Browsing by Subject "Nonlinear optics"

Collective behavior in many-body systems, where the dynamics of an individual element depend on the state of the entire ensemble, play an important role in both basic science research and applied technologies. Over the last twenty years, studies of such effects in cold atomic vapors have lead to breakthroughs in areas such as quantum information science and atomic and condensed matter physics. Nevertheless, in order to generate photon-mediated atom-atom coupling strengths that are large enough to produce collective behavior, these studies employ techniques that intrinsically limit their applicability. In this thesis, I describe a novel nonlinear optical process that enables me to overcome these limitations and realize a new regime of collective light-matter interaction.

My experiment involves an anisotropic cloud of cold rubidium atoms illuminated by a pair of counterpropagating optical (pump) fields propagating at an angle to the trap's long axis. When the pump beam intensities exceed a threshold value, a collective instability occurs in which new beams of light are generated spontaneously and counterpropagate along the trap's long axis. In order to understand the physical mechanism responsible for this behavior, I study first the system's nonlinear optical response when driven below the instability threshold. I find that the incident optical fields produce an optical lattice that causes the atoms to become spatially organized on the sub-wavelength length scale. This organization corresponds to the formation of an atomic density grating, which effectively couples the involved fields to one another and enables the transfer of energy between them. The loading of atoms into this grating is enhanced by my choice of field polarizations, which simultaneously results in cooling of the atoms from T~30 μK to T~3 μK via the Sisyphus effect. As a result, I observe a fifth-order nonlinear susceptibility χ^{(5)}=1.9x10^-12 (m/V)^4 that is 7 orders of magnitude larger than previously observed. In addition, because of the unique scaling of the resulting nonlinear response with material parameters, the magnitude of the nonlinearity can be large for small pump intensities (\ie, below the resonant electronic saturation intensity 1.6 mW/cm^2) while simultaneously suffering little linear absorption. I confirm my interpretation of the nonlinearity by developing a theoretical model that agrees quantitatively with my experimental observations with no free parameters.

The collective instability therefore corresponds to the situation where the cold vapor transitions spontaneously from a spatially-homogeneous state to an ordered one. This emergent organization leads to the simultaneous emission of new optical fields in a process that one can interpret either in terms of mirrorless parametric self-oscillation or superradiance. By mapping out the phase diagram for this transition, I find that the instability can occur for pump intensities as low as 1 mW/cm^2, which is approximately 50 times smaller than previous observations of similar phenomena. The intensity of the emitted light can be up to 20% of the pump beam intensity and depends superlinearly on the number of atoms, which is a clear signature of collective behavior. In addition, the generated light demonstrates temporal correlations between the counterpropagating modes of up to 0.987 and is nearly coherent over several hundred μs. The most significant attributes of the light, though, are that it consists of multiple transverse spatial modes and persists in steady-state. This result represents the first observation of such dynamics, which have been shown theoretically to lead to a rich array of new phenomena and possible applications.

As research in electromagnetics has expanded, it has given rise to the examination of metamaterials, which possess nontrivial electromagnetic material properties such as engineered permittivity and permeability. Aside from their application in the microwave industry, metamaterials have been associated with novel phenomena since their invention, including sub-wavelength focusing in negative refractive index slabs, evanescent wave amplification in negative index media, and invisibility cloaking and its demonstration at microwave frequency with controlled material properties in space.

Effective medium theory plays a key role in the development and application of metamaterials, simplifying the electromagnetic analysis of complex engineered metamaterial composites. Any metamaterial composite can be treated as a homogeneous or inhomogeneous medium, while every unit structure in the composite is represented by its permittivity and permeability tensor. Hence, studying an electromagnetic wave's interaction with complex composites is equivalent to studying the interaction between the wave and an artificial material.

This dissertation first examines the application of a magnetic metamaterial lens in wireless power transfer (WPT) technology, which is proposed to enhance the mutual coupling between two magnetic dipoles in the system. I examine and investigate the boundary effect in the finite sized magnetic metamaterial lens using a numerical simulator. I propose to implement an anisotropic and indefinite lens in a WPT system to simplify the lens design and relax the lens dimension requirements. The numerical results agree with the analytical model proposed by Smith et al. in 2011, where lenses are assumed to be infinitely large.

