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VIETNAM NATIONAL UNIVERSITY OF HANOI VIETNAM JAPAN UNIVERSITY PHAM DINH DAT STUDY OF LOW REFRACTIVE INDEX HOMOGENEOUS THIN FILM FOR APPLICATION ON METAMATERIAL MASTER’S THESIS HANOI, 2019 VIETNAM NATI[.]
VIETNAM NATIONAL UNIVERSITY OF HANOI VIETNAM JAPAN UNIVERSITY PHAM DINH DAT STUDY OF LOW REFRACTIVE INDEX HOMOGENEOUS THIN FILM FOR APPLICATION ON METAMATERIAL MASTER’S THESIS HANOI, 2019 VIETNAM NATIONAL UNIVERSITY OF HANOI VIETNAM JAPAN UNIVERSITY PHAM DINH DAT STUDY OF LOW REFRACTIVE INDEX HOMOGENEOUS THIN FILM FOR APPLICATION ON METAMATERIAL MAJOR: NANOTECHNOLOGY CODE: PILOT RESEARCH SUPERVISOR: Ph.D PHAM TIEN THANH HANOI, 2019 Acknowledgement First and foremost, I want to express my appreciation to my supervisor, Pham Tien Thanh Ph.D for his patient guidance and encouragement during my study and research at Vietnam Japan University I would like to thank Prof Kajikawa Kotaro and his students at Kajikawa Lab, Faculty of Electrical and Electronics Engineering, Tokyo Institute of Technology who helped us facilities to perform calculation, experiments and measurements I also would like to send my sincere thanks to the lecturers of Nanotechnology Program, Vietnam Japan University, who have taught and interested me over the past two years Besides, I am grateful to my family and my friends who are always there to share their experiences that help me overcome the obstacles of student’s life Hanoi, 17 June, 2019 Author Pham Dinh Dat i TABLE OF CONTENTS Acknowledgement i LIST OF FIGURES, SCHEMES iv LIST OF ABBREVIATIONS vi CHAPTER 1: INTRODUCTION .1 1.1 Metamaterial 1.2 Optical material relate to refractive index CHAPTER 2: FUNDAMENTAL THEORY 2.1 Effective Medium Theory 2.1.1 Effective medium 2.1.2 Permittivity calculation .8 2.2 Transfer Matrix for multilayer optics 10 2.3 Finite Difference Time Domain (FDTD) 14 CHAPTER 3: EXPERIMENTS 19 3.1 Silver nanoparticles synthesis 19 3.1.1 Chemicals 19 3.1.2 Process .19 3.2 Thin films fabrication 20 3.2.1 Chemicals 20 3.2.2 Process .20 3.3 Optical properties determination .21 3.4 Thin films thickness determination 21 CHAPTER 4: RESULTS AND DISCUSSION 22 4.1 Calculation results 22 ii 4.1.1 Index of refraction and index of extinction depend on element of particles 22 4.1.2 Index of refraction and index of extinction depend on volume fill fraction of silver nanoparticles on polymer matrix 25 4.1.3 Calculation for thin film following EMT using TMM 28 4.1.4 Calculation for thin film using FDTD method 31 4.1.5 Neighbor particles interaction 34 4.2 Experiment results 37 4.2.1 Properties of silver nanoparticles 37 4.2.2 Properties of thin films 40 CONCLUSION 45 iii LIST OF FIGURES, SCHEMES Fig 1.1: Multilayer structure and nanowires embedded structure metamaterial (A: metal-dielectric layered, B: wires in dielectric host) Fig 2.1: A material model of UEM Fig 2.2:Three simple model of UEM material classified following topology _6 Fig 2.3: A simple model for assumption limitation of volume fill fraction _7 Fig 2.4: Considered system of TMM problem 11 Fig 2.5: The arrangement of electric- and magnetic-field nodes in space and time 17 Fig 4.1: The index of refraction of PVP including 3% volume fill fraction of silver, gold and copper 22 Fig 4.2: The index of extinction of PVP including 3% volume fill fraction of silver, gold and copper 23 Fig 4.3: The index of refraction of PVA including 3% volume fill fraction of silver, gold and copper 24 Fig 4.4: The index of extinction of PVA including 3% volume fill fraction of silver, gold and copper 24 Fig 4.5: The index of refraction of PVP including 2%, 3%, 4% and 5% volume fill fraction of silver _25 Fig 4.6: The index of refraction of PVA including 2%, 3%, 4% and 5% volume fill fraction of silver _26 Fig 4.7: The index of extinction of silver and PVP including 2%, 3%, 4% and 5% volume fill fraction of silver 27 Fig 4.8: The index of extinction