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Here we demonstrate the control of magnetic dipole spontaneous emission at yellow light by polarization-independent hexagonally arrayed nanorods magnetic metamaterials. By embedding a magnetic dipole into a polarization-independent magnetic metamaterial consisting of hexagonal arrays of paired silver nanorods, the radiative emission enhancement and the Purcell factor around 590 nm have been dramatically increased 44 times for a significant general far-field emission enhancement and 57 times for a maximum general magnetic dipole near-field emission enhancement, respectively. Moreover, the polarization-independent enhancements are found to be a robust variation of the dipole’s positions and structure geometries, showing nice fabrication tolerance for practical applications.
© 2016 Optical Society of America
1. Introduction
In the past decade, some remarkable progresses have been obtained in the point-source emission enhancement, giving its high impacts on a range of applications such as nanolasers [1, 2], signals detection [3], and single-photon sources [4]. As the spontaneous emission rate is proportional to the photon local density of states [5], the main research on the Purcell factor and the radiative emission enhancement is focused on the control of electric dipole transition with micro- and nano-structures such as photonic crystals [6, 7], reflecting surfaces [8, 9], microcavities [10], and waveguides [11]. Very recently, due to the possibility of forming highly localized electric field, which is also well known as “hot spots”, plasmonic structures [12] have also been used to improve the dipole spontaneous emission.
In order to the control of electric dipole emission, the enhancement of magnetic dipole decay rate has provided a new way to enhance the spontaneous emission and has quickly gained considerable research attention in the past decade. Karaveli and Zia showed that magnetic dipole far-field emission can be increased 4 times in front of a gold mirror via the inhibition of electric dipole emission [13]. Soon after, Rolly et al. proposed theoretically that the magnetic dipole emission at 1.54 um can be enhanced 90 times through the lossless Mie resonances of silicon particles surrounded by trivalent erbium ions [14]. Later Albella et al. demonstrated that by coupling the emitting molecule to the gap between the dielectric particles, both electric dipole and magnetic dipole have high performance of radiative emission and quantum efficiency during the visible to near-infrared range [15]. In 2011 year, similar to the electric resonance hot spots, Feng et al. showed and numerically verified that the magnetic dipole radiative emission at 1.55 um can be increased around 360 times in an ideal single magnetic plasmonic structure [16]. Most of the previous reports are focused on the near-infrared wavelength range. Some of them can be extended to visible light range. In 2014 year, Lu et al. implemented two types of 1D grating with triangular and rectangular profile, obtaining a 10 times radiative enhancement at visible frequencies [17]. However, their radiative enhancement factors are only around ten, which is not too much different from microsized photonic structures. Recently, Hu et al. have proposed a magnetic metamaterial consisting of arrays of paired silver strips to control the spontaneous emission at visible range [18]. But the radiative enhancement is still polarization-dependent. Therefore, it is interesting to explore the possibility of polarization-independent dramatic enhancement of magnetic dipole emission at visible light range.
Owing to the self-organized hexagonal arrays of uniform parallel nanochannels, anodic aluminum oxide (AAO) film has been widely used as the template for nanoarray growth [19–22]. Many distinctive discoveries have been made in the nanosystems fabricated in AAO films [23–27]. As increasing emphasis is placed on low cost, high throughput, and ease of production, AAO template assisted nanoarray synthesis is becoming the method of choice for the fabrication of nanoarrays [28]. Here we study the control of magnetic dipole transition in a magnetic metamaterial, which consists of hexagonal arrays of paired silver nanorods. The corresponding magnetic resonance locates at the yellow light range around 590 nm. By embedding magnetic dipole into a polarization-independent magnetic metamaterial consisting of hexagonal arrays of paired silver nanorods, the radiative emission enhancement and the Purcell factor around 590 nm have been dramatically increased to 44 times for a significant general far-field emission enhancement and 57 times for a maximum general magnetic dipole near-field emission enhancement, respectively. Our numerical simulations also show that the polarization-independent enhancement of magnetic dipole emission is quite robust regardless of the spatial and spectral changes.