By manipulating the microwave properties of a magnetic metamaterial, the nonlinear properties come into the scope of this research. I chose split-ring resonators (SRR) loaded with varactors to develop nonlinear metamaterials. Analogous to linear metamaterials, I developed a nonlinear effective medium model to characterize nonlinear processes in microwave nonlinear metamaterials. I proposed both experimental and numerical methods here for the first time to quantify nonlinear metamaterials' effective properties. I experimentally studied three nonlinear processes: power-dependent frequency tuning, second harmonic generation, and three-wave mixing. Analytical results based on the effective medium model agree with the experimental results under the low power excitation assumption and non-depleted pump approximation. To overcome the low power assumption in the effective medium model for nonlinear metamaterials, I introduced general circuit oscillation models for varactor/diode-loaded microwave metamaterial structures, which provides a qualitative prediction of microwave nonlinear metamaterials' responses at relatively high power levels when the effective medium model no longer fits.

In addition to 1D nonlinear processes, this dissertation also introduces the first 2D microwave nonlinear field mapping apparatus, which is capable of simultaneously capturing both the magnitude and phase of generated harmonic signals from nonlinear metamaterial mediums. I designed a C-band varactor loaded SRR that is matched to the frequency and space limitation of the 2D mapper. The nonlinear field generation and scattering properties from both a single nonlinear element and a nonlinear metamaterial medium composite are experimentally captured in this 2D mapper, and the results qualitatively agree with numerical results based on the effective medium model.

Multinary chalcogenide semiconductors have long been a mainstay within optoelectronics industries. Chalcogenide materials consisting of at least four elements—i.e., quaternaries—have tunable structural, optical, and electronic properties, allowing the semiconductors to be tailored for specific applications. Recently, the I2-II-IV-X4 (I = Li, Cu, Ag; II = Ba, Sr, Pb, Eu; IV = Si, Ge, Sn; X = S, Se) family of materials has emerged as a source of promising semiconductors with applications in nonlinear optics and optoelectronics. A major challenge for these complex compounds is maintaining the ability to predictably control the desired properties. In this dissertation, solid-state chemistry methods are used to tackle three major goals: to investigate known I2-II-IV-X4-type compounds that have not been thoroughly explored; to develop predictable property trends within the wider family of materials; and to predict and make brand new semiconductors.

The study of the quaternary semiconductor Cu2BaGeSe4 and the mixing of Ge and Sn within this compound (to make Cu2BaGe1-xSnxSe4) serves as the platform for branching into new compounds in the I2-II-IV-X4 family. Using the structural analysis established in the work on Cu2BaGe1-xSnxSe4, a structural tolerance factor is developed to predict the probable crystal structure of hypothetical compounds that fit into the family of the I2-II-IV-X4-type materials. Four new semiconductors (Cu2PbGeS4, Cu2SrSiS4, Ag2SrSiS4, and Ag2SrGeS4) were made and found to conform to the anticipated crystal structures based on the structural tolerance factor. The newly synthesized Cu2SrSiS4, Ag2SrSiS4, and Ag2SrGeS4 are potential nonlinear optical materials, while each of the four semiconductors may be used as buffer or n-type layers in thin film solar cells. In the pursuit of new I2-II-IV-X4-type compounds, a family of cubic compounds is found to either co-exist and compete with the synthesized materials (Ag2Sr3Si2S8 & Ag2Sr3Ge2S8) or to be more stable than the hypothetical I2-II-IV-X4 materials (Ag2Pb3Si2S8 & Ag2Sr3Sn2S8) with the same elemental makeup. Of these four cubic semiconductors, Ag2Sr3Si2S8 and Ag2Pb3Si2S8 have not been reported by others. The compounds within this family have predictable trends of optical properties and have applications as nonlinear optical materials if large single crystals can be synthesized.

Finally, the solvothermal synthesis and properties of Ag2(NH4)AsS4 are explored, extending the scope of this dissertation from the I2-II-IV-X4 materials to those of the form Ag2-I’-V-X4 (I’ = NH4, K, Rb, Cs; V = As, Sb, Nb, Ta, V, P). Similar to the other studied Ag-based materials, Ag2(NH4)AsS4 has applications as a nonlinear optical material and as a buffer layer in solar cells. Understanding the Ag2(NH4)AsS4 synthesis technique allows future researchers to synthesize new Ag2-I’-V-X4-type semiconductors with the same methods or apply these principles to the fabrication of Ag2(NH4)AsS4 thin films. The work presented in this dissertation furthers the understanding of the synthesis and prediction of quaternary chalcogenide semiconductors and lays the foundation for future device and thin film studies using the semiconductors studied here.

