Topological photonics aims to utilize topological photonic bands and corresponding edge modes to implement robust light manipulation, which can be readily achieved in the linear regime of light-matter interaction. In this talk, I will review some recent results regarding nonlinear interactions of one-way edge-modes in frequency mixing processes in topological photonic crystals (PhCs) and graphene metasurfaces. In particular, I will demonstrate SHG via nonlinear interaction of double topological valley-Hall kink modes in PhCs with hexagonal lattice. I will first show that two topological frequency band gaps can be created around a pair of frequencies, ω0 and 2ω0, by gapping out the corresponding Dirac points. Importantly, I demonstrate that tunable, bidirectional phase-matched SHG via nonlinear interaction of the valley-Hall kink modes inside the two band gaps can be achieved. More specifically, by using Stokes parameters associated with the magnetic part of the valley-Hall kink modes, we introduce the concept of SHG directional dichroism, which is employed to characterize optical probes for sensing chiral molecules. I also show that these ideas can be extended to graphene metasurfaces, where the Kerr-type nonlinearity of graphene can be used to control the light transmission in topological domain-interface waveguides. In the second part of my talk I will illustrate how bound states in the continuum (BICs) of certain silicon nitride PhC slabs, engineered to possess sharp resonances with high quality factors at both the fundamental-frequency and second-harmonic, can be used to achieve an orders-of-magnitude enhancement of the SHG. Certain connections between the topological charge of the BICs and the properties of the nonlinear optical interaction (SHG) are also revealed.
The ability to confine and guide light makes photonic crystals (PhCs) a promising platform for large local field enhancement, which enables efficient nonlinear processes at the nanoscale. Here, we utilize optical bound states in the continuum (BICs) to engineer sharp resonances with high quality factors. By investigating the angleresolved reflection spectra, we demonstrate that two PhC slabs with different configuration but the same lattice constant support a pair of at-Γ and a pair of off-Γ resonances, respectively. In both cases, BIC-type resonances are observed at the fundamental frequency while BIC-like resonances are found at the second harmonic. This double-resonance phenomenon is subsequently used to significantly enhance the second-harmonic generation from PhC slabs. The maximum values of the SHG are several orders of magnitude larger than those corresponding to the reference slabs. We consider that our approach based on double-resonance BICs provides a novel way to realize enhanced harmonic generation in photonic nanodevices.
In this paper, optically controllable and topologically protected plasmon transport is implemented via a topological nanohole plasmonic waveguide coupled to a standard edge mode of a graphene metasurface. By introducing nanoholes with different sizes in the unit cell, one breaks the spatial-inversion symmetry of a graphene metasurface in which the topological waveguide is constructed, leading to the emergence of topologically protected modes located in a nontrivial band-gap. Based on the strong Kerr effect and tunable optical properties of graphene, the coupling between the edge and topological interface modes can be efficiently controlled by optical means provided by an optical pump beam injected in a bulk mode. In particular, by tuning the power inserted in the bulk mode, one can control the difference between the wave-vectors of the topological and edge modes and consequently the optical power coupled in the topological mode. Our results show that when the pump power approaches a specific value, the edge and topological modes become phase-matched and the topological waveguide mode can be efficiently excited. Finally, we demonstrated that the optical coupling is strongly dependent on the group-velocity of the pump mode, a device feature that can be important in practical applications.
Topological photonics aims to utilize topological photonic bands and corresponding edge modes to implement robust light manipulation. Importantly, topological photonics provide an ideal platform to study nonlinear interactions. In this talk, I will review some recent results regarding nonlinear interactions of one-way edge-modes in frequency mixing processes in topological photonic nanostructures. More specifically, I will discuss the band topology of 2D photonic crystals with hexagonal symmetry and demonstrate that SHG and THG can be implemented via one-way edge modes. Moreover, I will demonstrate that more exotic phenomena, such as slow-light enhancement of nonlinear interactions and harmonic generation upon interaction of backward-propagating edge modes can also be realized. Finally, FWM of topological plasmon modes of graphene plasmonic crystals and SHG upon interaction of valley-Hall topological modes of all-dielectric photonic crystals will be discussed.
Topologically protected plasmonic states with wide topological band gaps provide unprecedented robustness against disorder-induced backscattering. In this study, we design a graphene bi-layer metasurface that possesses valley-Hall topological plasmonic modes in a nontrivial bandgap. In particular, the breaking of mirror symmetry of two graphene layers is achieved via a horizontal shift of the hole lattice of the top layer, which leads to topologically protected edge modes in the nontrivial bandgap. The corresponding band dispersion of the topological edge modes shows unidirectional propagation features. Moreover, we have designed a sensitive molecular sensor based on such graphene bi-layer metasurfaces, using the fact that the chemical potential of graphene varies upon adsorption of gas molecules. This effect leads to a marked variation of the transmission of the topological mode, and thus a sensing device with large sensitivity can be realized.
