Spurious-free analysis of two-dimensional low-loss metallic gratings (original) (raw)
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The nature of transmission resonances in plasmonic metallic gratings
2010
Using the Fourier modal method (FMM) we report our analysis of the transmission resonances of a plasmonic grating with sub-wavelength period and extremely narrow slits for wavelengths of the incoming, transverse magnetic (TM)-polarized, radiation ranging from 240nm to 1500nm and incident angles from 0 degree to 90 degree. In particular, we study the case of a silver grating placed in vacuo. Consistent with previous studies on the topic, we highlight that the main mechanism for extraordinary transmission is a TM-Fabry-Perot (FP) branch supported by waveguide modes inside each slit. The TM-FP branch may also interact with surface plasmons (SPs) at the air/Ag interface through the reciprocal lattice vectors of the grating, for periods comparable with the incoming wavelength. When the TM-FP branch crosses a SP branch, a band gap is formed along the line of the SP dispersion. The gap has a Fano-Feshbach resonance at the low frequency band edge and a ridge resonance with extremely long lifetime at the high frequency band edge. We discuss the nature of these dispersion features, and in particular we describe the ridge resonance in the framework of guided-mode resonances (GMRs). In addition, we elucidate the connection of the coupling between the TM-FP branch and SPs within the Rayleigh condition. We also study the peculiar characteristics of the field localization and the energy transport in two topical examples.
Transmission resonances in plasmonic metallic gratings
Journal of the Optical Society of America B, 2011
Using the Fourier modal method (FMM) we report our analysis of the transmission resonances of a plasmonic grating with sub-wavelength period and extremely narrow slits for wavelengths of the incoming, transverse magnetic (TM)-polarized, radiation ranging from 240nm to 1500nm and incident angles from 0 0 to 90 0 . In particular, we study the case of a silver grating placed in vacuo. Consistent with previous studies on the topic, we highlight that the main mechanism for extraordinary transmission is a TM-Fabry-Perot (FP) branch supported by waveguide modes inside each slit. The TM-FP branch may also interact with surface plasmons (SPs) at the air/Ag interface through the reciprocal lattice vectors of the grating, for periods comparable with the incoming wavelength. When the TM-FP branch crosses a SP branch, a band gap is formed along the line of the SP dispersion. The gap has a Fano-Feshbach resonance at the low frequency band edge and a ridge resonance with extremely long lifetime at the high frequency band edge. We discuss the nature of these dispersion features, and in particular we describe the ridge resonance in the framework of guided-mode resonances (GMRs). In addition, we elucidate the connection of the coupling between the TM-FP branch and SPs within the Rayleigh condition. We also study the peculiar characteristics of the field localization and the energy transport in two topical examples.
Journal of the Optical Society of America A, 2007
The Fourier modal method (FMM), often also referred to as rigorous coupled-wave analysis (RCWA), is known to suffer from numerical instabilities when applied to low-loss metallic gratings under TM incidence. This problem has so far been attributed to the imperfect conditioning of the matrices to be diagonalized. The present analysis based on a modal vision reveals that the so-called instabilities are true features of the solution of the mathematical problem of a binary metal grating dealt with by truncated Fourier representation of Maxwell's equations. The extreme sensitivity of this solution to the optogeometrical parameters is the result of the excitation, propagation, coupling, interference, and resonance of a finite number of very slow propagating spurious modes. An astute management of these modes permits a complete and safe removal of the numerical instabilities at the price of an arbitrarily small and controllable reduction in accuracy as compared with the referenced true-mode method.
Description of the modes governing the optical transmission through metal gratings
Optics Express, 2011
An analytical model based on a modal expansion method is developed to investigate the optical transmission through metal gratings. This model gives analytical expressions for the transmission as well as for the dispersion relations of the modes responsible for high transmission. These expressions are accurate even for real metals used in the visiblenear-infrared wavelength range, where surface plasmon polaritons (SPP's) are excited. The dispersion relations allow the nature of the modes to be assessed. We find that the transmission modes are hybrid between Fabry-Pérot like modes and SPP's. It is also shown that it is important to consider different refractive indices above and below the gratings in order to determine the nature of the hybrid modes. These findings are important as they clarify the nature of the modes responsible for high transmission. It can also be useful as a design tool for metal gratings for various applications.