Nonlinear generation of optical fields has enabled many exciting breakthroughs in light science such as nonlinear imaging, all-optical switching and supercontinuum generation. The intrinsic nonlinear response from bulk materials is extremely weak and phase matching conditions need to be satisfied for efficient generation. Plasmonic structures have proven to be a promising platform to investigate nonlinear optics due to the capability to enhance and localize electromagnetic fields within subwavelength volumes beyond the diffraction limit. However, the origin of the large nonlinear response observed in the plasmonic structures is not fully understood and the investigations of nonlinear processes involving multiple excitation wavelengths are limited. Furthermore, simultaneous enhancement and precise manipulation of multiple nonlinear optical processes have not been experimentally demonstrated.

In this dissertation, I describe a specific film-coupled plasmonic nanogap cavity structure consisting of arrays of nanoparticles separated from a metallic ground plane by an ultrathin dielectric layer. Polarization-dependent, dual-band and spatially-overlapped resonances are obtained with arrays of rectangle nanoparticles where the two resonances can be tuned independently. Highly efficient third harmonic generation (THG) is achieved by integrating dielectric materials in plasmonic nanogap cavities, resulting in more than six orders of magnitude enhancement in the THG response compared with a bare gold film. Utilizing comprehensive spectral analysis and finite-element simulation, it is concluded that the main contributing nonlinear source is dielectric material in the gap. Furthermore, I demonstrate simultaneous enhancement of three nonlinear responses from THG, sum frequency generation (SFG) and four wave mixing (FWM) by integrating 1-7 nm Al2O3 layer in the nanocavities formed by a gold ground plane and silver nanorectangles. Enhancement up to 106-fold for both THG and FWM and 104-fold for SFG is achieved when the excitation wavelengths overlap with the resonance wavelengths from transverse and longitudinal modes of the nanorectangles. Precise control of the relative strength of these nonlinear responses is demonstrated either actively by varying the ratio between excitation powers or passively by changing the Al2O3 gap thickness. Moreover, a metasurface-based efficient frequency mixer is realized utilizing diamond and a novel polymer transfer process is employed for creating nanoparticle arrays. This new insight into the nonlinear response in ultrathin gaps between metals is expected to be promising for both the fundamental understanding of nonlinear optics at the deep nanoscale and efficient on-chip nonlinear devices such as ultrafast optical switching and entangled photon sources. The capability to precisely manipulate nonlinear optical processes at the nanoscale could find important applications for nonlinear imaging and quantum communication.

Dermatopathologists need more reliable tools for analyzing biopsies of lesions that are potentially melanomas and determining the best treatment plan for the patient. Previously inaccessible, the chemical and physical properties of melanin provide insight into melanoma biochemistry. Two-color, near-infrared pump-probe microscopy of unstained, human pathology slides reveals differences in the type of melanins and the distribution of melanins between melanomas and benign nevi. Because the pump-probe response of melanin is resilient to aging, even for hundreds of millions of years, this tool could prove useful in retrospective studies to correlate melanin characteristics with patient outcome, thus eliminating the pathologist's uncertainty from the development of this classification method.

Pump-probe spectroscopy of a variety of melanin preparations including melanins with varying amounts of metal ions and toxins, those that have been photo-damaged or chemically oxidized, and melanins with a homogeneous size distribution shows that the pump-probe response is sensitive to these chemical and physical differences, not just melanin type as previously hypothesized. When sampling the response at several pump wavelengths, the specificity of this technique is derived from the absorption spectra of the underlying chromophores. Therefore, hyperspectral pump-probe microscopy of melanin could serve as an indicator of the chemical environment in a variety of biological contexts. For example, the melanin chemistry of macrophages suggests that these cells oxidize, homogenize, and compact melanin granules; whereas melanocytes produce heterogeneous melanins.

