume ratio and therefore, surface dominant effects like surface plasmon come into play. In semiconductors quantum dots optical absorption and emission actually shift to the blue region of spectrum which means that to higher energies as the size of the dot increases. This we will see in detail which implies that inherently there is something changing in nano structured materials regarding the what you might call the electromagnetic structure or the band structure. The size reduction is more prominent in the case of semiconductors as compared to metals. To see the effect of say quantum confinement in metals we have to go down to smaller sizes as compared to that in semiconductor crystals. So, this effect comes prominent at larger sizes in semiconductor crystals and therefore, we will have lot of examples of semiconductor crystals being described here. We had also seen that at very small sizes metal nano particles can develop a band gap and can become a semiconductor or an insulator. So, this aspect we have seen that because of dimensional confinement the density of states we saw already changes between a bulk 3 d semiconductor normal metallic conductor to 2 d kind of a system where you get a staircase kind of a density of states. Then we saw we go down to 1 d semiconductor 1 d metal which actually develops a band gap that means when you are talking about 1 d metal that means you talk took a material like copper which is bulk metallic in the bulk and reduce its size. And you saw that the density of states now starts to behave like an e power minus half rather than e power half in the bulk and we saw that you actually develop a band gap. In other words the metals start to behave like a semiconductor on insulator in very small sizes. Then we also saw the case when we go down to a 0 dimensional a metal again metal in the bulk then you actually start to the material starts to behave like an atom that means you have discrete energy levels. So, all these possibilities we already have seen before for the case of a metal. Now, what happens in the case of semiconducting nanoparticles and films. So, these are very interesting things which start to happen in the case of semiconducting nanoparticles and films and on decreasing the size the electron gets confined to the particle and you confinement effect starts to dominating. And what is meant by this confinement effect will become clear when we discuss what is happening here. And this leads to two important effects one is increase in the band gap energy. This is very very important and this is at the heart of the blue shift we will be talking about. And the second is that the band levels get quantized. So, you have a bulk semiconductor as shown schematically in the diagram. So, you have the green region which is now my schematic of the valence band. And now you have the conduction band which is separated by an e g and this is now the bulk scenario. Now, when you make a nanoparticle you can clearly see two things are happening number one is that if you look at the band gap originally this was my band gap. Now, the new band gap in a semiconducting nanoparticle is this. So, the band gap has increased when you are talking about a semiconducting nanoparticle. The second effect is that the band gap levels get quantized. Of course, this is an obvious effect because now you in a nanoparticle even in a normal bulk material there are these discrete levels. But since they are placed space so closely and where there because there are now a mole of atoms or more you can continue consider them to be a continuous state which is called a band. So, this is just a mere approximation, but when the number of particles in the system actually reduces. Obviously, there are not enough levels to make it a what you might call a continuous or a semi continuous level. And therefore, you can see the discretization effect and you see that these levels start to become discrete. So, there are two important effects which come into play when you reduce the size of a nanoparticle one is in the increase in the band gap energy and number two is that the band gap levels get quantized or start to the discreteness of the level starts to come about or get starts to be felt. Another important effect which comes in semiconducting nanoparticles is the fact that surface states or trap states can form which lie in the band gap and become important. Because now the optical properties the nano crystals is going to be dominated by the surface states. And therefore, there may be absorption suppose I am talking about a surface state lying in the band gap somewhere here this is my band gap. This implies those surface states will absorb more strongly as compared to the inherent band gap edge or what you might call the inherent E G nano. And therefore, those will tend to dominate the proper optical properties of the semiconductor. So, the energy level spacing increases with decreasing dimension and this is called the quantum confinement effect. So, we have now we are talking about a semiconductor nanoparticle we have to take in additional factors compared to the bulk. Number one is that you have insufficient material leading to discretization of the band into separate energy levels. Number two is a fact that there is a increase in band gap energy which means now I have to supply higher energy coming of course, through an electromagnetic radiation like photon to via photon to actually excite an electron. Third thing we saw is that surface trap states can also start to play an important role in the absorption properties of the semiconductor. Now, how does the band gap or what you might call the effective band gap change with particle radius r. When you study this