Modeling OLED lighting using Monte Carlo ray tracing and rigorous coupling wave analyses

Optics Communications 380 (2016) 394–400

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Optics Communications journal homepage: www.elsevier.com/locate/optcom

Modeling OLED lighting using Monte Carlo ray tracing and rigorous coupling wave analyses An-Chi Wei a,n, Jyh-Rou Sze b a b

Graduate Institute of Energy Engineering, National Central University, Tao-Yuan City 320, Taiwan, ROC Instrument Technology Research Center, National Applied Research Laboratories, Hsinchu City 300, Taiwan, ROC

art ic l e i nf o

a b s t r a c t

Article history: Received 5 February 2016 Received in revised form 7 June 2016 Accepted 14 June 2016

Monte Carlo ray tracing and rigorous coupling wave analyses (RCWA) are linked together for modeling the lighting property of organic light-emitting diodes (OLED). The proposed method considers the thinfilm effect and the whole geometrical structure of OLED instead of a single exciton, realizing a mixedlevel and comprehensive model with reduced simulation complexity. According to experimental results, the proposed model has demonstrated an acceptable accuracy for the conventional planar OLED. Additionally, corrugated OLEDs are investigated for the blue spectrum enhancement. The simulations from the proposed model indicate that the reduced corrugated period or duty cycle contributes to blue-shift of the EL spectra. & 2016 Elsevier B.V. All rights reserved.

Keywords: OLED lighting Monte Carlo ray-tracing Rigorous coupling wave analyses Blue spectrum enhancement Periodic corrugated OLED

1. Introduction Organic light-emitting diodes (OLED) have drawn worldwide attention in recent decades owing to the characteristics of thin size, good color quality, and flexibility [1]. In order to investigate the optical properties of a practical OLED, some approaches, such as selecting an optimum color mixing spectrum [2], high color rendering index (CRI) performance [3–5], dipole transition and the transfer matrix method [6–16], have been developed and demonstrated. One of these approaches combined rigorous electromagnetic simulation techniques and Monte Carlo ray-tracing method, also called mixed-level method, to provide more practical results than those from individual simulation technique alone [17]. Since the mixed-level method included multiple rigorous electromagnetic simulation techniques, such as finite-difference timedomain (FDTD) and rigorous coupled wave analysis (RCWA), the data transformation between these techniques increased the complexity of the model. Thus, an OLED modeling approach exploiting mere RCWA and Monte Carlo ray tracing is proposed and investigated herein to simplify the model. Since RCWA has been widely employed in the literatures for analyzing thin layers, corrugated surfaces and periodic nanostructures [18–21], it is responsible for simulating the radiating TE and TM waves propagating through the layered thin films in the proposed model. As for n

Monte Carlo ray tracing, it has been widely implemented in commercial optical software, such as LightTools, ASAP and TracePro, and can deal with modern lighting problems such as adjustable illumination light field, effective color mixing, and illumination distribution of LEDs [22–26]. Then the Monte Carlo ray tracing is for random sampling the rays herein, starting from the thin films, reflected or refracting in the following geometrical ray paths toward the surrounding environment. Therefore, the proposed method not only inherits the ability of modeling both multilayered effects and geometrically optical characteristics of an OLED but also has the reduced simulation complexity.

2. Principles For a lighting device, one of the most important performance factors is the luminous intensity distribution, which affects the illuminance on the target surface as well as the brightness distribution. According to the basic emission mechanism of OLED, when the electrons and the holes meet within the emissive layer (EML), they recombine and form an exciton. Consequently, the exciton releases its energy by emitting light and returning to the lower energy level. Initially, the light emits in random directions, leading to the uniform luminous intensity distribution in the EML:

I (θo)=Io Corresponding author. E-mail address: [email protected] (A.-C. Wei).

http://dx.doi.org/10.1016/j.optcom.2016.06.040 0030-4018/& 2016 Elsevier B.V. All rights reserved.