of silver and PVA including 2%, 3%, 4% and 5% volume fill fraction of silver 27 Fig 4.9: Transmittance spectrum of 30 nm PVP-based films corresponding to different Ag fill fraction _28 Fig 4.10: Transmittance spectrum of 30 nm PVA-based films corresponding to different Ag fill fraction _29 Fig 4.11: The calculated transmittance spectrum of 200 nm PVP-based films corresponding to different Ag fill fraction using TMM _30 iv Fig 4.12: The calculated transmittance spectrum of 200 nm PVA-based films corresponding to different Ag fill fraction using TMM _31 Fig 4.13: The FDTD domain for calculation of 200nm film by x, y, z direction and 3D visions 32 Fig 4.14: The calculated transmittance spectrum of 200 nm PVP-based films corresponding to different Ag fill fraction using FDTD method 33 Fig 4.15: The calculated transmittance spectrum of 200 nm PVA-based films corresponding different Ag fill fraction using FDTD method 33 Fig 4.16: The simple model for consider neighbor-particles interaction 35 Fig 4.17: Calculated extinction spectra of two neighbor-particles with distance equal 3nm in medium that has refractive index equal 1.5 using FDTD 36 Fig 4.18: Calculated extinction spectra of neighbor-particles with distance equal 3nm in medium that has refractive index equal 1.5 using DDA _37 Fig 4.19: The images of silver nanoparticles solution after synthesis(a), after centrifugation(b) and after re-disperse on water(c). _38 Fig 4.20: SEM image of self-synthesis silver nanoparticles 39 Fig 4.21: Transmittance spectrum of self-synthesis and commercial silver nanoparticles solution _39 Fig 4.22: Molecular formula of PVP and PVA 40 Fig 4.23: Transmittance spectrum of PVA, PVP solution with and without existence of silver nanoparticles _41 Fig 4.24: Transmittance spectrum of drop-coating PVP, PVA films corresponding 3% fill fraction of silver nanoparticles 42 Fig 4.25: Transmittance spectrum of PVP-based films different fill fraction of silver nanoparticles 43 Fig 4.26: Transmittance spectrum of PVA-based films different fill fraction of silver nanoparticles 44 v LIST OF ABBREVIATIONS DDA: Discrete Dipole Approximation EMT: Effective Medium Theory EM: Effective Medium E-field: Electric field LSPR: Localized Surface Plasmon Resonance MGG: Maxwell Garnet geometry MGT: Maxwell Garnett theory FDTD: Finite Different Time Domain H-field: Magnetic field PVP: Poly Vinyl Pyrrolydone PVA: Poly Vinyl Alcohol PML: Perfect Match Layer SPR: Surface Plasmon Resonance TMM: Transfer Matrix Method UEM: Uniform Effective Medium vi CHAPTER 1: INTRODUCTION 1.1 Metamaterial Electromagnetic metamaterial is a class of material using for engineering electromagnetic space and controlling light propagation Metamaterials have shown their promise for the next generation optical materials with electromagnetic behaviors almost can’t be obtained in any conventional materials They have a plenty of application including cloaking [11,15,26], imagining [12,29,41], sensing [18,23,36], wave guiding [13,22,38], absorber [5], etc The metamaterial is fabricated based on the composite structures including inclusions that have sub-wavelength structures The inclusions have designed structure They can be totally artifact or emulate based on nature structure The inclusions are arranged on a host medium that is normally dielectric Due to the small size and distance of inclusion, the metamaterials can be considered as the homogeneous mediums The properties of material are represented through permittivity and permeability By changing shape and size of inclusion, permittivity and permeability of metamaterial can be adjusted to very high or low (even negative) value Under the consideration for permittivity and permeability, the material can be classified into groups [31] They are epsilon-negative material (ENG), mu-negative material (MNG), double positive material (DPS) and double negative material (DNG) The metamaterial is in