Summary of PSNR calculation.
\r\n\t
",isbn:"978-1-83968-760-0",printIsbn:"978-1-83968-759-4",pdfIsbn:"978-1-83968-761-7",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"cc49d6034d85f8f2e2890c6acc3cc629",bookSignature:"Dr. Abhijit Biswas",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/10285.jpg",keywords:"Mott Insulators, Semi Metals, Polycrystals, Single Crystals, Electronic Properties, Magnetic Properties, PLD, MBE, Topological Insulators, Topological Hall Effect, Devices Applications, Catalysis",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"September 9th 2020",dateEndSecondStepPublish:"October 7th 2020",dateEndThirdStepPublish:"December 6th 2020",dateEndFourthStepPublish:"February 24th 2021",dateEndFifthStepPublish:"April 25th 2021",remainingDaysToSecondStep:"5 months",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:null,kuFlag:!1,biosketch:"A pioneering researcher in the field of tailoring metal oxide crystal surfaces and growth as well as engineering of thin films for various emergent phenomena and energy applications. Dr. Biswas received his Ph.D. from POSTECH, South Korea.",coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"194151",title:"Dr.",name:"Abhijit",middleName:null,surname:"Biswas",slug:"abhijit-biswas",fullName:"Abhijit Biswas",profilePictureURL:"https://mts.intechopen.com/storage/users/194151/images/system/194151.png",biography:"Dr. Abhijit Biswas is a research associate at the Indian Institute of Science Education and Research (IISER) Pune, in India. His research goal is to design and synthesize highest quality epitaxial heterostructures and superlattices, to play with their internal degrees of freedom to exploit the structure–property relationships, in order to find the next-generation multi-functional materials, in view of applications and of fundamental interest. His current research interest ranges from growth of novel perovskite oxides to non-oxides epitaxial films, down to its ultra-thin limit, to observe unforeseeable phenomena. He is also engaged in the growth of high quality epitaxial layered carbides and two-dimensional non-oxide thin films, to exploit the strain, dimension, and quantum confinement effect. His recent work also includes the metal-insulator transitions and magneto-transport phenomena in strong spin-orbit coupled epitaxial perovskite oxide thin films by reducing dimensionality as well as strain engineering. He is also extremely interested in the various energy related environment friendly future technological applications of thin films. In his early research career, he had also extensively worked on the tailoring of metal oxide crystal surfaces to obtain the atomic flatness with single terminating layer. Currently, he is also serving as a reviewer of several reputed peer-review journals.\nDr. Biswas received his B.Sc. in Physics from Kalyani University, followed by M.Sc in Physics (specialization in experimental condensed matter physics) from Indian Institute of Technology (IIT), Bombay. His Ph.D., also in experimental condensed matter physics, was awarded by POSTECH, South Korea for his work on the transport phenomena in perovskite oxide thin films. Before moving back to India as a national post-doctoral fellow, he was a post-doc at POSTECH working in the field of growth and characterizations of strong spin-orbit coupled metal oxide thin films.",institutionString:"Indian Institute of Science Education and Research Pune",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"2",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"Indian Institute of Science Education and Research Pune",institutionURL:null,country:{name:"India"}}}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"20",title:"Physics",slug:"physics"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"205697",firstName:"Kristina",lastName:"Kardum Cvitan",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/205697/images/5186_n.jpg",email:"kristina.k@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. Whether that be identifying an exceptional author and proposing an editorship collaboration, or contacting researchers who would like the opportunity to work with IntechOpen, I establish and help manage author and editor acquisition and contact."