CAO Wen-jing，SUN Li-ze-tong，GUO Fu-zhou，SONG Jian-tong，LIU Xiao，CHEN Zhi-hui ，YANG Yi-biao，SUN Fei

（1. Key Laboratory of Advanced Transducer and Intelligent Control System, Ministry of Education and Shanxi Province, Taiyuan 030024, China；2. College of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan 030024, China）

Abstract: The technology of enhancing fluorescence emission can increase the sensitivity of fluorescence detection and the brightness of Light Emitting Diodes (LEDs), and is of great significance in improving the performance of light-emitting devices. Since the metal structure has a good effect in enhancing the local field and fluorescence emission, and the flexible dielectric material has flexible bendability characteristics, on the basis of above, we propose a flexible structure composed of Metal-Dielectric-Metal (MDM) to enhance the fluorescence emission. The influence of the structure on the directional emission enhancement of quantum dots is systematically studied by using the finite difference time domain method. Theoretical calculations show that the local undulations and arcs of the flexible MDM structure can promote fluorescence enhancement and increase the quantum efficiency of the quantum dots located at the center of the structure by about 7 times. They can alao change the refractive index and thickness of the dielectric to achieve the tunability of the target wavelength. At the same time, the experimental results shows that the flexible MDM structure does have a positive effect on the fluorescence enhancement. This discovery is valuable for future display technologies and flexible light-emitting devices. It is of certain guiding significance for the development and application of high-efficiency flexible devices.

Key words: fluorescence enhancement; flexible structure; directional emission; tunable wavelength

1 Introduction

With the well-known advantages such as high sensitivity and adjustable spectrum, fluorescence emission has made rapid development in optical imaging, biosensing, LED display and other fields.In particular, flexible LED has been widely used in display devices (such as foldable mobile phones,curved televisions and flexible e-books), flexible light sources and wearable devices due to its bendability, low structural cost, light weight, convenience and good performance. For example, in 2011,Wang et al. proposed an efficient OLED based on a flexible substrate, achieving an external quantum efficiency of up to 60% for green fluorescence[1]. In 2013, Kim et al. proposed an OLED that could be used in wearable displays and could still have certain stability even with a bending radius of 5 mm after 1 000 bending cycles[2]. In 2020, Shan et al.proposed a wearable and tonable perovskite luminescence/detection fiber with the narrowest luminescence spectrum of ～19 nm, which could simultaneously transmit and receive signals[3].

However, traditional fluorescence emission still has some limitations. For example, the fluorescence dependent on spontaneous photon emission is isotropic in all directions, which means that the fluorescence property is basically independent of the observation direction, resulting in a low quantum yield of fluorescence emission. For the fluorophore with low quantum yield, further enhancing the fluorescence emission can significantly improve the performance of relevant optical system (such as sensing sensitivity, imaging quality, luminance and stability)[4-8]. Therefore, in order to improve the fluorescence emission efficiency in practical applications and meet the miniaturization requirement for modern fluorescence devices, it is very important to control the emission direction in a cost-effective way and convert the original isotropic emission into directional emission. This research has also attracted considerable attention in recent years and is of great value to optical sensors, displays and light-emitting devices[9].

Previous work has proved that the fluorescence coupled with metal nanostructures[10], metal films[4]and photonic crystals[11-12]can enhance directional fluorescence emission. The fluorescence coupled with plasma substrate is enhanced by strong local field enhancement and surface plasmon resonance. The fluorescence coupled with photonic crystals is enhanced due to photonic band structure effect. The radiation of a fluorophore coupled with surface plasma resonance can be enhanced by applying a grating or fishnet structure on the metal layer or using a metal bilayer (silver-gold). In 2014,Jiang et al.[13]designed a subwavelength Ag-PMMA-Ag cavity structure with a 1D-period Ag grating at the top. By using the coupling effect in the structure and changing the dielectric thickness,grating period, groove width and depth and other structural parameters, the Full Width at Half Maximum (FWHM) of the fluorescence emission spectrum of the dye molecule became the narrowest and the fluorescence intensity became the maximum. In 2018, Ren et al.[14]designed and studied the fluorescence emission process of metal-dielectric-metal(MDM) fishnet metasurface structure, using the magnetic plasmons generated by the coupling effect between metal elements and arrays at the nanometer scale to control the wavelength of enhanced fluorescence and achieve the color-controlled wavelength tunability. However, the fabrication process of these structures is more complicated. It is still worth further research to obtain high directional fluorescence emission enhancement based on a simple fabrication process.

The MDM structure can effectively change the fluorescence emission characteristics by changing the quantum yield and directivity of fluorescence emission[15]. For a specific dielectric layer thickness,the coupling of fluorescence with Fabry-Perot cavity can cause fluorescence to be emitted in a direction perpendicular to the MDM structure[4,16]. In 2016, Shiekh et al.[17]proposed a planar MDM structure that used Surface Plasmon Coupled Emission(SPCE) to enhance single-molecule luminescence and increased the peak intensity and power of SPCE. In 2015, Sharmistha et al.[18]designed a planar MDM structure to control the fluorescence wavelength, angle dependence and emission polarization by changing the thickness of metal layer and dielectric medium. However, these structures are planar structures and are not applicable to flexible displays or light-emitting devices. Based on this, it is of great significance to proposing a relatively simple structure that can be applied to flexible displays or light-emitting devices.

Since the planar MDM structure can obtain the fluorescence emission perpendicular to its surface,this paper proposes a flexible MDM structure, in which the interaction between Fabry-Perot cavity and fluorescence can also produce the beam emission perpendicular to the structural surface to enhance the directional transmission of flexible lightemitting devices. In this work, the effects of different structural parameters on the fluorescence emission of quantum dots were studied to obtain the structural parameters that could achieve good coupling. Then, the structural parameters were compared with those of metal-dielectric structure and monolayer metal film structure. The results show that the local undulations and arcs of MDM structure can promote fluorescence enhancement in two ways, namely enhancing the quantum efficiency and obtaining highly directional fluorescence emission.Finally, the applicability of the structure in flexible fluorescence enhancement was verified by experiments.