(1)

where θo is an angle between a specific ray generated in the EML

A.-C. Wei, J.-R. Sze / Optics Communications 380 (2016) 394–400

Rs(θi ) =

cos θi −

Ni′ 2 − sin2θi

cos θi +

Ni′ 2 − sin2θi

and the normal of the EML surface. Consider the basic structure of a bottom-emitting OLED, or called substrate-emitting OLED [27], as illustrated in Fig. 1. According to the Snell's law, once the rays go through the transparent anode toward the air, refraction or total internal reflection (TIR) may take place, depend on the refractive indexes of media along their paths. Meanwhile, these rays passing through interfaces encounter certain energy decay caused by the Fresnel loss. Thus, the out-coupled luminous intensity distribution for the light emitting in the direction toward transparent anode is submitted to the thin-film theory, the Fresnel equation and the Snell's law:

Ia(θa)=I (θ0)M (θ0)F (θ0)

2

,

−Ni′ 2 cos θi +

R p(θi ) =

Fig. 1. The structure of a bottom-emitting OLED consists of a glass substrate, a transparent anode, organic layers, a metal cathode and passivation. The transparent anode and the metal cathode are usually ITO and Al, respectively.

395

Ni′ 2 cos θi +

Ni′ 2 − sin2θi Ni′ 2 − sin2θi

(4)

where the indexes of s and p denote the TE and TM modes, respectively, and θi can be obtained from the Snell's law with initially θ1 = θ0 . Meanwhile, Ts( θi) and Tp( θi) are the transmittance at that interface for TE and TM modes, respectively: 2

2 cos θi

Ts(θi ) =

,

Ni′ 2 − sin2θi

cos θi +

2

Tp(θi ) =

2Ni′ cos θi Ni′ 2 cos θi +

Ni′ 2 − sin2θi

(5)

The emission of exciton is assumed to be isotropic with the radiation power affected by the TE and TM modes evenly [29]; the transmittance Ti(θi ) and the reflectance Ri(θi ) both include these two orthogonal components with the same weight:

(

)

Ti(θi ) = Ts(θi ) + Tp(θi ) /2

(6)

(2)

(

)

Ri(θi ) = Rs(θi ) + R p(θi ) /2 where θa is an out-coupled angle in the air and calculated from the Snell's law, M (θ0) is modulation resulting from the thin-film layers, and F (θ0) represents synergetic results of the ray propagating in the glass substrate toward the air with the Fresnel equation considered. On the other hand, for the light radiating in the direction toward the metal cathode, the reflective characteristics of metal cathode should be considered. Then the out-coupled luminous intensity distribution for the ray toward metal cathode is:

Ia(θa)=I (θ0)R(θ0)M (θ0)F (θ0)

2

(3)

where R (θ0) is reflectance of the metal cathode in terms of radiation direction, while other parameters are defined as the mentioned ones. Since M(θ0) and R(θ0) in Eqs. (2) and (3) result from transmissive or reflective thin films, including the organic layers, the transparent electrode layer and the metal cathode, they can be calculated by means of the RCWA technique with the radiating wave decomposed as TE and TM modes. Remarkably, the RCWA technique is able to simulate not only the waves propagating through thin and planar layers but also those through the interfaces with one-dimensional or two-dimensional periodic structures. Once M (θ0) and R (θ0) are obtained, they can be characterized as a light source and imported into a Monte Carlo ray-tracing calculator. Along with the whole geometry of the OLED device, the model consisting of the mentioned light source can be built in the calculator. Then the calculator performs the non-sequential ray trace with the consideration of Fresnel equations, implying the calculation of F (θ0). Assume that the materials of all organic layers cause no absorption within the visible band and that the refractive indexes of all organic layers are even. Consider the complex refractive index of material: N = n + κ , where n and κ are the refractive index and the extinction index, respectively. For a ray incident to the ith interface with the incident angle of θi , when the relative complex index of refraction of the two media is assumed as Ni′ = Ni/Ni − 1, and N0 = n0 is the refractive index of organics, the reflectance at that interface can be derived as [28]:

(7)

Afterward, the Fresnel-equation-embedded ray tracing counts the refractive and reflective effects, inferring that F (θ0) is a synthetic result:

Fm(θ0) =

∏

⎡⎣T (θ ) + R (θ )⎤⎦ i, m i i, m i

i = 1 to l

(8)

where l is the maximum number of interfaces which a ray encounters, and m is the number of a ray, which specifies every individual ray. Meanwhile, Ti, m( θi) and Ri, m(θi ) follow the rules:

0 < Ti, m(θi ) + Ri, m(θi ) ≤ 1

Ti, m(θi )⋅Ri, m(θi ) = 0

(9)

(10)

Eq. (10) denotes that every ray path considers mere one direction at the interface. By means of randomly sampling the paths of rays, the Monte Carlo ray-tracing method is able to implement the above calculations and derives numerically representative results for the unpolarized and incoherent light source. From the analyses of the resultant ray data, the far-field intensity distribution Ia(θa ), can be obtained. It is noteworthy that when the Monte Carlo ray-tracing calculator is utilized, it is only suitable for simulating a light source propagating through a medium whose minimum feature size much larger than the wavelength of the light because the light propagation is analyzed by the ray optics instead of wave optics. In this study, the commercial optical simulation tools, GSolver and LightTools are utilized for the

Fig. 2. The concept of proposed model is combining the RCWA and the Monte Carlo ray- tracing techniques for modeling the thin-film characteristics and deriving the far-field performance of an OLED device.

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Fig. 5. Simulated luminous intensity in polar coordinates.

Fig. 3. Schematic of modeling flowchart.

Table 1 Parameters of OLED structure for simulating luminous intensity distribution. Layer

Material

Thickness

Refractive index

Passivation Cathode Organic layers Anode Substrate

Glass Al Organics ITO Glass

0.7 mm 100 nm 185–190 nm 150 nm 1 mm

1.5 0.85 þi6.38 1.78 1.951 þi0.043 1.5

Fig. 6. The fabricated samples are a kind of green phosphorescent OLED device. When the device was operated under 5 V and 40 mA, the averaged central luminous intensity was measured as 1.36 cd via a goniophotometer. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

was used to seal the sample. The emission area of the OLED sample was 10
10 mm2. A primary measurement indicated the peak wavelength of the sample as 521 nm. Such spectral information was incorporated into the proposed model. Other essential dimensional and optical parameters of the sample are listed in Table 1. 3.2. Results and discussions Fig. 4. The modulation ratios resulting from thin films, M (θ0) and M ( θ0)⋅R (θ0) are calculated for waves emitting to every direction. The emission angle is with respect to the normal of the layer interface. For the waves directly passing through transparent thin films, M (θ0) is considered, while for those reflected by the metal then passing through transparent thin films, M ( θ0)⋅R ( θ0) is considered.

RCWA simulation and the Monte Carlo ray tracing, respectively. The modeling concept and the flowchart are illustrated as shown in Figs. 2 and 3, respectively.

3. Model for luminous intensity distribution 3.1. Sample preparation A green bottom-emitting OLED has been fabricated to investigate the model. A glass substrate with the bottom area of 40
40 mm2 was firstly coated with ITO and the ITO was etched for the intended anode pattern. Then the organic layers were evaporated onto the patterned ITO, followed by the evaporation of Al to form the cathode. Finally, the glass passivation with the top area of 30
30 mm2 was allocated above the Al cathode and glue