}},relatedBooks:[{type:"book",id:"8356",title:"Metastable, Spintronics Materials and Mechanics of Deformable Bodies",subtitle:"Recent Progress",isOpenForSubmission:!1,hash:"1550f1986ce9bcc0db87d407a8b47078",slug:"solid-state-physics-metastable-spintronics-materials-and-mechanics-of-deformable-bodies-recent-progress",bookSignature:"Subbarayan Sivasankaran, Pramoda Kumar Nayak and Ezgi Günay",coverURL:"https://cdn.intechopen.com/books/images_new/8356.jpg",editedByType:"Edited by",editors:[{id:"190989",title:"Dr.",name:"Subbarayan",surname:"Sivasankaran",slug:"subbarayan-sivasankaran",fullName:"Subbarayan Sivasankaran"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1591",title:"Infrared Spectroscopy",subtitle:"Materials Science, Engineering and Technology",isOpenForSubmission:!1,hash:"99b4b7b71a8caeb693ed762b40b017f4",slug:"infrared-spectroscopy-materials-science-engineering-and-technology",bookSignature:"Theophile Theophanides",coverURL:"https://cdn.intechopen.com/books/images_new/1591.jpg",editedByType:"Edited by",editors:[{id:"37194",title:"Dr.",name:"Theophanides",surname:"Theophile",slug:"theophanides-theophile",fullName:"Theophanides Theophile"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3092",title:"Anopheles mosquitoes",subtitle:"New insights into malaria vectors",isOpenForSubmission:!1,hash:"c9e622485316d5e296288bf24d2b0d64",slug:"anopheles-mosquitoes-new-insights-into-malaria-vectors",bookSignature:"Sylvie Manguin",coverURL:"https://cdn.intechopen.com/books/images_new/3092.jpg",editedByType:"Edited by",editors:[{id:"50017",title:"Prof.",name:"Sylvie",surname:"Manguin",slug:"sylvie-manguin",fullName:"Sylvie Manguin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3161",title:"Frontiers in Guided Wave Optics and Optoelectronics",subtitle:null,isOpenForSubmission:!1,hash:"deb44e9c99f82bbce1083abea743146c",slug:"frontiers-in-guided-wave-optics-and-optoelectronics",bookSignature:"Bishnu Pal",coverURL:"https://cdn.intechopen.com/books/images_new/3161.jpg",editedByType:"Edited by",editors:[{id:"4782",title:"Prof.",name:"Bishnu",surname:"Pal",slug:"bishnu-pal",fullName:"Bishnu Pal"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"72",title:"Ionic Liquids",subtitle:"Theory, Properties, New Approaches",isOpenForSubmission:!1,hash:"d94ffa3cfa10505e3b1d676d46fcd3f5",slug:"ionic-liquids-theory-properties-new-approaches",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/72.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1373",title:"Ionic Liquids",subtitle:"Applications and Perspectives",isOpenForSubmission:!1,hash:"5e9ae5ae9167cde4b344e499a792c41c",slug:"ionic-liquids-applications-and-perspectives",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/1373.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"57",title:"Physics and Applications of Graphene",subtitle:"Experiments",isOpenForSubmission:!1,hash:"0e6622a71cf4f02f45bfdd5691e1189a",slug:"physics-and-applications-of-graphene-experiments",bookSignature:"Sergey Mikhailov",coverURL:"https://cdn.intechopen.com/books/images_new/57.jpg",editedByType:"Edited by",editors:[{id:"16042",title:"Dr.",name:"Sergey",surname:"Mikhailov",slug:"sergey-mikhailov",fullName:"Sergey Mikhailov"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"371",title:"Abiotic Stress in Plants",subtitle:"Mechanisms and Adaptations",isOpenForSubmission:!1,hash:"588466f487e307619849d72389178a74",slug:"abiotic-stress-in-plants-mechanisms-and-adaptations",bookSignature:"Arun Shanker and B. Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"878",title:"Phytochemicals",subtitle:"A Global Perspective of Their Role in Nutrition and Health",isOpenForSubmission:!1,hash:"ec77671f63975ef2d16192897deb6835",slug:"phytochemicals-a-global-perspective-of-their-role-in-nutrition-and-health",bookSignature:"Venketeshwer Rao",coverURL:"https://cdn.intechopen.com/books/images_new/878.jpg",editedByType:"Edited by",editors:[{id:"82663",title:"Dr.",name:"Venketeshwer",surname:"Rao",slug:"venketeshwer-rao",fullName:"Venketeshwer Rao"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"4816",title:"Face Recognition",subtitle:null,isOpenForSubmission:!1,hash:"146063b5359146b7718ea86bad47c8eb",slug:"face_recognition",bookSignature:"Kresimir Delac and Mislav Grgic",coverURL:"https://cdn.intechopen.com/books/images_new/4816.jpg",editedByType:"Edited by",editors:[{id:"528",title:"Dr.",name:"Kresimir",surname:"Delac",slug:"kresimir-delac",fullName:"Kresimir Delac"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"58005",title:"Structure-Induced Ultratransparency in Photonic Crystals",doi:"10.5772/intechopen.71274",slug:"structure-induced-ultratransparency-in-photonic-crystals",body:'\nPhotonic crystals (PhCs), as periodic arrangement of dielectrics, affect the motion of photons and electromagnetic (EM) waves in much the same way that semiconductor crystals affect the propagation of electrons, providing a new mechanism to control and manipulate the flow of light at wavelength scale [1, 2, 3, 4, 5]. The key property of the PhCs is the photonic band gap induced from the periodic modulation of photons and EM waves, which can block wave propagation in certain or all directions. As photonic band-gap materials, PhCs play vital roles in light confinement and optical manipulation, promising many important applications, such as omnidirectional reflectors [6, 7], waveguides [8, 9], fibers [10], high-Q nanocavities and laser [11, 12], and angular filters [13].
