Guide Fourier Modal Method and Its Applications in Computational Nanophotonics

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Box , Joensuu FI, Finland. We propose a scheme based on extraordinary transmission of light through a single nanoaperture, surrounded by periodic corrugations, for direct characterization of focal-region optical fields with subwavelength-scale structure. We describe the design of the device on the basis of rigorous diffraction theory and fabricate a prototype using a process that involves electron beam lithography, dry etching, and template stripping.

First experimental results performed with a transmission-type confocal optical microscope demonstrate the potential of the method. The ability of arrays of subwavelength apertures in a metal screen to transmit more light than geometrical considerations suggest has been known in grating theory for several decades see Sect. However, the interest in this phenomenon exploded only when Ebbesen et al.

Subsequent studies have shown, e. On the other hand, corrugations on the exit surface can give rise to directional emission from the aperture, known as the beaming effect. We refer to [ 3 - 6 ] for a detailed coverage of such effects and their applications in different fields of science and technology. In this paper, we study the possibility of using a single subwavelength aperture, surrounded by periodic corrugations on the exit side of the metal screen, in direct observation of the structure of tightly focused fields in the focal region.

The field in the focal region is scanned with a tiny aperture in a finitely conducting metal screen. Surface plasmons are generated on the exit side, which propagate along the surface away from the aperture; these surface-bound waves are coupled by the corrugations into a directional field propagating into a detector in the far zone of the aperture in practice, using a microscope objective. The system concept. The concept of the nanoslit-based probe for characterization of subwavelength-structured free fields.

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In the forthcoming sections, we describe the methods used to design the nanoscale field probe and to fabricate its first prototype. We also give preliminary experimental results on applying the prototype to measure directly the spot size of a tightly focused laser beam. For simplicity of design and fabrication, we employ in this study a slit aperture surrounded by straight-line corrugations, though the final goal is to use a circular aperture surrounded by a grating with concentric circular grooves.

Computational model. A schematic illustration of the computational cell with superperiod D containing the slit, N grooves, and a perfectly matched layer with thickness q. We used the following values: 1. The medium on the entrance side was assumed to be either air or water, and the NOA on the exit side could be assumed to extend to infinity because its thickness is several tens of micrometers.

Hence, the variables left for the FMM-based design are h , h m , d , and f.

Fourier Modal Method and Its Applications in Computational Nanophotonics – Bóksalan

The choice of these parameters will be discussed in the next section. A TM-polarized cylindrical Gaussian wave with its waist located at the entrance plane of the probe was assumed in the numerical simulations: the non-vanishing magnetic field component was taken to be of the following form:. In the FMM calculations, this field was represented using its sampled angular spectrum of plane waves, as usual, when dealing with incident fields of finite spatial extent. A nm-thick titanium dioxide film was added on top of the aluminum by atomic layer deposition to work as an etching mask and to cover the aluminum film against oxidation.

A 2-in, 0. A heat- and solvent-assisted process was used to ensure glue penetration into the narrow grating holes [ 9 ]. To achieve appropriate adhesion properties, two nanometers of Al 2 O 3 was added on the grating before glue. The process continued on the newly revealed Al surface.

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An alignment electron beam exposure was applied to write the slit structure, and the final etching steps followed the ones used on grating-side etching. The completed experimental device had an area of 1 mm 2 , with a 1-mm-long slit placed at the center of the device.

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Process flow. A Gaussian beam wavelength nm from a scanning confocal transmission microscope was used to illuminate the slit. Since a confocal microscope was used for illumination, the resolution measurements could be performed conveniently by scanning the incident spot perpendicularly across the slit and observing the output of the PMT detector. Measurement configuration.

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A schematic configuration for characterization of the field probe, which is placed in the object plane of a scanning confocal transmission microscope. The same geometry is used to measure the profile of the incident field by scanning it across the probe. The initial optimization of the parameters was performed by looking for optimal plasmon coupling by the corrugations.

