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Purpose: Extraprostatic extension (EPE) is an unfavorable prognostic factor and the grade of EPE is also shown to be correlated with the prognosis of prostate cancer. The current study assessed the value of prostate magnetic resonance imaging (MRI) in measuring the radial distance (RD) of EPE and the role of T2 WI signs in predicting the grade of EPE. Materials and methods: A total of 110 patients who underwent prostate MRI before radical prostatectomy are enrolled in this retrospective study. Eighty-four patients have organ confined disease and the remaining twenty-six patients have EPE all verified by histopathology. Prostate MRI examinations were conducted with 3T MRI scanner and phased array coil with the following sequences: T2 WI, T1 WI, DCE, DWI with ADC mapping, and high b-value at b = 1500 s/mm2. The likelihood of EPE with 5-point Likert scale was assigned, several MRI features were extracted for each dominant tumor identified by using T2 WI. Tumors with Likert scales 4–5 were evaluated further to obtain MRI-based RD. The relationship between pathological and MRI-determined RD was tested. Univariate and multivariate logistic regression models were developed to detect the grade of pathological EPE. The inputs were among the 2 clinical parameters and 4 MRI features. Results: There is a moderate correlation between pathological RD and MRI-determined RD (? = 0.45, P < 0.01). In univariate and multivariate models, MRI features and clinical parameters possess varying significance levels (univariate models; P = 0.048–0.788, multivariate models; P = 0.173–0.769). Multivariate models perform better than the univariate models by offering fair to good performances (AUC = 0.69–0.85). The multivariate model that employs the MRI features offers better performance than the model employs clinical parameters (AUC = 0.81 versus 0.69). Conclusion: Co-existence of T2 WI signs provide higher diagnostic value even than clinical parameters in predicting the grade of EPE. Combined use of clinical parameters and MRI features deliver slightly superior performance than MRI features alone. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Spatial filtering, an analog of frequency-domain filtering that can be obtained in the incidence angle domain at a fixed frequency is studied in the transmission mode for slabs of two-dimensional rod-type photonic crystals. In the present paper, the emphasis is put on the demonstration of the possibility to obtain various regimes of spatial filtering, i.e., band-stop, band-pass, and low-pass filtering in different frequency ranges in one simple configuration. The operation is based on the use of several Floquet-Bloch modes with appropriate dispersion properties, so that such one or two co-existing mode(s) contribute to the forming of a proper filter characteristic within each specific frequency range. It is shown that high-efficiency transmission and steep switching between pass and stop bands can be obtained in the angle domain for wide ranges of variation of the problem parameters. In particular, by varying the rod-diameter-to-lattice-constant ratio, one attains lots of freedom in the engineering of spatial filters with desired transmission characteristics. (C) 2015 Elsevier B.V. All rights reserved.

