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We have developed a scanning near-field microwave microscope that operates at cryogenic temperatures. Our system uses an open-ended coaxial probe with a 200 mm inner conductor diameter and operates from 77 to 300 K in the 0.01-20 GHz frequency range. In this paper, we present microwave images of the electric field distribution above a Tl2Ba2CaCu2O8 microstrip resonator at 77 K, measured at several heights. In addition, we describe the use of a frequency-following circuit to study the influence of the probe on the resonant frequency of the device., 4 pages, postscript file with 6 figures conference proceeding for the Applied Superconductivity Conference 1998

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.

Direct measurements of the complex conductivity spectra of thin-film La2−2x SrxCuO4 are made at frequencies of 5–40 cm−1. Narrow, intense Drude-type excitation is observed in the superconducting phase.

We present the first wide-band (5–400 cm−1) measurements of the dynamical conductivity and the dielectric permittivity spectra of La2−xSrxCuO4 (x ≈ 0.16). A narrow Drude-like band is observed in the spectra, which is consistent with a d-wave pairing state. We determine the plasma frequency, scattering rate, and mean free path of the unpaired charge carriers responsible for this band. For the first time, “coherence peak”-like behavior is observed in the temperature dependence of the submillimeter conductivity of La2−xSrxCuO4, associated with the temperature evolution of the band in the superconducting state.

We present a study of non-equilibrium superconductivity in DyBa2Cu3O7-d using photo induced activation of mm-wave absorption (PIAMA). We monitor the time evolution of the thin film transmissivity at 5 cm-1 subject to pulsed infrared radiation. In addition to a positive bolometric signal we observe a second, faster, decay with a sign opposite to the bolometric signal for T>40 K. We attribute this to the unusual properties of quasi-particles residing near the nodes of an unconventional superconductor, resulting in a strong enhancement of the recombination time., 4 pages, 3 figures

Using mm-wave transmission we obtain information about both the real and imaginary part of the dielectric function of superconducting thin films. This is done by fitting the Fabry-Perot resonance spectrum for the film plus substrate over a broad frequency range (110-180 GHz) using the full Fresnel equations and a two-fluid description for the dielectric function. Depending on the thickness of the film, the transmission is mainly determined by the real or the imaginary part of the dielectric function. For NbN we find a behavior consistent with the BCS-formalism. For DyBa_2Cu_3O_7, results on films of thicknesses ranging from 20 to 80 nm are presented. We find a quadratic temperature dependence of the penetration depth at low temperatures and a strongly enhanced conductivity below T_c, indicative of a strong reduction of the quasiparticle scattering. For the 20 nm film the transmission is dominated by the real part of the conductivity, even down to 60 K., Comment: Revtex, 7 pages including 7 eps-figures, submitted to Physica C

Infrared reflectivity measurements, using p-polarized light at a grazing angle of incidence, show an increased sensitivity to the optical conductivity of highly reflecting superconducting materials. We demonstrate that when this measurement technique is applied to the conventional s-wave superconductor NbN, the results are in perfect agreement with BCS theory. For the in-plane response of a ${\mathrm{La}}_{1.85}{\mathrm{Sr}}_{0.15}{\mathrm{CuO}}_{4}$ single crystal, in the superconducting state, we find a reduction of the optical conductivity in the frequency range below 20 meV. The observed frequency dependence excludes an isotropic s-wave gap, but agrees well with model calculations assuming a d-wave order parameter.

We show that from measurements of the reflectivity of a uniaxial medium taken at a finite incidence angle with s- and p-polarized light it is possible to determine the dielectric function both parallel and perpendicular to the optical axis. When applied to layered compounds with its surface parallel to the layers, this technique allows for an accurate determination of the loss function perpendicular to the layers. This is demonstrated for the example of c-axis oriented thin films of the high-${\mathit{T}}_{\mathit{c}}$ superconductor ${\mathrm{Tl}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{Ca}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{10}$, on which we carried out polarized reflectivity measurements at 45\ifmmode^\circ\else\textdegree\fi{} incidence angle above and below ${\mathit{T}}_{\mathit{c}}$.

The resonances of integrated tuning stubs in combination with SIS (superconductor-insulator-superconductor) detectors are measured and calculated. The predicted resonances are compared with measurements of stubs integrated with Nb-Al/sub 2/O/sub 3/-Nb junctions in a log-periodic antenna. Stubs of different lengths have been investigated on different substrates (on 200-mm thick quartz and on a 7-mm thick silicon membrane) and the results show a fairly good agreement with the model calculations. Quartz substrates showed resonances up to 640 GHz, while for silicon membranes stub resonances reach up to as 480 GHz. An observed resonance at 560 GHz is probably a substrate effect from the membrane. The gap frequency for all the samples is 670 GHz and no resonances are detected above this frequency. Up to the maximum detected frequency dispersion is found to be negligible. >

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.

