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Nanoscale Phenomena Underpinning Nanophotonics

This chapter explores the physical phenomena that distinguish nanophotonics from photonics. The chapter is organized in sections on photonic crystals (structures on the scale of the optical wavelength), metamaterials (structures much less than the optical wavelength), plasmonics (structures using the large, negative permittivity of metals to manipulate optical fields), and reduced dimensionality and quantum confinement (semiconductor nanostructures on the scale of electronic wave functions). Because many of the phenomena of nanophotonics are largely electromagnetic in origin, the discussion also includes applications to longer wavelengths (terahertz) to which the appellation “nano” no longer strictly applies. A very important caveat: the research areas discussed here are very active, with new developments being announced at a breakneck pace; the report provides a snapshot, frozen in time in the spring of 2007, of things that will inevitably have changed by the time the report is being circulated. Nonetheless, it is important to elucidate the fundamental concepts and to establish the vector along which the field of nanophotonics is progressing.

SPATIAL MODULATION AT FRACTIONS OF A WAVELENGTH—PHOTONIC CRYSTALS

Introduction

In a paper published in 1987, Yablonovitch anticipated the possibility of inhibited spontaneous emission in solid-state materials through the formation of a three-dimensionally periodic dielectric structure with spatial periodicity on the order of the wavelength of the light considered (Yablonovitch, 1987). Such periodic structures can be formed from two materials that have different indices of refraction—for example, air and SiO2. In the same time frame, S. John published a similarly visionary paper that speculated on strong localization of photons in “certain disordered superlattice microstructures of sufficiently high dielectric constant” (John, 1987). These papers formed the foundations of the tremendously fertile and productive research field of photonic crystals: this field involves engineered optical materials providing a multitude of ways to tailor the propagation of light through the control of the photonic crystal structure. While the first demonstrations of photonic crystal behavior were carried



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2 Nanoscale Phenomena Underpinning Nanophotonics This chapter explores the physical phenomena that distinguish nanophotonics from photonics. The chapter is organized in sections on photonic crystals (structures on the scale of the optical wavelength), metamaterials (structures much less than the optical wavelength), plasmonics (structures using the large, negative permittivity of metals to manipulate optical fields), and reduced dimensionality and quantum confinement (semiconductor nanostructures on the scale of electronic wave functions). Because many of the phenomena of nanophotonics are largely electromagnetic in origin, the discussion also includes applications to longer wavelengths (terahertz) to which the appellation “nano” no longer strictly applies. A very important caveat: the research areas discussed here are very active, with new developments being announced at a breakneck pace; the report provides a snapshot, frozen in time in the spring of 2007, of things that will inevitably have changed by the time the report is being circulated. Nonetheless, it is important to elucidate the fundamental concepts and to establish the vector along which the field of nanophotonics is progressing. SPATIAL MODuLATION AT FRACTIONS OF A WAVELENGTH—PHOTONIC CRYSTALS Introduction In a paper published in 1987, Yablonovitch anticipated the possibility of inhibited spontaneous emission in solid-state materials through the formation of a three-dimensionally periodic dielectric structure with spatial periodicity on the order of the wavelength of the light considered (Yablonovitch, 1987). Such periodic structures can be formed from two materials that have different indices of refrac- tion—for example, air and SiO2. In the same time frame, S. John published a similarly visionary paper that speculated on strong localization of photons in “certain disordered superlattice microstructures of sufficiently high dielectric constant” (John, 1987). These papers formed the foundations of the tremen- dously fertile and productive research field of photonic crystals: this field involves engineered optical materials providing a multitude of ways to tailor the propagation of light through the control of the photonic crystal structure. While the first demonstrations of photonic crystal behavior were carried 