\nHowever, little attention has been paid to the effect of enhancing transparency. Although there are pass bands in PhCs, they are usually reflective and, therefore, not transparent enough. As we know, transparent media are the foundation of almost all optical instruments, such as optical lens. However, perfect transparency has never been realized in natural transparent solid materials such as glass because of the impedance mismatch with free space. On the other hand, in the past decades, artificial EM materials like metamaterials [14, 15, 16, 17, 18, 19, 20] have been proposed to realize unusual EM properties beyond natural materials. However, most of the researches were focused on the realization of abnormal refractive behaviors such as negative refraction. Transparency over a large range of incident angle or a large frequency spectrum is theoretically possible, but the experimental realization is very difficult as complex and unusual parameters are required.
\nThe photonic band-gap effect is actually induced by the periodic modulation of the reflections on the surfaces of dielectrics. That is, the periodic modulation strengthens the reflections on the surfaces of dielectrics to form a complete band gap at particular frequencies. Then, a natural question is: Is it possible to rearrange the periodic modulation of the reflections on the surfaces of dielectrics to make them cancel each other for all incident angles, so that omnidirectional impedance matching and omnidirectional perfect transmission can be realized?
\nIn this chapter, we show the opposite effect of the band-gap effect in PhCs, i.e., the structure-induced ultratransparency effect [21, 22]. Ultratransparent PhCs not only have the omnidirectional impedance matching with the background medium, but also have the ability of forming aberration-free virtual images. The equal frequency contours (EFCs) of such ultratransparent PhCs are designed to be elliptical and “shifted” in the k-space and thus contain strong spatial dispersions and provide more possibilities for omnidirectional impedance matching. Interestingly, the combination of perfect transparency and elliptical EFCs satisfies the essential requirement of ideal transformation optics (TO) devices [23, 24, 25, 26, 27]. Therefore, such ultratransparent PhCs not only provide a low-loss and feasible platform for TO devices at optical frequencies, but also enable new freedom for phase manipulation beyond the local medium framework. Moreover, such ultratransparent PhCs have shown enormous potential applications in the designs of microwave transparent wall, nonreflection lens, omnidirectional polarizer, and so on.
\nIt is well known that the band-gap effect induced by the periodic distribution of dielectrics can block the propagation of EM waves in certain or all directions, as illustrated in Figure 1(a). The forbiddance of wave propagation is the result of lacking propagation modes within the PhCs, which can be seen from the EFCs in Figure 1(a). The circle in the left denotes the EFC of free space, and there is no dispersion of the PhCs within the band gap. Interestingly, we would like to rearrange the periodic array of dielectrics to obtain the omnidirectional impedance matching effect, which allows near 100% transmission of light at all incident angles, as illustrated in Figure 1(b).
\n(a) Total reflection by a PhC slab with complete photonic band gap. (b) Aberration-free virtual image formation through an ultratransparent medium without any reflection due to omnidirectional impedance matching. The arrows and dashed lines in (a) and (b) represent the light rays from a point source, and the back-tracing lines, respectively. The inset graphs show the corresponding EFCs.
Moreover, we expect such media to have the ability of forming aberration-free virtual images, which is absent in normal transparent media like glass. By using ray optics, it can be easily shown that transmitted rays from a point source behind a dielectric slab would form a “blurred” area of virtual image rather than a point image. For demonstration, we placed a point source on the left side of a glass slab (with a thickness of \n
The formation of “blurred” virtual image by a glass slab. (a) The existence of general reflection and aberration in virtual images behind a glass slab. (b) The zoom in “blurred” image in the region marked by dashed lines in (a). (c) The position of the virtual image for the observation from different positions.
Actually, such aberrations of the virtual image originate from the mismatch between the EFCs of free space and dielectrics, i.e., their EFCs do not have the same height in the transverse direction (i.e., the \n
where \n
Supposing that the rearrangement of the periodic array of dielectrics not only makes the whole structure impedance matched to free space for all incident angles, but also creates the unique EFC described by Eq. (1); thus, both omnidirectional 100% perfect transmission and aberration-free virtual imaging are enabled simultaneously. Apparently, such a level of transparency is superior to that of normal transparent media like dielectrics and is thus hereby denoted as ultratransparency.
