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Takehito Yokoyama - One of the best experts on this subject based on the ideXlab platform.
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Theory of charge transport in high-TC superconductor junctions from the view point of the mid gap Andreev Resonant State
Physica C-superconductivity and Its Applications, 2006Co-Authors: Yukio Tanaka, Yasuhiro Asano, Satoshi Kashiwaya, Takehito YokoyamaAbstract:Abstract In this paper, we report important features about high- T C superconductor junctions. It has been clarified that the most important property of high- T C junctions is the sign change of the pair potential on the Fermi surface reflecting on the d-wave pair potential. This unique feature induces the formation of the mid gap Andreev Resonant State (MARS) at the interface of the high- T C superconductor junctions. The MARS influences various physical quantities, e.g., quasiparticle current, Josephson effect and proximity effect. In d-wave superconductor, the MARS competes with the proximity effect. On the other hand, for triplet superconductor junctions, it can coexist. We can expect giant proximity effect enhanced by the MARS.
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theory of enhanced proximity effect by midgap andreev Resonant State in diffusive normal metal triplet superconductor junctions
Physical Review B, 2005Co-Authors: Yukio Tanaka, Satoshi Kashiwaya, Takehito YokoyamaAbstract:Enhanced proximity effect by the midgap Andreev Resonant State (MARS) in a diffusive normal-metal/insulator/triplet superconductor (DN/TS) junction is studied based on the Keldysh-Nambu quasiclassical Green's-function formalism. By choosing a $p$-wave superconductor as a typical example of the TS, conductance of the junction and the spatial variation of the quasiparticle local density of States (LDOS) in the DN are calculated as the function of the magnitudes of the resistance ${R}_{d}$, Thouless energy in the DN, and the transparency of the insulating barrier. The resulting conductance spectrum has a zero-bias conductance peak (ZBCP) and the LDOS has a zero energy peak (ZEP) except for $\ensuremath{\alpha}=\ensuremath{\pi}∕2$ $(0\ensuremath{\leqslant}\ensuremath{\alpha}\ensuremath{\leqslant}\ensuremath{\pi}∕2)$, where $\ensuremath{\alpha}$ denotes the angle between the lobe direction of the $p$-wave pair potential and the normal to the interface. The widths of the ZBCP and the ZEP are reduced with the increase of ${R}_{d}$ while their heights are drastically enhanced. These peaks are revealed to be suppressed by applying a magnetic field. When the magnitude of ${R}_{d}∕{R}_{0}$ is sufficiently large, the total zero voltage resistance of the junction is almost independent of the ${R}_{d}$ for $\ensuremath{\alpha}\ensuremath{\ne}\ensuremath{\pi}∕2$. The extreme case is $\ensuremath{\alpha}=0$, where total zero voltage resistance is always ${R}_{0}∕2$. We also studied the charge transport in ${p}_{x}+i{p}_{y}$-wave junctions, where only the quasiparticles with perpendicular injection feel the MARS. Even in this case, the resulting LDOS in the DN has a ZEP. Thus the existence of the ZEP in the LDOS of the DN region is a remarkable feature for DN/TS junctions which have never been expected for the DN/singlet superconductor junctions where the MARS and proximity effect compete with each other. Based on these results, a crucial test to identify triplet pairing superconductors based on tunneling experiments is proposed.