En este trabajo proporcionamos doce formas normales para todos los campos vectoriales polinomiales Hamiltonianos en el plano que tienen términos lineales más cúbicos homogéneos y que poseen en el origen un centro de tipo lineal o un centro nilpotente. Para estos sistemas caracterizamos sus retratos de fase globales en el disco de Poincaré y describimos sus diagramas de bifurcación. Las formas normales de estos sistemas las obtenemos utilizando las formas normales de los sistemas cúbicos homogéneos dados en [1], y añadiendo a estos los términos lineales de manera que el origen sea un centro de tipo lineal o un centro nilpotente. Luego describimos los retratos de fase globales en el disco de Poincaré de estas doce familias de sistemas. Para ello en primer lugar encontramos los retratos de fase en el infinito de esos sistemas, y luego encontramos los retratos de fase locales en los puntos singulares finitos. Usando estos dos resultados determinamos los posibles retratos de fase globales de cada familia. Para algunas familias los puntos singulares finitos son demasiado complicados para estudiar sus retratos de fase local, y en algunos otros casos ni siquiera podemos calcular los puntos singulares finitos. En estas situaciones primero determinamos el número máximo de puntos singulares finitos que los sistemas pueden tener, a continuación utilizando el hecho de que el índice total de todos los puntos singulares de un campo vectorial en la esfera de Poincaré con un número finito de puntos singulares es 2 (este resultado se conoce como el teorema de Poincaré–Hopf) determinamos el número posible de puntos singulares finitos y sus posibles retratos fase locales posibles. Para determinar los posibles retratos de fase globales posibles miramos el número de puntos de una recta que pasa por el origen que se encuentran en el mismo nivel de energía. Puesto que los polinomios Hamiltonianos de las doce familias de sistemas son de cuarto grado, no puede haber más que cuatro de tales puntos. Si encontramos que sólo un retrato de fase global es posible para una familia, entonces este es el retrato de fase de la familia. Si hay más de un retrato de fase global posible, entonces mostramos que podemos elegir los parámetros de forma que los retratos de fase se realicen. Por último, después de haber determinado los retratos de fase global para cada familia, describimos sus diagramas de bifurcación utilizando las dos diferencias principales entre estos retratos de fase: el número de puntos singulares finitos y el número de sillas en el mismo nivel de energía. [1] A. Cima and J. Llibre, “Algebraic and topological classification of the homogeneous cubic vector fields in the plane”, J. Math. Anal. and Appl. 147 (1990), 420–448., In this work we provide twelve normal forms for all the Hamiltonian planar polynomial vector fields having linear plus cubic homogeneous terms which possess a linear type center or a nilpotent center at the origin, and find their global phase portraits on the Poincaré disk. Moreover we provide the bifurcation diagrams of these differential systems. We obtain the normal forms of these systems using the normal forms of cubic homogeneous systems given in [1], and by adding to them the linear terms such that the origin is a linear type center or a nilpotent center. Then we describe the global phase portraits on the Poincaré disk of these twelve families of systems. To do this we first find the phase portraits at infinity of those systems, and then we find the local phase portraits at the finite singular points. Using these two results we determine the possible global phase portraits of each family. For some families the finite singular points are too complicated to study their local phase portraits, in some other cases we even cannot calculate the finite singular points. In these situations we first determine the maximum number of finite singular points that the systems can have, then using the fact that the total index of all the singular points of a vector field on the Poincaré sphere with a finite number of singular points is 2 (this result is known as the Poincaré–Hopf theorem) we determine the possible number of finite singular points and their possible local phase portraits. To determine the possible global phase portraits we look at the number of points of a straight line passing through the origin that are at the same energy level. Since the Hamiltonian polynomials of the twelve families of systems are quartic, there can be at most four such points. If we find only one possible global phase portrait for a family then we are done. If there are more than one possible global phase portrait then we show that for some specific choice of parameters those phase portraits are indeed realizable. Finally, after having determined the global phase portraits for each fam- ily, we describe their bifurcation diagrams using the two main differences between these phase portraits: the number of finite singular points and the number of saddles at the same energy level. [1] A. Cima and J. Llibre, “Algebraic and topological classification of the homogeneous cubic vector fields in the plane”, J. Math. Anal. and Appl. 147 (1990), 420–448.

The dispersion properties of rod-type chirped photonic crystals (PhCs) and non-channeled transmission in the direction of the variation of structural parameters from one cell of such a PhC to another are studied. Two types of configurations that enable multiple slow waves but differ in the utilized chirping scheme are compared. It is demonstrated that the multiple, nearly flat bands with a group index of refraction exceeding 180 can be obtained. For these bands, transmission is characterized by multiple narrow peaks of perfect transmission, strong field enhancement inside the slab, and large values of the Q-factor. Among the bands, there are some that show negative phase velocity. Symmetry with respect to the slab mid-plane must be kept in order to obtain constructive interferences that are necessary for reflection-free transmission. It is shown that 15 and more slow wave bands can be obtained in one configuration. The corresponding transmission peaks are well separated from each other, being the only significant feature of the transmission spectrum, while the Q-factor can exceed 10(5). The observed features are preserved in a wide range of the incidence angle variation. They can be used for tuning the locations and spectral widths of the transmission peaks. Some comparisons with the chirped multilayer structures have been carried out. (C) 2014 Optical Society of America, This work is supported by the projects DPT-HAMIT, ESF-EPIGRAT, and NATO-SET-181, and by TUBITAK under Project Nos., 107A004, 109A015, 109E301, and 110T306. A.E.S. thanks TUBITAK for partial support in the framework of the Visiting Researcher Program. H.K. and E.O. acknowledge partial support from the Turkish Academy of Sciences.