\nAccording to Fresnel equations, reflection of light on the surface of dielectrics is inevitable, except at a single-incident angle referred to as the Brewster angle under transverse magnetic (TM) polarization, as demonstrated in Figure 3(a). Here, we extend the impedance matching from one particular angle (i.e., Brewster angle) to all incident angles in a nonlocal or spatial dispersive medium, whose effective permittivity \n
(a) There exist reflected waves at the interface of free space and dielectrics except for the Brewster angle for TM polarization. (b) Nonreflection and total transmission on the surface of ultratransparent nonlocal media for all incident angles. The thin circle, thick circle, and curves in the inset graphs denote the EFCs of air, dielectrics, and the nonlocal media, respectively.
To begin with, we assume that the nonlocal medium exhibits an irregular-shaped EFC shown in Figure 3(b). An incident wave of transverse electric (TE) polarization with electric fields polarized in the \n
which determines the relationship between the components of wave vectors \n
In this case, the wave impedance of free space can be derived as \n
If Eq. (3) can be satisfied for all \n
An obvious local medium solution of Eq. (3) is that \n
Eq. (4) shows that when EM parameters possess spatial dispersions, there exist infinite solutions of \n
For the design of ultratransparent PhCs, we first propose a nonlocal effective medium theory for the homogenization of PhCs. Here, we consider uniform plane wave incidence. In this situation, the validity of the nonlocal effective medium theory lies in the satisfaction of the following four premises: (1) single-mode approximation [28], i.e., only one eigen-mode is excited; (2) the amplitudes of fields at the incident boundary are almost constant; (3) the phases of fields at the incident boundary obey the trigonometric functions; and (4) the electric and magnetic fields are in phase at the incident boundary. Although these premises are seemingly stringent, it turns out that most eigen-modes of the first few bands (e.g., monopolar and dipolar bands) can indeed satisfy these requirements (Figure 4).
\nSchematic graph of the unit cell for the nonlocal effective medium theory.
With the assumption of the abovementioned premises, eigen-fields of TE polarization at the boundary \n
where \n
On the other hand, the PhC satisfying previous premises generally can be described as a uniform medium with effective relative permittivity \n
Compared with Eqs. (5) and (6), the effective parameters can be derived as,
\n\n\n
With Eq. (7), the effective parameters of the PhC can be obtained by analyzing the eigen-fields with Bloch wave vector \n
PhCs contain strong spatial dispersions and thus provide the perfect candidate for realization of ultratransparency effect. Here, we demonstrate a type of PhCs composed of a rectangular array of dielectric rods in free space, with the unit cell shown in Figure 5(a). Under TE polarization, the band structure is presented in Figure 5(b), and the EFC of the third band is plotted in the reduced first Brillouin zone in Figure 5(c). The working frequency is chosen as \n
(a) Illustration of the unit cell of the ultratransparent PhC. (b) The band structure of the PhC. The dashed line denotes the working frequency \n\nfa\n/\nc\n=\n0.3183\n\n. (c) The EFC of the third band. The left and right dashed lines denote the EFCs of air and the PhC at the frequency \n\nfa\n/\nc\n=\n0.3183\n\n. (d) The impedance difference of the PhC and free space of the third band. Reprinted (figure) with permission from Ref. [21]. Copyright (2016) by the American Physical Society.
Figure 5(d) shows the impedance difference of the PhC and free space of the third band, i.e., \n
Moreover, in Figure 6(a), we present the effective parameters \n
(a) The effective parameters \n\n\nε\n\nz\n,\neff\n\n\n\n, \n\n\nμ\n\nx\n,\neff\n\n\n\n, and \n\n\nμ\n\ny\n,\neff\n\n\n\n retrieved from the eigen-fields based on Eq. (7) (symbols) and predicted by the ultratransparency condition based on Eq. (9) (dashed lines). (b) Calculated transmittance through a PhC slab with \n\nN\n\n (= 4, 5, 6, 15) layers of unit cells as the function of incident angles. Reprinted (figure) with permission from Ref. [21]. Copyright (2016) by the American Physical Society.
Now, by substituting the condition \n
The choice of \n
For further verification, the transmittance through such a PhC slab consisting of \n
In fact, for transparency in a relatively smaller range of incident angles, the design process is much easier and the effect can exist in much simpler structures. In the following, we demonstrate a simple ultratransparent PhC, which is verified by proof-of-principle microwave experiments. The PhC consists of rectangular alumina (\n
(a) Band diagram of the experimental PhC for TE polarization. The dashed line denotes the working frequency \n\nfa\n/\nc\n=\n0.4723\n\n. The inset is the illustration of the unit cell of the PhC. (b) EFCs in the frequency range \n\n0.397\n≤\nfa\n/\nc\n≤\n0.547\n\n. The left and right dashed lines denote the EFCs of air and the PhC at the frequency \n\nfa\n/\nc\n=\n0.4723\n\n. (c) The impedance difference of the PhC and the free space in the frequency range \n\n0.397\n≤\nfa\n/\nc\n≤\n0.547\n\n.