A patterned metasurface can strongly scatter incident light, functioning as an extremely low-profile lens, filter, reflector or other optical devices. Nonlinear metasurfaces‒combine the properties of natural nonlinear medium with novel features such as negative refractive index, magneto-electric coupling‒provide novel nonlinear features not available in nature. Compared to conventional optical components that often extend many wavelengths in size, nonlinear metasurfaces are flexible and extremely compact.

Characterization of a nonlinear metasurface is challenging, not only due to its inherent anisotropy, but also because of the rich wave interactions available. This thesis presents an overview of the work by the author in modeling and application of nonlinear metasurfaces. Analytical methods - transfer matrix method and surface homogenization method - for characterizing nonlinear metasurfaces are presented. A generalized transfer matrix method formalism for four wave mixing is derived, and applied to analyze nonlinear interface, film, and metallo-dielectric stack. Various channels of plasmonic and Fabry-perot enhancement are investigated. A homogenized description of nonlinear metasurfaces is presented. The homogenization procedure is based on the nonlinear generalized sheet transition conditions (GSTCs), where an optically thin nonlinear metasurface is modeled as a layer of dipoles radiating at fundamental and nonlinear frequencies. By inverting the nonlinear GSTCs, a retrieval procedure is developed to retrieve the nonlinear parameters of the nonlinear metasurface. As an example, we investigate a nonlinear metasurface which presents nonlinear magnetoelectric coupling in near infrared regime. The method is expected to apply to any patterned metasurface whose thickness is much smaller than the wavelengths of operation, with inclusions of arbitrary geometry and material composition, across the electromagnetic spectrum.

The second part presents the applications of nonlinear metasurfaces. First, we show that the third-harmonic generation (THG) can be drastically enhanced by the nonlinear metasurfaces – film-coupled nanostripes. The large THG enhancement is experimentally and theoretically demonstrated. With numerical simulations, we present methods to clarify the origin of the THG from the metasurface. Second, the enhanced two-photon photochormism is investigated by integrating spiropyrans with film-coupled nanocubes. This metasurface platform couples almost 100% energy at resonance, and induces isomerization of spiropyrans to merocyanines. Due to the large Purcell enhancement introduced by the film-coupled nanocubes, fluorescence lifetime measurements on the merocyanine form reveal large enhancements on spontaneous emission rate, as well as high quantum efficiency. We show that this metasurface platform is capable of storing information, supports reading and writing with ultra-low power, offering new possibilities in optical data storage.

The nonlinear interaction between light and atoms is an extensive field of study with a broad range of applications in quantum information science and condensed matter physics. Nonlinear optical phenomena occurring in cold atoms are particularly interesting because such slowly moving atoms can spatially organize into density gratings, which allows for studies involving optical interactions with structured materials. In this thesis, I describe a novel nonlinear optical effect that arises when cold atoms spatially bunch in an optical lattice. I show that employing this spatial atomic bunching provides access to a unique physical regime with reduced thresholds for nonlinear optical processes and enhanced material properties. Using this method, I observe the nonlinear optical phenomenon of transverse optical pattern formation at record-low powers. These transverse optical patterns are generated by a wave- mixing process that is mediated by the cold atomic vapor. The optical patterns are highly multimode and induce rich non-equilibrium atomic dynamics. In particular, I find that there exists a synergistic interplay between the generated optical pat- terns and the atoms, wherein the scattered fields help the atoms to self-organize into new, multimode structures that are not externally imposed on the atomic sample. These self-organized structures in turn enhance the power in the optical patterns. I provide the first detailed investigation of the motional dynamics of atoms that have self-organized in a multimode geometry. I also show that the transverse optical patterns induce Sisyphus cooling in all three spatial dimensions, which is the first observation of spontaneous three-dimensional cooling. My experiment represents a unique means by which to study nonlinear optics and non-equilibrium dynamics at ultra-low required powers.

In this work, a hybrid mixed order numerical framework is proposed for multiscale linear/ nonlinear nano optical computation. Starting from the principle of the spectral element boundary integral (SEBI) method, the mixed-order SEBI solver with homogeneous Green's function is first developed for the nano-scale linear and nonlinear electromagnetic scattering analyses. The SEBI realizes the exact radiation boundary condition with a set of surface integral equations (SIE's), and discretize the whole computation domain with the fast convergent Gauss-Lobatto-Legendre (GLL) basis function. The Bloch periodic boundary condition is applied for efficient simulation of structures with periodicities in one or two directions.

