Spatiotemporal coupled-mode theory of guided-mode resonant gratings

Bykov, Dmitry A.; Doskolovich, Leonid L.

doi:10.1364/oe.23.019234

Cited by 36 publications

(34 citation statements)

References 19 publications

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“…A promising theoretical platform in which to carry out this program is represented by temporal coupled-mode theory for optical resonators. Such framework has been fruitfully employed to study the transmission of layered photonic-crystal structures [16,21,22], gratings [23], coupled cavities and waveguides [24,25], and the scattering cross section of nanoparticles [17,26,27]. For the moment, however, coupled-mode theory has been typically restricted to a selection of only one or two modes of the optical system.…”

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confidence: 99%

Quasinormal-Mode Expansion of the Scattering Matrix

et al. 2017

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It is well known that the quasinormal modes (or resonant states) of photonic structures can be associated with the poles of the scattering matrix of the system in the complex-frequency plane. In this work, the inverse problem, i.e., the reconstruction of the scattering matrix from the knowledge of the quasinormal modes, is addressed. We develop a general and scalable quasinormal-mode expansion of the scattering matrix, requiring only the complex eigenfrequencies and the far-field properties of the eigenmodes. The theory is validated by applying it to illustrative nanophotonic systems with multiple overlapping electromagnetic modes. The examples demonstrate that our theory provides an accurate first-principle prediction of the scattering properties, without the need for postulating ad-hoc nonresonant channels.Scattering matrices have been playing a ubiquitous role in physics since the early history of quantum field theory [1]. Nowadays, scattering-matrix techniques represent an irreplaceable tool for scientists working in nuclear physics [2], electronic transport [3], or classically chaotic systems [4], just to mention some of the several fields of application. Scattering matrices also enjoy a well deserved popularity in electromagnetic modeling, ranging from microwave devices [5] to nanophotonics applications, such as scattering and transmission from nanostructured objects [6][7][8].Most of the systems that are usually investigated with scattering-matrix techniques display a highly structured resonant response as a function of the excitation frequency (or energy), with the resonances in the spectrum being directly related to the poles of the analytical continuation of the scattering matrix in the complexfrequency plane [9,10]. For electromagnetic systems, such poles correspond to quasinormal modes (also called resonant states), i.e., complex-frequency solutions of Maxwell's equations with outgoing-wave boundary conditions [11][12][13][14][15]. In a sense, quasinormal modes represent the bare skeleton around which the frequency-dependent response of the system is built. The interplay among different electromagnetic modes has proven to be crucial for explaining several intriguing phenomena, such as Fano resonances in optical systems [16], scattering dark states [17,18], and the optical analog of electromagnetically induced transparency and superscattering [19], and for designing new optical materials, such as optical metasurfaces for wavefront shaping [20]. For these reasons, it is desirable and extremely interesting to be able to reconstruct ab initio the entire scattering matrix of a system from the knowledge of its quasinormal modes. Not only would such quasinormal-mode expansion contribute to the understanding of complicated spectral features in terms of interference and superposition of resonant states, but it would also offer practical advantages from the numerical point of view, since a full eigenmode calculation is generally faster and more comprehensive than a large number of single-frequency simulations.A...

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Quasinormal-Mode Expansion of the Scattering Matrix

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“…As abovementioned, first-order spatial differentiation of the transverse profile of optical beams using guided-mode resonance gratings at oblique incidence was suggested in [21] and recently demonstrated with various grating structures and materials [22][23][24][25]. The mechanism of spatial differentiation can be simply understood on the basis of a one-dimensional spectral decomposition of the incoming beam and considering the transfer function of the grating in Fourier space based on a simple coupledmode model [64]. Denoting by G inc (k x ) and G tr (k x ) the spatial angular spectra of the incident and transmitted fields, respectively, the spatial transfer function of the grating is given by [21]…”

Section: B First-order Spatial Differentiation At Oblique Incidencementioning

confidence: 99%

Polarization-independent optical spatial differentiation with a doubly-resonant one-dimensional guided-mode grating

Darki,

Madsen,

Dantan

2021

Preprint

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We report on the design and experimental characterization of a suspended silicon nitride subwavelength grating possessing a polarization-independent guided-mode resonance at oblique incidence. At this resonant wavelength we observe that the transverse intensity profile of the transmitted beam is consistent with a first-order spatial differentiation of the incident beam profile in the direction of the grating periodicity, regardless of the incident light polarization. These observations are corroborated by full numerical simulations. The simple one-dimensional and symmetric design, combined with the thinness and excellent mechanical properties of these essentially loss-free dieletric films, is attractive for applications in optical processing, sensing and optomechanics.