In addition, the impedance difference between the PhC and the free space is calculated by using Eq. (5), as shown in Figure 7(c). Clearly, the impedance difference is very small on the EFC of \n
Moreover, the effective parameters obtained from Eq. (7) are presented in Figure 8(a) by solid lines with symbols, showing \n
(a) Effective parameters \n\n\nε\n\nz\n,\neff\n\n\n\n, \n\n\nμ\n\nx\n,\neff\n\n\n\n, and \n\n\nμ\n\ny\n,\neff\n\n\n\n retrieved from the eigen-fields based on Eq. (7) (solid lines with symbols) and predicted by the ultratransparency condition based on Eq. (11) (dashed lines). (b) Transmittance through a \n\nN\n\n (= 4, 5, 6, 15)-layered PhC slab as the function of incident angles.
In Figure 8(a), the dashed lines denote \n
Furthermore, we calculate the transmittance through the PhC slab with \n
Next, we show microwave experimental results to verify the above theory. A 23 × 5 array of such a PhC is assembled in the \n
(a) Photo of the PhC composed of alumina bars (white) placed inside the microwave field mapper. The measured electric-field distributions for microwave beams with incident angles of (b) 0°, (c) 30°, and (d) 45°. Reprinted (figure) with permission from Ref. [21]. Copyright (2016) by the American Physical Society.
The measured electric fields for 0°, 30°, and 45° incident angles are displayed in Figure 9(b), (c), and (d), respectively. Clearly, the reflection is barely noticeable, indicating impedance matching for all these incident angles. In Figure 10, the measured transmittance (triangular dots) coincides with simulation results (solid lines) quite well, both showing great enhancement compared with that through an alumina slab with the same thickness (dashed lines). Although the ultratransparency effect is hereby only verified at the microwave frequency regime, the principle can be extended to optical frequency regime by using PhCs composed of silicon or other dielectrics.
\nTransmittance through the PhC slab in simulations (solid lines) and experiments (triangular dots) and an alumina slab having the same thickness (dashed lines) as the function of incident angles. Reprinted (figure) with permission from Ref. [21]. Copyright (2016) by the American Physical Society.
In the above, we have shown the structure-induced ultratransparency in two-dimensional PhCs. In the following, we demonstrate the structure-induced ultratransparency in one-dimensional PhCs [22].
\nThe one-dimensional ultratransparent PhC we studied is composed of two dielectric materials A and B stacked along the \n
(a) and (b) show general reflection on the slab made of materials A and B, respectively. (c) Elimination of general reflection by a one-dimensional ultratransparent PhC composed of ABA unit cells. The orange arrows represent the rays of light emitted by a point source. Reprinted (figure) with permission from Ref. [22]. Copyright (2016) by the Optical Society.
Figure 12(a) presents the band structure of the PhC, whose unit cell is constructed in a symmetric form, i.e., ABA structure, as shown by the inset in Figure 12(a). The relative permittivity and filling ratio of the material A (B) are 2 (6) and 0.6 (0.4), respectively. The dashed line denotes the normalized frequency \n
(a) Band structures of the PhC for TE and TM polarizations. The dashed lines denote the working frequency \n\nfa\n/\nc\n=\n0.397\n\n. The inset denotes the illustration of the unit cell. (b, d) the EFCs of the PhC and (c, e) the impedance difference between PhC and free space in the second band for (b, c) TE and (d, e) TM polarizations. Reprinted (figure) with permission from Ref. [22]. Copyright (2016) by the Optical Society.
In Figure 12(b) and (d), the EFCs at the frequency \n
For further verification, the transmittance through the PhC slab composed of \n
(a) The numerical setup for the transmission computation. The color denotes the distribution of electric fields under \n\nθ\n=\n\n45\n∘\n\n\n incident angle. (b) Transmittance as the function of the incident angle when EM waves propagate through the PhC slab composed of \n\nN\n\n (= 4, 5, 6, 15) unit cells. Reprinted (figure) with permission from Ref. [22]. Copyright (2016) by the Optical Society.
Moreover, in Figure 14(a) and (b), the transmittance through a PhC slab (\n
Transmittance as the functions of the incident angle and the frequency for (a) TE- and (b) TM-polarized waves propagating through the PhC slab with 10 unit cells. Reprinted (figure) with permission from Ref. [22]. Copyright (2016) by the Optical Society.
