We acknowledge financial support by the Spanish Ministerio de Econom&#237;a y Competitividad through projects MAT2017-85232-R (AEI/FEDER,UE), Severo, Ochoa (SEV-2015-0496) and by the Generalitat de Catalunya (2017, SGR 1377), by CNPq &#8211; Brazil, and by the European Comission (Marie Sk&#322;odowska-Curie IF EMPHASIS - DLV-748429).

1. Mounting the setup
<ol>
	<li>Optics 
	NOTE: Build the setup as depicted in Figure 3A on an optical table with sufficient vibration isolation. To avoid spherical and other aberrations, center all the optical components (lenses, pinholes etc.) with respect to the beam. The optical arrangement is shown in Figure 2 with the distances between components indicated.
	<ol>
		<li>Guide the light from the white light source to a...

<ol>
	<li>Bayer, M., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Optical+Modes+in+Photonic+Molecules.">Optical Modes in Photonic Molecules.</a> Physical Review Letters. 81 (12), 2582-2585 (1998).</li><li>Blanco, A., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Large-scale+synthesis+of+a+silicon+photonic+crystal+with+a+complete+three-dimensional+bandgap+near+1.5+micrometres.">Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres.</a> Nature. 405 (6785), 437 (2000).</li><li>Rybin, M. V., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=High-Q+Supercavity+Modes+in+Subwavelength+Dielectric+Resonators.">High-Q Supercavity Modes in Subwavelength Dielectric Resonators.</a> Physical Review Letters. 119 (24), 243901 (2017).</li><li>Joannopoulos, J. D., Villeneuve, P. R., Fan, S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Photonic+crystals.">Photonic crystals.</a> Solid State Communications. 102 (2), 165-173 (1997).</li><li>Englund, D., Fushman, I., Vuckovic, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=General+recipe+for+designing+photonic+crystal+cavities.">General recipe for designing photonic crystal cavities.</a> Optics Express. 13 (16), 5961-5975 (2005).</li><li>Yablonovitch, E. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Inhibited+Spontaneous+Emission+in+Solid-State+Physics+and+Electronics.">Inhibited Spontaneous Emission in Solid-State Physics and Electronics.</a> Physical Review Letters. 58 (20), 2059-2062 (1987).</li><li>Yablonovitch, E. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Photonic+band-gap+structures.">Photonic band-gap structures.</a> JOSA B. 10 (2), 283-295 (1993).</li><li>Noda, S., Tomoda, K., Yamamoto, N., Chutinan, A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Full+Three-Dimensional+Photonic+Bandgap+Crystals+at+Near-Infrared+Wavelengths.">Full Three-Dimensional Photonic Bandgap Crystals at Near-Infrared Wavelengths.</a> Science. 289 (5479), 604-606 (2000).</li><li>John, S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Strong+localization+of+photons+in+certain+disordered+dielectric+superlattices.">Strong localization of photons in certain disordered dielectric superlattices.</a> Physical Review Letters. 58 (23), 2486-2489 (1987).</li><li>Krauss, T. F. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Slow+light+in+photonic+crystal+waveguides.">Slow light in photonic crystal waveguides.</a> Journal of Physics D: Applied Physics. 40 (9), 2666-2670 (2007).</li><li>Huang, X., Lai, Y., Hang, Z. H., Zheng, H., Chan, C. T. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Dirac+cones+induced+by+accidental+degeneracy+in+photonic+crystals+and+zero-refractive-index+materials.">Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials.</a> Nature Materials. 10 (8), 582-586 (2011).</li><li>Wagner, R., Heerklotz, L., Kortenbruck, N., Cichos, F. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Back+focal+plane+imaging+spectroscopy+of+photonic+crystals.">Back focal plane imaging spectroscopy of photonic crystals.</a> Applied Physics Letters. 101 (8), 081904 (2012).</li><li>Zhang, D., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Back+focal+plane+imaging+of+directional+emission+from+dye+molecules+coupled+to+one-dimensional+photonic+crystals.">Back focal plane imaging of directional emission from dye molecules coupled to one-dimensional photonic crystals.</a> Nanotechnology. 25 (14), 145202 (2014).</li><li>Vasista, A. B., Sharma, D. K., Kumar, G. V. P. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Fourier+Plane+Optical+Microscopy+and+Spectroscopy.">Fourier Plane Optical Microscopy and Spectroscopy.</a> Digital Encyclopedia of Applied Physics. , 1-14 (2019).