Nonlinearities give rise to intermodulation distortion in superconducting microwave devices and currently limit their use to low power applications. We have developed a cryogenic imaging technique to spatially resolve intermodulation distortion and used it to image an 8.2 GHz high temperature superconducting Tl2Ba2CaCu2O8 microwave resonator. The images reveal that the fundamental and intermodulation electric fields obey a fixed relation throughout the device. We note that further refinements of intermodulation theory in resonant devices may be required to fully describe the data.

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 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 present mm-wave transmission as a complementary technique to characterize the properties of superconducting thin films, obtaining information on both the real and imaginary part of the dielectric function. Examples are given to illustrate the strength of the technique to measure the response of di-electric materials and stratified systems. We demonstrate the BCS-behavior of a conventional superconductor NbN, and show furthermore the unconventional behavior in both the absorptive and reactive part of the conductivity of a 20 nm thick DyBa2Cu3O7-(delta ) film.

We use the experimental technique of thermal modulation reflectometry to study the relatively small temperature dependence of the optical conductivity of superconductors. Due to a large cancellation of systematic errors, this technique is shown to a be very sensitive probe of small changes in reflectivity. We analyze thermal modulation reflection spectra of single crystals and epitaxially grown thin films of YBa$_2$Cu$_3$O$_{7-\delta}$ and obtain the ${\alpha_tr}^2F(\omega)$ function in the normal state, as well as the superconductivity induced changes in reflectivity. We present detailed model calculations, based on the Eliashberg-Migdal extension of the BCS model, which show good qualitative and quantitative agreement with the experimental spectra. VSGD.93.12.th, Comment: 6 pages, figures on request. Revtex, version 2, Materials Science Center Internal Report Number VSGD.93.12.th

The frequency dependence of the coupling of niobium superconducting transmission lines is measured for frequencies up to and above the superconducting gap frequency. For this purpose superconducting microstrips are integrated in log-periodic planar antennas and the spectral response is measured by means of a Fourier transform spectrometer with 1 mum2 Nb/Al2O3/Nb SIS junctions as detectors. Resonances of microstrips are observed up to 650 GHz, the superconducting gap frequency of niobium, but above that frequency no resonances have been detected. The measured resonance frequencies are in good agreement with a dispersive model for superconducting transmission lines based on the Mattis-Bardeen theory. The radiation coupling is lower than calculated, indicating significant dielectric losses.

We show that from measurements of reflectivity of a uniaxial medium taken at a finite incidence angle with s - and p -polarized light it is possible to determine the dielectric function both parallel and perpendicular to the optical axis. When applied to a layered compound with its surface parallel to the layers, this technique allows for an accurate determination of the loss function perpendicular to the layers. This is demonstrated for the case of c -axis-oriented films of the high-temperature superconductor Tl 2 Ba 2 Ca 2 Cu 3 O 10 , on which we carried out polarized reflectivity measurements at 45° incidence angle above and below T c . We also studied the infrared response of La 1.85 Sr 0.15 CuO 4 single crystals with the light polarized parallel and perpendicular to the c -axis as a function of temperature. We confirm the results reported by Tamasaku [Phys. Rev. Lett. 69 (1992) 1455]: in the superconducting state a plasma branch occurs below the gap.

We study the charge dynamics of high-Tc superconductors with the electric field perpendicular to the planes, using polarized oblique-incidence reflectometry for thin films of Tl2Ba2Ca2Cu3O10 and normal incidence reflectometry for single crystals of La1.85Sr0.15CuO4. In Tl2Ba2Ca2Cu3O10 we observe no c-axis optical plasmon either above or below Tc. For E//c in La2−xSrxCuO4, no plasmon is observed in the normal state, but as soon as T drops below Tc, a plasma edge in the reflectivity occurs, which moves up to about 2kBTc for T→0. The electronic contribution to σ(ω)≈7ω−1 cm−1 is independent of frequency up to several hundred cm−1, which implies that the optical scattering rate (τc−1) is large compared to the c-axis plasma frequency (ωpc). We prove experimentally that h /τ c h ω pc ⪢ 3.5k E T c , hence the c-axis response is in a universality class different from the dirty (Mattis-Bardeen) limit, and the absence of a plasma edge in the normal state is due to overdamping. Recent experimental data of various groups show that this is a generic feature of high-Tc cuprates. There is no need to assume a large many-body reduction of the ab initio LDA-RPA plasma frequency along the c-axis. Yet the overdamping of the plasmon could be a many-body effect. The ‘confinement’ to the planes as was proposed by Anderson is therefore due to a strong scattering in the c-direction. In the dirty limit only the relatively small amount of oscillator strength in the below-gap region is transferred to the pair-response (the δ-function at zero frequency). As a result the plasma edge in the superconducting state occurs at about 3.4(k B T c h /τ) 0.5 ω pc ⪡3.5k B T c ⪡ h ω pc .