class of ENG, MNG and DNG materials Besides that, the metamaterial includes band gap material but it will not be considered in this research The three classes ENG, MNG and DNG of metamaterial show the noticeable of negative permittivity and permeability For example, the index of refraction of materials can become small than with structure like in Fig 1.1 It makes the refraction of light becomes very different when comparing with the original materials Fig 1.1: Multilayer structure and nanowires embedded structure metamaterial (A: metal-dielectric layered, B: wires in dielectric host) The metamaterials structuring as in Fig are called as hyperbolic metamaterial In this class of metamaterial, the refractive indexes and arrangement of components play a significant role to properties of metamaterial The below equations is used to calculate the anisotropic dielectric function of layered metamaterial ϵ𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 = ϵ𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 = 𝑑𝑑 + 𝑑𝑚 𝑑𝑚 𝑑𝑑 + 𝜖𝑚 𝜖𝑑 𝑑𝑚 𝜖𝑚 + 𝑑𝑑 𝜖𝑑 𝑑𝑑 + 𝑑 𝑚 with ϵ𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 and ϵ𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 are dielectric function following directions those are parallel and perpendicular with surface of multilayer structure; dd and dm are thickness; 𝜖𝑚 and 𝜖𝑑 are dielectric function of dielectric material and metal Following it, the very low refractive index n = √𝜖 can be achieved by this way [38] The problem is that the fabrication is very complex and expensive The distance between wires, the thickness of each layer must be very precise Here, we can see some issues of the metamaterial Firstly, the properties of metamaterial depend on not only structures but also nature of hosts and inclusions It suggests that along with structural changes, developing materials as host or inclusion also contribute to the metamaterials Most of the researches about the 𝑇𝑟 = t = (𝑇11 + 𝑇12 𝑟)2 (2.2.8) Now, the problem is finding the overall transfer matrix The propagation of light through mediums includes two ingredients The first is the propagation at the interface of medium i and medium j those have different refractive index For isotropic media, the transfer matrix for interface is a 2x2 matrix defined by: Mij = 𝑡𝑖𝑗 [ 𝑟𝑖𝑗 𝑟𝑖𝑗 ] (2.2.9) With 𝑡𝑖𝑗 and 𝑟𝑖𝑗 are the transmission and reflection amplitudes for light come from medium i to medium j Call that Ni and Nj is the reduced wave vector on propagation direction and 𝜖𝑖 and 𝜖𝑗 are complex dielectric constant of medium i and medium j The reflection and transmission amplitudes for s-polarized light are following [9]: 𝑟𝑖𝑗 = 𝑁𝑖 −𝑁𝑗 𝑁𝑖 +𝑁𝑗 and t 𝑖𝑗 = 2𝑁𝑖 (2.2.10) 𝑁𝑖 +𝑁𝑗 And the corresponding expressions for p-polarized light are: 𝑟𝑖𝑗 = 𝜖𝑖 𝑁𝑗 −𝜖𝑗𝑁𝑖 𝜖𝑖 𝑁𝑗 +𝜖𝑗𝑁𝑖 and t 𝑖𝑗 = 2(𝜖𝑖 𝜖𝑗) 1/2 𝑁𝑖 (2.2.11) 𝜖𝑖 𝑁𝑗 +𝜖𝑗𝑁𝑖 The second ingredient of propagation of light on our problem is the propagation on each medium The propagation matrix Pi of medium i is expressed following: P𝑖 = [ 𝑝𝑖 0 ] 𝑝̅𝑖 (2.2.12) With 𝑝𝑖 = exp(𝑖𝑁𝑖 𝑘0 𝑑𝑖 ) and 𝑝𝑖 = 𝑝̅𝑖 −1 (k0 is vacuum wave vector magnitude and di is thickness of material) Now, we can evaluate overall transfer matrix from two ingredients applying for propagation of light from medium to 3: T = M32 P2 M21 P1 (2.2.13) 13 By this way, the transmittance Tr13 can be calculated with determined complex dielectric constant and thickness of thin film Following Fressnel’s equation [14] the transmittance Trglass of light propagating from glass to To compare with experiment results, the final calculated transmittance is evaluated by: Tr = 𝑇𝑟13 × 𝑇𝑟𝑔𝑙𝑎𝑠𝑠 (2.2.14) 𝑇𝑟𝑔𝑙𝑎𝑠𝑠 This result correspond to measured transmittance of thin film on glass substrate with reference is glass 2.3 Finite Difference Time Domain (FDTD) The Finite-Difference Time-Domain (FDTD) method is the simplest fullwave techniques used to solve problems in electromagnetics The FDTD method can solve