</li><li>Belotelov, V. I., Doskolovich, L. L., Zvezdin, A. K. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Extraordinary+Magneto-Optical+Effects+and+Transmission+through+Metal-Dielectric+Plasmonic+Systems.">Extraordinary Magneto-Optical Effects and Transmission through Metal-Dielectric Plasmonic Systems.</a> Physical Review Letters. 98 (7), 077401 (2007).</li><li>Belotelov, V. I., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Enhanced+magneto-optical+effects+in+magnetoplasmonic+crystals.">Enhanced magneto-optical effects in magnetoplasmonic crystals.</a> Nature Nanotechnology. 6 (6), 370 (2011).</li><li>Chetvertukhin, A. V., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Magneto-optical+Kerr+effect+enhancement+at+the+Wood's+anomaly+in+magnetoplasmonic+crystals.">Magneto-optical Kerr effect enhancement at the Wood's anomaly in magnetoplasmonic crystals.</a> Journal of Magnetism and Magnetic Materials. 324 (21), 3516-3518 (2012).</li><li>Kataja, M., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Surface+lattice+resonances+and+magneto-optical+response+in+magnetic+nanoparticle+arrays.">Surface lattice resonances and magneto-optical response in magnetic nanoparticle arrays.</a> Nature Communications. 6, 7072 (2015).</li><li>Kataja, M., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Hybrid+plasmonic+lattices+with+tunable+magneto-optical+activity.">Hybrid plasmonic lattices with tunable magneto-optical activity.</a> Optics Express. 24 (4), 3652-3662 (2016).</li><li>Kalish, A. N., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Magnetoplasmonic+quasicrystals:+an+approach+for+multiband+magneto-optical+response.">Magnetoplasmonic quasicrystals: an approach for multiband magneto-optical response.</a> Optica. 5 (5), 617-623 (2018).</li><li>Borovkova, O. V., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=TMOKE+as+efficient+tool+for+the+magneto-optic+analysis+of+ultra-thin+magnetic+films.">TMOKE as efficient tool for the magneto-optic analysis of ultra-thin magnetic films.</a> Applied Physics Letters. 112 (6), 063101 (2018).</li><li>Kurvits, J. A., Jiang, M., Zia, R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Comparative+analysis+of+imaging+configurations+and+objectives+for+Fourier+microscopy.">Comparative analysis of imaging configurations and objectives for Fourier microscopy.</a> JOSA A. 32 (11), 2082-2092 (2015).</li><li>Cichelero, R., Oskuei, M. A., Kataja, M., Hamidi, S. M., Herranz, G. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Unexpected+large+transverse+magneto-optic+Kerr+effect+at+quasi-normal+incidence+in+magnetoplasmonic+crystals.">Unexpected large transverse magneto-optic Kerr effect at quasi-normal incidence in magnetoplasmonic crystals.</a> Journal of Magnetism and Magnetic Materials. 476, 54-58 (2019).</li><li>Cichelero, R., Kataja, M., Campoy-Quiles, M., Herranz, G. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Non-reciprocal+diffraction+in+magnetoplasmonic+gratings.">Non-reciprocal diffraction in magnetoplasmonic gratings.</a> Optics Express. 26 (26), 34842-34852 (2018).</li><li>Melo, L. G. C., Santos, A. D., Alvarez-Prado, L. M., Souche, Y. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Optimization+of+the+TMOKE+response+using+the+ATR+configuration.">Optimization of the TMOKE response using the ATR configuration.</a> Journal of Magnetism and Magnetic Materials. 310 (2, Part 3), e947-e949 (2007).</li><li>Regatos, D., Sep&#250;lveda, B., Fari&#241;a, D., Carrascosa, L. G., Lechuga, L. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Suitable+combination+of+noble/ferromagnetic+metal+multilayers+for+enhanced+magneto-plasmonic+biosensing.">Suitable combination of noble/ferromagnetic metal multilayers for enhanced magneto-plasmonic biosensing.</a> Optics Express. 19 (9), 8336-8346 (2011).</li><li>Polisetty, S., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Optimization+of+magneto-optical+Kerr+setup:+Analyzing+experimental+assemblies+using+Jones+matrix+formalism.">Optimization of magneto-optical Kerr setup: Analyzing experimental assemblies using Jones matrix formalism.</a> Review of Scientific Instruments. 79 (5), 055107 (2008).</li><li>Sato, K. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Measurement+of+Magneto-Optical+Kerr+Effect+Using+Piezo-Birefringent+Modulator.">Measurement of Magneto-Optical Kerr Effect Using Piezo-Birefringent Modulator.</a> Japanese Journal of Applied Physics. 20 (12), 2403 (1981).</li></ol>

