Search Results (54 total)

We discuss propagation effects in realistic, transparent, metallodielectric photonic band gap structures in the context of negative refraction and super-resolution in the visible and near infrared ranges. In the resonance tunneling regime, we find that for transverse-magnetic incident polarization, field localization effects contribute to a waveguiding phenomenon that makes it possible for the light to remain confined within a small fraction of a wavelength, without any transverse boundaries, due to the suppression of diffraction. This effect is related to negative refraction of the Poynting vector inside each metal layer, balanced by normal refraction inside the adjacent dielectric layer: The degree of field localization and material dispersion together determine the total momentum that resides within any given layer, and thus the direction of energy flow. We find that the transport of evanescent wave vectors is mediated by the excitation of quasistationary, low group velocity surface waves responsible for relatively large losses. As representative examples we consider transparent metallodielectric stacks such as Ag∕TiO₂ and Ag∕GaP and show in detail how to obtain the optimum conditions for high transmittance of both propagating and evanescent modes for super-guiding and super-resolution applications across the visible and near IR ranges. Finally, we study the influence of gain on super-resolution. We find that the introduction of gain can compensate the losses caused by the excitation of surface plasmons, improves the resolving characteristics of the lens, and leads to gain-tunable super-resolution.

We experimentally and theoretically investigate the second order nonlinear optical response of metallodielectric multilayer structures composed of Ag and Ta₂O₅ layers, deposited by magnetron sputtering. Second harmonic generation measurements were performed in reflection mode as a function of incidence angle, using femtosecond pulses originating from a Ti:sapphire laser system tuned at λ=800  nm. The dependence of the generated signal was investigated as a function of pump intensity and polarization state. Our experimental results show that the conversion efficiency from a periodic metallodielectric sample may be enhanced by at least a factor of 30 with respect to the conversion efficiency from a single metal layer, thanks in part to the increased number of active surfaces, pump field localization, and penetration inside the metal layers. The conversion efficiency maximum shifts from 70° for the single silver layer down to approximately 55° for the stack. The experimental results are found to be in good agreement with calculations based on coupled Maxwell-Drude oscillators under the action of a nonlinear Lorentz force term.

The present investigation is concerned with the study of pulsed second-harmonic generation under conditions of phase and group velocity mismatch, and generally low conversion efficiencies and pump intensities. In positive-index, nonmetallic materials, we generally find qualitative agreement with previous reports regarding the presence of a double-peaked second harmonic signal, which comprises a pulse that walks off and propagates at the nominal group velocity one expects at the second-harmonic frequency, and a second pulse that is “captured” and propagates under the pump pulse. We find that the origin of the double-peaked structure resides in a phase-locking mechanism that characterizes not only second-harmonic generation, but also χ⁽³⁾ processes and third-harmonic generation. The phase-locking mechanism that we describe occurs for arbitrarily small pump intensities, and so it is not a soliton effect, which usually relies on a threshold mechanism, although multicolor solitons display similar phase locking characteristics. Thus, in second harmonic generation a phase-matched component is always generated, even under conditions of material phase mismatch: This component is anomalous, because the material does not allow energy exchange between the pump and the second-harmonic beam. On the other hand, if the material is phase matched, phase locking and phase matching are indistinguishable, and the conversion process becomes efficient. We also report a similar phase-locking phenomenon in negative index materials. A spectral analysis of the pump and the generated signals reveals that the phase-locking phenomenon causes the forward moving, phase-locked second-harmonic pulse to experience the same negative index as the pump pulse, even though the index of refraction at the second-harmonic frequency is positive. Our analysis further shows that the reflected second-harmonic pulse generated at the interface and the forward-moving, phase-locked pulse appear to be part of the same pulse initially generated at the surface, part of which is immediately back-reflected, while the rest becomes trapped and dragged along by the pump pulse. These pulses thus constitute twin pulses generated at the interface, having the same negative wave vector, but propagating in opposite directions. Almost any break of the longitudinal symmetry, even an exceedingly small χ⁽²⁾ discontinuity, releases the trapped pulse which then propagates in the backward direction. These dynamics are indicative of very rich and intricate interactions that characterize ultrashort pulse propagation phenomena.