For nonlinear optical simulation, full-wave solver is developed self-consistently by iteratively solving the vector Helmholtz equations at each harmonic frequency. To further address the multiscale scattering analysis in nano optics, a hybrid framework is developed by combing the SEBI solver with the dyadic periodic layered medium Green's function (PLMGF) and the domain decomposition method (DDM). Formulating the SIE's with the dyadic PLMGF, all unknowns in the background layered medium are pushed to the radiation boundaries. Thus, the whole planar layered background can be truncated from the computation domain. Considering its highly singular analytical properties, the PLMGF is carefully and systematically formulated under matrix representation. A feasible and effective technique is proposed for the on-interface PLMGF singularity extractions. By extracting the primary and secondary terms' singularities separately, all PLMGF-related SIE components can be efficiently evaluated. The DDM further reduces the memory cost for electrically large problems and enhances the framework's flexibility. Finally, a scattered field perfectly matched layer - surface integral equation (PML-SIE) radiation boundary condition is proposed to enable the non-periodic modeling. With the hybrid radiation boundary condition, the periodic and non-periodic solvers are maximumly integrated together with the minimum maintenance cost.

Benefiting from the exponential convergence and flexibility of the SEBI, computationally challenging problem can be solved with considerably reduced number of samplings. As a typical application, the multilayer defects analysis in extreme ultraviolet (EUV) lithography is studied for both 2-D and 3-D models. The light absorption engineering of graphene is also investigated around the visible spectra. Benefiting from the accuracy of the full-wave nonlinear solver, couplings between the fundamental frequency (FF) field and the higher harmonic (HH) field ignored my most previous studies can also be self-consistently analyzed in nonlinear optical simulation. With this tool, the investigation is extended to the engineering of graphene's visible spectra absorption tuning and third harmonic generation (THG) enhancement. Graphene's Kerr effects are also studied under strong surface plasmonic resonance. The hybrid higher order method's efficiency and accuracy are further validated through various multiscale nano-optical cases.

All-optical devices have attracted many research interests due to their ultimately low heat dissipation compared to conventional devices based on electric-optical conversion. With recent advances in nonlinear optics, it is now possible to design the optical properties of a medium via all-optical nonlinear effects in a table-top device or even on a chip.

In this thesis, I realize all-optical control of the optical group velocity using the nonlinear process of stimulated Brillouin scattering (SBS) in optical fibers. The SBS-based techniques generally require very low pump power and offer a wide transparent window and a large tunable range. Moreover, my invention of the arbitrary SBS resonance tailoring technique enables engineering of the optical properties to optimize desired function performance,

which has made the SBS techniques particularly widely adapted for

various applications.

I demonstrate theoretically and experimentally how the all-optical

control of group velocity is achieved using SBS in optical fibers.

Particularly, I demonstrate that the frequency dependence of the

wavevector experienced by the signal beam can be tailored using

multi-line and broadband pump beams in the SBS process. Based on the theoretical framework, I engineer the spectral profile

to achieve two different application goals: a uniform low group velocity (slow light) within a broadband spectrum, and a group velocity with a linear dependence on the frequency detuning (group velocity dispersion or GVD).

In the broadband SBS slow light experiment, I develop a novel noise current modulation method that arbitrarily tailors the spectrum of a diode laser. Applying this method, I obtain a 5-GHz broadband SBS gain with optimized flat-topped profile, in comparison to the ~40 MHz natural linewidth of the SBS resonance. Based on the broadband SBS resonance, I build a 5-GHz optical buffer and use this optical buffer to delay a return-to-zero data sequence of rate 2.5 GHz (pulse width 200 ps). The fast noise modulation method significantly stabilizes the SBS gain and improves the signal fidelity. I obtain a tunable delay up to one pulse-width with a peak signal-to-noise ratio of 7. I also find that SBS slow light performance can be improved by avoiding competing nonlinear effects. A gain-bandwidth product of 344 dB.GHz is obtained in our system with a highly-nonlinear optical fiber.