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0 NANOphOTONICS out at microwave frequencies in scaled structures of 6 millimeter (mm) Al 2O3 spheres (Yablonovitch and Gmitter, 1989) or drill/etched Stycast 12 (Yablonovitch et al., 1991), current research on photonic crystals truly embodies the concepts of “nanophotonics,” with spatial index modulation (etched holes or solid rods) at the 100 nanometer (nm) scale, allowing compact, highly integrable waveguides, filters, resonators, and high-efficiency lasers. The original predictions of Yablonovitch and John have been realized: first reports of photonic crystal lasers were made in 1999 (Painter et al., 1999), and localiza- tion of photons within photonic crystal “defects” was first observed in 1991 in the microwave regime (Yablonovitch et al., 1991a). Photonic Band Gap A key idea for photonic crystal structures is the periodicity of the structure giving rise to the forma- tion of a forbidden gap in the electromagnetic spectrum, thus altering the properties of the light passing through the structure. One-, two-, and three-dimensional photonic crystals, as well as a photonic band structure are described in Figure 2-1. The photonic band gap defines a set of frequencies for which light cannot propagate in the crystal: the tunability of the band gap, through control of the dimensions and symmetry of the photonic structure, provides exquisite frequency control for multiple wavelength information processing (or wavelength division multiplexing, WDM). Various photonic crystal waveguides have been formed with deliberately engineered stop bands (e.g., Davanco et al., 2006; Fleming and Lin, 1999). Equally interesting, or perhaps more so, is the case in which the perfect translational symmetry of the photonic crystal is disrupted in a controlled manner. John (1987) alluded to these “certain disordered dielectric superlattices” in his 1987 paper, and Yablonovitch et al. (1991b) used the analogy of donor and acceptor modes in semiconductor crystals in defining these “defect” states: the disruption from symmetry providing a photonic state within the photonic band gap, making possible the localization of photons. a) b) FIGURE 2-1 (a) Simple examples of one-, two-, and three-dimensional photonic crystals. The different colors represent materials with different dielectric constants. (b) A notional dispersion diagram for a photonic crystal showing a band gap and regions of anomalous dispersion. SOURCE: Joannopoulos et al. (1995). Reprinted by permission of Princeton University Press.

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 NANOSCALE phENOMENA UNDERpINNING NANOphOTONICS Defects in Photonic Crystals: Localization of Light A linear defect, in which the field propagates along the direction of the defect and decays exponen- tially in the transverse direction, can serve as an on-chip optical waveguide with some exceptional prop- erties. More-typically-fabricated on-chip optical waveguides confine optical modes through differential indices of refraction and can display radiation losses—for example, at the bends of curved waveguides. Appropriately designed photonic crystal waveguides are prohibited from radiating into the surrounding bulk material, even for a 90° bend in the waveguide (Meade et al., 1994) (see Figure 2-2). The first experimental demonstration was carried out for a photonic crystal comprising alumina rods with a lattice constant of 1.27 mm, evidencing 80 percent transmission around a 90° bend (Faraon et al., 2007; Lin et al., 1998; Scherer et al., 2005). Various photonic crystal waveguides have since been fabricated with much smaller lattice constants (<0.4 micrometer [µm]) (e.g., Chutinan et al., 2002), and controlled interactions and light exchange between two or more waveguides are possible (Chong and Rue, 2004; Fan et al., 1998). The Control of Dispersion and the Slowing and Storage of Light An interesting and powerful consequence of the structure of the photonic band gap is the dispersion behavior near the band edge and the possibility of group velocities approaching zero. Such slowing of light has been observed in photonic crystal slab waveguides, etched into semiconductor materials (Notomi et al., 2001; Vlasov et al., 2005). The slowing of light and the control of the dispersion properties of the material hold important implications for compact, on-chip processing systems in which controlled delay and storage of optical signals would form important components of any optical-information- processing strategy. FIGURE 2-2 The field of a transverse-magnetic mode traveling around a sharp bend in a waveguide carved out of a photonic crystal square lattice. SOURCE: Joannopoulos et al. (1995). Reprinted by permission of Princeton University Press.

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 NANOphOTONICS High-Efficiency Optical Sources A “point defect” can localize photons, and the early predictions of possible high Q (low optical loss) have proven to be true (Meade et al., 1994). The combination of high Q and low modal volume possible with photonic crystal “defects” or cavities proves an extremely powerful one in producing ultralow-threshold lasers. Lasing was demonstrated in a quantum well (QW) gain medium in a photonic crystal structure (Painter et al., 1999) at low temperature, and subsequently in a dense quantum dot (QD) medium at room temperature (Yoshie et al., 2002). With lower density, QD and strategic matching of QD emission to photonic crystal cavity modal pattern, lasing has been observed at optical pump powers as low as 10s of nanowatts (nW), coupling to only 2 to 4 QDs (Strauf et al., 2006) (see Figure 2-3). Achieving lasing at such low thresholds is testimony to the control over spontaneous emission that formed the original vision for photonic crystals; numerous recent efforts have separately addressed these issues (Fujita et al., 2005; Lodahl et al., 2004; Ogawa et al., 2004). By changing the photon states accessible in the material, photonic crystal patterning of optical structures has also been shown to be an effective way of increasing the extraction efficiency of light- emitting diodes (LEDs), ideally converting optical guided modes within the device to extracted modes, with minimal loss. By designing the appropriate photonic crystal pattern for an LED structure, one can achieve efficient optical emission at particular wavelengths and angular directions (David et al., 2006; Oder et al., 2004; Orita et al., 2004; Wierer et al., 2004). The combination of high Q and low modal volume also makes photonic crystal cavities excellent testbeds for the validation of quantum computation schemes. Quantum dots or other emitters incorporated into the photonic crystal can be weakly or strongly coupled to the cavity: thus, control of the cavity (environment) can result in direct control of the emitters (qubits) within the environment (Badolato et al., 2005; Hennessy et al., 2007). (c) (a) (b) FIGURE 2-3 (a) Atomic force microscope showing ~5 quantum dots/μm2, mapped onto (b) simulation of mode strength in photonic crystal cavity, giving rise to (c) lasing characteristics with ultralow threshold. SOURCES: (a) Evelyn Hu, University of California at Santa Barbara; (b&c) Reprinted with permission from Strauf et al. (2006). Copyright 2006 by the American Physical Society. 2-3