We investigate topological photonic crystals specially designed such that the frequency band gaps appear around ω0, 2ω0, 3ω0 and, more importantly, each band gap contains exactly one unidirectional edge mode. These one-way edge modes are then utilized to implement key nonlinear frequency mixing processes, such as second- and third-harmonic generation.
Pulsed dynamics are rigorously studied in coupled silicon photonic crystal cavity-waveguide nanostructures by developing a computational model based on coupled-mode theory, which describes cavity-waveguide coupling effects, key nonlinear interactions, such as the Kerr effect, two-photon-absorption, free-carrier (FC) dispersion and FC absorption, as well as waveguide dispersion effects. Propagation of optical pulses in a photonic system consisting of two photonic crystal cavities coupled to a photonic crystal waveguide operating in the slow-light regime is analyzed. Moreover, the influence of different parameters on pulse dynamics is investigated, including the separation between cavities, the distance between the cavities and the waveguide, and the input pulse width.
We present several approaches for orders-of-magnitude enhancement of optical nonlinearities in specially engineered
nanostructures containing graphene and other 2D materials and illustrate how they apply to second- and third-harmonic
generation in such 2D-3D photonic heteromaterials. Applications to active photonic devices, such as nonlinear optical
gratings, are discussed as well.
Optical interconnects made of silicon are viewed as emerging efficient solutions for addressing the communication bottlenecks that plague high-performance computing systems and big-data centers. Due to large index contrast and optical nonlinearity of silicon, waveguides and active devices based on silicon can be scaled down to sub-wavelength size, making silicon photonics an ideal platform towards integrated on-chip photonic circuits. In order for this potential to be fulfilled, one needs to understand the factors that affect the quality of optical signals propagating in silicon optical interconnects, namely the bit-error ratio (BER), as well as the relationship between the parameters characterizing the optical signal and the BER.
In this work, an accurate approach to calculate the BER in single-channel silicon optical interconnects utilizing arbitrarily-shaped pulsed signals is presented. The optical interconnects consist of either strip single-mode silicon photonic waveguides (Si-PhWs) or silicon photonic crystal (PhC) waveguides (Si-PhCWs), and are linked to a direct-detection receiver. The optical signal consists of a superposition of Gaussian pulses and white noise. The signal dynamics in the silicon waveguides is modelled using a modified nonlinear Schrodinger equation, whereas the Karhunen-Loeve series expansion method is employed to calculate the system BER. Our analysis reveals that in the case of the Si-PhWs the pulse width is the main parameter that determines the BER, whereas in the case of Si-PhCWs the BER is mostly affected by the waveguide properties via the pulse group-velocity. A good system performance is achieved in centimeter-long Si-PhWs whereas similar system performance is obtained using 100× and 200× shorter Si-PhCWs operating in the fast- and slow-light regimes, respectively.
Peculiar physical properties of graphene offer remarkable potential for advanced photonics, particularly in the area of nonlinear optics at deep-subwavelength scale. In this article, we use a theoretical and computational analysis to demonstrate an efficient mechanism for enhancing the third-harmonic generation in graphene diffraction gratings. By taking advantage of the relation between the resonance wavelength of localized surface-plasmon polaritons of graphene ribbons and disks their specific geometry, we can engineer the spectral response of graphene gratings so as strong plasmonic resonances exist at both the fundamental frequency and third-harmonic (TH). As a result of this dual resonance mechanism for optical near-field enhancement, the intensity of the TH can be increased greatly.
We present an effective approach to evaluate the performance of multi-channel silicon (Si) photonic systems. The system is composed of strip Si photonic waveguides (Si-PhWs) with uniform cross-section or photonic-crystal (PhC) Si waveguides (Si-PhCWs), combined with a set of direct-detection receivers. Moreover, the optical field in each channel is the superposition of a continuous-wave nonreturn-to-zero ON-OFF keying modulated signal and a white Gaussian noise. In order to characterize the optical signal propagation in the waveguides, an accurate mathematical model describing all relevant linear and nonlinear optical effects and its linearized version is employed. In addition, two semi-analytical methods, time- and frequency-domain Karhunen-Loève series expansion, are used to assess the system bit-error-rate (BER). Our analysis reveals that Si-PhCWs provide similar performance as Si-PhWs, but for 100× shorter length. Importantly, much worse BER is achieved in Si-PhCWs when one operates in slow-light regime, due to the enhanced linear and nonlinear effects.
