Longitudinal Polarization States Research Articles

Manipulation of Longitudinally Inhomogeneous Polarization States Empowered by All‐Silicon Metasurfaces

AbstractPolarization plays a key role in fundamental science, and manipulating the evolutionary trends of longitudinal polarization states can provide new implements for light–matter interaction. However, existing 3D optical devices can only manipulate the polarization conversion in a single transverse plane. Recently, methods to control polarization by cascading bulky optical systems are miniaturized using metasurfaces. Nevertheless, it is quite challenging to generate focused beams with vectorial properties for metasurfaces carrying inhomogeneous polarization profiles. Here, a single‐layer all‐silicon metasurface operating in the terahertz (THz) band is demonstrated to address all those aforementioned challenges in one go, and pencil‐like beams with inhomogeneous polarization profiles can be imparted along the propagation direction. The introduction of a latitudinal polarization control factor representing the initial phase difference enables near‐even manipulation of the evolutionary trend of the longitudinal polarization state according to the extended focal depth. By manipulating the topological charges within two orthogonal circularly polarized channels to accomplish coherent superposition, a focused vortex beam with vectorial properties can be generated in desired planes. Two functional demonstrations based on this approach are established experimentally, offering promising opportunities for structured light on meta‐optics.

Generation of Nondiffracting Vector Beams with Ring-Shaped Plasmonic Metasurfaces

Optical nondiffracting vector beams, with their invariant transverse profiles and longitudinal polarization states, have drawn interest in many areas, from optical tweezers to imaging and metrology, but bulky optical components still limit their utilization. The authors design ultrathin, ring-shaped plasmonic metasurfaces to produce nondiffracting Bessel, Mathieu, and Weber vector beams across a broad wavelength range. These metasurfaces present a compact, effective platform for producing complex optical beams, and thus for advancing numerous applications related to conversion of spin and orbital angular momentum, optical manipulation, and optical communication.

Effect of deviation from purely transverse and longitudinal polarization states of acoustic waves on the anisotropy of acousto-optic figure of merit: the case of Tl3AsS4 crystals.

We analyze the effect of acoustic wave (AW) polarization states deviation from purely longitudinal and transverse on the anisotropy of the acousto-optic (AO) figure of merit for the case of AO interactions occurring in the principal crystallographic planes. In particular, we obtain phenomenological relations that describe the effective elasto-optic coefficient for the six types of AO interactions, which exhaust all of the possible isotropic AO diffractions. These relations are compared for the alternative cases when the deviations of polarization of the AWs from purely longitudinal and transverse ones are either taken into consideration or completely neglected. Our analysis carried out on the example of Tl3AsS4 crystals reveals that the deviation of AW polarization from its pure states influences the anisotropy of the AO figure of merit only when the AO interactions with quasi-transverse AWs are dealt with. This fact is caused by the peculiar acoustic and elasto-optic properties of Tl3AsS4. On the other hand, the situation can become different for other crystalline materials, where the angular dependences of the AO figure of merit can differ significantly in cases in which the deviation angle increases. This holds true for the AO interactions with both quasi-transverse and quasi-longitudinal AWs. Under these conditions, non-orthogonality of the AWs (or deviation from their longitudinal polarization states) affects essentially the AO characteristics. Finally, we determine the geometries of AO interactions for which the highest AO figures of merit are reached for the Tl3AsS4 crystals.

Quantization of the electromagnetic field at the presence of two dielectric slabs and application to the Casimir effect

The three dimensional formalism of the Green function method of the electro-magnetic field quantization is extended to quantize the electromagnetic field, at the presence of two dispersive and dissipative dielectric slabs. It is shown that the system decomposes into a singlet and a doublet parts. The singlet system corresponds to the normal polarization state of the electric field and the doublet system corresponds to the sum of parallel and longitudinal polarization states. Each part is quantized separately and vector potential operator of the each part is derived in terms of rightward and leftwards annihilation and creation operators. By using the assuming commutation properties of the noise current density, the equal time canonical commutation relations between the vector potential operator and its conjugate generalized momentum are verified for each part. Finally as an application, the explicit form of field operators are used to obtain an expression for the Casimir force between the two slabs via Maxwell stress tensor.