effect effective radius and now we have seen that the effective radius actually increases. So, you said these all originally where within the band have now become part of the band gap. Now, essentially we saw that we know that as r reduces the E G effective increases. So, if you look at the formula for E G effective as a function of r there is of course, the band gap energy of a bulk semiconductor at the first term, but there are two more terms one depends one is a positive term going as 1 by r square. And there is second a Coulombic term which is coming from which goes which is a negative term coming as 1 by r, but since the 1 by r square term dominates over the 1 by r term which is a negative term. This implies that though given individual terms for given the first term or the second term in the. So, this is my second term and this is my third term. The second term tells you that as r decreases the E G effective has to increase the third term tells you that as the r decrease the E G effective has to decrease as well the Coulombic attraction term, but as you can see this is an r square dependence therefore, this term dominates and overall the band gap energy increases as you decrease the size or the as you confine the semiconductor. These other terms in this are all constants which we have dealt with before. Now, the signature of this increase of what you might call the band gap can be seen in this nice interesting example, wherein which Lakshmi and co-workers studied bulk gallium arsenide and compared it with nano crystalline gallium arsenide. And typically they put this nano crystalline gallium arsenide as a thin film on an I T O substrate and studied this absorption properties. And if you look at the absorbance of now this what we call the nano gallium arsenide vis-a-vis the bulk gallium arsenide and you are here the x axis is the wave length you see that the bulk shows an increase in absorbance with wave length that means as the sorry decrease that means as the wave length increases the absorbance decreases that means as the. So, the wave length is increasing in the right hand direction the energy is actually increasing on the left hand side direction. So, this is my energy so with increasing energy you are seeing an increasing absorption. What is prominent in this absorption spectrum of course, one of the things is that you do not find an exciton, excitonic absorption because this is now at room temperature experiment wherein you expect that the exciton has been dissociated. Or if you look at their paper they plot this for the nano gallium arsenide they actually plot a peak like this and they call it the excitonic absorption. Now, what is really and this nano gallium arsenide has size range about 7 to 15 nanometer size nano crystals that means this is not a mono disperse system. In other words I have to consider the size variations also into take into account that means now I am not talking about a single band gap for this material there is a range of band gaps and which since there is a range of band gaps I would expect absorption to take place over a range of energies. And that is the reason that this peak is actually broaden and it is not a very sharp peak as you would expect if you had a mono disperse crystallite size. So, the broad excitonic peak occurs at about 526 nanometers so this is the range where it occurs and this corresponds to energy of about 2.36 e v and this is if you compare it with the band gap of the bulk gallium arsenide it is about 1.43 e v. That means that the frequency is blue shifted that means the band gap has effectively increased right the shift is 0.93 e v it is not the net the net is 2.36 e v that means now my band gap is 2.36 e v in the nano gallium arsenide while in the bulk gallium arsenide is 1.43 e v that means effective band gap has increased. And we already know if you are talking about true excitonic absorption then you would know that that has to lie in the band gap of the original semiconductor and therefore that would actually lead to a reduction in the or reduction in the band gap. So, this we can understand as not as excitonic absorption though the terminology is used as what you might call purely coming from confinement effect and increasing the band gap. So, to summarize this important slide you see that bulk gallium arsenide has a different absorption spectrum as compared to a nano gallium arsenide. In the nano gallium arsenide you observe that there is actually a very strong peak in the absorbance at 4 5 26 nanometers. And this strong absorption peak corresponds to a band gap of about 2.36 e v and this is what you might call blue shifted with respect to the bulk gallium arsenide. That means now this happens at higher frequencies or in other words at lower wavelengths. An additional fact which is seen from this curve is a fact that there is an overall increase in absorption of absorbance over the entire wavelength regime or the frequency regime in the case of the nano. That means the nano curve is shifted to higher absorbance values across the spectrum. And this is coming and this is attributed to the enhanced oscillator strength and oscillator strength is a dimensionless quantity to express the strength of the transition. And now we are talking about the transition from the valence band to the conduction band. And we have already noted that the exotonic peak or the absorption peak is broad because of the distribution of crystallite sizes. So here we have a clear cut example of a nano crystalline gallium arsenide film on an ITO substrate which shows an absorption property which is very very different from that of the bulk gallium arsenide. And the important thing to note is that the absorption peak