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 NANOSCALE phENOMENA UNDERpINNING NANOphOTONICS Photonic Crystal Waveguides and Fibers A number of powerful photonic crystal elements currently will allow on-chip, fairly dense integration of optical processing components: waveguides and filters of exceptionally high frequency resolution, the possibility of optical storage and delay through photon localization and control of group velocity, and extremely low threshold optical sources, with narrow spectral outputs that can be sensitively directed in-plane or out of plane. Tuning the band structure of these photonic crystal elements allows photon gen- eration, transmission, and coupling with minimal loss. The majority of the applications described above have been fabricated in a planar geometry, forming two- or three-dimensional photonic crystal device elements on a planar substrate. photonic crystal fibers represent a very powerful technology that applies many of the advantages previously described to the transmission and modulation of light propagating through optical fibers. These structures show a lateral periodic variation in the index of refraction (e.g., inclusion of air holes) along the entire length of the fiber. Examples of the cross sections of photonic crystal fibers are shown in Figure 2-4. From the initial demonstrations in the 1970s of low-loss (<20 decibels per kilometer [dB/km]) single- mode transmission, optical fiber technology has rapidly developed to become the predominant means of rapid, long-distance, low-loss transmission of optical signals. Conventional optical fibers employ stepped changes in the index of refraction to confine and guide light; the application of photonic crystal concepts allows the following: the engineering of index differences, beyond the choice of the fiber mate- rial alone; selective transmission of particular wavelengths; control of the dispersion properties of the FIGURE 2-4 Various photonic crystal fiber cross sections. SOURCE: Russell (2003). Reprinted with permission of AAAS. 2-04

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 NANOphOTONICS fiber; lower propagation loss; and lower loss from bending of the fiber. Additional optical properties, such as birefringence, can be engineered into the fiber, allowing the preservation of optical polarization information. Photonic crystal fibers can be formed with “hollow cores,” making possible a number of new appli- cations: very high power, ultrashort pulse propagation (Ouzounov et al. 2003), and nonlinear optical processes in gases that fill the hollow core (Knight, 2003; Russell, 2003). The relative ease of formation of photonic crystal fibers, its compatibility with existing optical fiber manufacturing techniques, and a natural scalability to the appropriate nanoscale modulation no doubt have all contributed to the rapid development of photonic crystal fibers between the time that the initial ideas were put forward in the 1990s and the current availability of commercial suppliers of such specialty fibers—for example, Crystal Fibres, Newport Corporation, and Corning International Corporation. Feasibility and Impact In a scant 20 years, the visionary predictions of the power of photonic crystal structures to modulate and control light have been dramatically proven to be accurate. Overcoming challenges of high-resolution fabrication, process imperfections, and materials loss, photonic crystal structures have shown the ability to filter and slow light, control spontaneous emission, and enhance optical efficiency. The impact of these structures is profound and wide-ranging, allowing top-down alteration of the fundamental optical prop- erties of the materials that are used as platforms for optical devices and systems. The challenges ahead with respect to photonic crystals lie in the achievement of superior performance of individual devices at reduced or equivalent cost and the ability to realize a major benefit of photonic crystal elements in the integration of multiple devices into high-performance, lightweight, compact systems. Further work will be required to achieve active electrical control and modulation of photonic crystal devices without loss. Much work needs to be done to improve understanding of long-term reliability and packaging issues associated with this technology. The link between potential benefits, feasibility, and impact of the photonic crystal technology can be demonstrated in the progress of photonic crystal fibers. With photonic crystals as vehicles for light transmission, the incorporation of photonic crystal modulation serves to make an inexpensive, outstand- ing technology even better, promising lower loss, control over dispersion, the possibility of optimization of transmission and various wavelengths (not just the wavelength determined by the core properties of the fiber), and the implementation of highly sensitive sensing and signal amplification. The benefits of the technology in this case are amplified and catalyzed by the existence of a manufacturable fabrica- tion strategy. Once similar technological challenges are met for planar dielectric photonic crystals, it is expected that their impact on optical information sensing and processing will be further realized. International Perspective The field of research in photonic structures has been an international endeavor from its very incep- tion, with substantial efforts taking place within the United States, Europe, Japan, and most recently China and Taiwan. Figure 2-5 illustrates some of the general trends in research as measured by publi- cations. Using the ISI Web of Knowledge and the Science Citation Index, all publications with any of the following topics: photonic band structure, or photonic crystal, or inhibited spontaneous emission, or localization of photons, were identified and separated into the time intervals 1986-1996, 1996-2001, and 2001-2007. The number of publications is plotted according to country or region and by time interval. “Europe” as used here refers to England, Germany, France, and Italy, which are generally the most pro-