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Theory of enhanced proximity effect by midgap Andreev Resonant State in diffusive normal-metal/triplet superconductor junctions
Physical Review B, 2005Co-Authors: Yukio Tanaka, Satoshi Kashiwaya, Takehito YokoyamaAbstract:Enhanced proximity effect by the midgap Andreev Resonant State (MARS) in a diffusive normal-metal/insulator/triplet superconductor (DN/TS) junction is studied based on the Keldysh-Nambu quasiclassical Green's-function formalism. By choosing a $p$-wave superconductor as a typical example of the TS, conductance of the junction and the spatial variation of the quasiparticle local density of States (LDOS) in the DN are calculated as the function of the magnitudes of the resistance ${R}_{d}$, Thouless energy in the DN, and the transparency of the insulating barrier. The resulting conductance spectrum has a zero-bias conductance peak (ZBCP) and the LDOS has a zero energy peak (ZEP) except for $\ensuremath{\alpha}=\ensuremath{\pi}∕2$ $(0\ensuremath{\leqslant}\ensuremath{\alpha}\ensuremath{\leqslant}\ensuremath{\pi}∕2)$, where $\ensuremath{\alpha}$ denotes the angle between the lobe direction of the $p$-wave pair potential and the normal to the interface. The widths of the ZBCP and the ZEP are reduced with the increase of ${R}_{d}$ while their heights are drastically enhanced. These peaks are revealed to be suppressed by applying a magnetic field. When the magnitude of ${R}_{d}∕{R}_{0}$ is sufficiently large, the total zero voltage resistance of the junction is almost independent of the ${R}_{d}$ for $\ensuremath{\alpha}\ensuremath{\ne}\ensuremath{\pi}∕2$. The extreme case is $\ensuremath{\alpha}=0$, where total zero voltage resistance is always ${R}_{0}∕2$. We also studied the charge transport in ${p}_{x}+i{p}_{y}$-wave junctions, where only the quasiparticles with perpendicular injection feel the MARS. Even in this case, the resulting LDOS in the DN has a ZEP. Thus the existence of the ZEP in the LDOS of the DN region is a remarkable feature for DN/TS junctions which have never been expected for the DN/singlet superconductor junctions where the MARS and proximity effect compete with each other. Based on these results, a crucial test to identify triplet pairing superconductors based on tunneling experiments is proposed.
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theory of enhanced proximity effect by midgap andreev Resonant State in diffusive normal metal triplet superconductor junctions
Physical Review B, 2005Co-Authors: Yukio Tanaka, Satoshi Kashiwaya, Takehito YokoyamaAbstract:Enhanced proximity effect by the midgap Andreev Resonant State (MARS) in a diffusive normal-metal/insulator/triplet superconductor (DN/TS) junction is studied based on the Keldysh-Nambu quasiclassical Green's-function formalism. By choosing a $p$-wave superconductor as a typical example of the TS, conductance of the junction and the spatial variation of the quasiparticle local density of States (LDOS) in the DN are calculated as the function of the magnitudes of the resistance ${R}_{d}$, Thouless energy in the DN, and the transparency of the insulating barrier. The resulting conductance spectrum has a zero-bias conductance peak (ZBCP) and the LDOS has a zero energy peak (ZEP) except for $\ensuremath{\alpha}=\ensuremath{\pi}∕2$ $(0\ensuremath{\leqslant}\ensuremath{\alpha}\ensuremath{\leqslant}\ensuremath{\pi}∕2)$, where $\ensuremath{\alpha}$ denotes the angle between the lobe direction of the $p$-wave pair potential and the normal to the interface. The widths of the ZBCP and the ZEP are reduced with the increase of ${R}_{d}$ while their heights are drastically enhanced. These peaks are revealed to be suppressed by applying a magnetic field. When the magnitude of ${R}_{d}∕{R}_{0}$ is sufficiently large, the total zero voltage resistance of the junction is almost independent of the ${R}_{d}$ for $\ensuremath{\alpha}\ensuremath{\ne}\ensuremath{\pi}∕2$. The extreme case is $\ensuremath{\alpha}=0$, where total zero voltage resistance is always ${R}_{0}∕2$. We also studied the charge transport in ${p}_{x}+i{p}_{y}$-wave junctions, where only the quasiparticles with perpendicular injection feel the MARS. Even in this case, the resulting LDOS in the DN has a ZEP. Thus the existence of the ZEP in the LDOS of the DN region is a remarkable feature for DN/TS junctions which have never been expected for the DN/singlet superconductor junctions where the MARS and proximity effect compete with each other. Based on these results, a crucial test to identify triplet pairing superconductors based on tunneling experiments is proposed.
Mark Doost - One of the best experts on this subject based on the ideXlab platform.