Two-mode nonlinear interaction (second-harmonic and second-subharmonic generation) in a planar waveguide with a small periodic corrugation at the surface is studied. Scattering of the interacting fields on the corrugation leads to constructive interference that enhances the nonlinear process provided that all the interactions are phase matched. Conditions for the overall phase matching are found. Compared with a perfectly quasi-phase-matched waveguide, better values of squeezing as well as higher intensities are reached under these conditions. Procedure for finding optimum values of parameters for squeezed-light generation is described.

We predict the existence of gap solitons in a nonlinear, quadratic Fabry-Pérot negative index cavity. A peculiarity of a single negative index layer is that if magnetic and electric plasma frequencies are different it forms a photonic band structure similar to that of a multilayer stack composed of ordinary, positive index materials. This similarity also results in comparable field localization and enhancement properties that under appropriate conditions may be used to either dynamically shift the band edge, or for efficient energy conversion. We thus report that an intense, fundamental pump pulse is able to shift the band edge of a negative index cavity, and make it possible for a weak second harmonic pulse initially tuned inside the gap to be transmitted, giving rise to a gap soliton. The process is due to cascading, a well-known phenomenon that occurs far from phase matching conditions that limits energy conversion rates, it resembles a nonlinear third-order process, and causes pulse compression due to self-phase modulation. The symmetry of the equations of motion under the action of either an electric or a magnetic nonlinearity suggests that both nonlinear polarization and magnetization, or a combination of both, can lead to solitonlike pulses. More specifically, the antisymmetric localization properties of the electric and magnetic fields cause a nonlinear polarization to generate a dark soliton, while a nonlinear magnetization spawns a bright soliton.

The properties of an entangled two-photon state antisymmetric in frequencies are studied. At a beam splitter, two entangled photons are perfectly anticorrelated. In addition, they cannot be detected at the same time instant despite the fact that their detection times are confined to a narrow time window, i.e., they are temporally antibunched. Using nonlinear photonic-band-gap structures made of GaN∕AlN, two schemes for generating such states are described.

We study second harmonic generation in a metallodielectric photonic-band-gap structure made of alternating layers of silver and a generic, dispersive, linear, dielectric material. We find that under ideal conditions the conversion efficiency can be more than two orders of magnitude greater than the maximum conversion efficiency achievable in a single layer of silver. We interpret this enhancement in terms of the simultaneous availability of phase matching conditions over the structure and good field penetration into the metal layers. We also give a realistic example of a nine-period, Si₃∕N₄Ag stack, where the backward conversion efficiency is enhanced by a factor of 50 compared to a single layer of silver.

In the spectral region where the refractive index of the negative index material is approximately zero, at oblique incidence, the linear transmission of a finite structure composed of alternating layers of negative and positive index materials manifests the formation of a new type of band gap with exceptionally narrow band-edge resonances. In particular, for TM-polarized (transverse magnetic) incident waves, field values that can be achieved at the band edge may be much higher compared to field values achievable in standard photonic band-gap structures. We exploit the unique properties of these band-edge resonances for applications to nonlinear frequency conversion, second-harmonic generation, in particular. The simultaneous availability of high field localization and phase matching conditions may be exploited to achieve second-harmonic conversion efficiencies far better than those achievable in conventional photonic band-gap structures. Moreover, we study the role played by absorption within the negative index material, and find that the process remains efficient even for relatively high values of the absorption coefficient.