2 Model and methodology

In order to verify the applicability of flexible MDM structure in flexible light-emitting devices,we proposed a flexible MDM structure, whose 3D front view is shown in Figure 1 (Color online). The minimum internal radius of the structure is defined asR, the thicknesses of the silver film in the upper and lower layers are bothd1, the thickness of the dielectric in the middle layer isd2, and the central angle corresponding to the structure isθ. The complex refractive index of silver comes from Palik Handbook[19], and the fixed refractive index of polyvinyl alcohol (PVA) material is set as 1.52. The geometric center of the dielectric layer in the structure is set as the originO, through which the horizontal axis isxand the vertical axis isy. The whole structure is placed in an air background (n=1).

The Finite Difference Time Domain (FDTD)method was used to simulate the MDM structure and calculate the fluorescence enhancement when the structure was coupled with a dipole light source(which could represent fluorescent molecules or quantum dots). The dipole light source is located at the originO, the simulation region is [x,y]=[?2.1∶2.1,?1.6∶5.0] μm, and the boundary conditions in bothxandydirections are Perfect Matching Layers (PML). One of the important factors affecting the quantum efficiency of fluorescent substances is radiation attenuation rate, which is positively correlated with the quantum efficiency of fluorescent molecules. The higher the radiation attenuation rate is, the higher the quantum yield of fluorescent molecules will be. In order to analyze the influence of MDM structure on fluorescence emission, the Purcell factor F is introduced to quantitatively represent the radiation attenuation rate of fluorescent molecules. Its mathematical definition is shown in Formula (1)[20-21]:

where Γradrepresents the radiation attenuation rate in the presence of the Hexible MDM structure,Pradrepresents the power radiated to the far field in the presence of the Hexible MDM structure, andandrepresent the radiation attenuation rate and the power radiated to the far field respectively in the absence of flexible MDM structure.

3 Results and discussion

3.1 Enhancement of quantum dot emission in different oscillation directions by MDM structure

In a uniform medium, the luminescence of quantum dots is isotropic. Several typical polarization states are usually selected for theoretical analysis. In this paper, we first studied the effect of quantum dots in three polarization states (x,yandz)on the fluorescence emission enhancement of quantum dots in a MDM structure. The minimum internal radius of the MDM structure isR=450 nm,the thickness of Ag film isd1=50 nm, the thickness of dielectric PVA layer is 120 nm, and the central angle corresponding to the structure isθ=60°. The fluorescence enhancement curves of the MDM structure coupled with the quantum dots in different polarization states were obtained by simulation calculation. As can be seen from the power curves shown in Fig. 2(a), the far-field fluorescence emission power of quantum dots in they-polarization state is small and its curve has no significant change, indicating that this structure has little influence on the fluorescence emission of quantum dots in they-polarization state. At the same time, compared with the oscillation of quantum dots in theydirection, the oscillation in thexandzdirections can achieve higher fluorescence enhancement and an obvious fluorescence emission peak. And when the quantum dots are in thex-polarization state, the fluorescence emission peak is the maximum. Because the fluorescence radiation distribution is perpendicular to the MDM structure when the oscilation in thexandzdirections, the interaction between fluorescence and the structure is enhanced. The coupling between fluorescence and structure model has increased the fluorescence power in the far field.In order to more intuitively analyze the physical mechanism of the interaction between the structure and the quantum dots in different polarization states,we obtained the electric field profiles of thex-yplane at 515 nm wavelength in three polarization states, as shown in Figure 2 (b?d) (Color online).

Fig. 1 Schematic diagram of the MDM structure model composed of silver and PVA, in which: the orange area represents the silver film with a thickness of d1;the blue area represents the dielectric PVA with a thickness of d2, the inner radius of the upper silver film is R, and the central angle corresponding to the structure is θ圖1 銀和PVA組成的MDM結(jié)構(gòu)模型示意圖，其中橙色區(qū)域代表銀膜，其厚度為d1；藍色區(qū)域代表電介質(zhì)PVA，其厚度為d2，上層銀膜內(nèi)半徑為R，結(jié)構(gòu)所對應(yīng)圓心角為θ

Fig. 2 (a) Power curves of quantum dots in different polarization states; (b?d) electric field profiles of quantum dots in different polarization states at 515 nm wavelength圖2 （a）不同偏振態(tài)下量子點的功率曲線；（b?d）不同偏振態(tài)的量子點在波長515 nm處的電場分布圖

Fig. 3 Power curves and Purcell factors of quantum dots for the MDM structures with different center angles圖3 在MDM不同圓心角下量子點的功率曲線及珀塞爾因子

It can be seen from the electric field profiles that the far-field electric field can be enhanced by the polarization of the dipole light source in thexandzdirections. Therefore, it can be concluded that when the radiation direction of quantum dots is perpendicular to the MDM structure, the MDM structure will be coupled with fluorescence emission to enhance the directional emission of the quantum dots, and a more obvious fluorescence enhancement effect will be yielded in thex-polarization state.Therefore, in the following research, we will select the quantum dots in thex-polarization state for research and analysis.

3.2 Effects of the MDM structure with different central angles on fluorescence emission

Based on the above study, we know that the MDM structure will produce different fluorescence enhancement effects when coupled with the quantum dots in different polarization states. Next,we study the effect of different arc lengths corresponding to the changing central angle on fluorescence emission. Here, we compared and analyzed the MDM structures with the central angleθranging from 0° to 180°. Seven values were selected with 30° as the step size, and other parameters remained unchanged. The power curves and radiation attenuation rate curves were obtained through numerical simulation, as shown in Figure 3 (Color online). As can be seen from Figure 3(a), compared with the fluorescence emission of quantum dots in the bare light source (corresponding to the central angle of 0°) and in the flexible PVA substrate, the MDM structure demonstrates good far-field fluorescence enhancement effect at different central angles.This finding indicates that the non-planar flexible structure has stable performance in enhancing the fluorescence emission. In addition, when the central angle corresponding to the structure is 60°, the farfield fluorescence peak is the maximum so that the optimal luminescence enhancement effect can be achieved. As can be seen from Figure 3(b), the radiation attenuation rate (Purcell factor) of the MDM structure coupled with fluorescent QDs has a significant peak in the wavelength range of 450?550 nm,indicating that the fluorescence emitted by the dipole light source resonates in the FP cavity of the MDM structure and achieves about 5.3 times of fluorescence enhancement.