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Resonant State expansion for Transverse Electric modes of two-dimensional open optical systems
arXiv: Optics, 2017Co-Authors: Mark DoostAbstract:The Resonant State expansion (RSE), a rigorous perturbative method in electrodynamics, is formulated for Transverse Electrodynamic modes of an effectively $2$-dimensional system. The RSE is a perturbation theory based on the Lippmann Schwinger Green's function equation and requires knowledge of the Green's function of the unperturbed system constructed from Resonant-States. I use the analytic Green's function for the magnetic field to normalize the modes appearing in the corresponding spectral Green's function. This use of the residue and cut of the analytic Green's function is a solution to the failure of the flux volume integral method of normalization for continuum States, a problem which is discussed in detail in this manuscript. In brief, the flux volume integral fails for continuum States because they are not true resonance. An analytic relation between normalized magnetic and electric modes is developed as part of the solution to these difficulties.The complex eigenfrequencies of modes are calculated using the RSE for the case of a homogeneous perturbation.
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Resonant-State-expansion Born approximation with a correct eigen-mode normalisation
Journal of Optics, 2016Co-Authors: Mark DoostAbstract:The Born approximation (Born 1926 Z. Phys. 38 802) is a fundamental result in physics, it allows the calculation of weak scattering via the Fourier transform of the scattering potential. As was done by previous authors (Ge et al 2014 New J. Phys. 16 113048) the Born approximation is extended by including in the formula the Resonant-States (RSs) of the scatterer. However in this study unlike previous studies the included eigen-modes are correctly normalised with dramatic positive consequences for the accuracy of the method. The normalisation of RSs used in the previous RS expansion Born approximation or Resonant-State expansion (RSE) Born approximation made in Ge et al (2014 New J. Phys. 16 113048) has been shown to be numerically unstable in Muljarov et al (2014 arXiv:1409.6877) and by analytics here. The RSs of the system can be calculated using my recently discovered RSE perturbation theory for dispersive electrodynamic scatterers (Muljarov et al 2010 Europhys. Lett. 92 50010; Doost et al 2012 Phys. Rev. A 85 023835; Doost et al 2013 Phys. Rev. A 87 043827; Armitage et al 2014 Phys. Rev. A 89; Doost et al 2014 Phys. Rev. A 90 013834) and normalised correctly to appear in spectral Green's functions and hence the RSE Born approximation via the flux-volume normalisation which I recently rigorously derived in Armitage et al (2014 Phys. Rev. A 89), Doost et al (2014 Phys. Rev. A 90 013834), Doost (2016 Phys. Rev. A 93 023835). In the case of effectively one-dimensional systems I find a RSE Born approximation alternative to the scattering matrix method.
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Resonant-State-expansion Born approximation for waveguides with dispersion
Physical Review A, 2016Co-Authors: Mark DoostAbstract:The Resonant-State expansion (RSE) Born approximation, a rigorous perturbative method developed for electrodynamic and quantum mechanical open systems, is further developed to treat waveguides with a Sellmeier dispersion. For media that can be described by these types of dispersion over the relevant frequency range, such as optical glass, I show that the perturbed RSE problem can be solved by diagonalizing a second-order eigenvalue problem. In the case of a single resonance at zero frequency, this is simplified to a generalized eigenvalue problem. Results are presented using analytically solvable planar waveguides and parameters of borosilicate BK7 glass, for a perturbation in the waveguide width. The efficiency of using either an exact dispersion over all frequencies or an approximate dispersion over a narrow frequency range is compared. I included a derivation of the RSE Born approximation for waveguides to make use of the resonances calculated by the RSE, an extension of the well-known Born approximation.
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Resonant-State-expansion Born approximation with a correct eigen-mode normalisation
Journal of Optics, 2016Co-Authors: Mark DoostAbstract:The Born approximation (Born 1926 Z.Phys.38.802) is a fundamental result in physics, it allows the calculation of weak scattering via the Fourier transform of the scattering potential. As was done by previous authors (Ge et al 2014 New J. Phys. 16 113048) the Born approximation is extended by including in the formula the Resonant-States (RSs) of the scatterer. However in this study unlike previous studies the included eigen-modes are correctly normalised with dramatic positive consequences for the accuracy of the method. The normalisation of the RSs used in the previous RSE Born approximation or Resonant-State-expansion Born approximation made in Ge et al (2014 New J. Phys. 16 113048) has been shown to be numerically unstable in Muljarov et al (2014 arXiv:1409.6877) and by analytics here. The RSs of the system can be calculated using my recently discovered RSE perturbation theory for dispersive electrodynamic scatterers (Muljarov et al 2010 Europhys. Lett. 92 50010; Doost et al 2012 Phys, Rev. A 89; Doost et al 2014 Phys. Rev. A 90 013834) and normalised correctly to appear in the spectral Green's functions and hence the RSE Born approximation via the flux-volume normalisation which I recently rigorously derived in Armitage et al (2014 Phys. Rev. A 89), Doost et al (2014 Phys. Rev. A 90 013834)(2016 Phys. Rev. A 93 023835). In the case of effectively one-dimensional systems I find an RSE Born approximation alternative to the scattering matrix method.