Study ofB¯d,s⁎0→Dd,s+M-Decays with QCD Factorization Approach

Motivated by theb-physics experiments at running LHC and upcoming SuperKEKB/Belle-II, the nonleptonicB¯q⁎0→Dq+M-(q=d,sandM=π,K,ρ,K⁎) weak decays are studied within QCD factorization framework. The observables of these decay modes are first predicted. It is found that the tree-dominated and CKM-favoredB¯q⁎0→Dq+ρ-decays have the largest branching fractions~O(10-8)and thus are hopefully to be measured. TheB¯q⁎0→Dq+V-decays are dominated by the longitudinal polarization states. In addition, associating with the relevantBmeson decays, some interesting phenomena and relations are discussed in detail; for example,RB≡B(B¯q→Dq⁎P)/B(B¯q⁎→DqP)≃3τB/τB⁎, andfL,∥(B¯q→Dq⁎V)≃fL,∥(B¯q⁎→DqV).

Study of NonleptonicBq∗→DqVandPqD∗Weak Decays

Motivated by the powerful capability of measurement for thebhadron decays at LHC and SuperKEKB/Belle-II, the nonleptonicB-∗→DD-∗,Dρ-,DK∗-,πD∗, andKD∗decays are studied. With the amplitudes calculated with factorization approach and the form factors evaluated with the BSW model, branching fractions and polarization fractions are firstly presented. Numerically, the CKM-favoredB-q∗→DqDs∗-andDqρ-decays have branching fractions ~10−8, which should be sought for with priority and firstly observed by LHC and Belle-II. TheB-q∗→DqK∗andDqρdecays are dominated by the longitudinal polarization states, while the parallel polarization fractions ofB-q∗→DqD-∗decays are comparable with the longitudinal ones; numerically,f∥+fL≃95% andfL:f∥≃5:4. Some comparisons betweenB-q∗0→DqVand their correspondingB-q0→Dq∗Vdecays are performed, and the relationfL,∥(B-∗0→DV)≃fL,∥(B-0→D∗V)is found. With the implication ofSU(3)flavor symmetry, the ratiosRduandRdsare discussed and suggested to be verified experimentally.

Erratum: Branching ratios and polarization inB→VV,VA,AAdecays [Phys. Rev. D78, 094001 (2008)

We present a detailed study of charmless two-body B decays into final states involving two vector mesons (VV) or two axial-vector mesons (AA) or one vector and one axial-vector meson (VA), within the framework of QCD factorization, where $A$ is either a $^3P_1$ or $^1P_1$ axial-vector meson. The main results are as follows. (i) In the presence of NLO nonfactorizable corrections, effective Wilson coefficients $a_i^h$ are helicity dependent. For some penguin-dominated modes, the constructive (destructive) interference in the negative-helicity (longitudinal-helicity) amplitude of the $B\to VV$ decay will render the former comparable to the latter and push up the transverse polarization. (ii) In QCD factorization, the transverse polarization fraction can be large for penguin-dominated charmless $VV$ modes by allowing for sizable penguin annihilation contributions. (iii) Using the measured $\bar K^{*0}\rho^-$ channel as an input, we predict the branching ratios and polarization fractions for other $\ov B\to \bar K^*\rho$ decays. (iv) The smallness of the axial-vector decay constant of the $^1P_1$ axial vector meson can be tested by measuring various $b_1\rho$ modes to see if $\Gamma(\bar B^0\to b_1^-\rho^+)\ll \Gamma(\bar B^0\to b_1^+\rho^-)$ and $\Gamma(B^-\to b_1^-\rho^0)\ll \Gamma(B^-\to b_1^0\rho^-)$. (v) For the penguin-dominated modes $a_1K^*$ and $b_1K^*$, it is found that the former are dominated by transverse polarization amplitudes, whereas the latter are governed by longitudinal polarization states.