The authors have nothing to disclose.

We have introduced a measurement setup and protocol to obtain angular resolved magneto-optical spectra of optical crystals. In particular, the case of ferromagnetic materials, that requires additional data analysis to account for the nonlinear permeability of the material, has been laid out. Angular resolved magneto-optical spectroscopy presents an additional advantage over non-angular resolved methods that the confined modes can be more readily identified as they appear as clearly defined bands in both optical and magne...

Confined electromagnetic modes in photonic crystals can arise from a variety of different origins, such as plasmon resonances around metal/dielectric interfaces or Mie resonances in high refractive index dielectric nanostructures1,2,3, and can be designed to appear at specifically defined frequencies4,5. Their presence gives rise to many fascinating phenomena such as photonic band gaps6,7,8, strong photon localization9, slow light10 and Dirac cones11. Fourier plane microscopy and spectroscopy are basic tools for characterization of photonic nanostructures as they enable capturing many essential properties of confined modes occurring in them. In Fourier space microscopy, as opposed to conventional real plane imaging, the information is presented as the function of angular coordinates12,13. It is alternatively known as back focal plane (BFP) imaging as the angular decomposition of the light emanating from the sample is recorded from the back focal plane of the microscope objective. The angular spectrum, i.e., the far field emission pattern of the sample is related to the momentum of light emanating from it (&#295;k). In particular, it represents its in-plane momentum (kx,ky) distribution14.
In magneto-optically active samples, the presence of confined photonic excitations has been shown to result in considerable enhancement of the magneto-optical response15,16,17,18,19. Magneto-optical effects depend on the mutual geometry of the magnetic field and the incident electromagnetic radiation. Most commonly encountered magneto-optical geometries for linearly polarized light and their nomenclature are depicted in Figure 1. Here, we demonstrate a setup that can be used to explore two magneto-optical effects that are observed in reflection: transverse and longitudinal magneto-optical Kerr effects, abbreviated, respectively, as TMOKE and LMOKE. TMOKE is an intensity effect, where the reflectivities of the opposing magnetization states are different while LMOKE manifests as a rotation of the reflected light polarization axis. The effects are distinguished by the orientation of the magnetization with respect to the light incidence, where for LMOKE, the magnetization is oriented parallel to the in plane component of the wave vector of the light while for TMOKE it is transverse to it. For normally incident light, both in-plane components of the momentum of light are null (kx = ky = 0) and, consequently, both effects are zero. Configurations where both effects are present can be easily conceived. However, to simplify the data analysis, in this demonstration we limit ourselves to situations where only one of the effects is present, namely TMOKE.
Several optical configurations can be used to measure the angular distribution of light emitted from magnetophotonic crystals. For example, in Kalish et al.20 and Borovkova et al.21, such a setup was successfully used in transmission geometry to unveil plasmon influence on magneto-optical phenomena. As an illustration, in Kurvits et al.22, some possible configurations are presented for a microscope that uses an infinity corrected objective lens. In our configuration, depicted in Figure 2A, we use an infinity corrected lens where the light coming from a given point in the sample is directed by the objective lens into collinear beams. In Figure 2A, beams emerging from the top (dashed lines) and the bottom (solid lines) of the sample are schematically depicted. Then, a collecting lens is used to refocus these beams to form an image at the image plane (IP). A second lens, also known as Bertrand lens, is then placed after the image plane to separate the incoming light at its focal plane into angular components, depicted in Figure 2A in red, blue and black. From this back focal plane, the angular distribution of the light emitted by the sample can be measured with a camera. Effectively, the Bertrand lens performs a Fourier transform on the light beam arriving at it. The spatial intensity distribution at the BFP corresponds to the angular distribution of the incident radiation. A full reciprocal space reflectance map of the sample can be established by illuminating the sample with the same objective that is used to collect the response of the sample. The incoming and out going beams are separated using a beam splitter. The complete setup is depicted in Figure 3A. To obtain a spectrum, a tunable light source or a monochromator is needed. The measurement can then be repeated over different wavelengths, keeping in mind that due to the spectrum of standard light sources, the results need to be normalized to the reflectivity of a control sample. For this purpose, one can use a mirror or a part of the sample that has been purposefully left unpatterned to allow for a high reflectivity. To assist in positioning, we show how to integrate the setup with an additional optical system that enables real-space imaging of the sample, shown in Figure 2B.
We now proceed to establish a method for measuring the angular resolved magneto-optical spectrum of a photonic crystal, using as a representative sample, a DVD grating covered with an Au/Co/Au film where the presence of ferromagnetic cobalt gives rise to considerable magneto-optical activity23. The periodic corrugation of the DVD grating enables surface plasmon polariton (SPP) resonances at distinct wavelength-angle combinations that are given by 
<img alt="Equation 1" src="/files/ftp_upload/60094/60094equ01.jpg" /> 
where n is the refractive index of the surrounding environment, k0 the wave vector of light in free space, &#952;0 the incidence angle, d the periodicity of the grating and m is an integer denoting the order of the SPP. The SPP wave vector is given by <img alt="Equation 2" src="/files/ftp_upload/60094/60094equ02.jpg" /> where &#949;1 and &#949;2 are the permittivities of the metallic layer and the surrounding dielectric environment. Due to the thickness of the gold/cobalt multilayer film, we can assume that SPPs are only excited on top of the multilayer film.