A scheme based on photonic crystal technology is proposed as an ultrabright source of entangled photons on a miniaturized scale. The geometry consists of a multilayer microcavity, excited by a resonant pump frequency, such that the emitted photons are guided transversally to the direction of the incident pump. The entanglement occurs in direction, frequency, and polarization, and the bandwidth of the emitted photons is of the order of 1  nm. We propose a feasible design based on Al_0.3Ga_0.7As∕Al₂O₃ structures and predict an emission rate 10⁵  pairs  per  second with 100  mW pump power. These results are promising for realization of chip and future quantum computer applications.

We derive an expression for the Minkowski momentum under conditions of dispersive susceptibility and permeability, and compare it to the Abraham momentum in order to test the principle of conservation of linear momentum when matter is present. We investigate cases when an incident pulse interacts with a variety of structures, including thick substrates, resonant, free-standing, micron-sized multilayer stacks, and negative index materials. In general, we find that for media only a few wavelengths thick the Minkowski and Abraham momentum densities yield similar results. For more extended media, including substrates and Bragg mirrors embedded inside thick dielectric substrates, our calculations show dramatic differences between the Minkowski and Abraham momenta. Without exception, in all cases investigated the instantaneous Lorentz force exerted on the medium is consistent only with the rate of change of the Abraham momentum. As a practical example, we use our model to predict that electromagnetic momentum and energy buildup inside a multilayer stack can lead to widely tunable accelerations that may easily reach and exceed 10¹⁰  m∕s² for a mass of 10⁻⁵  g. Our results suggest that the physics of the photonic band edge and other similar finite structures may be used as a testing ground for basic electromagnetic phenomena such as momentum transfer to macroscopic media.

We have developed a rigorous quantum model of spontaneous parametric down-conversion in a nonlinear 1D photonic-band-gap structure based upon expansion of the field into monochromatic plane waves. The model provides a two-photon amplitude of a created photon pair. The spectra of the signal and idler fields, their intensity profiles in the time domain, as well as the coincidence-count interference pattern in a Hong-Ou-Mandel interferometer are determined both for cw and pulsed pumping regimes in terms of the two-photon amplitude. A broad range of parameters characterizing the emitted down-converted fields can be used. As an example, a structure composed of 49 layers of GaN∕AlN is analyzed as a suitable source of photon pairs having high efficiency.

We predict a large enhancement of interface second-harmonic generation near the zero-n̅ gap of a Bragg grating made of alternating layers of negative- and positive-index materials. Field localization and coherent oscillations of the nonlinear dipoles located at the structure’s interfaces conspire to yield conversion efficiencies at least an order of magnitude greater than those achievable in the same length of nonlinear, phase-matched bulk material. These findings thus point to a new class of second-harmonic-generation devices made of standard centrosymmetric materials.

We numerically study the nonlinear optical properties of metal-dielectric photonic band gap structures in the pulsed regime. We exploit the high χ⁽³⁾ of copper metal to induce nonlinear effects such as broadband optical limiting, self-phase modulation, and unusual spectral narrowing of high intensity pulses. We show that in a single pass through a typical, chirped multilayer stack nonlinear transmittance and peak powers can be reduced by nearly two orders of magnitude compared to low light intensity levels across the entire visible range. Chirping dielectric layer thickness dramatically improves the linear transmittance through the stack and achieves large fields inside the copper to access the large nonlinearity. At the same time, the linear properties of the stack block most of the remaining electromagnetic spectrum.

Resonant cavities have been widely used in the past to enhance material, nonlinear response. Traditional mirrors include metallic films and distributed Bragg reflectors. In this paper we propose negative index material mirrors as a third alternative. With the help of a rigorous Green function approach, we investigate second harmonic generation from single and coupled cavities, and theoretically prove that negative index material mirrors can raise the nonlinear conversion efficiency of a bulk material by at least four orders of magnitude compared to a bulk medium.

We show that by using the internal resonances of a grating, it is possible to design a filter working for multiple wavelengths. We study the characteristics of the device with respect to the constituting parameters and we propose a realization process.