Although a wide-angle (\n
In the above, we have demonstrated the ultratransparency in both one- and two-dimensional PhCs. In the following, we show some applications of such ultratransparent PhCs. It is interesting to note that the omnidirectional perfect transparency and elliptical EFCs of the ultratransparent media are essential for ideal TO devices. The theory of TO [23, 24, 25, 26, 27] promises many novel and interesting applications, such as invisibility cloaks [23, 25, 31, 32], concentrators [33], illusion optics devices [34, 35, 36], and simulations of cosmic phenomena [37, 38]. Generally, the TO devices are realized by using metamaterials [14, 15, 16, 17, 18, 19, 20], which require complicated designs of electric and magnetic resonances, hindering the realization and applications in practice. In fact, most of the previous TO experiments were realized by using the so-called reduced parameters, which maintain the refractive behavior, but sacrifice the impedance matching as well as the perfect transparency [25, 39, 40, 41, 42, 43, 44, 45]. Moreover, at optical frequencies, the inherent loss in metallic components of metamaterials makes the realization of perfect transparency as well as the ideal nonreflecting TO devices extremely difficult [46, 47], if not impossible. Interestingly, we find that the ultratransparent PhCs provide a low-loss and feasible platform for TO devices at optical frequencies.
\nTo begin with, we consider a TO medium obtained by stretching the coordinate along the \n
where \n
Considering Eq. (12), the dispersion of the TO medium, i.e., \n
which has the similar form as that of Eq. (1). The EFC of the TO medium is an ellipse having the same height as the EFC of air in the \n
(a) Upper inset: the EFCs of air (the left circle) and TO media obtained by stretching air in the \n\nx\n\n direction (the right ellipse). Lower inset: scheme of the TO medium slab (with loose mesh) in the background medium of air (with dense mesh). (b) Upper: the EFC of the ultratransparent PhC (the right ellipse with solid lines), which has a “shift” in the \n\n\nk\nx\n\n\n direction compared with the EFC of the TO media (dashed lines). Lower inset: the ultratransparent PhC is used to replace the TO medium slab in (a).
The only difference of the EFCs between the TO medium and the ultratransparent medium is that there may exist a “shift” of \n
For demonstration, we show a specific example in Figure 16. The ultratransparent PhC is one-dimensional and composed of components I and II. The unit cell is constructed in a symmetric way with a lattice constant of \n
(a) The EFCs of the PhC for TE polarization. The solid line and dashed line denote the EFCs of the PhC and the TO medium at the normalized frequency \n\nfa\n/\nc\n=\n0.402\n\n, respectively. (b, c) The snapshot of electric fields for wave propagating through a TO medium slab (upper inset) and a PhC slab (lower inset) under an incident angle of 45°. The thickness of the TO medium slab is (b) \n\n5\na\n\n, (c) \n\n6\na\n\n, and the number of unit cells of the PhC slab is (b) 5, (c) 6.
Moreover, simulations of wave propagation through the TO medium slab with a thickness of \n
Next, we show an example of TO device by using one-dimensional ultratransparent PhCs. The design process is shown in Figure 17(a), in which the original shell of a concentrator [33] is discretized into four layers and each layer is further replaced by a corresponding ultratransparent PhC. Figure 17(b) shows the parameters of the discretized layers of TO media and the ideal profile. The corresponding four types of ultratransparent PhCs are of the same lattice constant \n
(a) Illustration of the design process from a concentrator composed of discretized layers of TO media (upper) to one composed of ultratransparent PhCs (lower). (b) Parameters of the discretized layers of TO media and the ideal profile. (c) EFCs of the discretized layers of TO media (dashed lines) and the corresponding PhCs (solid lines). Reprinted (figure) with permission from Ref. [21]. Copyright (2016) by the American Physical Society.
The detailed parameters of the PhCs are presented in Figure 18. The insets present the illustrations of unit cells, relative permittivities, and thicknesses of each component of the four different PhCs. Moreover, the transmittance through PhC slabs with 10 unit cells is plotted as the function of incident angles, as shown by the solid lines in Figure 18(a–d). During the calculation, the background media are chosen as the discretized TO media (Figure 17(b)) with the parameters \n
Transmittance through the PhC slabs with 10 unit cells as the function of incident angles. The PhCs in (a), (b), (c), and (d) correspond to the PhCs in regions A, B, C, and D, respectively. The insets are the structure, the relative permittivities, and the thicknesses of the components of the PhCs.
Moreover, numerical simulations are performed to demonstrate the functionality of the concentrator. Figure 19(a) and (b) corresponds to the concentrator composed of the original discretized TO media and the ultratransparent PhCs, respectively. It is seen that under an incident beam of Gaussian wave from the lower left, both concentrators exhibit good concentration effects in the core areas and induce almost no scattering of waves. Interestingly, the waves inside the core areas exhibit a distinct phase difference of \n
Electric field distributions in the concentrators made of (a) discretized TO media and (b) ultratransparent PhCs. Reprinted (figure) with permission from Ref. [21]. Copyright (2016) by the American Physical Society.
