When a planar dielectric medium has a permittivity profile that is an analytic function in the upper or lower half of the complex position plane x = x' + ix'' then the real and imaginary parts of its ...permittivity are related by the spatial Kramers-Kronig relations. We find that such a medium will not reflect radiation incident from one side, whatever the angle of incidence. Using the spatial Kramers-Kronig relations, one can derive a real part of a permittivity profile from some given imaginary part (or vice versa) such that the reflection is guaranteed to be zero. This result is valid for both scalar and vector wave theories and may have relevance for designing materials that efficiently absorb radiation or for the creation of a new type of anti-reflection surface.
We propose a design concept for tailoring the local density of optical states (LDOS) in dielectric nanostructures, based on the phase distribution of the scattered optical fields induced by ...point-like emitters. First we demonstrate that the LDOS can be expressed in terms of a coherent summation of constructive and destructive contributions. By using an iterative approach, dielectric nanostructures can be designed to effectively remove the destructive terms. In this way, dielectric Mie resonators, featuring low LDOS for electric dipoles, can be reshaped to enable enhancements of 3 orders of magnitude. To demonstrate the generality of the method, we also design nanocavities that enhance the radiated power of a circular dipole, a quadrupole, and an arbitrary collection of coherent dipoles. Our concept provides a powerful tool for high-performance dielectric resonators and affords fundamental insights into light-matter coupling at the nanoscale.
Deep-inelastic scattering, in the laboratory and on the lattice, is most instructive for understanding how the nucleon is built from quarks and gluons. The long-term goal is to compute the associated ...structure functions from first principles. So far this has been limited to model calculations. In this Letter we propose a new method to compute the structure functions directly from the virtual, all-encompassing Compton amplitude, utilizing the operator product expansion. This overcomes issues of renormalization and operator mixing, which so far have hindered lattice calculations of power corrections and higher moments.
When light propagates through opaque material, the spatial information it holds becomes scrambled, but not necessarily lost. Two classes of techniques have emerged to recover this information: ...methods relying on optical memory effects, and transmission matrix (TM) approaches. Here we develop a general framework describing the nature of memory effects in structures of arbitrary geometry. We show how this framework, when combined with wavefront shaping driven by feedback from a guide-star, enables estimation of the TM of any such system. This highlights that guide-star assisted imaging is possible regardless of the type of memory effect a scatterer exhibits. We apply this concept to multimode fibres (MMFs) and identify a 'quasi-radial' memory effect. This allows the TM of an MMF to be approximated from only one end - an important step for micro-endoscopy. Our work broadens the applications of memory effects to a range of novel imaging and optical communication scenarios.
Abstract Maxwell’s equations and the Dirac equation are the first-order differential relativistic wave equation for electromagnetic waves and electronic waves respectively. Hence, there is a notable ...similarity between these two wave equations, which has been widely researched since the Dirac equation was proposed. In this paper, we show that the Maxwell equations can be written in an exact form of the Dirac equation by representing the four Dirac operators with 8 × 8 matrices. Unlike the ordinary 4 × 4 Dirac equation, both spin–1/2 and spin–1 operators can be derived from the 8 × 8 Dirac equation, manifesting that the 8 × 8 Dirac equation is able to describe both electrons and photons. As a result of the restrictions that the electromagnetic wave is a transverse wave, the photon is a spin–1 particle. The four–current in the Maxwell equations and the mass in the electronic Dirac equation also force the electromagnetic field to transform differently to the electronic field. We use this 8 × 8 representation to find that the Zitterbewegung of the photon is actually the oscillatory part of the Poynting vector, often neglected upon time averaging.
The forward Compton amplitude describes the process of virtual photon scattering from a hadron and provides an essential ingredient for the understanding of hadron structure. As a physical amplitude, ...the Compton tensor naturally includes all target mass corrections and higher twist effects at a fixed virtuality, Q2. By making use of the second-order Feynman-Hellmann theorem, the nucleon Compton tensor is calculated in lattice QCD at an unphysical quark mass across a range of photon momenta 3 ≲ Q2 ≲ 7 GeV2. This allows for the Q2 dependence of the low moments of the nucleon structure functions to be studied in a lattice calculation for the first time. The results demonstrate that a systematic investigation of power corrections and the approach to parton asymptotics is now within reach.
FLAG Review 2019 Aoki, S.; Aoki, Y.; Bečirević, D. ...
The European physical journal. C, Particles and fields,
02/2020, Volume:
80, Issue:
2
Journal Article
Peer reviewed
Open access
We review lattice results related to pion, kaon,
D
-meson,
B
-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More ...specifically, we report on the determination of the light-quark masses, the form factor
f
+
(
0
)
arising in the semileptonic
K
→
π
transition at zero momentum transfer, as well as the decay constant ratio
f
K
/
f
π
and its consequences for the CKM matrix elements
V
us
and
V
ud
. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of
S
U
(
2
)
L
×
S
U
(
2
)
R
and
S
U
(
3
)
L
×
S
U
(
3
)
R
Chiral Perturbation Theory. We review the determination of the
B
K
parameter of neutral kaon mixing as well as the additional four
B
parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for
m
c
and
m
b
as well as those for
D
- and
B
-meson decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant
α
s
. Finally, in this review we have added a new section reviewing results for nucleon matrix elements of the axial, scalar and tensor bilinears, both isovector and flavor diagonal.
We review lattice results related to pion, kaon,
D
- and
B
-meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the ...determination of the light-quark masses, the form factor
f
+
(
0
)
, arising in the semileptonic
K
→
π
transition at zero momentum transfer, as well as the decay constant ratio
f
K
/
f
π
and its consequences for the CKM matrix elements
V
u
s
and
V
u
d
. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of
S
U
(
2
)
L
×
S
U
(
2
)
R
and
S
U
(
3
)
L
×
S
U
(
3
)
R
Chiral Perturbation Theory. We review the determination of the
B
K
parameter of neutral kaon mixing as well as the additional four
B
parameters that arise in theories of physics beyond the Standard Model. The latter quantities are an addition compared to the previous review. For the heavy-quark sector, we provide results for
m
c
and
m
b
(also new compared to the previous review), as well as those for
D
- and
B
-meson-decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. Finally, we review the status of lattice determinations of the strong coupling constant
α
s
.
Accessing hadronic form factors at large momentum transfers has traditionally presented a challenge for lattice QCD simulations. Here, we demonstrate how a novel implementation of the ...Feynman-Hellmann method can be employed to calculate hadronic form factors in lattice QCD at momenta much higher than previously accessible. Our simulations are performed on a single set of gauge configurations with three flavors of degenerate mass quarks corresponding to mπ≈470 MeV. We are able to determine the electromagnetic form factors of the pion and nucleon up to approximately 6 GeV2, with results for the ratio of the electric and magnetic form factors of the proton at our simulated quark mass agreeing well with experimental results.
We experimentally demonstrate a Purcell effect-based design technique for improved impedance matching, and thus enhanced the reflection coefficient from a small microwave emitter. Using an iterative ...process centred on comparing the phase of the radiated field of the emitter in air with that of the emitter in a dielectric environment, we optimise the structure of a dielectric hemisphere above a ground plane surrounding a small monopolar microwave emitter in order to maximise its radiation efficiency. The optimised system shows very strong coupling between the emitter and two omnidirectional radiation modes at 1.99 GHz and 2.84 GHz, yielding Purcell enhancement factors of 1762 and 411 times increase respectively, and near perfect radiation efficiency.
PDF
