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A photonic band-gap resonator to facilitate GHz-frequency conductivity experiments in pulsed magnetic fields
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Image of FIG. 1.
FIG. 1.

(Color online) (a) Fabry-Pérot geometry photonic band-gap resonator with waveguide coupling. (b) A sample loaded in the dielectric resonator. This sample is approximately 1 mm long, wide. and thick. (c) Schematic of the resonator indicating the following dimensions: diameter of the optics , radius of curvature of the lens , and the separation of the dielectric mirrors .

Image of FIG. 2.
FIG. 2.

(Color online) Calculated transmission through the one-dimensional photonic band-gap structure described in the text as a function of frequency and angle of incidence. Positive angles correspond to TE or polarization and negative angles to TM or polarization. The lower dashed line is normal incidence and the upper the effective angle of incidence for the mode of the V-band rectangular waveguide.

Image of FIG. 3.
FIG. 3.

(Color online) Measured (dashed line) and calculated (solid line) transmission through four different multilayer structures illustrating the tunability of the band gap with layer thickness. Layer thicknesses and materials are as follows: (a) zirconium tin titanate, alumina; (b) zirconium tin titanate, alumina; (c) zirconium tin titanate, alumina; (d) zirconium tin titanate, alumina (note the logarithmic scale: ).

Image of FIG. 4.
FIG. 4.

(Color online) (a) Room temperature transmission spectrum of the Fabry-Pérot style resonator, illustrating the low-transmission photonic band-gap region and well separated resonant modes labeled by their longitudinal mode index . (b) Tuning the resonance in the region of the band edge, note that the increased coupling is accompanied by an increase in the width of the resonance, a degradation of the factor.

Image of FIG. 5.
FIG. 5.

(a) factor of a 64 GHz mode as a function of the number of periods of the dielectric multilayer. The triangles mark the range of the observed factor, and the solid points and dashed line are the simulation described in the text. (b) factor of a single mode as it is tuned to the edge of the photonic band gap. The crosses are data and the line is the simulation described in the text. The data in both (a) and (b) were measured at room temperature using a Fabry-Pérot style resonator with one dielectric multilayer and one spherically curved copper mirror. The aperture coupling through the copper mirror limits its effective reflectivity to and is responsible for the saturation of the factor in both (a) and (b). (c) Oscillations in the factor of the Fabry-Pérot style photonic band-gap resonator. The data (crosses) correspond to multiple modes of the resonator, tuned to near the center of the photonic band gap via the length of the air gap between the lens and one of the dielectric mirrors. The simulation (dashed line) uses a lens reflectivity, , of 95% and a dielectric mirror reflectivity, , of 99.7% to account for the observed amplitude of oscillation. The period and decay are predicted via the lens geometry as described in the text.

Image of FIG. 6.
FIG. 6.

(Color online) Schematic of the cylindrical puck geometry resonator.

Image of FIG. 7.
FIG. 7.

Radial and azimuthal field patterns for the mode of the puck resonator (a), the mode pattern for the rectangular waveguide (b), and the mode of the puck resonator (c). The inner circle in (a) and (c) represents the circumference of the dielectric puck (in this case chosen to be 6 mm in diameter) and the outer circle is the circumference of the resonator (14 mm in diameter). The waveguide and resonator are drawn to scale so as to illustrate the similarities between the magnetic field distribution when aligned centrally.

Image of FIG. 8.
FIG. 8.

(Color online) Observed resonant frequency of the mode (the solid circles) as a function of the cavity radius for a 2 mm long cavity (a) and cavity length for a 6 mm diam cavity (b). The frequencies of other observed modes are shown as open circles. The calculated frequency of the TE and TM and HEM modes are the dashed, dotted-dashed, and thin solid lines, respectively. The thick solid lines represent the cutoff frequencies: above the upper cutoff the puck is not shorter than half the free-space wavelength and below the lower cutoff the puck is shorter than the dielectric medium wavelength. Note that the strong agreement between the measured and calculated frequency of the is an indication of the degree to which the dielectric multilayers and the geometry suppress the fringe fields.

Image of FIG. 9.
FIG. 9.

(Color online) Transmission spectra illustrating tuning of the mode of the dielectric-puck geometry photonic band-gap resonator. The puck is a 6 mm diam Rexolite 1422 cylinder of various lengths between 1.57 and 2.44 mm. The dielectric multilayers are periods of zirconium tin titanate and alumina, which are 14 mm in diameter.

Image of FIG. 10.
FIG. 10.

(Color online) Transmission spectrum of the unloaded puck resonator measured at 2.1 K. The puck is a Rexolite 1422 cylinder, 2 mm long and 6 mm in diameter, and the dielectric multilayers are periods of zirconium tin titanate and alumina, which are 14 mm in diameter. Both the and modes are clearly visible.

Image of FIG. 11.
FIG. 11.

Flow diagram of the pulsed-field microwave detection system including the MVNA.

Image of FIG. 12.
FIG. 12.

(Color online) (a) Predicted (solid lines) and measured (square data points, dc field; round data points, pulsed field) magnetic field/frequency dependence of the EPR lines in for an applied magnetic field parallel to the axis. (b). Line shape of the EPR lines measured in pulsed magnetic field, at a temperature of 2.1 K. (c) Line shape of the EPR lines measured in a dc magnetic field, at a temperature of 1.5 K. The lines are offset vertically for clarity. Note that, despite the superior factor and data averaging in the dc field measurements, the signal-to-noise ratio is similar for both data sets.

Image of FIG. 13.
FIG. 13.

(Color online) Frequency magnetic field dependence of the EPR features observed at low fields in . The inset shows the corresponding spectrum measured at a frequency of 47.1 GHz and a temperature of 2.1 K.

Image of FIG. 14.
FIG. 14.

(Color online) GHz-frequency magnetoconductivity of measured at a temperature of 2.1 K and a frequency of 64 GHz. Note the Josephson plasma resonance at low field and the quantum oscillations at higher fields. The data in this figure were acquired during a single magnet pulse. The insets show the Fourier spectrum of the quantum oscillations and the associated Fermi-surface orbits.


Generic image for table
Table I.

The calculated mode frequencies for the puck geometry resonator with a 3 mm radius, 2 mm long cylindrical Rexolite puck.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A photonic band-gap resonator to facilitate GHz-frequency conductivity experiments in pulsed magnetic fields