3.3 Effects of the MDM structures with different radius on fluorescence emission

Then we analyzed the effect of radius on fluorescence enhancement, which is another factor affecting the arc length. The central angle corresponding to the structure wasθ=60°. The MDM structures with the minimum internal radiusRranging from 350 nm to 750 nm were compared and analyzed. Five values were selected with the step size of 100 nm, and other parameters remained unchanged. The obtained power curves and radiation attenuation rate curves are shown in Fig. 4 (Color online). As can be seen from the power curves in Figure 4(a), compared with the quantum dot emission in the flexible PVA substrate, all the MDM structures have an emission peak in the waveband of 450?550 nm. Compared with the planar structure with an infinite radius, the flexible MDM structure will enhance the far-field fluorescence intensity.When the internal radius of the structure is 450 nm,the power peak value reach the maximum. With the increase of the internal radius, the fluorescence emission peak will be slightly red-shifted, because the structure with a smaller size can be easily coupled with short-wavelength fluorescence emission to achieve fluorescence enhancement. This also indicates that the different bending radians of the MDM structures used in flexible light-emitting devices will slightly affect the wavelength of fluorescence enhancement. This result provides theoretical guidance for the research and development of flexible light-emitting devices based on MDM structures. As can be seen from the radiation attenuation rate curves in Figure 4(b), when the MDM structure is coupled with fluorescent quantum dots, the radiation attenuation rate has an obvious peak; when the structure radius is 450 nm, the radiation attenuation rate reach its maximum.

Fig. 4 Power curves and Purcell factors of quantum dots for the MDM structures with different radii圖4 MDM半徑不同時，量子點的功率曲線及珀塞爾因子

Fig. 5 Luminous power curves of quantum dots for the MDM structures with different dielectric layer thicknesses and refractive indexes圖5 MDM電介質(zhì)層厚度及折射率不同時量子點發(fā)光功率曲線

Fig. 6 Luminous power curves and Purcell factors of quantum dots for the MDM structures with different upper and lower silver film thicknesses圖6 MDM不同上下層銀膜厚度時量子點發(fā)光功率曲線和珀塞爾因子

3.4 Effects of the MDM structures with different dielectric thicknesses and refractive indexes on fluorescence emission

Through the above study, it can be concluded that when the internal radius of the structure is 450 nm, FP cavity mode can be best coupled with quantum dot fluorescence to increase the fluorescence enhancement factor of quantum dots. To explore the specific influence of intermediate dielectric thickness and refractive index variation on the tunability of fluorescence emission wavelength,we first compared and analyzed the MDM structures with intermediate dielectric thicknessd2varying from 100 nm to 140 nm. Six values were selected with 10 nm as the step size. The central angle corresponding to the structure wasθ=60°, and the internal radius of the structure was 450 nm. Other parameters remained the same. As shown in Figure 5(a) (Color online), the fluorescence emission peak of the structure will be red-shifted with the increase of intermediate dielectric layer thickness. The far-field fluorescence emission peak reach its maximum when the dielectric layer thickness is 115 nm.

By using this characteristic, the MDM structures with different dielectric thicknesses can be coupled with different fluorescence emission wavelengths of quantum dots to achieve the flexible tunability of directional emission enhancement of the fluorescence in different target colors. Secondly,we studied the fluorescence emission power when the MDM structures with different dielectric refractive indexes were coupled with quantum dots. The obtained results are shown in Figure 5(b) (Color online). It can be seen that, the change of refractive index of intermediate dielectric layer in the MDM structure has little influence on fluorescence enhancement effect. With the increase of refractive index of the intermediate layer, the fluorescence peak is continuously red-shifted and reduced slightly.

3.5 Effects of the MDM structures with different silver-film thicknesses on fluorescence emission

Through the study of the influence of the above multiple structural parameters on fluorescence emission, it can be concluded that the central angle and internal radius of the structure have a certain influence on the value of fluorescence emission peak,whose position, however, mainly depends on the refractive index and thickness of intermediate dielectric layer of the structure. Next, we studied the effects of different upper and lower silver film thicknesses on fluorescence emission. We compared and analyzed the MDM structures with silver film thicknessd1changing from 20 nm to 60 nm. Five values were selected with the step size of 10 nm, the central angle corresponding to the structure wasθ=60°,the minimum internal radius of the structure was 450 nm, and the thickness of intermediate dielectric layer was 115 nm. Other parameters remained unchanged. The results are shown in Figure 6(Color online). When the thickness of upper and lower silver films is 40 nm and the wavelength is 490 nm, the far-field fluorescence peak reach the maximum.

3.6 Effects of metal and metal-dielectric structures on fluorescence emission

In order to receive highly directional outgoing light from quantum dots, we designed an MDM arc structure with an internal radiusR=450 nm, a central angle 60°, an upper/lower silver film thicknessd1=40 nm and a dielectric layer thicknessd2=115 nm. In order to study the directional fluorescence emission effect of this structure, we comparatively studied the far-field fluorescence-induced electric field distribution of M, MD and MDM are structures at the central wavelength of 490 nm, and obtained the results as shown in Figure 7(a)?7(c)(Color online). It can be found that compared with M and MD nanostructures, the flexible MDM structure can achieve stronger far-field fluorescence enhancement and highly directional emission. The farfield power curves and Purcell enhancement curves of flexible M, MD and MDM structures are shown in Fig. 7(d)?7(e) (Color online). It can be found that compared with flexible M and MD structures, the far-field power of flexible MDM structure is significantly enhanced. As can be seen from Figure 7e,the radiation attenuation rate of MDM structure at 490 nm wavelength increases by a factor of about 7,indicating that the use of this structure can enhance the fluorescence quantum efficiency by a factor of about 7. Compared with M and MD structures, the MDM structure can effectively enhance and directionally modulate the fluorescence emission due to the excellent characteristics of its FP cavity.