Alternatively, one might consider using the integrated radiant intensity in the positive half-space, i. The best criterion would in principle be the integrated radiant intensity within the NA of the collection optics, but this would depend on the type of detection scheme used. The optimum values of the parameters differ somewhat, with zeroth-order criterion giving a somewhat larger period and a considerably smaller groove depth than the criterion based on total transmission.

Although high-numerical-aperture collection optics was used in our experiments, we chose the former criterion, which would allow the use of a detector without any collection optics provided that it covers a reasonable solid angle in the far field. Corrugation design.

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  7. The final step in the design of the field probe is to choose the optimum thickness h of the Al layer. They exhibit a typical Fabry-Perot-like variation of transmittance through a subwavelength-width metal-insulator-metal waveguide of finite length h. Transmission efficiency. Comparison of the green and blue lines illustrates the improvement of transmission achieved by final optimization of the corrugation on the exit face of the Al layer. Hence, if the light efficiency of the system is a critical factor which was not the case in our experiments , the use of high-numerical-aperture collection optics is recommended despite of the beaming effect being utilized in the design.

    Let us next consider in more detail the advantages gained by adding the corrugations on the rear side of the Al film. A close inspection of these figures shows the interference of the reflected and the incident fields, the high intensity inside the slit, and the slight penetration inside all the metal surfaces. Also seen are the plasmon waves that propagate away from the slit; these are particularly apparent on the exit side. Simulated diffraction from a slit without corrugations. Simulated diffraction from a slit with corrugations.

    The complete field probe with the slit surrounded by corrugations is considered. In the case of a slit without corrugations, the far zone is effectively reached after a propagation distance of just a few wavelengths, while in the case of the corrugated rear interface, this requires propagation over a few tens of wavelengths. The corrugations increase the side lobe level considerably even at the best focus, indicating that the field immediately behind the exit plane of the probe contains strong phase variations.

    While the aberrations of grating-based plasmonic collimation systems are worth more careful studies, the increased side lobe level is of little concern in the present application: the area of the detector placed at the image plane can be chosen large enough to capture all side lobes with significant amplitude. We now proceed to simulate the effects of such scanning. Therefore, also the field amplitude distributions in the focal region are virtually independent on the position of the incident field; only the measured intensity changes and therefore allows the profiling of the incident field without moving the detector.

    For the convenience of resolution judgment, the peak values of both profiles have been normalized to unity, and the profiles are identical almost within the plotting precision. The simulated measured profile is slightly wider than the true incident field owing to the finite width of the slit.

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    Here, we compare the peak values of the measured signal with and without the corrugations as a function of the numerical aperture of the collection optics. Without the corrugations, the beaming effect disappears, and hence, the sensitivity gain for small numerical apertures is as high as 3 to 4. Simulated transmittance. For comparative measurements, we also fabricated a probe without the corrugations.

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    Summary Most available books on computational electrodynamics are focused on FDTD, FEM, or other specific technique developed in microwave engineering. Features Provides a comprehensive guide to the principles, methods, and mathematics of the Fourier modal method Explores the emerging field of computational nanophotonics Presents clear, step-by-step, practical explanations on how to use the Fourier modal method for photonics and nanophotonics applications Includes the necessary MATLAB codes, enabling readers to construct their own code Using this book, graduate students and researchers can learn about nanophotonics simulations through a comprehensive treatment of the mathematics underlying the Fourier modal method and examples of practical problems solved with MATLAB codes.

    Reviews [The authors] provide researchers and graduate students with a detailed mathematical framework for the sound numerical analysis of nanophotonics phenonema as well as the practical skills and source code required for implementing the Fourier model method on MATLAB. Request an e-inspection copy. Share this Title. Recommend to Librarian. Shopping Cart Summary.

    Fourier Modal Method and Its Applications in Computational Nanophotonics

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