complicated problems, but it consumes a lot of computation resource Solutions may demand a large amount of memory and computation time The FDTD method loosely fits into the category of “resonance region” techniques, i.e., ones in which the characteristic dimensions of the domain of interest are somewhere on the order of a wavelength in size If an object is very small compared to a wavelength, quasi-static approximations generally provide more efficient solutions Alternatively, if the wavelength is exceedingly small compared to the physical features of interest, ray-based methods or other techniques may provide a much more efficient way to solve the problem [36] The FDTD method is mainly based on the central-difference approximation This approximation can be applied to both the spatial and temporal derivative in Maxwell’s equation Now, we consider the Taylor series expansions of the function 𝛼 f(x) expanded about the point x0 with an offset of ± : 𝛼 𝛼 𝛼 2 2! f (x0 + ) = f(x0 ) + f ′ (x0 ) + ( ) f ′′ (x0 ) + ⋯ 14 (2.3.1) 𝛼 𝛼 𝛼 2 2! f (x0 − ) = f(x0 ) − f ′ (x0 ) + ( ) f ′′ (x0 ) − ⋯ (2.3.2) where the primes indicate differentiation Subtracting the equation (2.3.1) to the equation (2.3.2), we have: 𝛼 𝛼 2 f (x0 + ) − f (x0 − ) = 𝛼f ′ (x0 ) + ⋯ (2.3.3) Dividing both side to 𝛼 : 𝛼 𝛼 f(x0 + )− f(x0 − ) 𝛼 = f ′ (x ) + ⋯ (2.3.4) Here, we see that with 𝛼 is very small, the parts including high derivative of f(x) are neglect able So, we have an approximation following: df(x) dx x=x0 = 𝛼 𝛼 f(x0 + )− f(x0 − ) (2.3.5) 𝛼 This is the central-difference approximation Since the lowest power of 𝛼 being ignored is the second order, the central difference is said to have second-order accuracy or second-order behavior This implies that if 𝛼 is reduced by a factor of 10, the error in the approximation should be reduced by a factor of 100 (at least approximately) In the limit as 𝛼 goes to zero, the approximation becomes exact The FDTD algorithm as first proposed by Kane Yee in 1966 employs second-order central differences The algorithm can be summarized as follows [36]: Replace all the derivatives in Ampere’s and Faraday’s laws with finite differences Discretize space and time so that the electric and magnetic fields are staggered in both space and time Solve the resulting difference equations to obtain “update equations” that express the (unknown) future fields in terms of (known) past fields Evaluate the magnetic fields one time-step into the future so they are now known (effectively they become past fields) 15 Evaluate the electric fields one time-step into the future so they are now known (effectively they become past fields) Repeat the previous two steps until the fields have been obtained over the desired duration Here, let’s consider dimension problem of FDTD method We assumed that the E-field only has a z component and there are only variations in x direction Following Maxwell’s equation, we can derive two scalar equations corresponding to Faraday’s law and Ampere’s: μ ϵ 𝜕𝐻𝑦 𝜕𝑡 𝜕𝐻𝑦 𝜕𝑡 = = 𝜕𝐸𝑧 (2.3.6) 𝜕𝑥 𝜕𝐸𝑧 (2.3.7) 𝜕𝑥 where μ and ϵ are permeability and permittivity of medium, respectively Then, we could replace the derivatives in (2.3.6) and (2.3.7) with finite differences To convenient, the below notation will be used to indicate the location in space and time that the fields are considered: 𝑞 E𝑧 (x, t) = E𝑧 (m∆x, q∆t) = E𝑧 [m] 𝑞 H𝑦 (x, t) = H𝑦 (m∆x, q∆t) = H𝑦 [m] (2.3.8) (2.3.9) where ∆x is the spatial offset between sample points and ∆t is the temporal offset The index m corresponds to the spatial step, effectively the spatial location, while the index q corresponds to the temporal step Time and x direction can be considered as two independence dimension So, the arrangement of electric- and magnetic-field nodes in space and time is showed in Fig 2.5 Assume that all the fields below the dashed line are known—they are considered to be in the past— while the fields above the dashed