<table>
	<tbody>
		<tr>
			<td>Beam splitter</td>
			<td>Thorlabs</td>
			<td>BSW27</td>
			<td></td>
		</tr>
		<tr>
			<td>Bertrand lens</td>
			<td>Thorlabs</td>
			<td>LA1608</td>
			<td>f = 75 mm</td>
		</tr>
		<tr>
			<td>CCD Camera</td>
			<td>Thorlabs</td>
			<td>1500M-GE-TE</td>
			<td>Camera for real space imaging</td>
		</tr>
		<tr>
			<td>Collecting lens</td>
			<td>Thorlabs</td>
			<td>ITL200</td>
			<td>f = 200 mm</td>
		</tr>
		<tr>
			<td>Collimating lens</td>
			<td>Zeiss</td>
			<td>420640-9800</td>
			<td>Magnification 10x NA 0.3</td>
		</tr>
		<tr>
			<td>Flip mirror</td>
			<td>Thorlabs</td>
			<td>CCM1-P01/M</td>
			<td></td>
		</tr>
		<tr>
			<td>Flip mirror mount</td>
			<td>Thorlabs</td>
			<td>FM90/M</td>
			<td></td>
		</tr>
		<tr>
			<td>L1-lens</td>
			<td>Thorlabs</td>
			<td>LA1986</td>
			<td>f = 125 mm</td>
		</tr>
		<tr>
			<td>L2-lens</td>
			<td>Thorlabs</td>
			<td>LA1461</td>
			<td>f = 250 mm</td>
		</tr>
		<tr>
			<td>Objective lens</td>
			<td>Nikon</td>
			<td>MUE10500</td>
			<td>Magnification 50x NA 0.8</td>
		</tr>
		<tr>
			<td>Pinhole</td>
			<td>Thorlabs</td>
			<td>ID8/M</td>
			<td></td>
		</tr>
		<tr>
			<td>Polarizer</td>
			<td>Thorlabs</td>
			<td>GTH10M</td>
			<td>For LMOKE measurements, two polarizers are needed</td>
		</tr>
		<tr>
			<td>sCMOS camera</td>
			<td>Andor</td>
			<td>ZYLA-4.2P-USB3</td>
			<td></td>
		</tr>
	</tbody>
</table>

spectral and angle-resolved magneto-optical characterization of photonic nanostructures