Therefore, we have demonstrated that ultratransparent media can work as the TO media to realize TO devices. Such ultratransparent media not only provide a low-loss and feasible platform for TO devices at optical frequencies, but also enable new freedom for phase manipulation beyond the local medium framework.
\nIn the microwave regime, the ultratransparent media are also very useful and may have many applications in the design of radome, transparent wall, and so on. Here, we show an example of microwave transparent wall which allows the WiFi and 4G signals to pass through freely, and thus may find applications in architectural designs.
\nThe microwave transparent wall is composed of one-dimensional ultratransparent PhCs with ABA unit cells. Materials A and B are chosen as polypropylene (\n
Transmittance with respect to the incident angle and the frequency for EM waves propagating through a slab made of (a) material A for the TE polarization, (b) material B for the TE polarization, (c, d) 10 unit cells of ABA for the (c) TE and (d) TM polarizations. Reprinted (figure) with permission from Ref. [22]. Copyright (2016) by the Optical Society.
In this chapter, we introduced the recent results of the structure-induced ultratransparency effect in both one- and two-dimensional PhCs, which allow near 100% transmission of light for all incident angles and create aberration-free virtual images. The ultratransparency effect is well explained by nonlocal effective medium theory for PhCs and verified by both simulations and proof-of-principle microwave experiments. The design principle lies in systematic tuning of the microstructures of the PhCs based on the retrieved nonlocal effective parameters.
\nWith the ultratransparent media, many applications can be expected such as the perfectly transparent optical lens, ideal TO devices, microwave transparent devices, and solar cell packaging. Interestingly, the ultratransparent media with “shifted” elliptical EFC not only provides a low-loss and feasible platform for TO devices at optical frequencies, but also enables new degrees of freedoms for phase manipulation beyond the local medium framework. In addition, microwave transparent walls allowing the WiFi and 4G signals to pass through freely can also be realized.
\nAlthough the ultratransparency effect is mainly demonstrated for TE polarization here, the principle is general and can be extended to TM polarization, or even both polarizations. Polarization-independent ultratransparency has wide and important applications. On the other hand, polarization-dependent ultratransparent media could also have some special applications. For instance, if the PhC is ultratransparent for TE polarization, while the working frequency falls in an omnidirectional band gap for TM polarization, such a PhC would work as an omnidirectional polarizer.
\nThe concept and theory of ultratransparency give a guideline for pursuing solid materials with the ultimate transparency, i.e., broadband, omnidirectional, and polarization-insensitive total transparency. In the future, ultratransparent solid materials may be optimized to exhibit an unprecedented level of transparency and find vital applications in various fields.
\nThis chapter is supported by National Natural Science Foundation of China (No. 11374224, 11574226, 11704271), Natural Science Foundation of Jiangsu Province (No. BK20170326), Natural Science Foundation for Colleges and Universities in Jiangsu Province of China (No. 17KJB140019), Jiangsu Planned Projects for Postdoctoral Research Funds (1701181B) and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).
\nCompression of images is an important application in the field of satellite image processing as it is suitable for optimization of storage space and sharing over internet with optimum bandwidth utilization. For compression of satellite images, it is performed either directly from the image or from transformed part of the images. As discussed in [1] the compression of satellite images is based on Block Truncation Coding (BTC) technique. It first converts RGB satellite image into HSV planes. After that, each of the H and S planes are encoded using block truncation coding with quad clustering and V plane is encoded with BTC based bi-clustering or tri clustering depending on the edge information present in the plane. This method is better than previous BTC methods compared to visual quality of the output image. [2] discussed the image compression method based on evidence theory and k-Nearest Neighbor (KNN) algorithm. The main drawback is that the information loss is large [2]. To improve the quality of the output image, Fourier Transform and Huffman Coding is used for modification the previous technique. In both method, visual quality of satellite image is poor. [3] discusses the use of integer wavelet regression by increasing temporal correlation, which consequently improves the compression gain. [4] discusses a satellite image compression technique using discrete wavelet transform for noise removal to compress satellite images. [5] has discussed the use only hardware-based solutions in this lossless compression technique of X Sat images. [6] has analyzed the use of Discrete Wavelet Transform in their lossy image compression work and performance of different wavelets for satellite image compression. [7] has used the conventional Discrete Cosine Transform system for lossless image compression. [8] proposes an image compression technique using multiplexing and encryption by optical grating method [9, 10, 11, 12].