Fig. 7 The electric field distribution diagrams, power curves and Purcell factors for quantum dots in metal-dielectric-metal structure, metal-dielectric structure and metal structure at 490 nm wavelength圖7 490 nm波長下，金屬-電介質(zhì)-金屬結(jié)構(gòu)、金屬-電介質(zhì)結(jié)構(gòu)、金屬結(jié)構(gòu)中量子點發(fā)光的電場分布圖、功率曲線和珀塞爾因子

Fig. 8 Far-field fluorescence power curves of (a) two coherent dipole sources and (b) two incoherent dipole sources located at different positions in the MDM structure and flexible PVA substrate圖8 位于MDM結(jié)構(gòu)和柔性PVA基底中不同位置的（a）兩相干光源和（b）兩非相干光源的遠場熒光功率曲線

Fig. 9 Preparation process flow chart of MDM structure圖9 MDM結(jié)構(gòu)制備工藝流程圖

3.7 Effects of adjacent dipole light sources on fluorescence emission

Due to the relatively large structural size of the actual flexible light-emitting devices and the large number of light sources, we considered the influence of two adjacent dipoles on fluorescence emission. By analyzing the influence of the relative position between the two dipole sources in the flexible MDM structure and the flexible PVA substrate on far-field fluorescence emission, their far-field fluorescence power curves were obtained, as shown in Figure 8 (Color online). The power curves of two coherent and two incoherent dipole sources are given in Figure 8(a) and Figure 8(b) respectively. It can be seen that the emission of two dipole sources,either coherent or incoherent, is stronger than that of a single dipole source. With the decrease of the relative position between the two dipole sources, the value of fluorescence emission peak will increase gradually, but its position will remain unchanged.This is because when two adjacent dipole sources are close to each other, the emitted light from the sources will interact with each other in the near field to increase the emission intensity. Secondly, in a flexible PVA substrate, the far-field fluorescence emission of two dipole sources is not affected by their relative position. Compared with the doubledipole emission in a flexible PVA substrate, the double-dipole or single-dipole emission of flexible MDM structure can achieve far-field fluorescence enhancement. This finding is of certain guiding significance to applying the proposed MDM structure in flexible light-emitting devices.

4 Experiment and results analysis

In order to verify that the flexible MDM structure can enhance the luminescence of fluorescent substances, coumarin 6 is selected here as the fluorescent substance for experimental verification. The process for preparing the MDM structure is shown in Figure 9 (Color online). The glass slide was cleaned with alcohol in an ultrasonic cleaner for 15 min. After air-drying, a layer of polydimethylsiloxane (PDMS), which was a transparent flexible medium, was placed on the glass slide. A silver film with a thickness of 40 nm (99.999% purity)was prepared by depositing a silver layer on PDMS through LN-1084SC organometallic vapor deposition system and adjusting the deposition rate(～1.0 nm/min). Then, 100 μm coumarin 6(C20H18N2O2S, MW=350; the central wavelength is 515 nm after the dissolution in alcohol) was mixed with 3% aqueous PVA solution (MW=44.05). The required PVA dielectric layer thickness of 115 nm could be obtained by spin-coating the solution on silver layer at the set speed of 3 000 r/min[22]. Subsequently, a second silver layer (40 nm) was evaporated by vapor deposition on the PVA layer to obtain the MDM structure, as shown in Figure 10.

The sample was placed on the optical microscope platform. The bent MDM structure was observed with an optical microscope. Its bright field image and dark field image under 375 nm laser irradiation are shown in Figure 11 (Color online). It can be seen that the bent MDM has a certain radian, and that the fluorescent material at the focal point emits blue and green light under 375 nm laser irradiation,as observed from the designed MDM structure. The existence of irregular texture on the surface of MDM structure indicates that the evaporation process has a certain influence on the final morphology of MDM structure. Subsequently, a continuous laser with a wavelength of 488 nm was used to irradiate the sample, and the PL of the sample was collected by spectrometer. The collection process of structural PL is shown in Fig. 12.

Fig. 10 MDM structures. (a) planar; (b) curved (top view)圖10 MDM結(jié)構(gòu)。（a）平面；（b）彎曲（俯視圖）

Fig. 11 (a) Bright field image of MDM structure under optical microscope; (b) dark field luminescence image under 375nm laser irradiation圖11 光學顯微鏡下MDM結(jié)構(gòu)的（a）明場圖像；（b）375nm激光照射下的暗場發(fā)光圖像

Fig. 12 PL collection process圖12 PL收集過程

Fig. 13 PL curve obtained from the experiment圖13 實驗所得PL曲線

The PL of coumarin in PVA on PDMS substrate and that of the obtained planar MDM structure and the bent MDM structure were detected. The collected PL curves are shown in Figure 13 (Color online). It can be seen that compared with the quantum dot emission in PVA and planar MDM structure, the flexible curved MDM structure can further enhance the fluorescence emission of quantum dots, which is consistent with theoretical analysis results. In addition, this structure has a relatively wide fluorescence emission spectrum.However, in the experimental process, the mixingratio error of PVA solution will affect the thickness of dielectric layer after spin-coating, and then affect the position of fluorescence emission peak. In addition, the thickness, homogeneity and bending angle of the evaporated Ag film have certain influence on fluorescence enhancement factor.

5 Conclusion

In this paper, a flexible curved MDM structure is proposed. The simulation and experimental results show that this structure can achieve the directional emission enhancement of far-field fluorescence. By using the FDTD method, we systematically studied the effects of different radius central angles, dielectric thicknesses, dielectric refractive indexes and silver film thicknesses on fluorescence enhancement as well as the effects of adjacent dipole sources on fluorescence emission. The results show that the local undulations and arcs of the MDM structure can promote fluorescence enhancement in that they can not only highly modulate the directionality of the outgoing light of quantum dots,but also improve the radiation attenuation rate of quantum dots. In addition, different structure radius and central angles can enhance the far-field fluorescence emission of flexible curved MDM structure and achieve good directionality. The tunability of target wavelength can be achieved by changing the refractive index and thickness of the dielectric layer.Compared with metal structure and metal-dielectric structure, the curved MDM structure has the most significant fluorescence enhancement effect. When the quantum dots are located in the middle of the MDM structure, the high directionality of far-field fluorescence emission can be achieved, and the farfield power enhancement factor can reach about 7.This study verifies the applicability of flexible MDM structure in flexible devices, demonstrating that this structure can be used to enhance the luminescence intensity of flexible light-emitting devices and achieve high-sensitivity fluorescence sensing.

