Critical coupling in cavity-resonant integrated-grating filters (CRIGFs).

We experimentally demonstrate critical coupling in miniature grating-coupled resonators known as cavity-resonant integrated-grating filters (CRIGFs). Using previously proposed asymmetric grating coupler designs for non-linear CRIGFs, and introducing a dedicated variant of a coupled-modes theory model to estimate physical properties out of the measured reflection and transmission characteristics of these resonators, we demonstrate fine control over the in-and out-coupling rate to the resonator while keeping constant both the internal losses and the resonant wavelength. Furthermore, the critical coupling condition is also observed to coincide with the maximum enhancement of the second harmonic generation signal.

Extreme enhancement of the quality (Q)-factor and mode field intensity in cavity-resonator gratings.

In this paper, dielectric Cavity-Resonant Integrated-Grating Filters (CRIGFs) are numerically optimized to achieve extremely high-quality factors, by optimizing the cavity in/out-coupling rate and by introducing apodizing mode-matching sections to reduce scattering losses. Q-factors ranging between 0.1 and 50 million are obtained and two different domains are distinguished, as a function of the perturbation parameter which controls the cavity in/out-coupling rate. When the cavity coupling Q-factor is lower than the Q-factor of the uncoupled Fabry-Perot cavity, corresponding to the over-coupling regime, the reflectivity response exhibits a high resonance maximum. On the contrary, in the under-coupling regime the resonant reflectivity maximum is much weaker since the scattering losses of the uncoupled cavity dominate. Between these two domains, the so-called critical coupling condition leads to very strong field enhancement inside the device, reaching up to 104 times the incident field amplitude. This theoretical work paves the way towards the practical implementation of CRIGFs with much higher Q-factors than currently demonstrated, potentially reaching performance on a par with other resonators such as photonic crystal cavities or whispering gallery mode resonators. These results can serve to optimize the design of narrow-band planar grating filters, particularly for application in non-linear optics.

Cavity-resonator integrated bi-atom grating coupler for enhanced second-harmonic generation.

We report on the design of cavity-resonator integrated grating couplers for second-harmonic generation. The key point is that the base pattern of our grating coupler (GC) is made of two ridges with different widths (bi-atom). Thus, we reach extremely high Q-factors (above 105) with structures whose fabrication is not challenging, since the bi-atom base pattern is close to that of the surrounded distributed Bragg reflectors (DBR). Yet, the parameters of the structure have to be chosen cautiously to reduce the transition losses between each section (GC, DBR). We numerically demonstrate conversion efficiencies η of several tenths per Watt, even doubled when we include a phase-matching grating within the structuration. Such efficiencies are comparable to those obtained with waveguides and nano-resonators.

Cavity resonator-integrated guided-mode resonance filters with on-chip electro- and thermo-optic tuning.

Cavity resonator grating filters (CRIGFs) integrated on lithium niobate on insulator (LNOI) with electrical tuning elements are reported. The resonance wavelength of the filters is in the 780 nm range. Integrated thermo-optical tuning range of 2.5 nm is measured using integrated resistors, whilst a 0.7 nm electro-optical tuning range using capacitive metallic pads is achieved with ±400V drive voltage.

Second-harmonic-generation enhancement in cavity resonator integrated grating filters.

We demonstrate numerically and experimentally second-harmonic generation (SHG) in a cavity resonator integrated grating filter (CRIGF, a planar cavity resonator made of Bragg grating reflectors) around 1550 nm. SHG is modeled numerically for several different systems, including a thin plane layer of LiNbO3 without and with a grating coupler to excite a waveguide mode. We demonstrate that when the waveguide mode is confined to a CRIGF, designed to work with focused incident beams, the SHG power is increased more than 30 times, compared to the case of a single grating coupler used with an almost collimated pump beam.

Semi-phenomenological effective permittivity approach to metallic periodic structures.

A detailed review of the theory of effective permittivity for one- and two-dimensional periodic structures shows its limited validity for metal-dielectric structures in the visible and near infra-red if the feature dimensions are comparable with the metal skin depth. We propose a phenomenological correction to the static formulae using a realistic assumption for the electric field behavior inside the metal features. This approach allows us to obtain analytical expressions for the effective permittivity in the case when the electric field is not sufficiently homogeneous within the unit cell of the gratings. A comparison with the numerical results of the Fourier modal method demonstrates the validity of the analytical formulae. Additional study is made on the impedance approximation at the outer boundaries of the periodical structure in order to propose analytical formulae for the reflection coefficient that permits better correspondence with the numerical results. The link between the values of effective permittivity and permeability defined as the ratios between the averaged fields, and the metamaterial permittivity and permeability is discussed.