Besides the slow light applications, I realize that group velocity dispersion is also optically controlled via the SBS process. In the very recent GVD experiment, I use a dual-line SBS resonance and obtain a tunable GVD parameter of 7.5 ns$^2$/m, which is 10$^9$ times larger than the value found in a single-mode fiber. The large GVD system is used to disperse an optical pulse with a pulse width of 28 ns, which is beyond the capability for current dispersion techniques working in the picosecond and sub picosecond region. The SBS-based all-optical control of GVD is also widely tunable and can

be applied to any wavelength within the transparent window of the

optical fiber. I expect many future extensions following this work

on the SBS-based all-optical GVD control using the readily developed SBS tailoring techniques.

Finally, I extend the basic theory of backwards SBS to describe the forward SBS observed in a highly nonlinear fiber, where asymmetric forward SBS resonances are observed at the gigahertz range. An especially large gain coefficient of 34.7 W$^{-1}$ is observed at the resonance frequency of 933.8 MHz. This is due to good overlap between the optical wave and the high order guided radial acoustic wave. The interplay from the competing process known as the Kerr effect is also accounted for in the theory.

If electronics are ever to be completely replaced by optics, a significant possibility in the wake of the fiber revolution, it is likely that nonlinear materials will play a central and enabling role. Indeed, nonlinear optics is the study of the mechanisms through which light can change the nature and properties of matter and, as a corollary, how one beam or color of light can manipulate another or even itself within such a material. However, of the many barriers preventing such a lofty goal, the narrow and limited range of properties supported by nonlinear materials, and natural materials in general, stands at the forefront. Many industries have turned instead to artificial and composite materials, with homogenizable metamaterials representing a recent extension of such composites into the electromagnetic domain. In particular, the inclusion of nonlinear elements has caused metamaterials research to spill over into the field of nonlinear optics. Through careful design of their constituent elements, nonlinear metamaterials are capable of supporting an unprecedented range of interactions, promising nonlinear devices of novel design and scale. In this context, I cast the basic properties of nonlinear metamaterials in the conventional formalism of nonlinear optics. Using alternately transfer matrices and coupled mode theory, I develop two complementary methods for characterizing and designing metamaterials with arbitrary nonlinear properties. Subsequently, I apply these methods in numerical studies of several canonical metamaterials, demonstrating enhanced electric and magnetic nonlinearities, as well as predicting the existence of nonlinear magnetoelectric and off-diagonal nonlinear tensors. I then introduce simultaneous design of the linear and nonlinear properties in the context of phase matching, outlining five different metamaterial phase matching methods, with special emphasis on the phase matching of counter propagating waves in mirrorless parametric amplifiers and oscillators. By applying this set of tools and knowledge to microwave metamaterials, I experimentally confirm several novel nonlinear phenomena. Most notably, I construct a backward wave nonlinear medium from varactor-loaded split ring resonators loaded in a rectangular waveguide, capable of generating second-harmonic opposite to conventional nonlinear materials with a conversion efficiency as high as 1.5\%. In addition, I confirm nonlinear magnetoelectric coupling in two dual gap varactor-loaded split ring resonator metamaterials through measurement of the amplitude and phase of the second-harmonic generated in the forward and backward directions from a thin slab. I then use the presence of simultaneous nonlinearities in such metamaterials to observe nonlinear interference, manifest as unidirectional difference frequency generation with contrasts of 6 and 12 dB in the forward and backward directions, respectively. Finally, I apply these principles and intuition to several plasmonic platforms with the goal of achieving similar enhancements and configurations at optical frequencies. Using the example of fluorescence enhancement in optical patch antennas, I develop a semi-classical numerical model for the calculation of field-induced enhancements to both excitation and spontaneous emission rates of an embedded fluorophore, showing qualitative agreement with experimental results, with enhancement factors of more than 30,000. Throughout these series of works, I emphasize the indispensability of effective design and retrieval tools in understanding and optimizing both metamaterials and plasmonic systems. Ultimately, when weighed against the disadvantages in fabrication and optical losses, the results presented here provide a context for the application of nonlinear metamaterials within three distinct areas where a competitive advantage over conventional materials might be obtained: fundamental science demonstrations, linear and nonlinear anisotropy engineering, and extremely compact resonant all-optical devices.