It is experimentally demonstrated that the combination of diode and splitter functions can be realized in one broadband reciprocal device. The suggested performance is based on the dielectric photonic crystal grating whose structural symmetry is broken owing to non-deep corrugations placed at one of the two interfaces. The study has been performed at a normally incident beam-type illumination obtained from a microwave horn antenna. The two unidirectionally transmitted, deflected beams can show large magnitude and high contrast, while the angular distance between their maxima is 90 degrees and larger. The dual-band unidirectional splitting is possible when using TM and TE polarizations. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4800147]

We study single-beam deflection and asymmetry in transmission, two aspects of the same phenomenon that appear in the topologically simple, nonsymmetric, photonic crystal (PhC)-based structures without corrugations at the interfaces. Strong diffractions enabling efficient blazing, i.e., redistribution of the incident wave energy in favor of the desired higher diffraction order(s), can be achieved owing to the defect-like layer(s) embedded in a regular slab of PhC. The main features, together with the peculiarities of the two basic transmission types and relevant coupling and deflection scenarios, are discussed, for one of which a part of the PhC works in the evanescent-wave regime. Performances are suggested, in which efficient single-beam deflection and asymmetry in transmission can be obtained even when the irregular layer is deeply embedded. More than 97% of the incident wave energy can be converted into a single deflected beam that is associated with the first negative diffraction order, even though the entire structure is nonsymmetric and the diffractive element is located at some distance from the incidence interface. (C) 2016 Optical Society of America

It is shown that strong diffractions and related dual-beam splitting can be obtained at transmission through the nonsymmetric structures that represent two slabs of photonic crystal (PhC) separated by a single coupled-cavity type defect layer, while there are no grating-like corrugations at the interfaces. The basic operation regimes include unidirectional and bidirectional splitting that occur due to the dominant contribution of the first positive and first negative diffraction orders to the transmission, which is typically connected with different manifestations of the asymmetric transmission phenomenon. Being the main component of the resulting transmission mechanism, diffractions appear owing to the effect exerted by the defect layer that works like an embedded diffractive element. Two mechanisms can co-exist in one structure, which differ, among others, in that whether dispersion allows coupling of zero order to a wave propagating in the regular, i.e., defect-free PhC segments or not. The possibility of strong diffractions and efficient splitting related to it strongly depend on the dispersion properties of the Floquet-Bloch modes of the PhC. Existence of one of the studied transmission scenarios is not affected by location of the defect layer. Published by AIP Publishing.

Cataloged from PDF version of article. Wideband suppression of zero order and relevant strongly asymmetric transmission can be obtained in photonic crystal gratings that are made of linear isotropic materials and show the broken structural (axial) symmetry, even if zero diffraction order may be coupled to a Floquet-Bloch (FB) wave at the incidence and exit interfaces. The studied mechanism requires that the peculiar diffractions at the corrugated exit interface inspire strong energy transfer to higher orders, including those not coupled to an FB wave. At the opposite direction of incidence, transmission due to zero and some higher orders that may be coupled at the corrugated input interface can vanish. This leads to the alternative scenario of wideband unidirectional transmission, which itself does not need but can coexist with the other scenario based on the merging of asymmetric diffraction and dispersion of the FB mode. © 2012 Optical Society of America.

Planar metamaterials, which have incident to normal plane excitation unlike SRR-type structures and that are easily fabricated in multilayer form, have received great interest in recent years. In this paper, one-dimensional and polarization independent circular fishnet metamaterials and their equivalent discontinuous slab-pair modeling for tuning resonance frequencies are introduced. After the numerical and experimental demonstration of the inclusions, the standard retrieval characterization methods and the correspondent/related backward-wave propagation observation are realized in order to check the physical explanation mentioned in the paper. In addition, a detailed phase analysis is performed in order to demonstrate the application of the suggested structure as a phase compensator. (C) 2012 Elsevier B.V. All rights reserved.

Hybridization of the unit lattice along the propagation direction was demonstrated to produce a negative-phase-velocity transmission band in the absence of the contributions from the higher diffraction orders for a stacked metallic fishnet grid with subwavelength apertures. This extraordinary transmission band is governed by the stacked resonators. The hybridized unit lattice configurations are not just slight modifications of the configurations with homogenous unit lattices. The volumetric proportions of different dielectric media are a key factor in the partitioned unit lattice for the estimation of the stacking and coupling effects between the resonators. The contribution of the coupling mechanisms enhances the transmission results almost by the same factor for the investigated lattice separations along the propagation direction in hybrid unit cells while the densely stacked resonators yield much higher transmission results, both around the regarding extraordinary transmission band that is associated with the negative phase velocity. A positive-phase-velocity transmission band was also exhibited by the hybridized unit lattice configuration when combined with a cavity resonator. Experimental transmission results of the hybrid configuration supported the theoretical predictions. The hybrid configurations are scalable to the near-infrared regime. (C) 2012 Society of Photo-Optical Instrumentation Engineers (SPIE). [DOI: 10.1117/1.JNP.6.061608]