Two-dimensional grating for narrow-band filtering with large angular tolerances.

A two-dimensional periodic sub-wavelength array of vertical dielectric cylinders on a glass substrate is studied numerically using three different electromagnetic approaches. It is shown that such structure can present a narrow-band spectral resonance characterized by large angular tolerances and 100% maximum in reflection. In particular, in a two-nanometer spectral bandwidth the reflectivity stays above 90% within angles of incidence exceeding 10 degrees for unpolarized light. Bloch modal analysis shows that these properties are due to the excitation of a hybrid mode that is created in the structure by a guided-like mode and a localized cavity mode. The first one is due to the collective effect of the array, while the second one comes from the mode(s) of a single step-index fiber.

Almost-total absorption of light in thin, biperiodic, weakly-absorbing semiconductor gratings.

We consider the design of optical systems capable of providing near 100% absorption of visible light, consisting of a structured thin layer of a weakly absorbing semiconductor placed on top of a dielectric spacer layer and a metallic mirror layer. We generalise a system recently studied semi-analytically and experimentally by Stürmberg et al [Optica 3, 556 2016] which incorporated a grating layer of antimony sulphide and delivered high, narrow-band absorptance of normally-incident light for a single polarisation. We demonstrate that bi-periodic gratings can be optimised to deliver near-perfect absorptance of unpolarised light in the system, and comment on the wavelength and angular ranges over which the absorptance remains near 100%. We show that the properties of the systems studied depend on the interaction of multiple modes, and cannot be accurately modelled within the quasistatic approximation.

Optimized 2D array of thin silicon pillars for efficient antireflective coatings in the visible spectrum.

Light reflection occuring at the surface of silicon wafers is drastically diminished by etching square pillars of height 110 nm and width 140 nm separated by a 100 nm gap distance in a square lattice. The design of the nanostructure is optimized to widen the spectral tolerance of the antireflective coatings over the visible spectrum for both fundamental polarizations. Angle and polarized resolved optical measurements report a light reflection remaining under 5% when averaged in the visible spectrum for both polarizations in a wide angular range. Light reflection remains almost insensitive to the light polarization even in oblique incidence.

Comparative study of total absorption of light by two-dimensional channel and hole array gratings.

A detailed study of light absorption by silver gratings having two-dimensional periodicity is presented for structures constructed either of channels or of holes with subwavelength dimensions. Rigorous numerical modelling shows a systematic difference between the two structures: hole (cavity) gratings can strongly absorb light provided the cavity is sufficiently deep, when compared to the wavelength, whereas very thin channel gratings can induce total absorption. A detailed analysis is given in the limit when the period tends towards zero, and an explanation of the differences in behavior is presented using the properties of effective optical index of the metamaterial layer that substitutes the periodical structure in the limit when the period tend to zero.

Plasmonic antiresonance through subwavelength hole arrays.

It has been shown both experimentally and numerically that the phenomenon of extraordinary transmission through subwavelength hole arrays is generally associated with a drop in transmission located very close to it. Paradoxically, this antiresonant drop occurs at the wavelength that, at first glance, should provoke a resonant excitation of a surface plasmon propagating along the metallic surface of the screen. The present paper gives a theoretical demonstration of this phenomenon, which dispels the paradox. Our theory is supported by numerical calculations.

Impact of electron-beam lithography irregularities across millimeter-scale resonant grating filter performances.

We investigated the impact of electron-beam lithography writing imperfections on the performance of two-dimensional resonant grating notch filters. This large area photonic device provides an interesting benchmark to assess the acceptable limits of unavoidable fabrication errors. We found that field stitching errors up to 100 nm have no detrimental effect on the filter linewidth, whereas a 2.5 nm electron-beam writing resolution, responsible for digitization disorder, is tolerable only for high-index contrast filter designs. Such an electron-beam writing strategy could also be beneficial for photonic crystal guiding structures or any periodic nanopatterned device with which the optical mode interacts with a large number of periodic elementary units.

Experimental demonstration of ultrasharp unpolarized filtering by resonant gratings at oblique incidence.

The peaks in the reflectivity spectrum of waveguide gratings observed when the incident beam couples to a mode of the structure are promising features for many applications. However their weak angular tolerance and their strong polarization sensitivity, especially under oblique incidence, limit their interest in practice. These problems can be overcome by forming slow degenerate modes outside the usual high symmetry points of the Brillouin zone with a complex periodic pattern [Fehrembach, Appl. Phys. Lett. 86, 121105 (2005)]. We show experimentally that spectrally sharp, lambda/Deltalambda approximately 4000, polarization-independent, angularly tolerant optical resonances can be obtained by exciting these modes under oblique incidence.

