cross resonators

microstrip cross resonators

The ability to control the polarization of high frequency microwaves in resonant cavities is of special importance since it allows selection of transitions between different spin states. The ability to discriminate spin transitions becomes of crucial relevance for spin-based architectures in quantum information and computation applications.

Fig. 1 shows the assembly of our polarizable resonator. Two equal microstrip resonators designed to work at a frequency on the order of 530 GHz for its fundamental oscillation mode (L ~ /2) are put together forming a square cross. The geometry of the microstrip device (i.e. width of the line, w, and thickness of the dielectric substrate, h, separating the line from the metallic bottom plate) has been calculated to match the impedance of the microwave coaxial lines (50 ).

Note that in our case, where h < /2, the signal transmission corresponds to a quasi-TEM mode in each of the resonator lines. At their fundamental resonant mode, the microwave magnetic field components, and , are maximum and perpendicular to each other at the center of the resonators (see red and blue arrows in Fig. 1). The cross resonator is connected to ports P1 and P2 through feeding lines separated by a coupling gap, gc. The gaps are designed to critically couple the resonator to the feed lines, resulting in a loaded quality factor, QL = Q0/2, on the order of 100 when critically coupled. A third line, connected to port P3, is coupled to an opposite resonator arm through a transmission gap, g_t (>g_c), which is designed to allow measuring in transmission mode (i.e. S₂₁ parameter), without affecting the response of the resonator at resonance. Semi-rigid coaxial lines are used to connect the three ports of the resonator, which is housed at the base of a cryostat, to a 50 GHz Agilent Technologies PNA vector network analyzer. A power splitter, a phase shifter and variable attenuators are used to control the magnitude and phase of the input signals at ports P1 and P2.

Reflection (S₁₁) and transmission (S₃₁) parameters measured on a 10 GHz microstrip cross resonator at room temperature. Two resonances are observed at 9.7 and 11.5 GHz. Dotted lines correspond to simulated data. The graphics show the current density at each of the resonances when microwave stimulus is applied only to port P1.




	Microstrip cross resonators were presented in April 2007 in an worldwide itinerant exhibition of Art and Science during the 2007 UCF Research Week with the tile: “Polarizable Microstrip Resonators: X-ing the Waves In-Situ”.

In the figures above: a) EPR spectra obtained at 300 mK on a magnetically dilute single crystal of Fe₁₇Ga molecular magnets. The two curves correspond to two different phase delays, -90 and +90 degrees, between the microwave signals at ports P1 and P2 of the cross resonator. The inset shows and sketch of the Fe₁₇Ga molecular wheel, in which one Fe (S = 5/2) ion has been supplanted by a Ga (S = 0), resulting in a frustrated molecular spin S = 5/2 at low temperatures. b) Modulation of the normalized EPR peak height as a function of the phase delay between the signals. A 82% degree of circular polarization is achieved over the central area of the resonator.

Our polarizable microstrip cross resonator allows an arbitrary control of the polarization of high frequency microwaves without adjustable or moving mechanical actuators. The electronic control of the polarization provided by our microstrip cross resonator together with its low dimensions allows its integration in microscale devices for use in processes requiring fast modulation of the polarization (i.e. pulse EPR). In addition, the ability to measure in transmission mode allows working at low temperatures, where long coaxial lines needed to wire the cryostat mask the reflected signals. Moreover, the idea of our microstrip cross resonator can be extended to microstrip cross lines or coplanar cross waveguides to generate circular polarized microwaves in a broad range of frequencies.