line are future fields and hence unknown The FDTD algorithm provides a way to obtain the future fields from the past fields 16 Fig 2.5: The arrangement of electric- and magnetic-field nodes in space and time Now, let consider the space-time point ((m + 1/2)∆x, q∆t) by equation (2.3.6): μ 𝜕𝐻𝑦 𝜕𝑡 (𝑚 + 𝟏/𝟐)∆𝑥,𝑞∆𝑡 = 𝜕𝐸𝑧 (2.3.10) 𝜕𝑥 (𝑚 + 𝟏/𝟐)∆𝑥,𝑞∆𝑡 Using the central approximation, we can see that it possible to derive 𝑞+1/2 unknown value H𝑦 𝑞 𝑞−1/2 [m + 1/2] from available values H𝑦 [m + 1/2] , 𝑞 E𝑧 [m] and E𝑧 [m + 1] following: 𝑞+1/2 μ H𝑦 𝑞−1/2 [m+ ]−H𝑦 𝑞 [m+1/2] = ∆𝑡 𝑞+1/2 Solving this to take H𝑦 𝑞+1/2 H𝑦 𝑞−1/2 [m + ] = H𝑦 𝑞 E𝑧 [m+1]−E𝑧 [m] ∆𝑥 (2.3.11) [m + 1/2]: ∆𝑡 𝜇∆𝑥 [m + ] + 𝑞 𝑞 E𝑧 [m + 1] − E𝑧 [m] (2.3.12) This is known as an update equation, specifically the update equation for the Hy field And by the same way applying for equation (2.3.7), we can derive the update equation for the Ez field After these update equation applying to every 17 electric-field node in the grid, the dividing line between what is known and what are unknown moves forward another one-half temporal step They would be updated again, then the electric fields would be updated, and so on It is often convenient to represent the update coefficients ∆t/ϵ∆x and ∆t/μ∆x in terms of the ratio of how far energy can propagate in a single temporal step to the spatial step The maximum speed electromagnetic energy can travel is the speed of light in free space c = 1/√ϵ0 𝜇0 and hence the maximum distance energy can travel in one time step is c∆t (in all the remaining discussions the symbol c will be reserved for the speed of light in free space) The ratio c∆t/∆x is often called the Courant number which we label Sc It plays an important role in determining the stability of a simulation The more detail consideration about 3D problem and the boundary condition is important to understand clearly about FDTD method but it’s not suitable to discus in here The deeper discussions are provide in many the other relation document [8,17,21,28,30,37] In this study, I use the FullWAVE software by RSOFT design group to process the calculation for materials It allows me to simulate the material in form of thin film or particles to predict optical properties of object The purpose is optimizing grid, boundary condition and domain arrangement to archive good prediction for optical properties of research object 18 CHAPTER 3: EXPERIMENTS 3.1 Silver nanoparticles synthesis 3.1.1 Chemicals Silver nitrate: AgNO3 (Sigma Aldrich) Poly Vinyl Pyrrolidone (PVP) powder Sodium borohydride: NaBH4 (Sigma Aldrich) Distilled water 3.1.2 Process Step 1: Take 0.51 g Poly Vinyl Pyrrolidone and dissolve in 20 mg distilled water, stirring in 60 minutes (solution M2) Step 2: Take 0.05 mg NaBH4 and dissolve in 50 ml distilled water, stirring in 20 minutes (Solution M3) Step 3: Take 0.01 g AgNO3 and dissolve in 10 ml distilled water, stirring in 20 minutes (Solution M1) Step 4: After all the solutes are completely dissolved, Add solution M1 to solution M2, string in 15 minutes (Mixture M) Step 5: After that, drop slowly solution M3 to mixture M The drop flow is less than 1l/second Step 6: After that, keep the string in hour or more Step 7: Purification by centrifugation at 11000 rounds per minutes The centrifugation is repeated times with 20 minutes each time Step 8: The cleaned samples is redistributed into distilled water 19 3.2 Thin films fabrication 3.2.1 Chemicals Poly Vinyl Pyrrolidone (PVP) powder Poly Vinyl Alcohol (PVA) powder Silver nanoparticles solution (Sigma Aldrich) Distilled water 3.2.2 Process Step 1: The solution used to film fabricate is prepared from 20nm diameter silver nanoparticles solution (Sigma Aldrich) with sodium citrate is used as stabilizer and water as solvent It has two types of solution: Solutions made by PVP and silver nanoparticles were prepared by adding nanoparticles solution to PVP powder The mass ratios of