2. Polarization-independent optical nanorod metamaterials characterizations
Firstly, Feng et al. [16] simply used an ideal single model as the magnetic plasmonic structure, which is not practical for structure fabrication. Secondly, the conventional rare earth dopant Eu3+ has two main transitions 5D0→7F1 (magnetic dipole transition) and 5D0→7F2 (electric dipole transition) with emission wavelengths around 590 nm and 620 nm respectively [29, 30]. Taking above issues into consideration, we design the following nanorod structure, which can enhance the emission of magnetic dipoles and create strong magnetic resonance at 590 nm. The schematic picture of polarization-independent magnetic metamaterial consisting of hexagonal arrays of paired silver nanorods is depicted in Fig. 1(a). The red rectangle exhibits a simulation unit in simulations. It consists of arrays of paired thin silver nanorods on a glass substrate. The diameter and periodicity of paired thin silver nanorods are set at D = 91 nm and p = 182 nm respectively. The periodic arrangement can guarantee the plasmonic mode to scatter to the far-field. Figure 1(b) illustrates the cross-section of the paired silver nanorods. An alumina spacer with thickness of d = 30 nm is sandwiched by a pair of thin silver nanorods with same thickness of t = 30 nm. The alumina layers serve as the host of the dipoles in our simulation, and the pairs of silver create magnetic and electric resonances. These parameters are designed to obtain quite strong magnetic response in the alumina spacer. Considering the fabrication stability, two thin alumina layers with 10 nm thickness are added upon and underneath the silver pair.
Fig. 1 (a) Solid pattern and (b) cross-sectional schematic of the nanorod structure. The black areas, violet areas and blue areas represent alumina, silver and glass substrate respectively.
The magnetism in a grating structure has been extensively studied in [31–33]. To characterize the magnetic response and “hot spot” created inside alumina spacer, we calculated the reflection spectrum, transmission spectrum and magnetic field enhancement by 3D simulation using commercial finite element software (COMSOL Multiphysics). The material properties of silver, alumina and the glass substrate are the same as the parameters used in [31]. In visible light range, Tx polarization incident light (see Fig. 1(b)) is that E is along x-direction, Ty polarization incident light (see Fig. 1(b)) is that E is along y-direction. The results are shown in Fig. 2(a) and 2(b), where two transmission spectrum dips can be observed around 450 nm and 585 nm under Tx polarization incident light and Ty polarization incident light respectively.
Fig. 2 The reflection spectrum (dash line), transmission spectrum (dot line) and F|H|2 (solid line) as a function of wavelength under Tx polarization incident light. (a) and Ty polarization incident light(b), 3D view of magnetic field distribution around the magnetic resonance of 1/4 paired silver nanorods under Tx polarization incident light (c) and Ty polarization incident light (d), 2D xoz (e) plane and yoz plane (g) view of the electric displacement and magnetic field distribution around the magnetic resonance of 1/4 paired silver nanorods under Tx polarization incident light, 2D xoz (f) plane and yoz plane (h) view of the electric displacement and magnetic field distribution around the magnetic resonance of 1/4 paired silver nanorods under Ty polarization incident light.
Similar to previous reports [18], these two resonances correspond to the electrical resonance and magnetic resonance respectively. Then “hot spots” with electric and magneticfields localized in the spacer can be formed around these two resonances. In general, compared with the predominately one-directional electric displacement around the electric resonance, a closed loop of electric displacement at magnetic resonance can form quite strong artificial magnetism inside it. Thus we will focus on the magnetic resonance around 590 nm in this study. Figure 2(c) shows the 3D view of magneticfield distribution around the magnetic resonance of 1/4 paired silver nanorods under Tx polarization incident light. Figures 2(e) and 2(g) shows the 2D xoz plane and yoz plane view of the electric displacement and magneticfield distribution around the magnetic resonance of 1/4 paired silver nanorods under Tx polarization incident light. We can see that the currents flowing in the upper and lower silver nanorods are anti-symmetric and thus form a closed loop. And a magnetic hot spot can be observed inside the alumina spacer. Figure 2(d) shows the 3D view of magneticfield distribution around the magnetic resonance of 1/4 paired silver nanorods under Ty polarization incident light. Figures 2(f) and 2(h) shows the 2D xoz plane and yoz plane view of the electric displacement and magneticfield distribution around the magnetic resonance of 1/4 paired silver nanorods under Ty polarization incident light. We can also see that the currents flowing in the upper and lower silver naorods are anti-symmetric and thus form a closed loop. And a magnetic hot spot can be observed inside the alumina spacer.