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 NANOSCALE phENOMENA UNDERpINNING NANOphOTONICS lific European countries working in this area of research. The data in Figure 2-5 are intended simply to provide a general picture of the activity in the area of photonic crystal research by country or region and over time. Obvious trends are the accelerating activity in this area (comparing the number of publications in the 10-year period from 1986 through 1995 to the number in the roughly 6-year period from 2001 to the present) and the recent dramatic rise in publication activity in the People’s Republic of China. It would be interesting (but probably more difficult) to similarly monitor the changing patent port- folios in this area. At present, there are few examples of commercial products based on photonic crystal technology, with the exception of photonic crystal fibers, which are produced by companies in Europe and in the United States (Crystal Fibre in Denmark and Newport in the United States). Commercial opportuni- ties may give rise to photonic crystal technology for enhanced light extraction in LEDs in the nearer term, although increased manufacturing costs and as-yet not fully proven enhancements will prove to be formidable barriers. 1800 1986-96 1600 1996-2001 1400 2001-2007 1200 Number of Publications 1000 800 600 400 200 0 USA JAPAN EUROPE ISRAEL CANADA RUSSIA CHINA S. KOREA Region FIGURE 2-5 Analysis of photonic crystal research by country or region between 1986 and 2007, from the ISI Web of Knowledge and the Science Citation Index. NOTE: “Europe” as used here refers to England, Germany, France, and Italy. 2-5

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 NANOphOTONICS METAMATERIALS—SPATIAL INDEx MODuLATION AT A SCALE LESS THAN A WAVELENGTH Electromagnetic radiation exists from below the radio frequency (rf) to x-rays and above. However, this committee takes the field of nanophotonics to apply to the much more restricted range of frequen- cies spanning the infrared (IR) (~20 terahertz [THz] to 350 THz), the visible, and the ultraviolet (UV) spectral regions. In these regions the scale of the wavelength ranges from tens of micrometers to hun- dreds of nanometers, and consequently the size of the structures devised to manipulate this radiation is commensurate with developing nanoscale fabrication and integration technologies. Background We are accustomed to describing electromagnetic interactions with materials in terms of continuum constitutive relations (electric permittivity, ε; magnetic permeability, µ). Materials, of course, consist of atoms and molecules with a spatial scale much less than the optical wavelength, so these continuum approximations are appropriate. With some important exceptions, the permittivity and permeability are related primarily to the density of the material constituents and are relatively independent of their organization. The emerging field of metamaterials is largely concerned with the fabrication of individual structures, on a scale much less than the wavelength, with localized electromagnetic resonances and their combination into macroscopic materials with novel electromagnetic responses, for which an effective permittivity and permeability are appropriate descriptors. Nature provides a wealth of materials with a wide range of electromagnetic properties. Dielectric (nonconducting) materials such as oxides exhibit dielectric permittivities (over their respective trans- parency ranges) from about 2 up to about 3. Semiconductors typically have larger permittivities; from approximately 5 up to about 20. Metals have by far the largest available permittivities, because the free electrons in metals respond to screen an applied electric field; the metal permittivity is negative below the plasma frequency (which is in the UV for most metals) and can be quite large. For example, for gold (Au) at 5 µm, ε = –433 + i37, where the imaginary part is a result of electron-scattering processes in the metal. The metal ε is also quite dispersive, following a Drude model 1/ω dependence across the infrared, with a complex behavior, with more losses, in the visible and ultraviolet as a result of contributions from bound transitions in addition to the free-electron contribution (Shelby et al., 2001). In contrast to the wide diversity of electrical permittivity, there is no magnetic response (i.e., µ = 1) for all known materials. At lower radio frequncy and microwave frequencies, magnetic materials (ferrites) are available, but they involve collective excitations and therefore have limited frequency response. Over the wavelength range being considered here, there are no naturally occurring magnetic materials. Therefore, the emphasis of the effort in metamaterials has been to construct materials with a mag- netic response. Since there are no magnetic monopoles, the building blocks of magnetic materials are magnetic dipoles (subwavelength current loops). In order to get a large magnetic response at specific frequencies, it is often necessary to provide resonant structures (inductor-capacitor tank circuits). The first of these structures was the split-ring resonator (Pendry et al., 1999). The current state of this research is reviewed in the next subsection. Status The field of spatial index modulation began in the late 1990s with the theoretical prediction and the first demonstration of split-ring resonators with a negative permeability in the rf (Pendry et al., 1999; Shelby et al., 2001). The frequency of operation has been steadily increased, first to 1.2 THz and