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Resonant-State expansion for a simple dispersive medium
arXiv: Optics, 2015Co-Authors: Mark Doost, Wolfgang Werner Langbein, Egor A MuljarovAbstract:The Resonant-State expansion (RSE), a rigorous perturbative method developed in electrodynamics for non-dispersive optical systems is applied to media with an Ohm's law dispersion, in which the frequency dependent part of the permittivity scales inversely with the frequency, corresponding to a frequency-independent conductivity. This dispersion has only a single pole at zero frequency, which is already present in the non-dispersive RSE, allowing to maintain not only the linearity of the eigenvalue problem of the RSE but also its size. Media which can be described by this dispersion over the relevant frequency range, such as optical glass or doped semiconductors, can be treated in the RSE without additional complexity. Results are presented using analytically solvable homogeneous spheres, for doped silicon and BK7 glass, both for a perturbation of the system going from non-dispersive to dispersive media and the reverse, from dispersive to non-dispersive media.
Alexey I. Fokin - One of the best experts on this subject based on the ideXlab platform.
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Resonant dissociative electron attachment by acetone, acetamide and acetic acid in the rydberg States energy region
Rapid Communications in Mass Spectrometry, 1997Co-Authors: Mars V. Muftakhov, Alexey I. FokinAbstract:Resonant dissociative electron attachment to molecules of carbonyl compounds in an electron energy region 5.5-7.5 eV has been studied. Resonant States at 5.75 eV in CH3CONH2, at 5.65 eV in CH3COOH and at 6.25 eV in CH3COCH3 have been related to the 2[n 3s2] type State by analogy with the 2[n 3s2] Resonant State at 6.34 eV in CH3COH. A Resonant State at 6.05 eV in CH3CONH2 and a Resonant State at 6.75 eV in CH3COOH have been related to States corresponding to the Resonant States of 2[nN 3s2] type in NH3 and 2[nO 3s2] type in H2O, respectively. © 1997 John Wiley & Sons, Ltd.
Yukio Tanaka - One of the best experts on this subject based on the ideXlab platform.
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midgap andreev Resonant State affected by superconducting proximity effect of high tc cuprate attached to diffusive normal metal
Journal of Physics: Conference Series, 2009Co-Authors: Iduru Shigeta, Y Tanuma, Yasuhiro Asano, Masahiko Hiroi, Yukio TanakaAbstract:We report how a midgap Andreev Resonant State (MARS) is affected by the superconducting proximity effect at an interface of diffusive normal metal/insulator/dx.2_y2-wave superconductor (DN/I/DS) junctions. A zero-bias conductance peak (ZBCP) was observed for the (110)-oriented interface in Ag/SiO/Bi2Sr2CaCu2O8+δ (Bi-2212) planar junctions. The experimental ZBCP was analyzed by the extended circuit theory, which was improved by the introduction of spatial variations of the pair potential in a DS electrode near the junction interface. Our experimental results are well explained by the extended circuit theory for DN/I/DS junctions.
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Theory of charge transport in high-TC superconductor junctions from the view point of the mid gap Andreev Resonant State
Physica C-superconductivity and Its Applications, 2006Co-Authors: Yukio Tanaka, Yasuhiro Asano, Satoshi Kashiwaya, Takehito YokoyamaAbstract:Abstract In this paper, we report important features about high- T C superconductor junctions. It has been clarified that the most important property of high- T C junctions is the sign change of the pair potential on the Fermi surface reflecting on the d-wave pair potential. This unique feature induces the formation of the mid gap Andreev Resonant State (MARS) at the interface of the high- T C superconductor junctions. The MARS influences various physical quantities, e.g., quasiparticle current, Josephson effect and proximity effect. In d-wave superconductor, the MARS competes with the proximity effect. On the other hand, for triplet superconductor junctions, it can coexist. We can expect giant proximity effect enhanced by the MARS.