——中文對照版——

1 引 言

熒光發(fā)射具有高靈敏、光譜可調(diào)等眾多優(yōu)勢，已經(jīng)在光學成像、生物傳感、LED顯示等領(lǐng)域取得了飛速發(fā)展。特別是柔性LED由于具有可彎曲、結(jié)構(gòu)成本低、輕薄便捷、性能優(yōu)良等特點，使得其在折疊手機、曲屏電視、柔性電子書等顯示器件、柔性光源和可穿戴設(shè)備等方面具有廣泛的應(yīng)用。例如：2011年，Wang等人提出了一種基于柔性基底的高效OLED，對于綠色熒光實現(xiàn)了高達60%的外量子效率[1]。2013年，Kim等人提出了一種可用于可穿戴顯示器的OLED，在彎曲半徑為5 mm的1 000次循環(huán)彎曲后依然具有一定的穩(wěn)定性[2]。2020年，Shan等人提出了一種可穿戴和可調(diào)色的鈣鈦礦發(fā)光/檢測雙功能光纖，具有最窄的～19 nm的發(fā)光光譜，可以同時發(fā)射和接收信號[3]。

但傳統(tǒng)熒光發(fā)射仍存在一些局限性，比如依賴于光子自發(fā)發(fā)射的熒光在所有方向上均是各向同性的，這也就意味著熒光性質(zhì)基本上與觀測方向無關(guān)，使得熒光發(fā)射的量子產(chǎn)率較低。而對于低量子產(chǎn)率的熒光團，進一步增強熒光發(fā)射可以顯著改善相關(guān)光學系統(tǒng)的性能（例如，傳感靈敏度，成像質(zhì)量和發(fā)光亮度、穩(wěn)定性等）[4-8]。因此為了提高實際應(yīng)用中的熒光發(fā)射效率，滿足現(xiàn)代熒光器件小型化的要求，以一種經(jīng)濟有效的方式控制發(fā)射方向，將原始的各向同性發(fā)射轉(zhuǎn)化為定向發(fā)射是非常重要的。這一研究近年來也引起了相當大的關(guān)注，對于光學傳感器、顯示器和發(fā)光器件有很大的價值[9]。

之前的工作已經(jīng)證明了熒光與金屬納米結(jié)構(gòu)[10]、金屬薄膜[4]、光子晶體[11-12]耦合可使得熒光定向發(fā)射增強。等離子體襯底由于強局域場增強和表面等離子體激元共振而增強熒光；光子晶體則由于光子帶結(jié)構(gòu)效應(yīng)而增強熒光；通過在金屬層上使用光柵、漁網(wǎng)結(jié)構(gòu)或使用銀和金的金屬雙層，可以實現(xiàn)熒光團與表面等離子體共振耦合的輻射增強。例如：2014年，Jiang等人[13]設(shè)計了頂部是1D周期Ag光柵的亞波長Ag-PMMA-Ag腔結(jié)構(gòu)，利用結(jié)構(gòu)中的耦合效應(yīng)，并通過改變介電層厚度、光柵周期、溝槽寬度和深度等結(jié)構(gòu)參數(shù)使得染料分子的熒光發(fā)射光譜的半峰全寬變得最窄、熒光強度最大。2018年，Ren等人[14]設(shè)計研究了金屬-介質(zhì)-金屬（MDM）漁網(wǎng)超表面結(jié)構(gòu)的熒光發(fā)射過程，利用納米尺度的金屬元素與陣列之間的耦合效應(yīng)產(chǎn)生的磁等離子體激元模式來控制增強熒光的波長，實現(xiàn)顏色可控的波長可調(diào)諧性。但這些結(jié)構(gòu)制作工藝都比較復雜?；诤唵蔚闹谱鞴に嚕玫礁叩臒晒舛ㄏ虬l(fā)射增強仍是一個值得繼續(xù)研究的課題。

MDM結(jié)構(gòu)通過改變熒光發(fā)射的量子產(chǎn)率和方向性，可以有效地改變熒光發(fā)射特性[15]。而對于特定的電介質(zhì)層厚度，熒光與法布里-珀羅腔模式的耦合可以使熒光向垂直于MDM結(jié)構(gòu)的方向發(fā)射[4,16]。2016年，Shiekh等人[17]提出了一種MDM平面結(jié)構(gòu)，其使用表面等離子體耦合發(fā)射(SPCE)來增強單分子發(fā)光，提高了SPCE的峰值強度和功率。2015年，Sharmistha等人[18]設(shè)計了MDM平面結(jié)構(gòu)，通過改變金屬層和介質(zhì)厚度來控制熒光波長、角度依賴性和發(fā)射極化。但這些結(jié)構(gòu)都是平面結(jié)構(gòu)，不適合用于柔性顯示或發(fā)光器件。

本文基于平面MDM結(jié)構(gòu)可以使熒光向垂直于其表面發(fā)射的特性，在柔性結(jié)構(gòu)的基礎(chǔ)上，提出了一種MDM柔性結(jié)構(gòu)，該結(jié)構(gòu)中的法布里-珀羅腔模式與熒光相互作用也可以產(chǎn)生垂直于結(jié)構(gòu)表面的光束發(fā)射，有望用于增強柔性發(fā)光器件中的定向發(fā)射。本工作首先研究了不同結(jié)構(gòu)參數(shù)對量子點熒光發(fā)射的影響，得到可實現(xiàn)良好耦合的結(jié)構(gòu)參數(shù)。然后，在此結(jié)構(gòu)參數(shù)下，將其與金屬-電介質(zhì)結(jié)構(gòu)、單層金屬薄膜結(jié)構(gòu)進行了對比。計算結(jié)果表明，MDM結(jié)構(gòu)的局部起伏和弧度對熒光增強起促進作用，不但可以實現(xiàn)量子效率的增強，同時還可以得到高度定向的熒光出射。最后，通過實驗驗證了結(jié)構(gòu)在柔性熒光增強方面的適用性。