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“…The method is based on the framework of temporal coupledmode theory for optical resonators [3,10]. Such framework has been effectively used to study the transmission of gratings and photonic-crystal structures [3,[10][11][12] and the scattering cross section of nanoparticles [4]. However, in these applications, coupled-mode theory has been usually restricted to only one or two modes of the optical system, with the residual spectral response being taken into account with a slowly varying frequency-dependent background, fitted from independent simulation data [3,10,11].…”

Section: Introductionmentioning

confidence: 99%

Reconstructing the scattering matrix of photonic systems from quasinormal modes

Alpeggiani

Parappurath

Verhagen

et al. 2017

2017 19th International Conference on Transparent Optical Networks (ICTON)

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The scattering matrix is a fundamental tool to quantitatively describe the properties of resonant systems. In particular, it enables the understanding of many photonic devices of current interest, such as photonic metasurfaces and nanostructured optical scatterers. In this contribution, we show that the scattering matrix of a photonic system is completely determined by its quasinormal modes, i.e., the self-sustaining electromagnetic excitations at a complex frequency. On the basis of temporal coupled-mode theory, we derive an expression for the expansion of the scattering matrix on quasinormal modes, which is directly applicable to an arbitrary number of modes and input/output channels. Our theory does not require any ad-hoc assumptions, such as the fitting of an additonal nonresonant background. We validate and discuss the theoretical formalism with some illustrative examples. This demonstrates that the theory represents a powerful and predictive tool for calculating the highly structured spectra of resonant nanophotonic systems, and, at the same time, a key for unravelling the physical mechanisms at the heart of such intricate spectral structures. Keywords: scattering matrix, quasinormal modes, resonant states, theoretical photonics, photonic crystals. INTRODUCTIONThe scattering matrix constitutes an important tool in multiple fields of science, such as nuclear physics, electronic transport, or classical electrodynamics [1,2]. In particular, it plays an essential role in helping us to understand intriguing optical phenomena, such as Fano resonances in optical systems [3] or scattering dark states [4], and to tailor the properties of novel photonic devices, like photonic metasurfaces [5] or hybrid plasmonicphotonic nanoresonators [6].These electromagnetic systems typically display a highly structured spectral response, with multiple resonances in the spectrum. The resonances are associated with quasinormal modes (also called resonant states), i.e., complex-frequency solutions of Maxwell's equations with outgoing-wave boundary conditions [7][8][9]. In order to decipher, understand, and engineer the behaviour of complex optical systems, it is vital to unravel the connection between the scattering matrix and the underlying quasinormal modes.In this contribution, we develop a rigorous and general theory for the expansion of the scattering matrix of electromagnetic systems on quasinormal modes. The method is based on the framework of temporal coupledmode theory for optical resonators [3,10]. Such framework has been effectively used to study the transmission of gratings and photonic-crystal structures [3,[10][11][12] and the scattering cross section of nanoparticles [4]. However, in these applications, coupled-mode theory has been usually restricted to only one or two modes of the optical system, with the residual spectral response being taken into account with a slowly varying frequency-dependent background, fitted from independent simulation data [3,10,11]. Our theory provides a direct and general relation ...

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Spatiotemporal coupled-mode theory of guided-mode resonant gratings

Cited by 36 publications

References 19 publications

Quasinormal-Mode Expansion of the Scattering Matrix

Quasinormal-Mode Expansion of the Scattering Matrix

Polarization-independent optical spatial differentiation with a doubly-resonant one-dimensional guided-mode grating

Reconstructing the scattering matrix of photonic systems from quasinormal modes

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