Photonic crystals are periodic nanostructures that can support a variety of confined electromagnetic modes. Such confined modes are usually accompanied by local enhancement of electric field intensity that strengthens light-matter interactions, enabling applications such as surface-enhanced Raman scattering (SERS) and surface plasmon enhanced sensing. In the presence of magneto-optically active materials, the local field enhancement gives rise to anomalous magneto-optical activity. Typically, the confined modes of a given photonic crystal depend strongly on the wavelength and incidence angle of the incident electromagnetic radiation. Thus, spectral and angular-resolved measurements are needed to fully identify them as well as to establish their relationship with the magneto-optical activity of the crystal. In this article, we describe how to use a Fourier-plane (back focal plane) microscope to characterize magneto-optically active samples. As a model system, here we use a plasmonic grating built out of magneto-optically active Au/Co/Au multilayer. In the experiments, we apply a magnetic field on the grating in situ and measure its reciprocal space response, obtaining the magneto-optical response of the grating over a range of wavelengths and incident angles. This information enables us to build a complete map of the plasmonic band structure of the grating and the angle and wavelength dependent magneto-optical activity. These two images allow us to pinpoint the effect that the plasmon resonances have on the magneto-optical response of the grating. The relatively small magnitude of magneto-optical effects requires a careful treatment of the acquired optical signals. To this end, an image processing protocol for obtaining magneto-optical response from the acquired raw data is laid out.

Figure 4A shows a scanning electron microscope (SEM) micrograph of a commercial DVD grating covered with Au/Co/Au multilayer that was used a demonstration sample in our experiments. Its optical and magneto-optical spectra are shown in Figure 4B,C respectively. Details on sample fabrication are presented elsewhere23. Black lines in Figure 4A,B show the plasmon...

Watch this Scientific Journal Video about Spectral and Angle-Resolved Magneto-Optical Characterization of Photonic Nanostructures at JoVE.com

Spectral and Angle-Resolved Magneto-Optical Characterization of Photonic Nanostructures

Photonic band structure enables understanding how confined electromagnetic modes propagate within a photonic crystal. In photonic crystals that incorporate magnetic elements, such confined and resonant optical modes are accompanied by enhanced and modified magneto-optical activity. We describe a measurement procedure to extract the magneto-optical band structure by Fourier space microscopy.

Photonic crystals are periodic nanostructures that can support a variety of confined electromagnetic modes. Such confined modes are usually accompanied by ...