is now blue shifted. That means it is occurring across a larger band gap and there is a peak where there was no peak in the case of the bulk gallium arsenide. So this is a very important difference between the optical property of what you might call a bulk semiconductor vis-a-vis and nano semiconductor. And we will take up some more examples in the coming slides to see the difference between this what you might call bulk versus nano in the four semiconductors. After considering the example of gallium arsenide nano crystalline thin film, we take up an equivalent example the case of the P B S E nano crystals where in again we see this dramatic effect of blue shift which is coming from quantum confinement effects in these semiconductor nano crystals. Now we have already noticed that the density of states becomes more quantized and the band gap shifts to higher energies which is the root cause for this blue shift. In the case of P B S E nano crystals again we are plotting the wave length as a function of the absorbance. And we know of course these curves have been shifted vertically. So, that they we can make a comparison and that is why the y axis is in arbitrary units. We note that there is a dramatic change in the absorption peak as you go from say for instance the 9 nanometer particles of P B S E to 5.5 nanometer particles to the 4.5 and to the 3 nanometer particles. And we will soon see an effect with respect to the surface plasmon absorbance in the case of metals that there this effect of shift is actually negligible and it is actually small when you actually change the particle size. So, here you see that there is actually a blue shift in the peak and you can see the peak shifts to higher frequencies or in other words lower wave lengths and in other words the energy of the transition becomes high. And therefore, the material absorbs at higher energies when you actually reduce the particle size and this particle size is only by a factor of about 3 from 9 nanometer to 3 nanometers. And the wave length you can see for absorbance shift to something like about 1100 nanometers from something more than something which is 2000 nanometers. So, clear cut there is this quantum confinement effect in these nanocrystals which effects its optical properties. The counterpart side the other side of this absorbance is what is called photoluminescence in other words if a material is put into an excited state then it is going to relax to its ground state and in the process may actually emit a photon. In some cases of course, there can be radiation less transitions, but if there is a possibility here that the excited state will relax to the ground state by the emission of photons. And this is the phenomena of photoluminescence and when this relaxation in a semiconductor takes place by recombination of electron and hole the photon is emitted. And if this emitted photons energy lies in their range of about 1.8 to 3.1 electron volts then the radiation will be in the visible range and often this phenomena is called luminescence. Now, by changing the size of the nanoparticles I have a handle on the band gap now in other words in the bulk material I had just had one single band gap to deal with, but now I can tailor the band gap by actually changing the particle size. And therefore, I can tailor the emission and in other words I get a handle on even the color of the particle which I see which we will take up a startling example coming up soon. And even in these cases the emission case not unexpectedly you observe a blue shift of frequencies with reduction in particle size. So, when we are talking about photoluminescence which is the phenomena where which is the phenomena which is called the other side of the coin of absorbance which is the emission of a photon when a system is excited in other words the recombination of the electron and hole takes place and there is an emission of photon and this emission of photon can actually happen in the visible region in which case you call it luminescence. Of course, this need not always take place in the visible range that depends on the band gap and if the band gap happens to be in about 1.8 to 3.1 volts then this will happen to be in the visible region. The dramatic effect can be seen in what we might call the core shell nanostructures wherein there is one semiconductor as the core another semiconductor as the shell. Some examples of these are cadmium sulphide coated with MOS4, zinc selenide coated with CDSE, CDSE coated with CDS and etcetera. And in this case we notice that the band gaps are tunable near the IR in which case they can be used as an IR biological luminescent markers also. That means not only can the emission be in the visible region it can also be in the IR region and you have a handle on the frequency of emission and therefore, you can tune the what you call the frequency which is emitted. The in such core shell structures the luminescent properties are typically characteristic of the core and we will take up an example and the shell actually leads to an enhancement of the luminescent properties of the core. The shell we said when we talked about core shell structures in detail before we said that the shell could actually be performing many roles. One of the roles could be a mere passive layer which is actually protecting the core from the environment. But we also pointed out that we will take up an example at that some later stage wherein we will talk about enhancement of properties of the core. And this is a nice example wherein actually you will find that there is this enhancement of the luminescent properties of the core when you have a shell around it of a semiconductor. Now typically deposition of the of a