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 NANOSCALE phENOMENA UNDERpINNING NANOphOTONICS then to the IR (Linden et al., 2004; Yen et al., 2004; Yen et al., 2005). Initially, there was some skepti- cism that continued scaling from the lower frequencies would be possible because of the extremely small dimensions involved. At higher frequencies, the inductance is dominated by the inertia (mass) of the free electrons, and the geometric loop structure is no longer needed. This advance has led to a dramatic increase in the ability to fabricate metamaterials; a simple metal-dielectric-metal structure with transverse dimensions less than the relevant wavelength provides a simple, manufacturable route to negative-permeability metamaterials. As an aside, this structure is closely related to a gap-mode surface plasma wave, and there is a strong connection between metamaterials and plasmonics (see the section on “Plasmonics” in this chapter). A major driver of this technology has been the development of negative-index materials (materials with both a negative permittivity and a negative permeability). The negative permittivity is easy to accomplish with metals; the negative permeability is the difficult part. Recently, three experimental groups (two in the United States and one in Germany) have demonstrated negative-index materials using negative-permeability metamaterials (Dolling et al., 2006; Shalaev et al., 2005; Zhang et al., 2005b). The wavelength has rapidly advanced from near infrared (2 µm) to visible (800 nm). At present, the best results have been obtained with a “fishnet” structure in a stacked metal-dielectric-metal film (Chettiar et al., 2006; Ku and Brueck, 2007). Spatial Index Modulation Metamaterials: Anisotropy The classical prescription of Pendry to realize negative-index metamaterials is to construct resonant elements with negative electric susceptibilities (χE < 0) and magnetic susceptibilities (χM < 0). If the magnitudes of the susceptibilities and the number densities r of the elements are sufficiently large, then the electric permittivity e = e0 (1 + rE χE) and the magnetic permeability m = m0 (1 + rM χM) will both be negative, and a negative refactive index n = εµ can be realized. To avoid scattering of radiation, the resonant elements must be much smaller than the wavelength at which the metamaterial is to operate. Since metals have negative dielectric permittivity at frequencies below the plasma frequency, metallic nanowires can provide negative susceptibility. The depolarizing factors arising from their shape introduce resonances in their response, with the result that their susceptibility is very different—possibly even in sign—for electric fields parallel and perpendicular to their length. Since all known natural materials have positive magnetic permeabilities, negative magnetic sus- ceptibility can only be realized through a resonant response. Metallic split-ring resonators and similar structures, which function like LC circuits, can give rise to large negative magnetic susceptibility, but only near resonance and only when the magnetic field is perpendicular to the plane of the ring or ring- like planar structure. Both types of elements are inherently anisotropic; that is, their susceptibility depends on the orien- tation of the applied fields relative to the elements. Metamaterials consisting of regular lattices of such elements tend to be anisotropic. Anisotropy, which implies polarization dependence, is not desirable, but may be acceptable for some applications. It may be eliminated by incorporating elements with different orientation in the metamaterial, but the orientationally averaged susceptibilities of the elements may be far from ideal, and significant loss in performance may result. An alternate strategy for high-definition imaging has been proposed; it relies on anisotropy and may overcome the problem of losses (Jacob et al., 2006; Liu et al., 2007). The basic idea is to abandon nega-

