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 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.
