Analysis of target response of FM-CW radar

Detection and location of different targets buried in ground or constructional walls depends to a great extent on the knowledge of expected target return response. The analysis of the target-radar response for FM-CW ground probing radar is performed with the aid of a signal flow diagram relating the target response and the radar performance. A plane wave model for the radar radiated electromagnetic waves is adopted and the analysis is carried out for two typical targets; a finite thickness slab and a sphere. Computed returns based on this analysis are compared with those obtained experimentally from a 1-2 GHz FM-CW radar scheme and a very close agreement is found. A computational study is conducted on the response of planar target model, and important conclusions are reached upon relevant to ground probing problem.     

Shallow-Etch Mesa Isolation of Graded-Bandgap “W”-Structured Type II Superlattice Photodiodes

Shallow-etch mesa isolation (SEMI) of graded-bandgap “W”-structured type II superlattice (GGW) infrared photodiodes provides a powerful means for reducing excess dark currents due to surface and bulk junction related processes, and it is particularly well suited for focal-plane array fabrication. In the n-on-p GGW photodiode structure the energy gap is increased in a series of steps from that of the lightly p-type infrared-absorbing region to a value typically two to three times larger. The wider gap levels off about 10 nm short of the doping-defined junction, and continues for another 0.25 μm into the heavily n-doped cathode before the structure is terminated by an n ⁺-doped InAs top cap layer. The increased bandgap in the high-field region near the junction helps to strongly suppress both bulk tunneling and generation–recombination (G–R) current by imposing a much larger tunneling barrier and exponentially lowering the intrinsic carrier concentration. The SEMI approach takes further advantage of the graded structure by exposing only the widest-gap layers on etched surfaces. This lowers surface recombination and trap-assisted tunneling in much the same way as the GGW suppresses these processes in the bulk. Using SEMI, individual photodiodes are defined using a shallow etch that typically terminates only 10 nm to 20 nm past the junction, which is sufficient to isolate neighboring pixels while leaving the narrow-gap absorber layer buried 100 nm to 200 nm below the surface. This provides for separate optimization of the photodiode’s electrical and optical area. The area of the junction can be reduced to a fraction of that of the pixel, lowering bulk junction current, while maintaining 100% optical fill factor with the undisturbed absorber layer. Finally, with the elimination of deep, high-aspect-ratio trenches, SEMI simplifies array fabrication. We report herein results from SEMI-processed GGW devices, including large-area discrete photodiodes, mini-arrays, and a focal-plane array. Current–voltage data show strong suppression of side-wall leakage relative to that for more deeply etched devices, as well as scaling of dark current with junction area without loss of quantum efficiency.     

Invariant Euler–Lagrange Equations and the Invariant Variational Bicomplex

In this paper, we derive an explicit group-invariant formula for the Euler–Lagrange equations associated with an invariant variational problem. The method relies on a group-invariant version of the variational bicomplex induced by a general equivariant moving frame construction, and is of independent interest.     

High-yield flip-chip bonding and packaging of low-threshold VCSEL arrays on sapphire substrates

Oxide-confined top-emitting 850 nm and bottom-emitting 980 nm vertical-cavity surface-emitting laser (VCSEL) 8/spl times/8 arrays were designed and fabricated for applications of optical interconnects. The arrays were flip-chip bonded onto sapphire substrates that contain complimentary metal-oxide-semiconductor (CMOS) driver and fan-out circuitries. The off-sited bonding contacts and minimized bonding force produced very high yield of the hybridization process without causing damage to the VCSEL mesas. The hybridized devices were further mounted either on printed circuit board (PCB) or in 68-pin pin-grid-array (PGA) packages. The transparent sapphire substrate allowed optical outputs from the top-emitting VCSEL arrays to transmit directly through without additional substrate removal procedure. Lasing thresholds below 250 /spl mu/A for 850 nm VCSELs and 800 /spl mu/A for 980 nm VCSEL were found at room temperature. The oxide confinement apertures of VCSELs were measured to be around 6 /spl mu/m in diameter. High-speed data transmission demonstrated a bandwidth of up to 1 Gbits/s per channel for these hybridized VCSEL transmitters.     

Experimental determination of attenuation in corrugated circular waveguides

The attenuation of the HE11 mode in a brass corrugated circular waveguide of internal diameter 8 cm is measured in the frequency range 8?10 GHz by means of a resonant-cavity technique. Attenuation values of the order of 4 dB/m are observed. The mean attenuation level exceeds the theoretical value for a perfect corrugated waveguide by about 25%, which is within the experimental accuracy. The attenuation measured is substantially less than that predicted for the H11 mode in a smooth-wall waveguide of comparable size and is, in fact, close to that predicted for the H01 mode.     

Single-mode operation of low-attenuation corrugated waveguide

The operation of a corrugated waveguide is described under conditions where the HE11 mode is the only mode of propagation. Its attenuation is then predicted to be significantly less than that of other single-mode waveguides operating at the same frequency. Verification of the theory is provided by resonant-cavity experiments. Results lie within a range which can be accounted for in terms of surface roughness of the cavity irises.     

A nonlinear Hamiltonian structure for the Euler equations

The Euler equations for inviscid incompressible fluid flow have a Hamiltonian structure in Eulerian coordinates, the Hamiltonian operator, though, depending on the vorticity. Conservation laws arise from two sources. One parameter symmetry groups, which are completely classified, yield the invariance of energy and linear and angular momenta. Degeneracies of the Hamiltonian operator lead in three dimensions to the total helicity invariant and in two dimensions to the area integrals reflecting the point-wise conservation of vorticity. It is conjectured that no further conservation laws exist, indicating that the Euler equations are not completely integrable, in particular, do not have soliton-like solutions.     

Normalizability of one-dimensional quasi-exactly solvable Schrödinger operators

We completely determine necessary and sufficient conditions for the normalizability of the wave functions giving the algebraic part of the spectrum of a quasi-exactly solvable Schrödinger operator on the line. Methods from classical invariant theory are employed to provide a complete list of canonical forms for normalizable quasi-exactly solvable Hamiltonians and explicit normalizability conditions in general coordinate systems.Supported in Part by DGICYT Grant PS 89-0011Supported in Part by an NSERC GrantSupported in Part by NSF Grant DMS 92-04192     

Joint Invariant Signatures

A new, algorithmic theory of moving frames is applied to classify joint invariants and joint differential invariants of transformation groups. Equivalence and symmetry properties of submanifolds are completely determined by their joint signatures, which are parametrized by a suitable collection of joint invariants and/or joint differential invariants. A variety of fundamental geometric examples are developed in detail. Applications to object recognition problems in computer vision and the design of invariant numerical approximations are indicated. August 25, 1999. Final version received: May 3, 2000. Online publication: xxxx.