Taking the center point O of the nanorod in Fig. 2(c) and 2(d) as an example, we have studied the dependence of |H|2 enhancement factor (F|H|2) on the wavelength under Tx polarization incident light and Ty polarization incident light respectively. The result is summarized as solid line in Fig. 2(a) and 2(b). We can still see two peaks of enhancement around 410 nm and 590 nm under Tx polarization incident light and Ty polarization incident light respectively. Consistent with our expectation, the enhancement factor at the magnetic resonance is much higher than that around electric resonance. The maxima value around 590 nm can be as high as 78 times under Tx polarization incident light and 78 times under Ty polarization incident light, which relates to the strong magnetic coupling caused by polarization-independent paired silver nanorods. This value is even comparable to that of the metamagnetism structures working in near-infrared wavelength range, where metal loss is much smaller [16]. Most importantly, this nanorod structure with hexagonal arrays (see in Fig. 1(a)) can ensure that the magnetic resonance can cover large amounts of magnetic dipole in the spacer layers. Therefore, we confirm that the arrays of paired thin silver nanorods is polarization-independent and can be good candidates to control the magnetic dipole transition at visible light range.
3. Magnetic dipole inside the polarization-independent sandwich nanorod structure
According to Fermi's golden rule, the relationship between spontaneous emission decay rate (γ) and local density of states (ρm) of a magnetic light emitter located at γ0 with transition frequency ω 0 and magnetic dipole moment m can be expressed as the following equations [34]:
where nm is the unit vector in magnetic dipole direction, is the magnetic Green function, is the reduced Planck constant, is the permittivity of the vacuum and c is vacuum speed of light respectively. Hence the spontaneous emission decay rate γ of magnetic dipole is determined by the partial local density of states, which can be increased by highly localized magnetic field. As the paired thin silver nanorods exhibit magnetic resonance and localize magnetic field in the narrow gap, the structure has the strength to enhance magnetic dipole transitions. By embedding a magnetic light emitter within the sandwich nanorods with appropriate orientation and location, the magnetic resonance of the structure can modify the local environment of the emitter to achieve huge local density of states, leading to a great enhancement of spontaneous emission rate.Here we use two factors, namely the Purcell factor (Fp) and radiative emission enhancement factor (RE), to represent the magnetic dipole emission change at near-field and far-field domain respectively. Fp is defined as the ratio between the total decay rate in structure (γ) and the spontaneous emission rate in free space without structure (γ0) and RE is equal to the ratio between the radiative decay rate (γr) and γ0. For the structure with power loss, the total decay rate is usually divided into γr and nonradiative decay rate (γnr). Therefore, Fp and RE can be expressed as the following equations:
where Pr is the power that radiates into the far-field, Pabs is the power absorbed by metal, and P0 is the power in free space without the nanorod structure.In order to calculate the emitter-plasmonic coupling in the nanorods accurately, we design the structure according to Fig. 1 in 3D simulation. In the simulation a single magnetic dipole emitter is placed at the O point in Fig. 2(c) and 2(d) with the dipole moment direction parallel to x-axis and y-axis respectively. In this 3D simulation Pabs is the ohmic loss of the Ag nanorods. Pr and P0 are the out flowing energy along z-axis at the far field with and without nanorod structure. Figure 3(a) shows Fpx and REx as a function of wavelength with the dipole moment direction parallel to x-axis. The maximum REx reaches near 67 times around 590 nm, which is consistent with the strongest magnetic resonance wavelength in Fig. 2(b). Meanwhile, we can see that both the central wavelength and the full-width half max (FWHM) of REx are very similar to the enhancement of |H|2 in Fig. 2(b). Figure 3(b) shows Fpy and REy as a function of wavelength with the dipole moment direction parallel to y-axis. The maximum REy reaches near 66 times around 590 nm, which is also consistent with the strongest magnetic resonance wavelength in Fig. 2(a). Meanwhile, we can also see that both the central wavelength and the full-width half max (FWHM) of REy are very similar to the enhancement of |H|2 in Fig. 2(a). All these information confirm the relation between significant enhancement of spontaneous emission and the magnetic resonance.