We present a new numerical method for the analysis of second-harmonic generation (SHG) in one- and two-dimensional (1D, 2D) diffraction gratings containing centrosymmetric quadratically nonlinear materials. Thus, the nonlinear optical properties of a material are determined by its symmetry properties: non-centrosymmetric materials lack inversion symmetry and therefore allow local even-order SHG in the bulk of the material, whereas this process is forbidden in centrosymmetric materials. The inversion symmetry of centrosymmetric materials is broken at their surface whence they allow local surface SHG. Additionally, centrosymmetric materials give rise to nonlocal (bulk) SHG.
Our numerical method extends the linear generalized source method (GSM), which is an efficient numerical method for solving the problem of linear diffraction in periodic structures of arbitrary geometry. The nonlinear GSM is a three-step algorithm: for a given excitation at the fundamental frequency the linear field is computed using the linear GSM. This field gives rise to a nonlinear source polarization at the second harmonic (SH) frequency. This nonlinear polarization comprises surface and bulk polarizations as additional source terms and is subsequently used to compute the nonlinear near- and far-field optical response at the SH.
We study the convergence characteristics of the nonlinear GSM for 1D and 2D periodic structures and emphasize the numerical intricacies caused by the surface SH polarization term specific to centrosymmetric materials. In order to illustrate the practical significance of our numerical method, we apply it to metallic gratings made of Au and Ag as well as dielectric grating structures made of silicon and investigate the relative contribution of the bulk and surface nonlinearity to the nonlinear optical response at the SH. Particular attention is paid to optical effects that have a competing influence to the nonlinear optical response of the grating structures, namely the resonant local field enhancement and optical losses.
We theoretically investigate the fluorescence enhancement of a representative set of dye-molecules excited by three classes of nanoantennae, using a fully vectorial three-dimensional finite-difference time-domain (3D FDTD) method. Through these 3D FDTD calculations, in conjunction with analytic guidance using temporal coupled-mode (TCM) theory, we develop a design procedure for antennae assemblies that allow achieving fluorescence enhancements of 200-900 over the emission intensity in the bare dye molecule. The enhancement from these commercially available fluorochrome conjugates, namely, CFTM568, CFTM660R and CFTM790 are fully investigated using spherical-dimer, elliptical-dimer, and bowtie nanoantennae. These results demonstrate a method for rationally designing arbitrary metallic nanoparticle/emitter assemblies prior to their synthesis and assembly to achieve optimum fluorescence enhancement.
We present recent results pertaining to pulse reshaping and optical signal processing using optical nonlinearities of silicon-based tapered photonic wires and photonic crystal waveguides. In particular, we show how nonlinearity and dispersion engineering of tapered photonic wires can be employed to generate optical similaritons and achieve more than 10× pulse compression. We also discuss the properties of four-wave mixing pulse amplification and frequency conversion efficiency in long-period Bragg waveguides and photonic crystal waveguides. Finally, the influence of linear and nonlinear optical effects on the transmission bit-error rate in uniform photonic wires and photonic crystal waveguides made of silicon is discussed.
We demonstrate enhanced conversion efficiency (CE) and parametric amplification of optical pulses via quasiphase- matched four-wave-mixing (FWM) in long-period Bragg waveguides made of silicon. Our study is based on a rigorous theoretical model that describes optical pulse dynamics in a periodically, adiabatically modulated silicon photonic waveguide and a comprehensive set of numerical simulations of pulse interaction in such gratings. More specifically, our theoretical model takes into account all of the relevant linear and nonlinear optical effects, including free-carriers generation, two-photon absorption, and self-phase modulation, as well as modal frequency dispersion up to the fourth-order. Due to its relevance to practical applications, a key issue investigated in our work is the dependence of the efficiency of the FWM process on the waveguide parameters and the operating wavelength. In particular, our analysis suggests that by varying the waveguide width by just a few tens of nanometers the wavelengths of the phase-matched waves can be shifted by hundreds of nanometers. Our numerical simulations show also that, in the anomalous group-velocity dispersion regime, a CE enhancement of more than 20 dB, as compared to the case of a waveguide with constant width, can be easily achieved.