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 NANOphOTONICS tive magnetic permeability, with its requirement of operating very near resonance and the high attendant losses. Instead, it is noted that evanescent waves occur when the magnitude of the wave vector carrying image information is greater than 2pn / lO. If the refractive index n could be made sufficiently large, then arbitrarily high resolution image information could be carried by the wave without the wave vector exceeding the limit of 2pn / lO and thus without evanescent decay. In uniaxial anisotropic media, there are two modes of propagation, with the dispersion relation for the extraordinary mode being k⊥ k||2 ω 2 2 + = ε || ε ⊥ c 2 where k┴ and k┴ are components of the wave vector perpendicular and parallel to the optic axis. If one of the principal values of the dielectric tensor is negative, then the magnitude of k, that is, the refractive index n, may be arbitrarily large. Thus, anisotropic metamaterials, consisting of positive and negative dielectric components, such as oriented metallic nanowires in a dielectric host, should be capable of subwavelength imaging with modest losses. Issues To date, experimental metamaterials rely predominantly on metallic structures and current flow to produce the negative permeability, and the associated losses are too large to allow many applications. A figure of merit, –Re(n)/Im(n), has been introduced to capture the loss information. Table 2-1 presents the reported results. Fabrication is another major issue. To date, the demonstrations have all been in thin-film materials with a total thickness (for all three layers) of much less than a wavelength. Recently, a theoretical predic- tion suggested that a thicker stack of material (up to 10 layers) would have a lower loss and a dramatically improved figure of merit (Zhang et al., 2005c). No experiments have yet been reported. This is still a thin film, and it does not seem likely that the current approach will yield bulk materials, both because of the excessive losses and because of the difficulty of extending thin-film approaches to macroscopic scales. Two different fabrication techniques have been used to date: electronic-beam direct write and interferometric lithography (Dolling et al., 2006; Shalaev et al., 2005; Zhang et al., 2005a; 2005b). Direct write is a serial technology that is not scalable to large volumes of material. Interferometric lithography, as a simpler version of traditional optical lithography, is a large-area technique that is directly scalable to manufacturing volumes. Additional discussion of fabrication approaches is presented in Chapter 3. TABLE 2-1 Reported Metamaterials Experiments in the Near Infrared Spectral Region Figure of Merit Material Structure [–Re(n)/Im(n)] Reference λλ(μm) Au/Al2O3/Au Two-dimensional perforated films 2.0 0.5 Zhang et al. (2005b) (symmetric) Au Metal line pairs 1.5 0.1 Shalaev et al. (2005) Au/Al2O3/Au Two-dimensional perforated films 2.0 1.0 Zhang et al. (2006a) (asymmetric) Ag/MgF2/Ag Two-dimensional perforated films 1.4 3.0 Dolling et al. (2006) (asymmetric fishnet)

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 NANOSCALE phENOMENA UNDERpINNING NANOphOTONICS An exciting new direction is the introduction of active materials (gain) and the integration of these negative-index materials with semiconductor and other gain media. The challenges are large as a result of the short range of the interactions and the nonradiative losses introduced by the close proximity of the gain media to the metal films. Impact New and improved optical materials have always led to advances in optical systems. Currently, the first tentative steps at realizing these materials are under way. As always, the materials are too difficult to work with and too lossy to realize the benefits. However, these are very early days in this process, and it is clear on the basis of analogies with other major advances in optical characteristics that there will be many new capabilities associated with these hitherto-unavailable characteristics. Some promising directions include nonlinear optics, subwavelength cavities and field concentration for both sources and detectors, imaging at scales much less than a wavelength, negative dispersion and dispersion compensa- tion, and many others. These are discussed at length in later chapters in this report. To date, most of the work on metamaterials has focused on the fabrication and demonstration of homogeneous materials. Recently, the Duke group demonstrated an inhomogenous metamaterial lens by systematically varying the structure of the metamaterial elements (Driscoll et al., 2006). Because the lens is fabricated with only few metamaterial layers, it is much more lightweight than traditional approaches. In another set of experiments, the same group has demonstrated the “cloaking” of electromagnetic radia- tion by arranging an inhomogenous array of metamaterial elements in concentric rings around an object (Schurig et al., 2006). These experiments point to exciting new directions for metamaterials and confirm the hypothesis stated above—new materials lead to new functionality and to new applications. The enhancement associated with subwavelength apertures will be of particular importance in mid- and long-wave infrared applications such as focal plane arrays. Room-temperature IR detectors are either very noisy as a result of large thermal dark currents in narrow band-gap semiconductor materials or very slow as in microelectromechanical systems (MEMS)-based microbolometers because of the thermal response of the isolated materials. In both cases, plasmonic antenna concepts offer revolutionary new capabilities. The dark current scales with the detector area and the noise scales as the square root of the area; thus, the figure of merit is the relative signal for a small detector versus a large-area detector divided by the square root of the area ratio. For microbolometers, the speed scales directly as the area (capacitance and thermal time constant) of the small elements. Box 2-1 and Box 2-2 provide examples of optical system advances made possible by improved optical materials. PLASMONICS plasmonics is a subfield of nanophotonics concerned primarily with the manipulation of light at the nanoscale, based on the properties of surface plasmons. plasmons are the collective oscillations of the electron gas in a metal or a semiconductor. Rigorously, the plasmon is the quasi-particle resulting from the quantization of plasma oscillations, a hybrid of the electron plasma and the photon. Although plasmons are quantum mechanical in nature, their properties, most specifically with respect to the coupling of light to plasmon oscillations, can be described rigorously by classical electrodynamics. Surface plasmons (SPs) are the electromagnetic waves that propagate along metallic/dielectric interfaces; they can exist at any interface, and for any frequency region, where the complex dielectric constants of the media constituting the interface are of opposite sign and the sum of the dielectric constants are negative. SPs are supported by structures at all length scales. They largely determine the optical proper-