Experimental demonstration of a narrowband, angular tolerant, polarization independent, doubly periodic resonant grating filter.

Resonant grating filters are promising components for free-space narrowband filtering. Unfortunately, due to their weak angular tolerance, their performances are strongly deteriorated when they are illuminated with a standard collimated beam. Yet this problem can be overcome by resorting to a complex periodic pattern known as the doubly periodic grating [Lemarchand et al., Opt. Lett.23, 1149 (1998)]. We report what we believe to be the first experimental fabrication and characterization of a bidimensional doubly periodic grating filter. We obtained a 0.5 nm bandpass polarization independent reflection filter for telecom wavelengths (1520-1570 nm) that presents a transmittivity minimum of 18% with a standard incident collimated beam.

Single-scattering theory of light diffraction by a circular subwavelength aperture in a finitely conducting screen.

A perturbation theory based on a single-scattering approximation is developed from the rigorous differential theory of diffraction in cylindrical coordinates. It results in analytical formulas in the inverse space for the field amplitudes providing results that are in quantitative agreement with the results of the rigorous method, in both the near- and far-field regions, when a proper correction to the incident field inside the aperture is made by using the renormalized Born approximation. When working in reflection by a screen having permittivity high in modulus, the method proposes an equivalence with the simple model consisting of the emission by a single magnetic dipole excited inside the pierced layer, emission that is then transferred back into the cladding following the Fresnel's coefficients of transmission from the layer into the cladding. The theory predicts a directivity of the radiation pattern that increases for smaller values of modulus of permittivity, both for dielectrics and metals, thus independently of the possibility of plasmon surface wave excitation along the interface. The theory can take into account such surface wave resonances, as well as the waveguide supported by a dielectric slab, but cannot implicitly recognize the modes carried out by the cylindrical waveguide corresponding to the aperture. This fact limits its domain of validity when used in transmission, although the far- and near-field maps can be reconstructed sufficiently well within a multiplicative factor corresponding to the enhanced transmission due to the excitation of these modes.

Narrow-band filtering with whispering modes in gratings made of fibers.

We present a numerical study of whispering modes in gratings made of fibers. Due to the strong localization of the modes inside each fiber, it is possible to obtain narrow-band filters with very broad angular tolerance.

Enhanced transmission of light through a circularly structured aperture.

Using the differential theory of light diffraction by finite cylindrical objects, we study light transmission through a small circular aperture in a metallic screen with concentric corrugation around the nanohole. Poynting vector maps in the region below the screen show that the field enhancement compared with an unstructured aperture is obtained with corrugation lying on the entrance face of the screen. Corrugation on the exit face leads to a more directional radiation close to the normal to the screen. The spectral dependence of the transmission shows a sharp maximum linked with surface plasmon excitation.

Optimization of plasmon excitation at structured apertures.

Surface plasmon excitation that is due to a single or a structured circular aperture in a flat metallic screen is investigated theoretically and numerically with a view to enhancing the electric field close to the metallic surface. A systematic study of the homogeneous solution of the electromagnetic scattering problem is made with cylindrical coordinates, expanding Maxwell equations on a Fourier-Bessel basis. A perturbation analysis devoted to simple physical analyses of different types of cylindrical nanostructure is developed for the optimization of plasmon excitation by a normally incident linearly polarized monochromatic plane wave. The conclusions drawn from this analysis agree well with the results of rigorous electromagnetic calculations obtained with the differential theory of diffraction in cylindrical coordinates.

Angular tolerant resonant grating filters under oblique incidence.

Resonant grating filters have been proposed as a promising alternative to multilayer stacks for narrowband free-space filtering. The efficiency of such filters under normal incidence has been demonstrated. Unfortunately, under oblique incidence, the limited angular tolerance of the resonance forbids any filtering applications with use of standard collimated incident beams. Using a multimode planar waveguide and a bi-atom grating, we show how to increase the angular tolerance up to the divergence of standard beams (0.2 deg) without modifying the spectral bandwidth (0.1 nm), under any oblique angle of incidence.

Study of waveguide grating eigenmodes for unpolarized filtering applications.

The dispersion relation of eigenmodes of two-dimensional waveguide gratings is studied with a perturbative model. The analytic expression of the complex wavelength of the modes permits us to predict the shape of the anomalies in the grating reflectivity with respect to the wavelength and the polarization of the incident plane wave. The simultaneous excitation of two independent modes is necessary for obtaining high-efficiency filtering of unpolarized light. We show how this requirement can be met.