2 模型和方法

為了驗證MDM柔性結(jié)構(gòu)在柔性發(fā)光器件中的適用性。本文提出了金屬-電介質(zhì)-金屬（MDM）柔性結(jié)構(gòu)，其三維模型主視圖如圖1（彩圖見期刊電子版）所示。結(jié)構(gòu)的最小內(nèi)半徑定義為R，上下層銀膜厚度均為d1，中間層電介質(zhì)厚度為d2，結(jié)構(gòu)所對應(yīng)的圓心角大小為θ，銀的復折射率參數(shù)來自于Palik手冊[19]，聚乙烯醇（PVA）材料設(shè)為固定折射率1.52。設(shè)定該結(jié)構(gòu)中電介質(zhì)層的幾何中心為原點O，通過原點O沿著水平方向為x軸、豎直方向為y軸。整個結(jié)構(gòu)置于空氣背景（n=1）中。利用時域有限差分方法（FDTD）對該MDM結(jié)構(gòu)進行仿真計算，分析計算了結(jié)構(gòu)和偶極子光源（可代表熒光分子或量子點）耦合時的熒光增強。偶極子光源位于原點O處，仿真區(qū)域為[x，y]=[?2.1∶2.1，?1.6∶5.0] μm，x和y方向的邊界條件都是完美匹配層（PML）。影響熒光物質(zhì)量子效率的重要因素之一是輻射衰減率，而輻射衰減率與熒光分子的量子效率呈正相關(guān)關(guān)系，輻射衰減率越大，熒光分子的量子產(chǎn)率也就越高。為了分析MDM結(jié)構(gòu)對熒光發(fā)射的影響，引入珀塞爾因子F來定量表示熒光分子的輻射衰減率，其數(shù)學定義式如公式（1）所示[20-21]：

式中 Γrad表示柔性MDM結(jié)構(gòu)存在時的輻射衰減率，Prad表示柔性MDM結(jié)構(gòu)存在情況下輻射到遠場的功率，相應(yīng)地，和分別表示柔性MDM結(jié)構(gòu)不存在時的輻射衰減率和輻射到遠場的功率。

3 結(jié)果和討論

3.1 MDM結(jié)構(gòu)對不同振蕩方向量子點發(fā)射的增強

在均勻介質(zhì)中，量子點的發(fā)光是各向同性的。而在理論分析時通常選取幾個典型的偏振態(tài)進行研究。本文中首先研究了量子點處于x，y，z3種不同偏振態(tài)對MDM結(jié)構(gòu)中量子點熒光發(fā)射增強的影響。MDM結(jié)構(gòu)最小內(nèi)半徑R=450 nm，Ag膜厚度d1=50 nm，電介質(zhì)PVA層厚度為120 nm，結(jié)構(gòu)所對應(yīng)的圓心角θ=60°。通過仿真計算得到了MDM結(jié)構(gòu)與不同偏振態(tài)的量子點耦合時的熒光增強曲線。從圖2（a）所示的功率曲線可以發(fā)現(xiàn)：y偏振態(tài)下的量子點的遠場熒光發(fā)射功率較小且其曲線無明顯變化，表明該結(jié)構(gòu)對y偏振態(tài)下的量子點熒光發(fā)射影響不大。同時，相比于量子點在y方向上的振蕩，在x和z方向振蕩時，可以實現(xiàn)較高的熒光增強，并且在x和z方向振蕩時可以觀察到一個明顯的熒光發(fā)射峰。且當量子點處在x偏振態(tài)時，熒光發(fā)射峰值最大。因為在x和z方向振蕩時，熒光輻射分布垂直于MDM結(jié)構(gòu)，熒光與結(jié)構(gòu)的相互作用增強，熒光通過和結(jié)構(gòu)模式的耦合使得遠場熒光功率增強。為了更直觀地分析結(jié)構(gòu)與不同偏振態(tài)下量子點的相互作用物理機制，得到了515 nm波長處x-y平面在3種偏振態(tài)下的電場分布圖，結(jié)果如圖2（b）～2（d）所示。從其電場圖可以看出，偶極子光源在x和z方向偏振下，可使遠場電場得到增強。因此可以得到：當量子點的輻射方向垂直于MDM結(jié)構(gòu)時，MDM結(jié)構(gòu)與熒光發(fā)射耦合，使得量子點的定向發(fā)射得到增強，并且在x偏振態(tài)下得到了更為明顯的熒光增強效果。因此，在接下來的研究中，選擇x偏振的量子點進行分析。

3.2 不同圓心角的MDM結(jié)構(gòu)對熒光發(fā)射的影響

通過上面的研究得知，MDM結(jié)構(gòu)與不同偏振態(tài)量子點耦合時會產(chǎn)生不同的熒光增強效果。接下來將研究圓心角變化所對應(yīng)的不同弧長結(jié)構(gòu)對熒光發(fā)射的影響。這里比較分析了圓心角θ從0°到180°變化的MDM結(jié)構(gòu)，以30°為步長選取了7個值，其他參數(shù)保持不變。通過數(shù)值模擬計算得到了如圖3所示的功率曲線和輻射衰減速率變化曲線。從圖3（a）可以看出，相比于裸光源（對應(yīng)圓心角為0°）和PVA柔性基底中的量子點熒光發(fā)射，MDM結(jié)構(gòu)在不同的圓心角下都有很好的遠場熒光增強效果。這一發(fā)現(xiàn)表明該非平面柔性結(jié)構(gòu)具有穩(wěn)定的熒光發(fā)射增強效果。此外，當結(jié)構(gòu)所對應(yīng)的圓心角大小為60°時，遠場熒光峰值最大，可以達到最優(yōu)的發(fā)光增強效果。從圖3（b）中可以看到，MDM結(jié)構(gòu)和熒光量子點耦合時的輻射衰減率（即珀塞爾因子）在450～550 nm波長范圍內(nèi)有一個明顯的峰值，這表明在MDM結(jié)構(gòu)的FP腔模式下偶極子光源發(fā)射的熒光產(chǎn)生共振，并且實現(xiàn)了約為5.3倍的熒光增強。