The nano-scaled thin films, including the organic layers and electrodes, were firstly constructed in the RCWA simulation tool. Because of the close optical characteristics, the multiple organic layers were regarded as one layer. Then the emissive wave was assumed to be generated in that organic layer and decomposed as TE and TM modes. For the waves emitting toward the passivation, the thin-film modulation ratio M (θ0) , representing the transmittance from the organic layer to the glass substrate, was then calculated and averaged for the orthogonal orientations by means of the RCWA technique. On the other hand, since those emissive waves toward the metal cathode encountered a reflective interface, the intensity distribution was additionally influenced by the reflectance R (θ0) of the cathode. After reflected by the metal film, these waves also propagated through the transparent thin films. Therefore, the effects from the metal reflection and thin films were expressed as M ( θ0)⋅R ( θ0), which were also counted via the RCWA technique. The calculated M (θ0)and M ( θ0)⋅R (θ0) for the waves directly passing through transparent thin films and those reflected by the metal then passing through transparent thin films are plotted in Fig. 4, respectively. Such data computed from RCWA were then inputted into the Monte Carlo ray-tracing tool as

A.-C. Wei, J.-R. Sze / Optics Communications 380 (2016) 394–400

Fig. 8. Structure of periodic corrugated OLED in referred literature.

° Fig. 7. Comparison of simulated and experimental luminous intensity distributions. The red squares show the measured luminous intensity distribution, while the green line indicates the one simulated by the proposed model. As references, the blue dash line represents the intensity distribution from a Lambertian source and the error bars indicate the measurement deviation. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

multiple ray sources. The ray-tracing tool incorporated the geometry and the optical characteristics of the glass substrate and the passivation, along with the ray sources, to form an OLED model. To investigate the optical performance of such a device, a virtual farfield receiver was established in the ray-tracing tool. Considering the Fresnel equation at the interfaces, the ray-tracing tool traced the rays until the far-field receiver. By means of calculations and analyses of simulated ray data, the out-coupled intensity Ia(θa ) was obtained, as shown in Fig. 5. From the simulated luminous power accumulated in the far-field receiver, the light extraction efficiency was counted as 18.6%. The OLED sample was lit under 5 V and 40 mA, as shown in Fig. 6. The efficacy was measured as 22.3 lm/W by means of a commercial integration sphere, and the luminous intensity measurement was done by a goniophotometer. The measured luminous intensity distribution is plotted as red squares in Fig. 7, and the simulated data is plotted as the green line in the same graph. The results show that the intensity distribution simulated by the proposed model is close to the measured one. Another blue dash line is the intensity distribution from a Lambertian source as a reference, indicating a curve obeys the Lambert's cosine law. It shows that the Lambertian intensity distribution also fits closely to the measured data. In fact, with regard to the measurement deviation, both the simulated and Lambertian intensity distributions are within the acceptable accuracy as the error bars indicated in Fig. 7. To further improve the simulation accuracy, the proposed model should modify the imprecise input parameters, such as the refractive indexes of the organic layers, requiring further works of measuring the complex refractive index of each layer accurately. Since such index measurement of organic layers with reliable and repeatable results is beyond the scope of this study, the details are not discussed here. Another factor which may be insufficiently precise is the orientation of emitting wave. Although the output power is assumed from TE and TM modes evenly in this study, some literatures reported non-isotropic and predominantly parallel emitter orientation for the OLED emission, and such nonisotropic orientation was demonstrated to increase out-coupling efficiency [30,31]. Therefore, precise measurement of the orientation of OLED emission is also essential for improving the model accuracy. In addition, the proposed model was so far implemented on two separate platforms, one for RCWA and the other for Monte Carlo ray-tracing calculations, requiring the effort of manual data transferring and incurring inefficient simulation speed. A multi-physics platform may be more suitable for performing the proposed OLED modeling with the improved

397

simulation pace.