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theory of enhanced proximity effect by midgap andreev Resonant State in diffusive normal metal triplet superconductor junctions
Physical Review B, 2005Co-Authors: Yukio Tanaka, Satoshi Kashiwaya, Takehito YokoyamaAbstract:Enhanced proximity effect by the midgap Andreev Resonant State (MARS) in a diffusive normal-metal/insulator/triplet superconductor (DN/TS) junction is studied based on the Keldysh-Nambu quasiclassical Green's-function formalism. By choosing a $p$-wave superconductor as a typical example of the TS, conductance of the junction and the spatial variation of the quasiparticle local density of States (LDOS) in the DN are calculated as the function of the magnitudes of the resistance ${R}_{d}$, Thouless energy in the DN, and the transparency of the insulating barrier. The resulting conductance spectrum has a zero-bias conductance peak (ZBCP) and the LDOS has a zero energy peak (ZEP) except for $\ensuremath{\alpha}=\ensuremath{\pi}∕2$ $(0\ensuremath{\leqslant}\ensuremath{\alpha}\ensuremath{\leqslant}\ensuremath{\pi}∕2)$, where $\ensuremath{\alpha}$ denotes the angle between the lobe direction of the $p$-wave pair potential and the normal to the interface. The widths of the ZBCP and the ZEP are reduced with the increase of ${R}_{d}$ while their heights are drastically enhanced. These peaks are revealed to be suppressed by applying a magnetic field. When the magnitude of ${R}_{d}∕{R}_{0}$ is sufficiently large, the total zero voltage resistance of the junction is almost independent of the ${R}_{d}$ for $\ensuremath{\alpha}\ensuremath{\ne}\ensuremath{\pi}∕2$. The extreme case is $\ensuremath{\alpha}=0$, where total zero voltage resistance is always ${R}_{0}∕2$. We also studied the charge transport in ${p}_{x}+i{p}_{y}$-wave junctions, where only the quasiparticles with perpendicular injection feel the MARS. Even in this case, the resulting LDOS in the DN has a ZEP. Thus the existence of the ZEP in the LDOS of the DN region is a remarkable feature for DN/TS junctions which have never been expected for the DN/singlet superconductor junctions where the MARS and proximity effect compete with each other. Based on these results, a crucial test to identify triplet pairing superconductors based on tunneling experiments is proposed.
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Theory of enhanced proximity effect by midgap Andreev Resonant State in diffusive normal-metal/triplet superconductor junctions
Physical Review B, 2005Co-Authors: Yukio Tanaka, Satoshi Kashiwaya, Takehito YokoyamaAbstract:Enhanced proximity effect by the midgap Andreev Resonant State (MARS) in a diffusive normal-metal/insulator/triplet superconductor (DN/TS) junction is studied based on the Keldysh-Nambu quasiclassical Green's-function formalism. By choosing a $p$-wave superconductor as a typical example of the TS, conductance of the junction and the spatial variation of the quasiparticle local density of States (LDOS) in the DN are calculated as the function of the magnitudes of the resistance ${R}_{d}$, Thouless energy in the DN, and the transparency of the insulating barrier. The resulting conductance spectrum has a zero-bias conductance peak (ZBCP) and the LDOS has a zero energy peak (ZEP) except for $\ensuremath{\alpha}=\ensuremath{\pi}∕2$ $(0\ensuremath{\leqslant}\ensuremath{\alpha}\ensuremath{\leqslant}\ensuremath{\pi}∕2)$, where $\ensuremath{\alpha}$ denotes the angle between the lobe direction of the $p$-wave pair potential and the normal to the interface. The widths of the ZBCP and the ZEP are reduced with the increase of ${R}_{d}$ while their heights are drastically enhanced. These peaks are revealed to be suppressed by applying a magnetic field. When the magnitude of ${R}_{d}∕{R}_{0}$ is sufficiently large, the total zero voltage resistance of the junction is almost independent of the ${R}_{d}$ for $\ensuremath{\alpha}\ensuremath{\ne}\ensuremath{\pi}∕2$. The extreme case is $\ensuremath{\alpha}=0$, where total zero voltage resistance is always ${R}_{0}∕2$. We also studied the charge transport in ${p}_{x}+i{p}_{y}$-wave junctions, where only the quasiparticles with perpendicular injection feel the MARS. Even in this case, the resulting LDOS in the DN has a ZEP. Thus the existence of the ZEP in the LDOS of the DN region is a remarkable feature for DN/TS junctions which have never been expected for the DN/singlet superconductor junctions where the MARS and proximity effect compete with each other. Based on these results, a crucial test to identify triplet pairing superconductors based on tunneling experiments is proposed.