3.3 不同半徑的MDM結(jié)構(gòu)對熒光發(fā)射的影響

接著分析了影響弧長的另一因素—半徑，對熒光增強的影響，結(jié)構(gòu)所對應(yīng)的圓心角θ=60°。比較分析了結(jié)構(gòu)最小內(nèi)半徑大小R從350 nm到750 nm變化時的MDM結(jié)構(gòu)，以100 nm為步長選取了5個值，其他參數(shù)保持不變。所得功率曲線和輻射衰減速率如圖4所示。由圖4（a）的功率曲線可以發(fā)現(xiàn)：相對于PVA柔性基底中的量子點發(fā)射，該MDM結(jié)構(gòu)在450～550 nm波段內(nèi)均有一個發(fā)射峰，并且相對于半徑無限大的平面結(jié)構(gòu)，該柔性MDM結(jié)構(gòu)會使得遠場熒光強度增強。當結(jié)構(gòu)內(nèi)半徑為450 nm時，功率峰值最大。隨著結(jié)構(gòu)內(nèi)半徑的增大，熒光發(fā)射峰位有略微紅移，這是因為尺寸較小的結(jié)構(gòu)容易與短波長熒光發(fā)射耦合使熒光增強。這也表明MDM結(jié)構(gòu)在實際應(yīng)用于柔性發(fā)光器件時，不同的彎曲程度會對熒光增強的波長略有影響，為基于MDM結(jié)構(gòu)的柔性發(fā)光器件的研發(fā)提供了一定的理論指導。從圖4（b）輻射衰減率變化曲線可以得到，MDM結(jié)構(gòu)和熒光量子點耦合時，輻射衰減率對應(yīng)出現(xiàn)一個明顯的峰值且當結(jié)構(gòu)半徑為450 nm時輻射衰減率最大。

3.4 不同電介質(zhì)厚度及折射率的MDM結(jié)構(gòu)對熒光發(fā)射的影響

通過以上研究可以得到：當結(jié)構(gòu)內(nèi)半徑為450 nm時，F(xiàn)P腔模式和量子點熒光耦合效果最好，使得量子點的熒光增強倍數(shù)得到提高。為了探究結(jié)構(gòu)中間層電介質(zhì)厚度及折射率變化對熒光發(fā)射波長可調(diào)的具體影響，首先，比較分析了結(jié)構(gòu)中間層電介質(zhì)厚度d2變化的MDM結(jié)構(gòu)，從100 nm到140 nm以10 nm為步長選取了6個值，結(jié)構(gòu)所對應(yīng)圓心角θ=60°，內(nèi)半徑為450 nm，其它參數(shù)保持不變。從圖5（a）所示結(jié)果可以得到：隨著中間電介質(zhì)層厚度的增加，該結(jié)構(gòu)熒光發(fā)射峰紅移，且當電介質(zhì)層厚度為115 nm時，遠場熒光發(fā)射峰值最大。根據(jù)這一特性，可以利用不同中間層電介質(zhì)厚度的MDM結(jié)構(gòu)與量子點的不同熒光發(fā)射波長耦合，達到不同目標顏色熒光定向發(fā)射增強的靈活可調(diào)諧性。其次，研究了不同電介質(zhì)折射率的MDM結(jié)構(gòu)和量子點耦合時的熒光發(fā)射功率，結(jié)果如圖5（b）所示，MDM結(jié)構(gòu)中間電介質(zhì)層折射率發(fā)生變化對熒光增強效果影響不大。隨著結(jié)構(gòu)中間層介質(zhì)折射率的增加，熒光峰值不斷紅移且略有減小。

3.5 不同銀膜厚度的MDM結(jié)構(gòu)對熒光發(fā)射的影響

通過以上多個結(jié)構(gòu)參數(shù)對熒光發(fā)射影響的研究得到：結(jié)構(gòu)所對應(yīng)圓心角大小、內(nèi)半徑這些因素對結(jié)構(gòu)的發(fā)射峰值有一定的影響，而熒光發(fā)射峰位主要取決于結(jié)構(gòu)中間層電介質(zhì)折射率及厚度。接下來研究了不同上下層銀膜厚度的MDM結(jié)構(gòu)對熒光發(fā)射的影響。比較分析了結(jié)構(gòu)上下層銀膜厚度大小d1從20 nm到60 nm變化的MDM結(jié)構(gòu)，以10 nm為步長選取了5個值，結(jié)構(gòu)所對應(yīng)圓心角θ=60°，結(jié)構(gòu)最小內(nèi)半徑為450 nm，中間電介質(zhì)層厚度為115 nm，其他參數(shù)保持不變。所得結(jié)果如圖6所示，當上下層銀膜厚度為40 nm，波長490 nm處遠場熒光峰值最大。

3.6 金屬、金屬-電介質(zhì)結(jié)構(gòu)對熒光發(fā)射的影響

為了實現(xiàn)量子點高定向的出射光，設(shè)計了內(nèi)半徑R=450 nm、圓心角為60°、上下層銀膜厚度d1=40 nm、電介質(zhì)層厚度d2=115 nm的MDM有弧度結(jié)構(gòu)。為了研究該結(jié)構(gòu)的熒光定向發(fā)射效果，對比研究了有弧度的M、MD、MDM結(jié)構(gòu)中心波長490 nm下的遠場熒光電場分布，所得結(jié)果如圖7（a）～7（c）所示?？梢园l(fā)現(xiàn)相比于M和MD納米結(jié)構(gòu)，MDM柔性結(jié)構(gòu)可以實現(xiàn)較強的遠場熒光增強和高度定向發(fā)射。M、MD和MDM柔性結(jié)構(gòu)的遠場功率曲線和珀塞爾增強曲線如圖7（d）～7（e）所示?？梢园l(fā)現(xiàn)相比M和MD柔性結(jié)構(gòu)，MDM柔性結(jié)構(gòu)遠場功率明顯增強。從圖7（e）可以看出，MDM柔性結(jié)構(gòu)在波長490 nm處的輻射衰減率約為7倍，即表明該結(jié)構(gòu)使得熒光量子效率增強倍數(shù)達到7倍左右。相比于M和MD結(jié)構(gòu)，MDM柔性結(jié)構(gòu)由于其FP腔的優(yōu)異特性，可以對熒光的出射進行有效增強和定向調(diào)制。