semiconductor with a larger band gap than the core results in what you might call luminescence enhancement and this occurs due to suppression of radiation less recombination. And this radiation less recombination typically is mediated by surface states. So, if you had a raw semiconductor then you have the surface states which lie in the band gap and the transition to these surface states may sometime may not lead to luminescence. And therefore, having a shell layer enhances your luminescent properties of the semiconductor. The one of the beautiful examples available is the case of the CDAC nanoparticles. And now we are talking about change in CDAC nanoparticle size from about 5.5 nanometers which is on the right hand side a small nanoparticle to a size. So, this is my 5.5 nanometer particle to a size of about 2.3 nanometer particle a factor of about 2 to 3. Now in these core shell nanostructures of course, there is a shell of zinc sulphide. And we will look at the properties of luminescence in the absence of the shell and also in the presence of the shell. So, we have a case where there is no zinc sulphide and we will compare it to the properties where there is actually in zinc sulphide shell. And the most beautiful and marking what you call characteristic signature of this change in size is the change in color of the colloid. And this is cited usually as one of the beautiful properties emerging in nanostructure this is given as what one of those what we call the typical or the outstanding examples given. And wherein here I have schematically shown the change in color that in the way of 5.5 nanometer particles on the left hand side you notice that you have emission or photo emission in the red region of the spectrum. When you reduce the size to 2.3 nanometer which is on the right hand side you notice that the emission shifts to the blue color. And clearly that is why this phenomena is known as blue shift because now there is a change in color from red to the blue. That means from lower energies to higher energies when you reduce the particle size which again is coming from the phenomena of this quantum confinement which is leading to a increase in the band gap. Now this is a very striking and startling example. And if now if I plot my intensity versus wavelength and now this intensity is not the absorbing intensity but is the emission intensity. So, it is the other side of the coin of absorbance we just now saw and we are again plotting it with respect to wavelength. So, when the particle size is 5.5 nanometer which is the case corresponding to the figure on the right hand side. So, this is this case the red case you notice that there is an emission in the frequency wavelength region 60 to 600 to 650 in the red color regime. Now the important point is that in the absence of the shell you see that the emission has a certain intensity. But when you have a shell around it there is a clear cut market enhancement in the intensity in the presence of the shell. So, I can show that there is a enhancement in the presence of the shell. So, this is clearly you can see that an important effect of putting a shell around the core. Now as you change the particle size you can see that the frequencies are seeing a blue shift the peak is shifting to blue side. And you can see that in each one of these cases the core shell structure has an higher emission as compared to the bare core or the bare core implying only the core. And in the core is shown by the dotted lines the core shell structure is shown by the peak. The overall peak of the emission does not shift much. So, there can be a small shift as you can see from the fact that the peak of the bare core lies slightly to the what you call in other words the shell adds a slight red shift to this. But that is not a very significant effect the important effect is the enhancement in the intensity. So, there is a beautiful example here of a core shell structure wherein in the absence of a core you still have a red shift or sorry a blue shift when you reduce the particle size. And there is an enhancement of the photo emission or enhancement in the fluorescence when you have a shell around the core. And this is as I said typically given as a beautiful example there are beautiful nice pictures wherein they show that how this dramatic effect takes place because of reduction in particle size. And here again note that the particle size reduction is not too much it is not an order of magnitude it is only a by a few factor of a few. Now, if you look at on the other hand metallic nanoparticles the metallic nanoparticles you will see we had pointed out the size does not affect is not it does not have a very profound effect. Now, for instance gold nanoparticles have been used as a pigment because of their in ruby colored stained glass dating back to about 17th century. So, if anybody has gone to an old church where there is stained glass the color in the stained glass is coming from these nano gold particles typically about 1 to 10 nanometer in size. And we had said that this is this phenomena is coming this color is coming because of surface plasmon resonance. We had also pointed out that the surface plasmon are transverse in nature as compared to the bulk plasmon which are longitudinal character. Now, we already noted that thin films of gold can be partially transparent about 10 100 nanometers are less and they will essentially transmit blue violet light. Now, the color of these metallic nanoparticles depends on the size in a nano scale regime, but again now we have to see a larger size changes to see the change in color. Bulk gold is yellow in color nanoparticles of gold can have red purple or blue color. So, there is again a