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theory of enhanced proximity effect by midgap andreev Resonant State in diffusive normal metal triplet superconductor junctions
Physical Review B, 2005Co-Authors: Yukio Tanaka, Satoshi Kashiwaya, Takehito YokoyamaAbstract:Enhanced proximity effect by the midgap Andreev Resonant State (MARS) in a diffusive normal-metal/insulator/triplet superconductor (DN/TS) junction is studied based on the Keldysh-Nambu quasiclassical Green's-function formalism. By choosing a $p$-wave superconductor as a typical example of the TS, conductance of the junction and the spatial variation of the quasiparticle local density of States (LDOS) in the DN are calculated as the function of the magnitudes of the resistance ${R}_{d}$, Thouless energy in the DN, and the transparency of the insulating barrier. The resulting conductance spectrum has a zero-bias conductance peak (ZBCP) and the LDOS has a zero energy peak (ZEP) except for $\ensuremath{\alpha}=\ensuremath{\pi}∕2$ $(0\ensuremath{\leqslant}\ensuremath{\alpha}\ensuremath{\leqslant}\ensuremath{\pi}∕2)$, where $\ensuremath{\alpha}$ denotes the angle between the lobe direction of the $p$-wave pair potential and the normal to the interface. The widths of the ZBCP and the ZEP are reduced with the increase of ${R}_{d}$ while their heights are drastically enhanced. These peaks are revealed to be suppressed by applying a magnetic field. When the magnitude of ${R}_{d}∕{R}_{0}$ is sufficiently large, the total zero voltage resistance of the junction is almost independent of the ${R}_{d}$ for $\ensuremath{\alpha}\ensuremath{\ne}\ensuremath{\pi}∕2$. The extreme case is $\ensuremath{\alpha}=0$, where total zero voltage resistance is always ${R}_{0}∕2$. We also studied the charge transport in ${p}_{x}+i{p}_{y}$-wave junctions, where only the quasiparticles with perpendicular injection feel the MARS. Even in this case, the resulting LDOS in the DN has a ZEP. Thus the existence of the ZEP in the LDOS of the DN region is a remarkable feature for DN/TS junctions which have never been expected for the DN/singlet superconductor junctions where the MARS and proximity effect compete with each other. Based on these results, a crucial test to identify triplet pairing superconductors based on tunneling experiments is proposed.
Egor A Muljarov - One of the best experts on this subject based on the ideXlab platform.
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Full electromagnetic Green's dyadic of spherically symmetric open optical systems and elimination of static modes from the Resonant-State expansion
Physical Review A, 2020Co-Authors: Egor A MuljarovAbstract:A general analytic form of the full 6 × 6 dyadic Green’s function of a spherically symmetric open optical system is presented, with an explicit solution provided for a homogeneous sphere in vacuum. Different spectral representations of the Green’s function are derived using the MittagLeffler theorem, and their convergence to the exact solution is analyzed, allowing us to select optimal representations. Based on them, more efficient versions of the Resonant-State expansion (RSE) are formulated, with a particular focus on the static mode contribution, including versions of the RSE with a complete elimination of static modes. These general versions of the RSE, applicable to nonspherical optical systems, are verified and illustrated on exactly solvable examples of a dielectric sphere in vacuum with perturbations of its size and refractive index, demonstrating the same level of convergence to the exact solution for both transverse electric and transverse magnetic polarizations.