3.7 相鄰偶極子光源對熒光發(fā)射的影響

由于實際的柔性發(fā)光器件結(jié)構(gòu)尺寸相對較大，所包含發(fā)光源的數(shù)量較多，因此考慮兩個相鄰偶極子對熒光發(fā)射的影響。通過分析位于柔性MDM結(jié)構(gòu)中和柔性PVA基底中的兩個偶極子光源之間的相對位置對遠場熒光發(fā)射的影響，得到了其遠場熒光功率曲線，如圖8所示。其中圖8（a）和圖8（b）分別為兩相干偶極子光源和兩非相干偶極子光源的功率曲線，從中可以看到，無論是兩相干光源還是非相干光源，兩個偶極子光源的發(fā)射均比單個偶極子光源的發(fā)射強，并且，隨著兩個偶極子光源相對位置的減小熒光發(fā)射峰值逐漸增大，但是熒光發(fā)射峰位保持不變。這是因為當兩相鄰偶極子源之間距離較近時，光源的發(fā)射光會在近場相互作用使得發(fā)射強度得到增強。其次，在PVA柔性基底中，兩偶極子光源的遠場熒光發(fā)射不受其相對位置的影響。相對PVA柔性基底中的雙偶極子光源發(fā)射，柔性MDM結(jié)構(gòu)在雙偶極子光源發(fā)射和單偶極子光源發(fā)射的情況下均可實現(xiàn)遠場熒光增強。這一發(fā)現(xiàn)使得本文提出的MDM結(jié)構(gòu)對應(yīng)用于柔性發(fā)光器件有一定的指導意義。

4 實驗制備及結(jié)果分析

為了驗證柔性MDM結(jié)構(gòu)可使得熒光物質(zhì)的發(fā)光增強，這里選取香豆素6作為熒光物質(zhì)進行實驗驗證。制備MDM結(jié)構(gòu)的工藝流程如圖9所示，將玻璃載玻片用酒精在超聲波清洗器中清洗15 min，風干后在玻璃載玻片上放置一層透明柔性介質(zhì)聚二甲基硅氧烷（PDMS）。用LN-1084SC型有機金屬氣相沉積系統(tǒng)在PDMS上沉積銀薄膜，通過調(diào)節(jié)沉積速率（～1.0 nm/min）制備了厚度為40 nm的銀膜（純度99.999%）。然后用100 μM香豆素6（C20H18N2O2S，MW=350，溶于酒精后的中心波長約為515 nm）與濃度約為3%的聚乙烯醇PVA（MW=44.05）水溶液混合，在金屬銀膜表面進行旋涂，設(shè)置轉(zhuǎn)速為3 000 r/min可以獲得所需的約115 nm厚時PVA電介質(zhì)層[22]。隨后在PVA層繼續(xù)使用氣相沉積蒸鍍第二層金屬銀層（40 nm），制備得到的MDM結(jié)構(gòu)如圖10所示。

將樣品置于光學顯微鏡平臺。采用光學顯微鏡觀察彎折后的MDM結(jié)構(gòu)，其明場圖像和375 nm激光照射下的暗場圖像如圖11（彩圖見期刊電子版）所示。從其明場和暗場圖像可以看出經(jīng)彎曲后MDM具有一定弧度，并且在375 nm激光照射下聚焦點處熒光物質(zhì)發(fā)藍綠光，與設(shè)計的MDM結(jié)構(gòu)相似。MDM結(jié)構(gòu)表面存在不規(guī)則紋理, 說明蒸鍍過程對MDM結(jié)構(gòu)的最終形貌有一定影響。隨后，使用波長為488 nm的連續(xù)激光器照射樣品，并通過光譜儀采集樣品的PL，結(jié)構(gòu)PL收集過程如圖12所示。

檢測得到了PDMS基板上PVA中香豆素的PL和所得平面MDM結(jié)構(gòu)及將MDM結(jié)構(gòu)彎曲之后的PL。采集到的PL曲線如圖13（彩圖見期刊電子版）所示，從中可以看出，相對于PVA和平面MDM結(jié)構(gòu)中的量子點發(fā)射，柔性有弧度MDM結(jié)構(gòu)可使得量子點的熒光發(fā)射得到進一步增強，與理論分析結(jié)果一致，并且具有相對較寬的熒光發(fā)射譜。但在實驗過程中，PVA溶液的配比誤差會影響旋涂后電介質(zhì)層的厚度，進而影響熒光發(fā)射峰位。此外，蒸鍍Ag膜的厚度、均勻性以及彎折角度會對熒光增強倍數(shù)有一定的影響。

5 結(jié) 論

本文提出了一種由金屬-電介質(zhì)-金屬組成的MDM柔性有弧度結(jié)構(gòu)，仿真模擬和實驗結(jié)果表明，該結(jié)構(gòu)可以實現(xiàn)遠場熒光的定向發(fā)射增強，通過時域有限差分法系統(tǒng)地研究了該MDM結(jié)構(gòu)的不同半徑、圓心角、電介質(zhì)層厚度和電介質(zhì)層折射率及銀膜厚度對熒光增強的影響，并研究了相鄰偶極子光源對熒光發(fā)射的影響。計算結(jié)果表明MDM結(jié)構(gòu)局部起伏和弧度對熒光增強起促進作用。不但可以對量子點出射光的定向性進行高度調(diào)制，同時可以提高量子點的輻射衰減率。不同結(jié)構(gòu)半徑和圓心角對MDM柔性有弧度結(jié)構(gòu)的遠場熒光發(fā)射都有一定的增強效果并且可以達到好的定向性，而且通過改變電介質(zhì)的折射率和厚度可以實現(xiàn)目標波長的可調(diào)諧性。相比于單層金屬結(jié)構(gòu)和金屬-電介質(zhì)組成的復合結(jié)構(gòu)，該MDM有弧度結(jié)構(gòu)的熒光增強效果最為顯著。當量子點位于MDM結(jié)構(gòu)中間位置時，可以實現(xiàn)遠場熒光發(fā)射的高度定向性，遠場功率增強倍數(shù)達7倍左右。本文工作驗證了MDM柔性結(jié)構(gòu)在柔性器件中的適用性，可用于增強柔性發(fā)光器件發(fā)光強度，也可用于高靈敏度熒光傳感。