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 NANOphOTONICS Quantum Cascade Lasers Quantum cascade lasers are one of the most dramatic examples of a completely new device operat- ing principle emerging from the ability to confine electron levels in reduced-dimensionality structures. The first QCL was demonstrated in 1994, at a wavelength of 4.2 μm (Faist et al., 1994). QCLs operate by engineering the electron energy levels and tunneling coefficients in a multilayer structure. The device is an all-electron device, with the only the conduction band having any influence on its operation, and it can be fabricated in many material systems but is typically made with InGaAs/InAlAs or AlGaAs/GaAs heterostructures. While many design variations exist, a single cell or “unit period” of the QCL can be thought of as a three-level structure where the energy separations between the levels are completely engineered, allowing the designer to choose the operating wavelength. Electrons are injected electrically into the upper energy level and transition to the middle level by emitting a desired photon. The electron transition to the lowest level from the middle level is engineered to keep the middle energy level at a very low population, enabling population inversion between the top two levels. Since the electrons are still in the conduction band, by clever use of band structure engineering and tunneling, the electrons are transported from the lowest level into the highest level of the next cell, allowing the process to be repeated. By stacking many cells together—up to 200 or more for the longest wavelengths—sufficient gain can be achieved that the structure will produce lasing. Thus, a single electron will emit a photon for each cell it traverses, resulting in a cascade-like motion as it moves through the QCL structure, which is of course the origin of the name for the device. QCLs are a triumph of band structure engineering, simulation and modeling, and high-precision epitaxial growth techniques. The energy levels, tunneling probabilities, wavefunction distributions, and decay rates must all be extremely well designed and controlled. A typical design is to space the middle and lowest levels apart by the optical phonon energy, ensuring that the middle level is rapidly depopu- lated so that population inversion can occur. QCL emission wavelengths are limited to less than the conduction band offset in the host ternary compound semiconductor system—for example, to less than the conduction band offset energy in the material system (and in actuality about half the offset). In practice, QCLs have been demonstrated with wavelengths between 3 to 24 microns and between 60 and 200 microns, covering large portions of the electromagnetic spectrum from the mid-infrared out to the terahertz. Their advantages, in addition to a broad range of wavelength ranges, include high power and high-temperature operation. (Of course, achievable powers and operating temperatures are a strong function of wavelength. Record powers are near 10 watts (W) in the mid-IR and 250 milliwatts (mW) in the terahertz, while record operating tem- peratures are >300 K in the mid-IR and up to 164 K in the terahertz. Terahertz Quantum Cascade Lasers The first quantum cascade laser to operate in the terahertz frequency range was reported in 2001 (Kohler et al., 2002). Now terahertz QCLs have been demonstrated to operate with frequencies from 1.6 THz to 4.9 THz and record powers of 250 mW (pulsed) and 140 mW (continuous wave) (Williams et al., 2006). Prior to this, the standard for continuous-wave terahertz lasers was molecular gas lasers. These bulky and expensive systems consist of a meter-long gas tube, pumped by a CO2 laser in another meter- long tube, and weigh on the order of 100 kilograms (kg). The development of terahertz QCLs enables highly compact (less than 1 mm long), low-weight, and inexpensive laser sources in this frequency regime. By integrating terahertz QCLs with coherent detectors, it may be possible to build compact terahertz transceivers with far greater sensitivity and frequency resolution than that of direct detection