A complementary bilayer cross-wire chiral metamaterial is proposed and studied experimentally and numerically. It exhibits giant optical activity and a small circular dichroism. The retrieval results reveal that a negative refractive index is realized for right circularly polarized waves due to the strong chirality. Our numerical results show that the mechanism of the chiral behavior at the resonance of lower frequency can be interpreted as the coupling effects between two sets of mutually twisted virtual magnetic dipoles, while the resonance of higher frequency shows complicated nonlocal features. (C) 2011 American Institute of Physics. [doi:10.1063/1.3574909]

Cataloged from PDF version of article. Spatial filtering is demonstrated at beam-type excitations by utilizing finite thickness slabs of two-dimensional dielectric photonic crystals (PCs) showing exotic Fabry-Perot resonances that are preserved over a wide range of variation of the incidence angle. Bandstop and dual-bandpass filtering effects are illustrated theoretically and the corresponding filters are validated in the microwave experiments by using square-lattice PCs. It is shown that the basic transmission features that were observed earlier for a plane-wave illumination are also recognizable at beam-type excitations. The proposed spatial filtering mechanism exhibits directional beaming. The desired widths and the locations of the passbands and stopbands are attainable in the angle domain with a proper choice of the operating frequency for the given excitation characteristics. c 2010 American Institute of Physics. [doi:10.1063/1.3498810]

A uniaxial chiral metamaterial is constructed by double-layered four "U" split ring resonators mutually twisted by 90 degrees. It shows a giant optical activity and circular dichroism. The retrieval results reveal that a negative refractive index is realized for circularly polarized waves due to the large chirality. The experimental results are in good agreement with the numerical results., Comment: 4 pages, 4 figures, Published as cover on APL

Cataloged from PDF version of article. We report astonishingly high transmission enhancement factors through a subwavelength aperture at microwave frequencies by placing connected split ring resonators in the vicinity of the aperture. We carried out numerical simulations that are consistent with our experimental conclusions. We experimentally show higher than 70,000-fold extraordinary transmission through a deep subwavelength aperture with an electrical size of lambda/31x lambda/12 (width x length), in terms of the operational wavelength. We discuss the physical origins of the phenomenon. Our numerical results predict that even more improvements of the enhancement factors are attainable. Theoretically, the approach opens up the possibility for achieving very large enhancement factors by overcoming the physical limitations and thereby minimizes the dependence on the aperture geometries. (C) 2010 Optical Society of America

A pair of mutually twisted metallic cross-wires can produce giant optical activity. When this single chiral layer is stacked layer by layer in order to build a thick chiral metamaterial, strong coupling effects are found between the two adjacent chiral layers. We studied these coupling effects numerically and experimentally. The results show that the existing coupling between chiral layers can make the chiral properties of a two-layered chiral metamaterial different from the constituting single chiral layers. It is explained qualitatively that the coupling effects are generated from the coupling of metallic cross-wires belonging to different chiral layers. Our experimental results are in good agreement with the simulation results. (C) 2010 Optical Society of America

Date of Conference: 12-16 April 2010 Bandpass and bandstop spatial filters based on the dielectric-rod EBG structures are proposed and validated for the frequency range from 18 to 25 GHz. The obtained experimental results are well consistent with the theoretical predictions. The exploited mechanism utilizes, in particular, anisotropic-like dispersion, which can occur in the conventional EBG structures made of isotropic materials.

We report an enhanced transmission through a single circular subwavelength aperture that is incorporated with a split ring resonator (SRR) at the microwave regime. Transmission enhancement factors as high as 530 were observed in the experiments when the SRR was located in front of the aperture in order to efficiently couple the electric field component of the incident electromagnetic wave at SRR's electrical resonance frequency. The experimental results were supported by numerical analyses. The physical origin of the transmission enhancement phenomenon was discussed by examining the induced surface currents on the structures. © 2009 American Institute of Physics.