Plasmonic band edge effects on the transmission properties of metal gratings
AIP Advances, 2011
We present a detailed analysis of the optical properties of one-dimensional arrays of slits in metal films. Although enhanced transmission windows are dominated by Fabry-Perot cavity modes localized inside the slits, the periodicity introduces surface modes that can either enhance or inhibit light transmission. We thus illustrate the interaction between cavity modes and surface modes in both finite and infinite arrays of slits. In particular we study a grating that clearly separates surface plasmon effects from Wood-Rayleigh anomalies. The periodicity of the grating induces a strong plasmonic band gap that inhibits coupling to the cavity modes for frequencies near the center of the band gap, thereby reducing the transmission of the grating. Strong field localization at the high energy plasmonic band edge enhances coupling to the cavity modes while field localization at the low energy band edge leads to weak cavity coupling and reduced transmission.
Third International Workshop on Theoretical and Computational Nanophotonics - Tacona-Photonics 2010, 2010
We study the extraordinary transmission of electromagnetic wave in structures composed of two gratings with subwavelength slits in films and the conditions at which the transmittance is equal to zero. Effects of various geometric parameters on these phenomena are analyzed. The study is performed by numerical simulations using the Fourier modal method.
Physical mechanism of extraordinary electromagnetic transmission in dual-metallic grating structures
Physical Review B, 2008
Very recently, in a short letter ͓Appl. Phys. Lett. 91, 111111 ͑2007͔͒, we outlined some important results of electromagnetic transmission in dual-metallic grating structures composed of two identical single-metallic gratings with periodic subwavelength slit arrays. Here we describe and explain our theoretical study on the propagation property of the electromagnetic radiation in such structures in detail. The results manifest that the longitudinal interval and lateral displacement between the two single-metallic gratings strongly influence the electromagnetic transmission behavior in the dual-metallic grating structures. We discover some interesting phenomena such as the frequency shift and splitting of the high transmission peak, and the transmission suppression over a broad frequency region. We reveal that the coupling between the two single-metallic gratings is responsible for those phenomena. In addition, the case of oblique incidence is also explored.
Antennas and Propagation Society …, 2005
Due to the filtering and diffractive effects of their periodic structures, dielectric gratings have found different applications in controlling the propagation of electromagnetic waves. Different numerical and semi-analytical techniques, such as method of moments, modal analysis and transverse resonance method, were proposed for solving dielectric grating structures [1]-[3]. The main advantage of semi-analytical techniques compared with the numerical techniques is the less computational effort to obtain the characteristics of the grating structure. Modal analysis showed significant advantage over the transverse resonance approach for modeling one-dimensional grating structure where the complexity of the former does not increase with the number of dielectric slabs present in the unit cell as it is usually happens in the later approach [1]. Another important advantage of modal analysis compared with the transverse resonance method is that it can be extended to two-dimensional structure as it is used for solving a waveguide filled with inhomogeneous materials [4]. The present work extends the modal analysis of one-dimensional dielectric grating to the case of two-dimensional dielectric grating.
Transmission Resonances on Metallic Gratings with Very Narrow Slits
Physical Review Letters, 1999
In this letter we show how transmission metallic gratings with very narrow and deep enough slits can exhibit transmission resonances for wavelengths larger than the period of the grating. By using a transfer matrix formalism and a quasi-analytical model based on a modal expansion, we show that there are two possible ways of transferring light from the upper surface to the lower one: by the excitation of coupled surface plasmon polaritons on both surfaces of the metallic grating or by the coupling of incident plane waves with waveguide resonances located in the slits. Both mechanisms can lead to almost perfect transmittance for those particular resonances.
Theory of electromagnetic wave transmission through metallic gratings of subwavelength slits
Journal of Optics A: Pure and Applied Optics, 2007
We present FDTD calculations for transmission of light and other electromagnetic waves through periodic arrays of slits in a metallic slab. The results show resonant, frequency dependent, transmittance peaks for subwavelength widths of the slits which can be up to a factor of ten with respect to those out of resonance. Although our conclusions agree with previous work by Lezec and Thio as regards both the magnitude of the enhancement and the lack of contribution of surface plasmon polaritons of the metal surface to this effect, we derive an interpretation from a theory that deals with emerging beam-Rayleigh anomalies of the grating, and with Fabry-Perot resonances of the perforated slab considered as an effective medium.