nanoparticles solution and PVP powder correspond to 3%, 4% and 5% fill fraction of silver nanoparticles on thin films Solutions made by PVA and silver nanoparticles were prepared by add nanoparticles solution into prepared PVA 10%w.t solution with water as solvent The mass ratios of nanoparticles solution and PVA correspond to 3%, 4% and 5% fill fraction of silver nanoparticles on thin films Step 2: Before film making, the solutions are sonicated for 30 minutes using ultrasonicator bath The thin film was fabricated on glass substrate following methods: Drop coating: 10l prepared solution were dropped into side of glass substrates Then, samples were dried on vacuum at 60oC for more than hours Spin coating: 10l prepared solution were dropped into side of glass substrates The spin program is following: 1500rpm on 60 seconds 500 20 rpm on 10 seconds Then, samples were dried on vacuum at 60oC for more than hours 3.3 Optical properties determination The optical property of thin films is determined by UV – VIS spectrophotometer The measurement investigates transmittance of thin films and solutions on wavelength region from 300nm to 800nm The glass substrates which have thin films are placed directly into measuring chamber The solutions are packaged in cuvettes The reference is glass substrate in case of thin films or distilled water in case of solution The scan speed is 40nm/minute 3.4 Thin films thickness determination The thickness of thin films is determined by the Alpha-step profiler It investigates the height difference of area with and without thin film to derive thickness of thin films The scan mode is 2D on region 10000m The resolution is approximate scan point/m The thickness deviation of this system is around 30nm The thickness of each film is sampled four times then took average 21 CHAPTER 4: RESULTS AND DISCUSSION 4.1 Calculation results 4.1.1 Index of refraction and index of extinction depend on element of particles In this study, it has two host materials which are Poly Vinyl Pyrrolidone (PVP) and Poly Vinyl Alcohol (PVA) Their dielectric functions are considered as constants because they are stable over visible wavelength The considered inclusions are by copper, gold and main object – silver The complex dielectric constants of these elements are functions of wavelength The dielectric constants used for calculations are taken from the available database [30] The calculated index of refraction and index of extinction of types of material based on PVP as host medium following UEM are described in Figure 4.1 and Figure 4.2, respectively The calculation is processed using Maxwell Garnett expression for effective dielectric constant ϵ𝑒𝑓𝑓 The host is PVP with index of refraction as 1.5523 and neglected index of extinction [24] The inclusions are gold, copper and silver with volume fill fraction 3% Index of refraction 2.5 1.5 PVP_Ag3% PVP_Au3% PVP_Cu3% 0.5 0.3 0.4 0.5 0.6 Wavelength (m) 0.7 0.8 Fig 4.1: The index of refraction of PVP including 3% volume fill fraction of silver, gold and copper 22 Index of extinction 1.8 1.6 1.4 1.2 0.8 0.6 0.4 0.2 PVP_Ag3% PVP_Au3% PVP_Cu3% 0.3 0.4 0.5 0.6 Wavelength (m) 0.7 0.8 Fig 4.2: The index of extinction of PVP including 3% volume fill fraction of silver, gold and copper Following Fig 4.1, it’s easily to see that silver nanoparticles should be the most suitable element for low refractive index material It shows the index of refraction about on wavelength region from 390 to 410 nm Comparing with index of refraction of PVP (approximate 1.55), the existence of silver, gold or copper also can decrease index of refraction But, the purpose is fabricating a material which has index of refraction approximate refractive index of air So, silver nanoparticle is chosen as inclusion of material Just composite materials including polymer and silver nanoparticles are considered on later part of thesis The other considered host medium is PVA