4. Model for corrugated OLED Although the green, red and blue phosphorescent OLEDs have demonstrated the high efficiency, the life-time of the blue phosphorescent OLED is still incompatible with those of green and red ones [32]. To enhance the performance of the blue OLED, methods involving host engineering for high efficient blue OLEDs, fluorescent and phosphorescent hybrid white organic light-emitting diodes (WOLEDs), and their related techniques have been reported [32–35]. Because of the longer lifetime, blue fluorescent emitters instead of blue phosphorescent emitters have been operated alone or combined with the phosphorescent red and green emitters in such methods and have demonstrated the improved performance. On the other hand, the periodic corrugated OLED has shown the enhancement of electroluminescence (EL) efficiency, because the light trapped in surface plasmon-polariton (SPP) and waveguide (WG) modes have been highly extracted through the structured cavity [36–38]. Then integrating the above techniques by applying the periodic corrugated structure to blue fluorescent emitters brings potential of enhancing both the efficiency and the lifetime of monochromatic blue OLEDs as well as WOLEDs [39]. The operation principle of such periodic corrugated OLEDs is explained as follows. Since the peaks of EL spectra indicate the wavelength regions for extracting SPP and WG modes [36], varying the period of corrugation results in the adjustment of the spectral peaks and brings light extraction for the designated wavelengths [39]. Thus, when a corrugated structure inducing a peak in the blue band is implemented for a blue emitter, the EL efficiency of that blue emitter can be enhanced. On the other hand, when such a corrugated structure bringing a peak in the blue band is applied to a green emitter whose emission spectrum covers that blue band, it contributes to the enhancement of the blue spectrum. Then this second scheme brings an opportunity to enhance a blue spectrum from a green OLED. In consideration of both the lifetime and the efficiency, the former scheme which improves the EL efficiency of blue emitters is specifically suitable for an OLED with a fluorescent blue emitter, while the later scheme which enhances the blue band of a green light source prefers an OLED comprising Table 2 Parameters of periodic corrugated OLED. Layer Passivation Cathode Organic layers Anode substrate

Material Glass Al Organics ITO Glass

Thickness/Corrugated depth a

0.7 mm 100 nm/40 nmb 120 nm/40 nmb 1 mma

Refractive index 1.5 Depend on λ 1.78 Depend on λ

a In RCWA simulation, the passivation and the substrate are assumed to be semi-infinite half spaces. b Parameters refer to the literature [36].

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the phosphorescent green emitter. Consequently, another application example of the proposed modeling method is to investigate candidate variants of the periodic corrugated OLED for enhancing the efficiency of the blue spectrum. 4.1. Device structure Referring to the periodic corrugated OLED demonstrated in the literature [36], we considered the device structure as ITO glass/ Organic layers (120 nm)/Al (100 nm), as illustrated in Fig. 8. The organic and cathode layers were corrugated, while the groove of corrugation was 40 nm in depth, and the duty cycle, defined as the width of groove divided by the period, was fixed as 50%. Such a corrugated structure had been realized via the interferometry ablation followed by the deposition process. According to the literature, when the periodic corrugated structure contributed to the light-coupling, several absorption maxima occurred. Thus, the EL spectrum of the periodic corrugated OLED was counted by its absorption spectrum. Additionally, when the incident light in simulation started from the ITO side, the absorption spectrum was able to be obtained from the complementary calculation of the reflective spectrum. Therefore, the EL spectra of both TE and TM waves were simulated by means of the reflective spectra derived from the proposed modeling approach, while essential factors, including the period and the duty cycle of the corrugated layers, were investigated for the enhancement of blue spectrum.

Fig. 9. Simplified structure of periodic corrugated OLED. The cross-section of the corrugated layers is assumed as rectangular fluctuation, while the duty cycle is defined as the ratio of the width of sunken portion to the period.