Fig. 3 Fp (circles in red solid line) and RE(circles in black solid line) for the magnetic dipole at various wavelengths with the dipole moment direction parallel to x-axis (a) and y-axis (b) respectively.
Taking the orientation into consideration, the general radiative enhancement for random orientation magnetic dipole is the average value of the radiative enhancement of magnetic dipoles with their dipole moment parallel to x, y, z axes, respectively. Due to no strong magnetic resonance can be formed in the structure when the magnetic dipole moment is along z-axis, which means that the general radiative enhancement and near field enhancement is nearly (REx + REy)/3 and (Fpx + Fpy)/3 respectively. Thus, the general radiative enhancement can get the maximum value over 44 times around 590 nm, which could not be realized by other previous researches. On the other hand, the general near field enhancement Fp can reach nearly 57 times at 590 nm in Fig. 3. The simulation results have also been verified by experimental results reported recently [17], demonstrating that at the resonant wavelength, due to strong electric or magnetic resonance dipole radiation can be greatly improved.
4. Magnetic dipoles sensitivity to spatial position and spectral misfit
From Fig. 2(c) and 2(d), the magnetic field distribution in the alumina spacer is anisotropic. Hence the enhancement of magnetic dipole emission is expected to be different at different positions. Figures 4(a), 4(c), and 4(e) presents the dependence of Fpx and REx versus magnetic dipole's positions along x, y, and z axes, respectively. When the magnetic dipole moves from spacer's center point O to the structure edges along x and y axes, the corresponding emission enhancement factors gradually decrease from the maxima values (see Fig. 4(a) and 4(c)). Such kind of trend can be confirmed by the electric displacement intensity and magnetic field distribution in Fig. 2(g) and 2(h). REx can reach more than 25 times for a wide position range along x and y axes unless the magnetic dipole is very close to the boundary. On the other hand, the magnetic resonance enhancement is more robust in z direction. In Fig. 4(e), when magnetic dipole moves along z-axis, Fpx and REx are very stable and maintain at values around 86 times and 67 times respectively. While contrary to the minimum value occurred near the structure in Fig. 4(a), the maximum Fpx and REx reach 113 times and 87 times exactly at the spacer's z-orientation edges, where the strongest electric displacement intensity happens.
Fig. 4 Fpx (circles in red solid line), REx (circles in black solid line) as a function of position a long x-axis (a), y-axis (c) and z-axis (e) at 590 nm. Fpy (circles in red solid line), REy (circles in black solid line) as a function of position a long x-axis (b), y-axis (d) and z-axis (f) at 590 nm. positive value of a and b mean the magnetic dipole is located on the right side of O along x-axis, and negative (positive) value of c means the magnetic dipole is located on the down (up) side of O along z -axis in Fig. 2 (c) and (d).