We discuss pulse propagation effects in generic, electrically and magnetically dispersive media that may display large material discontinuities, such as a surface boundary. Using the known basic constitutive relations between the fields, and an explicit Taylor expansion to describe the dielectric susceptibility and magnetic permeability, we derive expressions for energy density and energy dissipation rates, and equations of motion for the coupled electric and magnetic fields. We then solve the equations of motion in the presence of a single interface, and find that in addition to the now-established negative refraction process an energy exchange occurs between the electric and magnetic fields as the pulse traverses the boundary.

A description of spontaneous parametric down-conversion in finite-length one-dimensional nonlinear photonic crystals is developed using semiclassical and quantum approaches. It is shown that if a suitable averaging is added to the semiclassical model, its results are in very good agreement with the quantum approach. We propose two structures made with GaN∕AlN that generate both degenerate and nondegenerate entangled photon pairs. Both structures are designed so as to achieve a high efficiency of the nonlinear process.

Cross-phase-modulation-induced instability is identified as a significant mechanism for efficient parametric four-wave-mixing frequency conversion in photonic-crystal fibers. Fundamental-wavelength femtosecond pulses of a Cr, forsterite laser are used in our experiments to transform the spectrum of copropagating second-harmonic pulses of the same laser in a photonic-crystal fiber. Efficient generation of sidebands shifted by more than 80 THz with respect to the central frequency of the second harmonic is observed in the output spectrum of the probe field.

A new generalized nonlinear Schrödinger equation describing the propagation of ultrashort pulses in bulk media exhibiting frequency dependent dielectric susceptibility and magnetic permeability is derived and used to characterize wave propagation in a negative index material. The equation has new features that are distinct from ordinary materials (μ=1): the linear and nonlinear coefficients can be tailored through the linear properties of the medium to attain any combination of signs unachievable in ordinary matter, with significant potential to realize a wide class of solitary waves.

We numerically demonstrate that a planar waveguide in which the inner layer is a gas with refractive index n₀=1, sandwiched between two identical semi-infinite layers of a negative index material, can support both transverse electric and transverse magnetic guided modes with low losses. Recent developments in the design of metamaterials with an effective negative index suggest that this waveguide could operate in the infrared region of the spectrum.

A Kerr-nonlinearity-induced profile of the refractive index in the hollow core of a photonic-crystal fiber (PCF) changes the spectrum of propagation constants of air-guided modes, effectively shifting the passbands in fiber transmission, controlled by the photonic band gaps (PBGs) of the cladding. This effect is shown to allow the creation of fiber switches for high-intensity laser pulses. The Kerr-nonlinearity control of air-guided modes in PCFs and the performance of a PCF switch are quantified by solving the propagation equation for the slowly varying envelope of a laser pulse guided in Kerr-effect-modified PCF modes. The spatial dynamics of the light field in a PBG waveguide switch is analyzed with the use of the slowly varying envelope approximation, demonstrating high contrasts of optical switching with PBG waveguides and hollow PCFs.

We predict the existence of bright and dark gap solitons in a single slab of negative index material. The formation of gap solitons is made possible by the exceptional interplay between the linear dispersive properties of the negative index etalon and the effect of a cubic nonlinearity.

We have studied biaxial, birefringent, one-dimensional, multilayer structures and found a wavelength region where the phase of one specific polarization component of the transmitted field increases with wavelength, giving rise to unusual polarization dependent dispersive effects of the input beam. We discuss the conditions that lead to these effects, and examine possible ways to enhance them.

Self-phase-modulation-induced spectral broadening of laser pulses in air-guided modes of hollow photonic-crystal fibers (PCFs) is shown to allow the creation of fiber-optic limiters for high-intensity ultrashort laser pulses. The performance of PCF limiters is analyzed in terms of elementary theory of self-phase modulation. Experiments performed with 100 fs microjoule pulses of 800  nm Ti:sapphire laser radiation demonstrate the potential of hollow PCFs as limiters for 10  MW ultrashort laser pulses and show the possibility to switch the limiting level of output radiation energy by guiding femtosecond pulses in different PCF modes.