In this chapter, we proposed a scheme to compress multiple high-resolution satellite images by using phase grating. Each image is modulated by applying high value of spatial frequency and a fixed orientation angles. For each image, multiple bands have been generated due to modulation which are placed in the same spectrum plane (only three bands are clearly visible). The spectrum is encoded and filtered using Gauss filtering. To detect the location of maximum image information, an intensity graph has been plotted in the decrypted plane. All stored images can be securely and efficiently retrieved by applying inverse Regional Fourier Transform operation. This proposed technique is simple and suitable for optimization of storage space and bandwidth in satellite communication.
The chapter is organized as follows:
Section I describes the location and data used in this chapter
Section II discusses the proposed compression method
Section III presents proposed methodology of our research work
Section IV provides result of our research work and PSNR value of the extracted images
Section V concludes the paper and discuss why low compression ratio is desired for land cover analysis.
Images which are used in our research work, collected from Regional Remote Sensing Centre (East). The images are satellite picture of different areas in Kolkata Metropolitan Area.
All satellite images used in this paper are captured by LISS III 23 m sensor. LISS- III sensor is an optical sensor working in four spectral bands (Green, Red, Near Infrared and Short-Wave Infrared). It covers a 141 km- wide swath with a resolution of 23 meters in all spectral bands [13, 14].
According to rule of phase grating, value of the grating frequency (𝑢0) should be high. Low grating frequency is creating aliasing problem and therefore it would be very difficult to reconstruct the original image. In this chapter, we propose to select 𝑢0 = 1400, which is sufficient for filtering. In grating, value of the orientation angle (θ) varies from 0 to 3600. We have worked with 0 deg orientation angle.
The diffraction gratings used are illustrated in Figures 1 and 2.
Sinusoidal phase grating along x axis.
Spectrum of an image due to modulation.
Let us assume that image, denoted by
Invoking the well-known convolution theorem, the Fourier transform of this modulated object is given by,
The diffraction pattern, as given by Eq. (2) is a series of diffraction spots each containing the object spectrum. Considering the zero order and the first two orders of the spectrum, Eq. (2) may be represented by,
The reconstruction of images is achieved by decrypting the encrypted plane followed by plotting an intensity graph of the spectrum horizontally. This intensity graph is generated using the intensity values with respect to its location (pixel position). In the intensity graph, peak values indicate the brightest spots, where information of images are maximum. To avoid any human intervention, system automatically finds the intensity level horizontally, vertically and diagonally. In addition, regional Inverse Fourier Transform is applied around the peaks by using a fixed cut-off frequency. As only one sideband is enough for image reconstruction, hence we select one side-band. This spectrum is filtering using a cut-off value of 120. Proper operating frequency is selected and there is no overlapping during the band selection, so the extracted images are free from aliasing problem. As center band contains the information of all images, therefore filtering is not applied across center band.
PSNR value is calculated using Mean Square Error (MSE) approach:
Where
Satellite Images chosen for testing the algorithm described in Section III are shown in Figure 3(a)-(c). The dimensions of the selected images are 512 x 512.
Three high Resolution Satellite Images.
During zonal filtering operation, images 𝑓1(𝑥, 𝑦), 𝑓2(𝑥, 𝑦) and 𝑓3 (𝑥, 𝑦) have been extracted by Regional Inverse Fourier Transform taking upper spectrum from horizontal direction. Extracted images are shown in Figure 4(a)-(c), respectively. A summary of the PSNR calculation is presented in Table 1.
Three extracted images.
Image | Original image size (kB) | Compression ratio (compressed image/original image) | PSNR |
---|---|---|---|
𝑓1(𝑥, 𝑦) | 242 | 0.84 | 32.5 |
𝑓2(𝑥, 𝑦) | 240 | 0.81 | 31.73 |
𝑓3 (𝑥, 𝑦) | 254 | 0.86 | 31.6 |
Summary of PSNR calculation.
In this chapter, phase grating technique has been proposed for compressing the high- resolution satellite images in frequency domain. The original image is retrieved by applying Inverse Fourier Transform from the respective spectrum of the image. As presented here, since we have taken only few coefficients from the spectrum, the size of the output image is less than the main original image. It should be mentioned that in high resolution satellite image, compression should be as minimum as possible. The main reason for the requirement of low compression ratio is mainly due to large geographical area representation (as these images contain a lot of information). High compression ratio is not suitable for accurate land cover analysis. To maintain the same dimension with original image and to avoid aliasing effect, spectral area is carefully selected. Compared with earlier methods, visual quality of the selected satellite images is very good as it is captured by optical LISS-III sensor. Our proposed technique is simple and suitable for optimization of storage space and bandwidth in satellite communication.
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