Cataloged from PDF version of article. Nonuniform and nonperiodic grooves are used to enhance the transmission and directivity of emissions from a single metallic subwavelength aperture. By using nonuniform and nonperiodic grooves, the amplitude and phase of the diffracted power flow from each groove can be adjusted properly. As a result, the transmission and emission directivity can be further improved when compared to apertures with uniform and periodic grooves. Our experimental results are in good agreement with the finite difference time domain simulation results.

Cataloged from PDF version of article. Unidirectional transmission is studied theoretically and experimentally for the gratings with one-side corrugations (non-symmetric gratings), which are based on two-dimensional photonic crystals composed of alumina rods. The unidirectional transmission appears at a fixed angle of incidence as a combined effect of the peculiar dispersion features of the photonic crystal and the properly designed corrugations. It is shown that the basic unidirectional transmission characteristics, which are observed at a plane-wave illumination, are preserved at Gaussian-beam and horn antenna illuminations. The main attention is paid to the single-beam unidirectional regime, which is associated with the strong directional selectivity arising due to the first negative diffraction order. An additional degree of freedom for controlling the transmission of the electromagnetic waves is obtained by making use of the asymmetric corrugations at the photonic crystal interface. (C) 2010 Optical Society of America.

Cataloged from PDF version of article. A graded index photonic crystal (GRIN PC) configuration was placed at the input side of a photonic crystal waveguide (PCW) in order to efficiently couple the light waves into the waveguide. We compared the transmission efficiencies of light in the absence and presence of the GRIN PC structure. We report a significant improvement in coupling when the GRIN PC is incorporated with the PCW. The intensity profiles were obtained by carrying out the experiments at microwave frequencies. Finite difference time domain based simulations were found to be in good agreement with our experimental results.

Cataloged from PDF version of article. We describe an approach to implement graded index (GRIN) structures using two- dimensional photonic crystals (PCs). The lattice spacing along the transverse direction to propagation is altered and we show, both theoretically and experimentally, that such a spatial perturbation is an effective way to obtain GRIN PC. The response of the structure to spatially wide incident beams is investigated and strong focusing behavior is observed. The large spot size conversion ratio can be attainable and is mainly limited by the finite size of the structure. The designed GRIN PC shows promise for use in optical systems that require compact and powerful focusing elements compared to the traditional bulky lenses. (C) 2008 American Institute of Physics. [DOI: 10.1063/1.3009965]

A Photonic Crystal (PC) with a surface defect layer (made of dimers) is studied in the microwave regime. The dispersion diagram is obtained with the Plane Wave Expansion Method. The dispersion diagram reveals that the dimer-layer supports a surface mode with negative slope. Two facts are noted: First, a guided (bounded) wave is present, propagating along the surface of the dimer-layer. Second, above the light line, the fast traveling mode couple to the propagating spectra and as a result a directive (narrow beam) radiation with backward characteristics is observed and measured. In this leaky mode regime, symmetrical radiation patterns with respect to the normal to the PC surface are attained. Beam steering is observed and measured in a 70 degrees angular range when frequency ranges in the 11.88-13.69GHz interval. Thus, a PC based surface wave structure that acts as a frequency dependent leaky wave antenna is presented. Angular radiation pattern measurements are in agreement with those obtained via numerical simulations that employ the Finite Difference Time Domain Method (FDTD). Finally, the backward radiation characteristics that in turn suggest the existence of a backward leaky mode in the dimer-layer are experimentally verified using a halved dimer-layer structure. (C) 2009 Optical Society of America

To provide asymmetric propagation of light, we propose a graded index photonic crystal (GRIN PC) based waveguide configuration that is formed by introducing line and point defects as well as intentional perturbations inside the structure. The designed system utilizes isotropic materials and is purely reciprocal, linear, and time-independent, since neither magneto-optical materials are used nor time-reversal symmetry is broken. The numerical results show that the proposed scheme based on the spatial-inversion symmetry breaking has different forward (with a peak value of 49.8%) and backward transmissions (4.11% at most) as well as relatively small round-trip transmission (at most 7.11%) in a large operational bandwidth of 52.6 nm. The signal contrast ratio of the designed configuration is above 0.80 in the telecom wavelengths of 1523.5-1576.1 nm. An experimental measurement is also conducted in the microwave regime: A strong asymmetric propagation characteristic is observed within the frequency interval of 12.8 GHz-13.3 GHz. The numerical and experimental results confirm the asymmetric transmission behavior of the proposed GRIN PC waveguide. (C) 2014 AIP Publishing LLC.