Branching ratios and polarization inB→VV,VA,AAdecays

We present a detailed study of charmless two-body $B$ decays into final states involving two vector mesons ($VV$) or two axial-vector mesons ($AA$) or one vector and one axial-vector meson ($VA$), within the framework of QCD factorization, where $A$ is either a $^{3}P_{1}$ or $^{1}P_{1}$ axial-vector meson. The main results are as follows. (i) In the presence of next-to-leading-order nonfactorizable corrections, effective Wilson coefficients ${a}_{i}^{h}$ are helicity-dependent. For some penguin-dominated modes, the constructive (destructive) interference in the negative-helicity (longitudinal-helicity) amplitude of the $\overline{B}\ensuremath{\rightarrow}VV$ decay will render the former comparable to the latter and push up the transverse polarization. (ii) In QCD factorization, the transverse polarization fraction can be large for penguin-dominated charmless $VV$ modes by allowing for sizable penguin-annihilation contributions. (iii) Using the measured ${\overline{K}}^{*0}{\ensuremath{\rho}}^{\ensuremath{-}}$ channel as an input, we predict the branching ratios and polarization fractions for other $\overline{B}\ensuremath{\rightarrow}{\overline{K}}^{*}\ensuremath{\rho}$ decays. (iv) The smallness of the axial-vector decay constant of the $^{1}P_{1}$ axial-vector meson can be tested by measuring various ${b}_{1}\ensuremath{\rho}$ modes to see if $\ensuremath{\Gamma}({\overline{B}}^{0}\ensuremath{\rightarrow}{b}_{1}^{\ensuremath{-}}{\ensuremath{\rho}}^{+})\ensuremath{\ll}\ensuremath{\Gamma}({\overline{B}}^{0}\ensuremath{\rightarrow}{b}_{1}^{+}{\ensuremath{\rho}}^{\ensuremath{-}})$ and $\ensuremath{\Gamma}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{b}_{1}^{\ensuremath{-}}{\ensuremath{\rho}}^{0})\ensuremath{\ll}\ensuremath{\Gamma}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{b}_{1}^{0}{\ensuremath{\rho}}^{\ensuremath{-}})$. (v) For the penguin-dominated modes ${a}_{1}{K}^{*}$ and ${b}_{1}{K}^{*}$, it is found that the former are dominated by transverse polarization amplitudes, whereas the latter are governed by longitudinal polarization states. (vi) The rates of $B\ensuremath{\rightarrow}{K}_{1}(1270){K}^{*}$ and ${K}_{1}(1400){K}^{*}$ are generally very small. The decay modes ${K}_{1}^{\ensuremath{-}}{K}^{*+}$ and ${K}_{1}^{+}{K}^{*\ensuremath{-}}$ are of particular interest as they are the only $AV$ modes which receive contributions solely from weak annihilation. (vii) For tree-dominated $B\ensuremath{\rightarrow}AA$ decays, the ${a}_{1}^{+}{a}_{1}^{\ensuremath{-}}$, ${a}_{1}^{\ensuremath{-}}{a}_{1}^{0}$, ${a}_{1}^{\ensuremath{-}}{b}_{1}^{+}$, ${a}_{1}^{\ensuremath{-}}{b}_{1}^{0}$, ${b}_{1}^{+}{\ensuremath{\rho}}^{\ensuremath{-}}$ and ${b}_{1}^{0}{\ensuremath{\rho}}^{\ensuremath{-}}$ modes have sizable branching ratios, of order $(20--40)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. (viii) There are many penguin-dominated $B\ensuremath{\rightarrow}AA$ decays within the reach of $B$ factories: ${K}_{1}(1270)({a}_{1},{b}_{1}^{\ifmmode\pm\else\textpm\fi{}})$, ${K}_{1}(1400)({b}_{1},{a}_{1}^{\ifmmode\pm\else\textpm\fi{}})$, ${K}_{1}(1270)({f}_{1}(1285),{f}_{1}(1420))$ and ${K}_{1}(1400)({f}_{1}(1420),{h}_{1}(1170))$.

ZZγandZγγcouplings at lineare+e−collider energies with the effects ofZpolarization and initial state radiation

The constraints on the neutral gauge boson couplings, $ZZ\gamma$ and $Z\gamma\gamma$, are investigated at linear $e^{+}e^{-}$ collider energies through the $Z\gamma$ production with longitudinal and transverse polarization states of the final Z boson. Because of high energy of linear electron- positron beams, initial state radiation (ISR) considerably changes the production cross section. We obtain an increase in the cross section by a factor of 2-3 due to ISR for transverse polarization and by a factor of 10-100 for longitudinal polarization states depending on the energy. We find the 95% C.L. limits on the CP conserving form factors $h_{3}^{Z}$, $h_{4}^{Z}$, $h_{3}^{\gamma}$ and $h_{4}^{\gamma}$ with integrated luminosity 500$fb^{-1}$ and $\sqrt{s}=$0.5, 1, 1.5 TeV energies. It is shown that the longitudinal polarization of the Z boson, together with ISR, can improve sensitivities by factors 2-3.

Vector meson dominance predictions for single pion electroproduction

Predictions for π + electroproduction are obtained by using vector meson dominance to continue the pion photoproduction amplitudes to spacelike values of the virtual photon mass. The continuation is performed by formulating vector dominance in terms of invariant rather than helicity amplitudes, and the longitudinal polarization states of the virtual photon are given in terms of the photoproduction invariant amplitudes. Previous vector dominance predictions for electroproduction from vector meson production have encountered difficulty with the sign of the longitudinal-transverse interference term in the cross section. In the present model, however, the structure of this term is explained naturally in terms of the kinematical k 2 dependence of the longitudinal amplitudes, and excellent agreement with all the data is obtained. These results complete the unified description of vector meson production, pion photoproduction, and pion electroproduction in terms of a covariant vector meson dominance model.