Photonic band structures map out the dispersion relations of the confined electromagnetic modes in a photonic crystal and are associated with enhanced light-matter interactions such as magneto-optical effects. Our method enables the mapping out of magneto-optical effects in the reciprocal space of the photonic crystal so that we can directly study how magnetization modifies a photonic response. Magneto-optical crystals are interesting for their non-reciprocal optical properties.While we will demonstrate this technique with a simple plasmonic grating, it's applicable to many other types of photonic crystals. One particular challenge of this technique is that the magneto-optical effects are typically very weak so you have to take extra care to make sure that any noise is minimized. Begin by building the setup on an optical table with sufficient vibration isolation.The optics of the beam emerging from the sample should be set up as indicated with the infinity-corrected objective lens directing wave fronts emerging from each point of the sample into collinear beams. Place a collector lens with an f of 200 millimeters 330 millimeters from the objective to refocus the beams to form an image at the image plane. Insert a flip mirror after the image plane to enable real-space imaging of the sample and insert an L1-lens with an f of 125 millimeters so that the image plane is in focus.Place an L2-lens with an f of 250 millimeters at a 135-millimeter distance from L1.Place a camera 210 millimeters from the L2-lens to capture a magnified image of the image plane and move the L1-and L2-lens until a pinhole placed in the image plane is in good focus on the CCD camera. Place a pinhole into the image plane at 200 millimeters from the collector lens as needed to limit the imaged region to a small, patterned area. Place a Bertrand lens with an f of 75 millimeters 120 millimeters after the image plane to create a Fourier transform of the angular components of the image and place a camera 75 millimeters from the Bertrand lens.Using a small drop of silver paint, mount the sample, a commercial DVD grating covered with magnetoplasmonic gold-cobalt-gold-film, on the sample holder. Place the sample between the poles of an electromagnet then move the objective lens toward the sample until the sample is in good focus in the CCD camera. To perform an optical reflectivity measurement, using the real-space image of the sample, position the light spot over a reflective, unpatterned section of the sample and flip the mirror to visualize the back focal plane of the microscope.Select the area of the back focal plane that corresponds to the polarization state of interest and select an area of interest as a rectilineal cross-section of the objective back focal plane along the axis that corresponds to the transverse magneto-optical polarization. Click Measure Normalization Spectrum to measure the spectrum of the light source. As each wavelength yields a 1D set of data points, the full spectrum of the light source is saved as a 2D tensor in which each data point represents a combination of wavelength and angle.Using the real-space image of the sample, position the light source over the photonic crystal of interest and switch back to the back focal plane, ensuring that the plasmon modes are visible as dark lines crossing the back focal plane. Using the same areas of interest and measurement settings, click Measure Reflection Spectrum to measure the reflection spectrum of the photonic crystal. To perform a magneto-optical measurement, start by measuring a hysteresis loop using an angle and wavelength that are known to correspond to a good magneto-optical response.Using the hysteresis loop, select the range of magnetic fields to loop. For ferromagnetic samples, loop the fields from a fully saturated state to an oppositely saturated state, extending the range comfortably over the saturation field. Finally measure the intensity reflected by the sample at each defined magnetic field point, repeating over multiple loops as desired.Each wavelength and magnetization point will yield a single, 1D array of numerical data for which each point of the array corresponds to a particular angle. To account for the spectral variation in the light source intensity, normalize the obtained spectrum by the spectrum of the light source. This will yield a 2D array of numbers from zero to one for which one corresponds to fully reflective and zero corresponds to fully absorptive conditions.For data analysis, using the hysteresis loop of the sample, assign each measured frame to either of the saturated states or to the intermediate state, then discard the measured intensities for the intermediate states and subtract the saturated intensities separately for each angular and wavelength data point. In this figure, a scanning electron microscope micrograph of a commercial DVD grating covered with a gold-cobalt-gold multilayer can be observed. Here the optical and magneto-optical spectra of the grating can be observed.The lines show the plasmon dispersion relations calculated from equation one and correspond to a conspicuous dip in reflectivity that results from the incident radiation being converted into SPPs and dissipated via ohmic damping. In the magneto-optical spectrum of the plasmonic grating, the plasmon lines are accompanied by an increase in magneto-optical activity that abruptly reverses at the surface plasmon polariton. The line's shape can be explained by the fact that the magnetization slightly changes the surface plasmon polariton excitation conditions, thus resulting in two different surface plasmon polaritons for opposite magnetization states.Due to the small magnitude of the magneto-optical effects, the magnetic field needs to be applied in situ measuring each wavelength at the time to ensure optimal signal-to-noise ratio. This setup can be used for a variety of magneto-optical techniques, for example, for Kerr microscopy to study the dominant structure of magnetic materials. We have studied the magneto-optical effects in diffraction by restricting the angular spread of the incident light to observe the diffracted beams in the back focal plane.

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Electromagnetic Waves

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7.0K visualizações.  Institut de Ciència de Materials de Barcelona. Estruturas de banda fotônica mapeiam as relações de dispersão dos modos eletromagnéticos confinados em um cristal fotônico e estão associadas a interações aprimoradas de matéria-luz, como efeitos magneto-ópticos. Nosso método permite o mapeamento de efeitos magneto-ópticos no espaço recíproco do cristal fotônico para que possamos estudar diretamente como a magnetização modifica uma resposta fotônica. Cristais magneto-ópticos são interessantes por suas propriedades óptica...