We present a new numerical method for the analysis of second-harmonic generation (SHG) in one- and twodimensional (1D, 2D) diffraction gratings with arbitrary profile made of non-centrosymmetric optical materials. Our method extends the generalized source method (GSM), which is a highly efficient alternative to the conventional Fourier modal method, to quadratically nonlinear diffraction gratings. The proposed method consists of a two-stage algorithm. Initially, the electromagnetic field at the fundamental frequency is computed in order to obtain the second-harmonic polarization using the known second-order nonlinear susceptibility. Then the optical field at the second-harmonic frequency is computed using this polarization as an additional source term in the GSM. We show how to integrate this source term into the GSM framework without changing the structure of the basic algorithm. We use the proposed algorithm to investigate a doubly resonant mechanism that leads to strong enhancement of SHG in a nonlinear 2D circular GaAs grating mounted on top of a GaAs slab waveguide. We design this optical device such that slab waveguide modes at the fundamental and second-harmonic are simultaneously excited and phase matched by the grating. The numerically obtained resonance frequencies show good agreement with analytically computed resonance frequencies of the unperturbed slab waveguide.
We present a comprehensive study of generation and collision of optical similaritons in sub-micron silicon photonic wire waveguides. Our analysis of optical pulse dynamics in such wave guiding devices is based on a rigorous theoretical model that incorporates all of the relevant linear and nonlinear optical effects, including modal dispersion, free-carrier dispersion and absorption, self-phase modulation, two-photon absorption, frequency dispersion of the optical nonlinearity, and the free-carrier dynamics. In addition to the particular characteristics of the generation of optical similaritons in silicon photonic wires, we also investigate the dependence of the efficiency of this optical process on the physical parameters and temporal profile of the input pulse. The collision of optical similaritons that propagate both in the normal and anomalous dispersion regime is also analyzed. Guided by the target applications of our study, we considered two technologically relevant spectral regions, namely, telecom and mid-IR frequency domains.
Scanning second harmonic generation (SHG) microscopy is becoming an important tool for characterizing
nanopatterned metal surfaces and mapping plasmonic local field enhancements. Here we study G-shaped
and mirror-G-shaped gold nanostructures and test the robustness of the experimental results versus the
direction of scanning, the numerical aperture of the objective, the magnification, and the size of the laser
spot on the sample. We find that none of these parameters has a significant influence on the experimental
results.
KEYWORDS: Plasmonics, Absorption, Plasmons, Plasmonic sensors, Sensors, Near field optics, Signal to noise ratio, Optical microcavities, Electromagnetism, Nanowires
High fabrication costs of complex photonic nano-devices make it imperative to have access to high-performance
computational tools, which can greatly accelerate the device design process by reducing the design-fabricationtesting
cycle. To this end, in this article we briefly review a numerical method based on the multiple scattering
algorithm, which we used to describe the second-harmonic generation in plasmonic nanostructures. Then, by
using specific examples, we illustrate how this method can be employed to characterize the nonlinear optical
modes of microcavities made of plasmonic nanowires. In particular, we show that such plasmonic microcavities
have three distinct types of modes, namely, plasmonic cavity modes, multipole plasmon modes generated via
the hybridization of modes of single nanowires, and whispering gallery modes. We also show that due to the
sensitivity of the nonlinear plasmonic cavity modes to the changes in the environment, they are ideal candidates
for nano-scale sensing devices, e. g., plasmonic sensors.
We analyze the influence of the interchannel frequency separation on the transmission capacity of a soliton-based wavelength-division multiplexing (WDM) system. The input into the optical fiber is represented by a superposition of N single solitons with equal amplitudes and different frequencies. Two different cases are taken into account. In the first case, all solitons completely overlap but have different frequencies. It is found that there exists a critical frequency separation above which WDM is feasible. Furthermore, it is shown that this critical frequency increases with the number of transmission channels. In the second case, there is a time shift between the overlapping solitons in adjacent channels. It is demonstrated that this combination of time- and wavelength-division multiplexing yields the largest transmission capacity. In addition, it is discussed the case in which the interchannel frequency separation is smaller than the critical frequency. It is found that in this regime the soliton spectrum of the emerging optical field has a rich structure.
We apply the quasiadiabatic approximation for the femtosecond pulse propagation in a collection of excitons in the case of weak interaction between the optical pulse and the semiconductor medium. Using the semiconductor Maxwell-Bloch equations beyond the slowly varying envelope approximation we show that the dynamics of femtosecond pulse propagation is described by the modified Korteweg-de Vries equation. Bright solitons superimposed on a continuous wave background are found and their stability against low amplitude perturbations is investigated. Possible experiments in semiconductor systems such as GaAs/AlGaAs are discussed.
We used the Riemann Problem Method with a 3 X 3 matrix system to find the single soliton solution for a perturbed nonlinear Schrodinger equation in the most compact form. The considered equation describes bright ultrashort pulse propagation in properly tailored monomode optical fibers. The propagation of different single soliton solutions under the influence of the self-induced Raman effect was illustrated. Unlike the single soliton solution of the standard nonlinear Schrodinger equation we found that one of the our soliton solution can exhibit instability which leads to soliton fission.
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