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This paper discusses some of the major experimental features of microwave nonlinearity in high temperature superconductors, both intrinsic and extrinsic. The case is made for solving the problem of extrinsic nonlinearity through the use of localized measurements of microwave surface impedance and electromagnetic fields. Along these lines, a brief introduction is given to our work on scanning near-field microwave microscopy.

We have developed a scanning microwave microscope which can image features with 20 /spl mu/m spatial resolution. The microscope consists of a section of open-ended coaxial cable which is scanned over the surface of a planar sample. Images can be made in either passive mode, in which the reflectivity of the probe tip is measured as a function of position, or in active mode, in which stray fields from the sample are picked up by the scanning probe and measured with a vector demodulation circuit. We have imaged reflectivity variations of metallic and superconducting samples in passive mode to determine the spatial resolution of the technique. Images are also presented in active mode of a superconducting microwave device taken at liquid nitrogen temperature.

We describe a thin-film superconducting Nb microwave resonator, tunable to within 0.3 ppm of the hyperfine splitting of $^{87}$Rb at $f_{Rb}=6.834683$ GHz. We coarsely tuned the resonator using electron-beam lithography, decreasing the resonance frequency from 6.8637 GHz to 6.8278 GHz. For \emph{in situ} fine tuning at 15 mK, the resonator inductance was varied using a piezoelectric stage to move a superconducting pin above the resonator. We found a maximum frequency shift of about 8.7 kHz per 60-nm piezoelectric step and a tuning range of 18 MHz., accepted in AIP Advances

We describe a scanning near-field microwave microscope which uses a loop probe to measure local magnetic properties of metallic samples on a length scale of 200 μm. We demonstrate imaging at 6 GHz through spatiallyresolved ferromagnetic resonance experiments on a single crystal of the colossal magneto-resistive material La0.8Sr0.2MnO3. We find the experimental results are qualitatively and quantitatively well described by a simple model of the system.

We describe the use of a cryogenic near-field scanning microwave microscope to image microwave electric fields from superconducting and normal-metal microstrip resonators. The microscope employs an open-ended coaxial probe and operates from 77 to 300 K in the 0.01-20 GHz frequency range with a spatial resolution of about 200 mm. We describe the operation of the system and present microwave images of Cu and Tl2Ba2CaCu2O8 microstrip resonators, showing standing wave patterns at the fundamental and second harmonic frequencies., Comment: 9 pages, 3 eps figures

We describe quantitative imaging of the sheet resistance of metallic thin films by monitoring frequency shift and quality factor in a resonant scanning near-field microwave microscope. This technique allows fast acquisition of images at approximately 10 ms per pixel over a frequency range from 0.1 to 50 GHz. In its current configuration, the system can resolve changes in sheet resistance as small as 0.6 Ohms/sq for 100 Ohms/sq films. We demonstrate its use at 7.5 GHz by generating a quantitative sheet resistance image of a YBa2Cu3O7 (YBCO) thin film on a 5 cm-diameter sapphire wafer., 6 pages, 3 figures; To be published in Appl. Phys. Lett. (2/16/98); See also Steinhauer et al., Appl. Phys. Lett., vol. 71, p. 1736 (1997) cond-mat/9712142; See also http://www.csr.umd.edu/research/hifreq/micr_microscopy.html

We describe near-field imaging of sample sheet resistance via frequency shifts in a resonant coaxial scanning microwave microscope. The frequency shifts are related to local sample properties, such as surface resistance and dielectric constant. We use a feedback circuit to track a given resonant frequency, allowing measurements with a sensitivity to frequency shifts as small as one parts in 50000 for a 30 ms sampling time. The frequency shifts can be converted to sheet resistance based on a simple model of the system., 6 pages, 3 figures; for color versions of figures see www.csr.umd.edu/research/hifreq/micr_microscopy.html

We describe the operation of a simple near‐field scanning microwave microscope with a spatial resolution of about 100 μm. The probe is constructed from an open‐ended resonant coaxial line which is excited by an applied microwave voltage in the frequency range of 7.5–12.4 GHz. We present images of conducting structures with the system configured in either receiving or reflection mode. The images demonstrate that the smallest resolvable feature is determined by the diameter of the inner wire of the coaxial line and the separation between the sample and probe.

We describe the use of a near-field scanning microwave microscope to image the permittivity and tunability of bulk and thin film dielectric samples on a length scale of about 1 micron. The microscope is sensitive to the linear permittivity, as well as to nonlinear dielectric terms, which can be measured as a function of an applied electric field. We introduce a versatile finite element model for the system, which allows quantitative results to be obtained. We demonstrate use of the microscope at 7.2 GHz with a 370 nm thick barium strontium titanate thin film on a lanthanum aluminate substrate. This technique is nondestructive and has broadband (0.1-50 GHz) capability. The sensitivity of the microscope to changes in relative permittivity is 2 at permittivity = 500, while the nonlinear dielectric tunability sensitivity is 10^-3 cm/kV., 12 pages, 10 figures, to be published in Rev. Sci. Instrum., July, 2000

Superconducting microwave devices are now beginning to show significant potential for cellular telephone applications. The key limitations to this new technology, besides reliable inexpensive cryogenic cooling, are the problems of power dependence and nonlinearity. We have employed imaging techniques, including scanning near-field microwave microscopy of devices and materials, to begin examining the microscopic origins of nonlinearity.

We describe the use of a near-field scanning microwave microscope to quantitatively image the dielectric permittivity and tunability of thin-film dielectric samples on a length scale of 1 micron. We demonstrate this technique with permittivity images and local hysteresis loops of a 370 nm thick barium strontium titanate thin film at 7.2 GHz. We also observe the role of annealing in the recovery of dielectric tunability in a damaged region of the thin film. We can measure changes in relative permittivity as small as 2 at 500, and changes in dielectric tunability as small as 0.03 V$^{-1}$., Comment: 5 pages, 2 figures. To be published in Applied Physics Letters, Nov. 15, 1999

We describe a technique for extracting topographic information using a scanning near-field microwave microscope. By monitoring the shift of the system's resonant frequency, we obtain quantitative topographic images of uniformly conducting metal surfaces. At a frequency of 9.572 GHz, our technique allows for a height discrimination of about 55 nm at a separation of 30 microns. We present topographic images of uneven, conducting samples and compare the height response and sensitivity of the system with theoretical expectations., Accepted for publication Applied Physics Letters. To appear tentatively 4/6/98

By scanning a fine open-ended coaxial probe above an operating microwave device, we image local electric fields generated by the device at microwave frequencies. The probe is sensitive to the electric flux normal to the face of its center conductor, allowing different components of the field to be imaged by orienting the probe appropriately. Using a simple model of the microscope, we are able to interpret the system's output and determine the magnitude of the electric field at the probe tip. We show images of electric field components above a copper microstrip transmission line driven at 8 GHz, with a spatial resolution of approximately 200 $\mu$m., Comment: 10 pages, 3 eps-figures, accepted by Appl. Phys. Lett

We describe the near-field microwave microscopy of microwave devices on a length scale much smaller than the wavelength used for imaging. Our microscope can be operated in two possible configurations, allowing a quantitative study of either material properties or local electric fields., 4 pages, 8 figures, minor corrections to text and 2 figures