Modifying magnetic dipole spontaneous emission with nanophotonic structures

Tailoring of electromagnetic spontaneous emission predicted by E. M. Purcell more than 50 years ago has undoubtedly proven to be one of the most important effects in the rich areas of quantum optics and nanophotonics. Although during the past decades the research in this field has been focused on electric dipole emission, the recent progress in nanofabrication and study of magnetic quantum emitters, such as rare‐earth ions, has stimulated the investigation of the magnetic side of spontaneous emission. Here, we review the state‐of‐the‐art advances in the field of spontaneous emission enhancement of magnetic dipole quantum emitters with the use of various nanophotonics systems. We provide the general theory describing the Purcell effect of magnetic emitters, overview realizations of specific nanophotonics structures allowing for the enhanced magnetic dipole spontaneous emission, and give an outlook on the challenges in this field, which remain open to future research.

     

Electric and magnetic dipole couplings in split ring resonator metamaterials

In this paper, the electric and the magnetic dipole couplings between the outer and the inner rings of a single split ring resonator (SRR) are investigated. We numerically demonstrate that the magnetic resonance frequency can be substantially modified by changing the couplings of the electric and magnetic dipoles, and give a theoretical expression of the magnetic resonance frequency. The results in this work are expected to be conducive to a deeper understanding of the SRR and other similar metamaterials, and provide new guidance for complex metamaterials design with a tailored electromagnetic response.     

Near-field thermal emission from metamaterials

A closed form expression for the local density of electromagnetic states (LDOS) due to a thermally emitting metamaterial bulk is derived from Maxwell's equations combined with fluctuational electrodynamics. The final form is the same as that for nonmagnetic materials, where the influence of the magnetic permeability is embedded in the Fresnel reflection coefficients. Spectral distributions of LDOS near metallic- and dielectric-based metamaterials are investigated. Results reveal that LDOS profiles are dominated by surface polaritons (SPs) in both TE and TM polarization states. A detailed discussion is provided on the necessary conditions for exciting TM- and TE-polarized SPs via a dispersion relation analysis that accounts for losses. Beyond the conventional conditions for excitation of SPs, the lossy dispersion relation analysis demonstrates mathematically that SPs exist when the imaginary parts of the permittivity or permeability, as well as n′n″, are close to zero, where n′ and n″ are the real and imaginary parts of the refractive index, respectively. An asymptotic expression for the extreme near field LDOS is derived, showing a Δ^?3 power law relationship, as for nonmagnetic media, between LDOS and distance from the emitting bulk Δ. Results obtained from this study will assist in assessing material properties of arbitrarily electromagnetic materials in applications related to energy harvesting.     

Strong enhancement of magnetic dipole emission in a multilevel electronic system

The Purcell effect is commonly used to increase light emission by enhancing the radiative decay of electric dipole transitions. In this Letter, we demonstrate that the opposite effect, namely, the inhibition of electric dipole transitions, can be used to strongly enhance light emission via magnetic dipole transitions. Specifically, by exploiting the differing symmetries of competitive electric and magnetic dipole transitions in trivalent europium, we demonstrate a fourfold enhancement of the far-field emission from the (5)D(0)→(7)F(1) magnetic dipole transition in trivalent europium. We show that this strong enhancement is well predicted by a three-level model that couples the individual Purcell enhancement factors of competitive transitions from the same excited state.     

Spectral tuning by selective enhancement of electric and magnetic dipole emission

We demonstrate that magnetic dipole transitions provide an additional degree of freedom for engineering emission spectra. Without the need for a high-quality optical cavity, we show how a simple gold mirror can strongly tune the emission of trivalent europium. We exploit the differing field symmetries of electric and magnetic dipoles to selectively direct the majority of emission through each of three major transitions (centered at 590, 620, and 700 nm), and present a model that accurately predicts this tuning from the local electric and magnetic density of optical states.     

Controlling magnetic dipole transition with magnetic plasmonic structures

A plasmonic structure with double gold patches is proposed for enhancing the spontaneous emission of a magnetic dipole transition through a magnetic hot area. A Purcell factor of nearly 2000 can be obtained at optical frequencies together with a low sensitivity in spatial and spectral mismatches between the light emitter and the resonance mode. The associated resonance can be tuned from the visible to the IR frequencies, enabling efficient control of forbidden transitions using plasmonic structures.     

Spontaneous emission enhancement in metal-dielectric metamaterials

We study the spontaneous emission of a dipole emitter imbedded into a layered metal-dielectric metamaterial. We demonstrate ultra-high values of the Purcell factor in such structures due to a high density of states with hyperbolic isofrequency surfaces. We reveal that the traditional effective-medium approach greatly underestimates the value of the Purcell factor due to the presence of an effective nonlocality, and we present an analytical model which agrees well with numerical calculations.     

Moving finite-size dipole emission

Emission of a finite-size arbitrarily moving dipole is considered. It is shown that the dipole radiation intensity can be expressed in terms of the dipole moment of the system for wavelengths longer than the dipole size. In this case, the system radiation intensity is much lower than that of the unit charge. For wavelengths much shorter than the dipole size, the dipole radiation intensity is equal to the sum of radiation intensities of two charges. For wavelengths comparable to the dipole size, interference minima and maxima arise in the angular distribution of the radiation intensity.     