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Resonant-State expansion for planar photonic-crystal structures
Physical Review B, 2020Co-Authors: Sam Neale, Egor A MuljarovAbstract:We present a powerful concept in the field of photonic crystals and metamaterials, applying the Resonant-State expansion (RSE) to planar photonic crystal structures. The RSE allows us to understand and quantify optical resonances in photonic crystal structures in terms of the analytic Resonant States of a homogeneous planar waveguide. The RSE provides an efficient and reliable tool for accurate calculation of a complete set of the Resonant States of a photonic crystal slab, which is required for the correct description and a better understanding of its optical spectra. For the proof of principle, numerical verification of the RSE, and demonstration of its unprecedented accuracy and convergence, an infinite planar photonic crystal slab periodic in one dimension is taken as an example. To illustrate the power of this approach, we consider the mode evolution with the amplitude of the periodic modulation, revealing the role of the guided modes in the formation of bound States in the continuum.
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Applying the Resonant-State expansion to realistic materials with frequency dispersion
Physical Review B, 2020Co-Authors: Hame Sehmi, Wolfgang Werner Langbein, Egor A MuljarovAbstract:The dispersive Resonant-State expansion, developed for an accurate calculation of the Resonant States in open optical systems with frequency dispersion, is applied here to realistic materials, such as metallic nanoparticles and semiconductor microspheres. The material permittivity is determined by fitting the measured indices of refraction and absorption with a generalized Drude-Lorentz model containing a number of poles in the complex frequency plane. Each Drude or Lorentz pole generates an infinite series of Resonant States. Furthermore, for small nanoparticles, each of these poles produces a distinct surface plasmon polariton mode. The evolution of these multiple surface modes with increasing radius traces the transition from the electrostatic limit to significant retardation and radiation. Treating the optical phonon range in a semiconductor microsphere, a reststrahlen band separating the Resonant States is found. Considering a small energy range around the semiconductor band gap, the transition from absorption to gain is described by inverting the Lorentz pole weight, which results in the formation of lasing Resonant States. Interestingly, the series of Resonant States converging towards the absorption pole from the lower frequency side reshapes for a gain pole into a clockwise loop approaching the pole from the higher frequency side, being separated from a series spanning from low to high frequencies and containing the lasing modes.
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Resonant-State expansion applied to three-dimensional open optical systems: Complete set of static modes
Physical Review A, 2019Co-Authors: S. V. Lobanov, Wolfgang Werner Langbein, Egor A MuljarovAbstract:We present two alternative complete sets of static modes of a homogeneous dielectric sphere, for their use in the Resonant-State expansion (RSE), a rigorous perturbative method in electrodynamics. Physically, these modes are needed to correctly describe the static electric field of a charge redistribution within the optical system due to a perturbation of the permittivity. We demonstrate the convergence of the RSE toward the exact result for a perturbation describing a size reduction of the basis sphere. We then revisit the quarter-sphere perturbation treated by Doost et al. [Phys. Rev. A 90, 013834 (2014)], where only a single static mode for each angular momentum was introduced, and show that using a complete set of static modes leads to a small though non-negligible correction of the RSE result, improving the agreement with finite-element simulations. As another example of applying the RSE with a complete set of static modes, we calculate the Resonant States of a dielectric cylinder, also comparing the result with a finite-element simulation.
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Resonant-State expansion for planar photonic-crystal structures.
arXiv: Optics, 2019Co-Authors: Sam Neale, Egor A MuljarovAbstract:We present a new paradigm in the field of photonic crystals and metamaterials, applying the Resonant-State expansion (RSE) to planar photonic-crystal structures. The RSE allows us to understand and quantify optical resonances in photonic-crystal structures in terms of the analytic Resonant States of a homogeneous planar waveguide. The RSE provides an efficient and reliable tool for accurate calculation of a complete set of the Resonant States of a photonic-crystal slab, which is required for the correct description and a better understanding of its optical spectra. For the proof of principle, numerical verification of the RSE, and demonstration of its unprecedented accuracy and convergence, an infinite planar photonic crystal slab periodic in one dimension is taken as an example. To illustrate the power of the present approach, we consider the mode evolution with the amplitude of the periodic modulation, revealing the role of the guided modes in the formation of bound States in the continuum.