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 NANOSCALE phENOMENA UNDERpINNING NANOphOTONICS techniques. At present, such a system would still need to be cooled, limiting the extent to which it could be miniaturized. However, numerous schemes are being developed for higher-temperature operation, and much progress has been made. It is conceivable that room-temperature operation could be achieved in the not-too-distant future. As discussed in the applications section, the terahertz portion of the spectrum is important for a number of reasons. First, the rotational frequencies of many molecules, from simple diatomic chemicals to complex macromolecules, have stronger and more distinctive absorption and emission resonances in the terahertz than in either microwave or near-IR regions. Thus, terahertz has great promise for the chemical and biological (especially chemical) detection of various threats. (However, due to the severe attenuation of terahertz radiation in the atmosphere, this detection would have to be relatively short range.) In addition, terahertz has considerable promise for through-object imaging, including inspection of passengers for hidden objects and packages. The shorter wavelength of terahertz renders the imaging resolution far superior to that of microwaves, when needed. Finally, because of the atmospheric attenu- ation and the ability to produce highly directional beams of radiation, terahertz may also be useful for covert communication. REFERENCES Aifer, E.H., E.M. Jackson, G. Boishin, L.J. Whitman, I. Vurgaftman, J.R. Meyer, J.C. Culbertson, and B.R. Bennet. 2003. Very- long-wave ternary antimonide superlattice photodiode with 21 μm cutoff. Applied physics Letters 82(25):4411-4413. Albrecht, M.G., and J.A. Creighton. 1977. Anomalously intense Raman spectra of pyridine at a silver electrode. Journal of the American Chemical Society 99(15):5215-5217. Arakawa, Y., and H. Sakaki. 1982. Multidimensional quantum well laser and temperature dependence of its threshold current. Applied physics Letters 40(11):939-941. Asada, Masahiro, Yasuyuki Miyamoto, and Yasuharu Suematsu. 1986. Gain and the threshold of three-dimensional quantum- box lasers. IEEE Journal of Quantum Electronics 22(9):1915-1921. Ayato, Yusuke, Keiji Kunimatsu, Masatoshi Osawa, and Tatsuhiro Okada. 2006. Study of Pt electrode/Nafion ionomer interface in HClO4 by in situ surface-enhanced FTIR spectroscopy. Journal of the Electrochemical Society 153(2):A203-A209. Badolato, Antonio, Kevin Hennessy, Mete Atatüre, Jan Dreiser, Evelyn Hu, Pierre M. Petroff, and Atac Imamgolu. 2005. Deterministic coupling of single quantum dots to single nanocavity modes. Science 308(5725):1158-1161. Bahriz, M., V. Moreau, J. Palomo, R. Colombelli, D.A. Austin, J.W. Cockburn, L.R. Wilson, A.B. Krysa, and J.S. Roberts. 2006. Room-temperature operation of λ ≈ 7.5 μm surface-plasmon quantum cascade lasers. Applied physics Letters 88(18):181103. Berciaud, Stéphane, Laurent Cognet, Gerhard A. Blab, and Brahim Lounis. 2004. Photothermal heterodyne imaging of indi- vidual nonfluorescent nanoclusters and nanocrystals. physical Review Letters 93(25):257402. Berciaud, Stéphane, Laurent Cognet, Philippe Tamarat, and Brahim Lounis. 2005. Observation of intrinsic size effects in the optical response of individual gold nanoparticles. Nano Letters 5(3):3. Berger, Paul R., Kevin Chang, Pallab Bhattacharya, and Jasprit Singh. 1988. Role of strain and growth conditions on the growth front profile of InxGa1−xAs on GaAs during the pseudomorphic growth regime. Applied physics Letters 53(8):684-686. Bergman, D.J., and M.I. Stockman. 2003. Surface plasmon amplification by stimulated emission of radition: Quantum genera- tion of coherent plasmons in nanosystems. physical Review Letters 90(2):027402. Bethe, H.A. 1944. Theory of diffraction by small holes. physical Review 66(7-8):163-182. Bimberg, D., N. Kirstaedter, N.N. Ledentsov, Zh.I. Alferov, P.S. Kop’ev, and V.M. Ustinov. 1997. InGaAs-GaAs quantum-dot lasers. IEEE Journal of Selected Topics in Quantum Electronics 3(2):196-205. Biteen, Julie S., Nathan S. Lewis, Harry A. Atwater, Hans Mertens, and Albert Polman. 2006. Spectral tuning of plasmon- enhanced silicon quantum dot luminescence. Applied physics Letters 88(13):131109. Bozhevolnyi, Sergey I., Balentyn S. Volkov, Eloise Devaux, and Thomas Ebbesen. 2005. Channel plasmon-polariton guiding by subwavelength metal grooves. physics Review Letters 95(4):046802. Bozhevolnyi, Sergey I., Valentyn S. Volkov, Eloïse Devaux, Jean-Yves Laluet, and Thomas W. Ebbesen. 2006. Channel plasmon subwavelength waveguide components including interferometers and ring resonators. Nature 440(7083):508-511.

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