具有电与磁非线性效应超常介质中光束的聚焦特性

基于Drude模型,采用解析法与数值模拟法研究了具有电与磁非线性效应超常介质中光束的聚焦特性。结果表明超常材料中光束聚焦现象不但可以发生在自聚焦非线性介质中（正折射区）而且可以发生在自散焦非线性介质中（负折射区）,且光束中心频率离介质的等离子频率越近,其聚焦效应越明显。特别是当电与磁非线性极化率为异号时,超常介质的非线性符号可以通过调控电与磁等离子频率的相对大小控制,这为主动操控光束的传输提供一种新的自由度。     

Waves in magnetic metamaterials with strong coupling of elements

The properties of magnetic metamaterials composed of microresonators have been studied. Coupling of meta-atoms induces magnetoinductive waves, which determine the features of propagation of electromagnetic radiation in metamaterials. The complication of the coupling mechanism due to the radiation when the element sizes decrease as frequencies tend to optical ones is discussed.     

具有电与磁非线性效应超常介质中光束的聚焦特性

基于Drude模型,采用解析法与数值模拟法研究了具有电与磁非线性效应超常介质中光束的聚焦特性。结果表明超常材料中光束聚焦现象不但可以发生在自聚焦非线性介质中(正折射区)而且可以发生在自散焦非线性介质中(负折射区),且光束中心频率离介质的等离子频率越近,其聚焦效应越明显。特别是当电与磁非线性极化率为异号时,超常介质的非线性符号可以通过调控电与磁等离子频率的相对大小控制,这为主动操控光束的传输提供一种新的自由度。     

Surface waves guided by magnetic metamaterials

We consider electromagnetic waves guided by slabs of anisotropic resonant magnetic metamaterials in free space and in metal waveguides. It is shown that wave propagation is possible in a waveguide below cutoff with an insert of such a metamaterial. The dependence of the dispersion properties of waves on the geometric sizes of the insert and the waveguide are studied. The obtained results can be used for miniaturization of electrodynamic systems. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 7, pp. 618–625, July 2006.     

Knotted solitons in nonlinear magnetic metamaterials

We demonstrate that nonlinear magnetic metamaterials comprised of a lattice of weakly coupled split-ring resonators driven by an external electromagnetic field may support entirely new classes of spatially localized modes--knotted solitons, which are stable self-localized dissipative structures in the form of closed knotted chains. We demonstrate different topological types of stable knots for the subcritical coupling between resonators and instability-induced breaking of the chains for the supercritical coupling.     

Discrete breathers in nonlinear magnetic metamaterials

Magnetic metamaterials composed of split-ring resonators or U-type elements may exhibit discreteness effects in THz and optical frequencies due to weak coupling. We consider a model one-dimensional metamaterial formed by a discrete array of nonlinear split-ring resonators where each ring interacts with its nearest neighbors. On-site nonlinearity and weak coupling among the individual array elements result in the appearance of discrete breather excitations or intrinsic localized modes, both in the energy-conserved and the dissipative system. We analyze discrete single and multibreather excitations, as well as a special breather configuration forming a magnetization domain wall and investigate their mobility and the magnetic properties their presence induces in the system.     

Effect of metallic and hyperbolic metamaterial surfaces on electric and magnetic dipole emission transitions

Spontaneous emission patterns of electric and magnetic dipoles on different metallic surfaces and a hyperbolic metamaterial (HMM) surface were simulated using the dyadic Green’s function technique. The theoretical approach was verified by experimental results obtained by measuring angular-dependent emission spectra of europium ions on top of different films. The results show the modified behavior of electric and magnetic dipoles on metallic and HMM surfaces. The results of numerical calculations agree well with experimental data.     

A massive magnetic dipole

A solution of the Einstein-Maxwell equations representing a massive magnetic dipole is investigated. Problems of its physical interpretation are discussed and test particle motion is studied.     

Manipulating electromagnetic wave with the magnetic surface plasmon based metamaterials

In this work, we have investigated the optical properties of the magnetic metamaterials (MMs) consisting of periodically/randomly arranged ferrite rods. By calculating the photonic band diagrams and transmittance, we have identified a photonic band gap originating from the magnetic surface plasmon (MSP) resonance. In addition, by tuning the external magnetic field (EMF), an MM slab can be used as an optical switch. Our simulated results also suggest that the optical properties of the MMs are robust against the position disorder and the size fluctuation of the ferrite rods. Moreover, by examining the relation between the transmittance and the EMF, we can optimize the EMF to realize the best switching effect. With the retrieved effective constitutive parameters ε _eff and μ _eff obtained from the effective-medium theory, the optimal EMF can be understood in a more clear manner.     

Circular dichroism of planar chiral magnetic metamaterials

We propose, fabricate, and study a double-layer chiral planar metamaterial that exhibits pronounced circular dichroism at near-infrared wavelengths. The antisymmetric oscillation modes of the two coupled layers allow local magnetic-dipole moments and enhanced polarization effects compared with similar single-layer systems where only electric-dipole moments occur. Experiment and rigorous theoretical calculations are in good agreement.     

Line positions and strengths of magnetic dipole transitions of molecular oxygen from stratospheric emission spectra

Submillimeter emission spectra of the low stratosphere (24.5 km) between 30 and 110 cm^-1 have been used to determine line positions and strengths for many of the lines originating in magnetic dipole transitions of the homonuclear molecule O₂. Observed line positions are shown to be in excellent agreement with recently derived theoretical values. Line strengths for these lines, many of which have never been measured in the laboratory, have also been obtained from these spectra. Measurements were made by utilizing the equivalent blackbody envelope defined by the peaks of heavily saturated H₂O lines throughout the spectrum to determine equivalent widths from the O₂ lines. The resulting line strengths are found to be significantly higher than values calculated on the basis of recent theoretical work and, for those lines for which a comparison is possible, higher than previously obtained laboratory determinations. This general feature of the present data is vital not only for the establishment of basic molecular parameters for O₂, but also for the application of recent methods for H₂O and O₃ stratospheric concentration determination in which O₂ lines are used as an internal calibration of the balloon-borne instrumentation.