We also calculated refractive index for material with PVA as host material and inclusion as like as in case of PVP (material and fill fraction) The index of refraction and index of extinction by wavelength are illustrated on Fig 4.3 and Fig 4.4 Actually, both index of refraction and index of extinction of PVA based materials are quite similar as case of PVP The index of refraction of PVA – silver material is about on wavelength region from 385 to 400 nm However, the confirmation that PVP based and PVA based 23 material has similar indexes of refraction is necessary The experimental discussion about two types of material will be showed in more detail later Index of refraction 2.5 1.5 PVA_Ag3% PVA_Au3% PVA_Cu3% 0.5 0.3 0.4 0.5 0.6 Wavelength (m) 0.7 0.8 Fig 4.3: The index of refraction of PVA including 3% volume fill fraction of Index of extinction silver, gold and copper 1.8 1.6 1.4 1.2 0.8 0.6 0.4 0.2 PVA_Ag3% PVA_Au3% PVA_Cu3% 0.3 0.4 0.5 0.6 Wavelength (m) 0.7 0.8 Fig 4.4: The index of extinction of PVA including 3% volume fill fraction of silver, gold and copper 24 For both PVP and PVA cases, the main challenge is shown in Fig 4.2 and Fig 4.4 Although material including silver could have low index of refraction, the index of extinction of it is much higher than the others However, the extinction relate to both index of extinction and thickness of thin film For application for metamaterial, the thickness of thin film should much less than working wavelength that about 40nm in case of silver based material In this case, the extinction is acceptable 4.1.2 Index of refraction and index of extinction depend on volume fill fraction of silver nanoparticles on polymer matrix The index of refraction and index of extinction not only depend on type of material but also relate to fill fraction of inclusion on material The wavelength depend index of refraction for PVP-based and PVA-based material in number of fill fraction are shown in Fig 4.5 and Fig 4.6 Index of refraction Tải FULL (60 trang): https://bit.ly/3GbCZVS Dự phòng: fb.com/TaiHo123doc.net 3.3 PVP_Ag2% 2.8 PVP_Ag3% 2.3 PVP_Ag4% PVP_Ag5% 1.8 1.3 0.8 0.3 0.35 0.4 0.45 0.5 Wavelength (m) 0.55 Fig 4.5: The index of refraction of PVP including 2%, 3%, 4% and 5% volume fill fraction of silver 25 Index of refraction 3.3 PVA_Ag2% 2.8 PVA_Ag3% 2.3 PVA_Ag4% PVA_Ag5% 1.8 1.3 0.8 0.3 0.35 0.4 0.45 0.5 Wavelength (m) 0.55 Fig 4.6: The index of refraction of PVA including 2%, 3%, 4% and 5% volume fill fraction of silver Tải FULL (60 trang): https://bit.ly/3GbCZVS Dự phòng: fb.com/TaiHo123doc.net The fill fraction approximate is achieved in case fill fraction of silver about 3% and higher for both case PVP-based and PVA-based materials Consistent with results in the previous section, the deep of index of refraction spectrum of PVPbased material appears at longer wavelengths than PVA’s The trend of results for PVP-based materials are similar as available results that confirmed by experiment in [33] However, the confirmed results are just limited for wavelength over 500nm The reliability of prediction should be considered by comparison with experiments 26 Index of extiction 3.5 2.5 1.5 0.5 0.35 Ag PVP_Ag2% PVP_Ag3% PVP_Ag4% PVP_Ag5% 0.4 0.45 0.5 Wavelength (mm) 0.55 Fig 4.7: The index of extinction of silver and PVP including 2%, 3%, 4% and 5% Index of extinction volume fill fraction of silver 3.5 2.5 1.5 0.5 0.35 Ag PVA_Ag2% PVA_Ag3% PVA_Ag4% PVA_Ag5% 0.4 0.45 0.5 Wavelength (m) 0.55 Fig 4.8: The index of extinction of silver and PVA including 2%, 3%, 4% and 5% volume fill fraction of silver The dependence of index of extinction on fill fraction is described in Fig 4.7 and Fig 4.8 corresponding to PVP-based and PVA-based materials The position of peak on index of extinction spectrum is quite similar as confirmed result in [15] As inferring naturally, the higher fill fraction is, the greater extinction will be There is 27 6796303