possibility of twinning the color of these gold nanoparticles by changing the size. Not only does the color depend on the size, but it also depends on the shape and the next slide we will see that we will consider two kinds of particles one cylindrical particles and one spherical particles and we will see how the shape actually affects the frequency of emission or frequency of absorption. Not only does the particle shape and size play a role in this whole plasmon surface plasmon resonance, but also the dielectric properties of the medium because as we said that in the case of the stained glass this gold nanoparticles are embedded in a dielectric glass. You may also what you call suspend is gold nanoparticles in the form of a colloidal suspension and in which case the dielectric properties of the suspending medium plays an important role. Now, in this case of this gold nanoparticles the surface plasmon are excited by the incident electromagnetic radiations and few more points about that are in the next box surface plasmon have a lower energy than bulk plasmon. Now, when you have a gold or silver which has a mean free path of about 50 nanometers for smaller particles in this there will be no scattering within the particle and all the interactions will be on the surface. In other words when you have extremely small particles it is a surface which becomes important. That means we are we have to worry about the surface plasmon more than the bulk plasmon. In other words the bulk plasmon absorbance is going to be small and it is going to surface plasmon which are going to play the key role in determining the optical properties of such small metallic nanoparticles. And as we pointed out in particles with shape anisotropy and we are going to give an example of cylinder in the next slide more than one type of plasmon may be simultaneously excited and we may observe an absorption p corresponding to both longitudinal and transverse plasmon. So, the this is a beautiful example in this example we have three kinds of objects one a sphere one a long cylinder which is marked in green and also the corresponding curve is also in green and one is a short cylinder. In other words a sphere can be characterized by one dimension which is just the radius of the sphere. While on the other hand if you have a long cylinder not only does you have to specify the diameter of the cylinder, but additionally you have to specify the length that means two dimensions characterize a cylinder. And this can be sphere can be thought of as a quantum dot or a zero dimensional system of course this is slightly large, but on the other hand a cylinder can be thought of as in one dimensional nano crystal. And now in some of the previous curves when we talked about semiconductors we initially of course we plotted what you might call the absorbance. Then we switched to when we switched when we talked about photo luminescence we were actually plotting the emission part that means how an excited system relaxes by emission of light and we use the term fluorescence for that, but here again we are going back to absorbance that means what we are plotting here is absorption of wave length or absorption as a function of the frequency of the electromagnetic radiation. And here typically we are talking about visible regions. Now for a sphere of about 15 nanometer diameter and here is the blue sphere which is 15 nanometer diameter only transverse plasma peak is observed at lambda approximately about 520 nanometer. So, if I look at this blue curve corresponding to my transverse plasmon's absorbance you see that it has a peak around about 520 nanometer there is only one peak that is very very important to note. And this is coming from transverse plasmon in other words surface plasmon's. So, this absorbance spectra of this sphere is dominated by a single quantity which is now the absorbance of because of setting up transverse surface plasmon resonance. So, that is the key phenomena here now as I pointed out there is one key difference between semiconductor particles and metal nanoparticles that is the size dependence sensitivity to size dependence on this absorbance spectra. We noted in the case of semiconductors that if I change the size just from 3 nanometer to 4.5 nanometer is about a 50 percent increase you see that the peak shifts drastically. In other words for a 3 nanometer particle the peak is around about this may be considered 1200 in that range and this 3 nanometer particle is more than 1500. So, there is a drastic shift in the absorbance peak when you change the particle size nanoscale regime, but when you are talking about metal nanoparticles this is not the case and we have been talking about this previously. And so here is the right example to prove that point. Now, if I double the radius of the sphere I make it 30 nanometer the transverse absorb plasmon absorption peaks will only shift lightly. I have not plotted it on this curve here because that makes it what you might call too much complicated there will be too many curves lying on top of the other there, but the shift is only slight. This is unlike semiconductor nanoparticles where absorbance is a strong function of the nanoparticle size. So, you see that if I make my sphere from 30 nanometer to 50 nanometer or 50 nanometer to 15 to 30 there is not much shift in the peak and this peak is now coming from surface plasmon resonance. Now, the case of the cylinder is very interesting. Now, let me start with the long cylinder the 112 nanometer cylinder in the case of the 112 nanometer cylinder you would notice that there is two peaks at in fact there are two peaks one peak in the low wavelength or high frequency regime. And the other one is in the