Figures 4(b), 4(d), and 4(f) present the dependence of Fpy and REy versus magnetic dipole's positions along x, y, and z axes respectively. When the magnetic dipole moves from spacer's center point O to the structure edges along x and y axes, the corresponding emission enhancement factors also gradually decrease from the maxima values (see Figs. 4(b) and 4(d)). Such kind of trend can be confirmed by the electric displacement intensity and magnetic field distribution in Fig. 2(e) and 2(f). REy can also reach more than 25 times for a wide position range along x and y axes unless the magnetic dipole is very close to the boundary. On the other hand, the magnetic resonance enhancement is also more robust in z direction. In Fig. 4(f), when magnetic dipole moves along z-axis, Fpy and REy are very stable and maintain at values around 86 times and 66 times respectively. While contrary to the minimum value occurred near the structure in Fig. 4(b), the maximum Fpy and REy reach 114 times and 88 times exactly at the spacer's z-orientation edges, where the strongest electric displacement intensity happens.
Due to the fabrication limitation, the cross-sectional schematic of the structure in experiment actually is trapezoidal owing to an angular deviation (θ) depicted in the insert of Fig. 5(a) and 5(b), instead of rectangle depicted in Fig. 1(b). This diameter nonuniformity would lead to variation of resonance wavelength, which can change the coupling between magnetic dipole and magnetic resonance. Figure 5(a) shows the dependence of Fpx and REx on angular deviation (θ) with the central diameter of alumina spacer (D) unchanged. The curve denotes that the magnetic dipole emission enhancement decreases when the fabrication deviation becomes larger. But the coupling is still robust with enhancement of radiative and total emission over 31 times and 37 times even under 30° angular deviation. Figure 5(b) shows the dependence of Fpy and REy on angular deviation (θ) with the central diameter of alumina spacer (D) unchanged. The curve denotes that the magnetic dipole emission enhancement also decreases when the fabrication deviation becomes larger. But the coupling is still robust with enhancement of radiative and total emission over 32 times and 37 times even under 30° angular deviation.
Fig. 5 Fp (circles in red solid line) and RE (circles in black dashed line) at 590 nm as a function of angular deviation (θ) with the dipole moment direction parallel to x-axis (a) and y-axis (b) respectively. The insert is the trapezoidal cross-sectional schematic of structure.
In Fig. 6 we plot the dependence of the magnetic resonance wavelength (λres) on the average diameter (D) of the paired nanorod samples. By tuning the diameter of the nanorods with the coverage ratio of rods constant (50%), the magnetic resonance wavelengths cover broad visible spectrum from 450 nm to 750 nm. As depicted in Fig. 6(a) and 6(b) the magnetic resonance wavelength and the relevant magnetic resonance keeps a linear enhancement relationship with the diameter increment, which denotes that the magnetic resonance becomes stronger at longer wavelength. In [16], there is a width threshold beyond which the radiative enhancement drops down due to the interactive effect between the metal loss and magnetic field enhancement. However, both Fp and RE in our structure keep the same variation trend with F| H |2, which manifests that the strong influence of magnetic resonance is always the dominated factor on magnetic dipole radiative emission compared with the metal energy loss from 450 nm to 750 nm. Moreover, RE stays over a value of 65 times ranging from 570 nm to 610 nm, which provides significant applications for magnetic dipole transitions enhancement in the yellow light spectrum.
Fig. 6 Fp (red dot line), RE (black dot line), |H|2 (red solid line) and λres (black solid line) as a function of nanorod diameter with the dipole moment direction parallel to x-axis (a) and y-axis (b) respectively.
5. Conclusion
In summary, we have polarization-independent sandwiched nanorod metamaterials to enhance the spontaneous emission of magnetic dipole transition around 590 nm. A maximum general magnetic dipole near-field emission enhancement of 57 times and a significant general far-field emission enhancement of 44 times are attained near the interface between the metal and dielectric layer regardless of the strong metal absorption in visible spectrum. Meanwhile, the magnetic dipole emission enhancement shows low sensitivity to the space position change, magnetic dipole orientation and resonance mismatch. The variation of the structure geometry modulates the resonance and emission enhancement over the visible spectrum range. Therefore, the coupled nanorods structure can serve as a general building block to produce high magnetic field enhancement for managing magnetic dipole transition at visible spectrum.
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