longer wavelength regime these this long wavelength peak is coming from the longitudinal plasmon which is along the length of the cylinder of the along the length of the cylinder. And the lower wavelength peak which is here close to about may be slightly more than about or close to 500 nanometers this peak is coming from this peak is coming from the transverse plasmon. In other words based on the geometry of the cylinder now I got two peaks and these two peaks are coming from totally different mechanisms one from longitudinal plasmon and one is coming from surface plasmon. Now, if I make the cylinder short there is you can see there is a shift in the longitudinal plasmon peak was now that is along the length of the cylinder which is what is sensitive. While you can see that now for the short cylinder this is the red red curve and you can see that the red curve marks points on the red curve. The red curve the surface plasmon is in the same position because now if you look at the d of the long and short cylinder they are in the same place. So, the transverse plasmon peak appears at the same place as the case of the long cylinder, but then the longitudinal mode has actually shifted to shorter wavelengths. In other words higher frequencies this shift this shift is this peak is coming from the longitudinal plasmon. In other words now I have in the case of metal nanoparticles an important demonstration that the color depends on size obviously as we have seen and also on the shape of the particle. So, size and shape are the two important factors which we have seen in the previous graph which is now going to determine my plasmon absorption and we already seen that in the case of the shape the two peaks we observe one is coming from and that means the two peaks are from two different mechanisms one is coming from a surface plasmon resonance and other is coming from the longitudinal plasmon. So, there is a nice example here of metal nanoparticles which wherein the size and shape are determining the absorption of the material. Having said this that the we have to be careful that when we are comparing semiconductors with metals the mechanisms of absorption are obviously different, but add to that we are comparing the sensitivity to size and we are not definitely not saying that it is not size dependent. Obviously we seen the example that the absorption spectrum is size dependent, but it is not a sensitive function of the size that is the important thing we are saying. Now we take up another of the core shell examples in this core shell example we have a metal on a dielectric. In the previous example of core shell structure we saw we considered a semiconductor on a semiconductor and we took up the example of zinc sulphide shell on a C D S E which is a semiconductor nanoparticle. Now we take up the example of a metal shell and in this case we have a gold shell as I am highlighting in a low here the gold shell on a silicon dioxide core S I O 2 core. So, the core is a dielectric in other words a non conducting material and the shell is our metal and in we consider a case where we keep the core radius or core diameter constant and this core diameter is 60 nanometers. And what we do is we just change the shell size from about you can see that about 20 to 5 nanometers we keep on changing the shell size and we study the extinction intensity as a function of the wavelength. And we note that in this case when you are for the gold on S I O 2 cores the plasmon band shifts on changing the core radius and this depends on obviously the thickness of the shell because we are keeping the core radius constant increasing the core to shell ratio actually red shifts the plasmon resonance band. Because this I have taken up this example because this is right opposite of what we have been talking so far which is the blue shift. In other words here when I am reducing the metal thickness on this metal thickness of shell around this dielectric core then I am seeing that on decreasing the shell size I see that there is actually a red shift that means that when you have a shell which is thick then the frequency peak lies close to about 800 nanometers when you make the shell thin about 5 nanometers then I see that there is a shift towards the red region that means this is now towards the lower energy region. So, this shift is actually opposite to what we have been talking about so far for the case of the semiconductor nanoparticles. So, this is a very interesting case of a core shell structure. Now, we were when we talked about refractive index we said that there are very interesting class of materials known as materials with negative refractive index. So, metamaterials or negative refractive index materials or otherwise we might want to call them negative refractive index structures have a negative refractive index and when we said a negative refractive index suppose I am assuming a ray we said coming from vacuum or air into a medium which is colored blue here then we note that the refracted ray lies in the same side of the normal as the incident ray unlike normal refraction which is the green line shown here where in the refracted ray lies on the other side of the normal. Now, typically these are man made structures where in the refractive index as a negative value and this refractive index as a negative value typically over some kind of a frequency range and so far this has not been discovered in natural materials. And these metamaterials have or negative refractive index materials have negative effective permeability. Now, the refractive index we have noted before can be written as plus or minus epsilon into mu where one is the permeability another is the permeability and we have to note that when we are talking about positive refractive index or positive refractive index then we take the positive sign outside the square root and use the positive of both epsilon and mu. In negative refractive index structures use the negative sign outside the square root and use both the negative signs here. An important property of this negative refractive index materials is shown in the figure below in normal refraction what happens suppose you have a divergent set of rays then these rays of course, even after refraction will continue to be divergent. Within the medium the what you might call the angular regime of a diffraction may come down but they continue to diverge. But in negative refraction you can see that the this is now my red material is a negative refraction refractive index material the divergent rays will actually come to convergence. In other words such a material can be used as a convergent lens normally we know that when you talking about a lens which is converging like a double convex lens then it is actually the shape of the lens which alters what you might call the optical path length which is leading to the convergence. But here you are seeing that this even a flat surface of negative refractive index can act like a converging lens and this kind of a negative refractive index material can actually be used for focusing what you may not what is known as a evanescent component of the field. Now, what are the typical materials or structures which show this kind of a negative refractive index there are structures which are known as magnetic split ring resonators. And there is a schematic of such structures here all these gray regions in the figure below are these magnetic split ring detectors or a split ring resonators. And now there is a lattice of these structures and therefore, I make a crystal of these and you know that if the scale of these structures happens to be about 2 of the order of 200 nanometers then such a structure will show a negative refractive index close to the visible range. That means if I change the scale of this structure which I am making I can actually tune the regime in the electromagnetic spectrum wherein it shows what you might call negative refractive index property. So, if I make these structures even smaller then it will shift to the visible region, but if I make the scale of these structures larger then they will start to become negative refractive index only in the microwave or other regimes. So, these are what you might call very interesting materials, but the important thing to note from our course point of view that if I make these structures in the nano scale about 200 nanometers are less and each one of these what you might call these entities in this is what is called a magnetic split ring resonator then this structure as a whole starts to behave like a negative refractive index structures. So, people have been making various kinds of chiral materials and various kind of sculpted structures which can actually give this kind of a property of negative refractive index and for that negative refractive index to be in the optical regime we have to note that the scale of the structure has to be about less than about 200 nanometers. So, these are again very interesting materials and people who are interested in this area can investigate further with this we come to the end of this course. In this course which professor Kantesh Balani and myself are the instructors we have tried to give you a broad flavor of what are nano materials what are nano structures what kind of properties can they have and of course briefly we have also been talking about applications of these materials in some cases we have gone into details of these classification and some of the properties we have considered in lot of detail like the magnetic properties, but in many other cases we have only made a cursory what you might call remark or a superficial consideration of many of these topics. So, students are expected to follow up this with further reading and there of course there is an immense volume of material available in the literature now regarding nano materials nano structures their properties one of the biggest what you might call the mammoth volumes is about now initially there were 10 volumes of the handbook of nano materials by Harissing Nalwa and now 10 more volumes have been added that means now we have 20 volumes of reference material coming from a single handbook there are many others at similar handbooks there are beautiful review papers also available on any specific given topic for instance we also been trying to give references like the one for optics we had cited a book which you can refer and similarly we have talked about magnetism what books can you refer, but going through this course the students must have understood that behind each one of those fascinating properties which we have introduced you to or each one of those fascinating concepts we introduced you to when you come to nano materials let it be for instance super plasticity let it be inverse hall pitch effect or let it be super paramagnetism or it can even be a shift in the optical absorbance that lot of fundamental understanding is required in other words students may have to read lot of books to understand the fundamental concepts behind some of these fascinating properties and in a course like this it has not been possible for us to go into for instance all the details of the fundamentals though we have been giving flavor of some of the fundamentals from time to time. So the students may have to do a lot of reading to understand what are the fundamentals in this area and I hope they enjoy the material of the course thank you very much.