4.2. Simulated results The model of periodic corrugated OLEDs was constructed in the RCWA simulation platform according to the parameters listed in Table 2. To facilitate the modeling, the periodic corrugation was assumed as rectangular fluctuation, the period of corrugation was the variable ranging from 100 nm to 400 nm, and the normal incidence was considered, as illustrated in Fig. 9. Since the duty cycle was designated as 50%, the groove was 50 nm to 200 nm in width. In terms of the procedures mentioned in the previous subsection, the TE, TM and their synergetic modes of the model herein were simulated, and their absorption properties were analyzed for the EL spectra, as illustrated in Fig. 10. It shows that for the synergetic mode consisting of evenly TE and TM modes, blue-shift occurs when the period of the corrugation is reduced. Such result agrees with the measurement demonstrated in the literature [36]. Additionally, the corrugation structure which induces an EL maximum close to 800 nm has a harmonic peak around 410 nm, as shown in Fig. 10. It means that such a periodic corrugation structure contributes to enhance the emission from an 800-nm emitter primarily, and a 410-nm emitter secondarily. Although this structure can be applied to enhance the blue spectrum, it shall be noticed that if there is concurrently another emitter with the emitting wavelength close 800 nm, its emission will be also enhanced. Secondly, the duty cycle was examined to investigate its relationship with the blue spectrum. According to the results in Fig. 10, when the period of corrugation was 100 nm, the peak of EL spectrum was closer to the blue wavelength. Therefore, for the duty cycle examination, the period of corrugation was assigned as 100 nm, while the duty cycle ranged from 20% to 80%. Another simulation with the corrugated period of 200 nm and duty cycle of 60% was done for the comparisons. These simulated spectra are depicted in Fig. 11. The results indicate that the reduced duty cycle contributes to blue-shift of the EL spectrum but causes the decreased peak intensity. Meanwhile, modulation of the corrugated period and the duty cycle shows the effect of superposition. Thus, when both the corrugated period and the duty cycle are decreased, the peak of EL spectrum shifts to further low wavelength with its intensity further reduced.

Fig. 10. Simulated EL spectra of referred corrugated OLED under (a) TE mode, (b) TM mode and (c) synergetic mode composed of TE and TM modes evenly. Each curve represents a specific period of corrugation, ranging from 100 nm to 400 nm.

Further, the far-field property of the corrugated OLED was investigated by the proposed method. The period and the duty cycle of a corrugated OLED and the wavelength of emission were assumed as 100 nm, 40% and 480 nm, respectively, while other

A.-C. Wei, J.-R. Sze / Optics Communications 380 (2016) 394–400

Fig. 11. Simulated EL spectra of referred corrugated OLED for various duty cycles under the synergetic mode. The solid and dash lines result from the corrugated period of 100 nm and 200 nm, respectively.

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simulate the lighting property of an OLED device. The RCWA technique and Monte Carlo ray tracing in the model are responsible for calculating the thin-film effect and simulating the geometrically optical characteristics of OLEDs, respectively. Compared to other models in the literatures, the proposed model inherits the merits of a mixed-level modeling and the reduced simulation complexity. For validation of the model, a test sample has been fabricated and simulated. The simulated and experimental results have been compared, while the intensity distribution of an OLED device has been modeled by the proposed technique with acceptable accuracy. In addition to conventional planar structure, the periodic corrugated OLEDs have been investigated to enhance the spectrum of blue fluorescent OLEDs or the blue band of the OLEDs comprising phosphorescent non-blue emitters. According to the calculated results, decreasing the corrugated period or the duty cycle has shown the contribution to blue-shift of EL spectrum but the decrement of the peak intensity. For further improvement of modeling accuracy, the characteristics of every lamination, such as the refractive index, shall be measured precisely. Also, the orientation of OLED emission shall be examined for higher accurate parameters inputted into the model.

Acknowledgments The authors appreciate the partially financial support from the Ministry of Science and Technology, Taiwan under the contract No. MOST 104-3113-E-008-004.

References

Fig. 12. Simulated luminous intensity distribution of presumed corrugated OLED. The period, the duty cycle and the wavelength of emission were set as 100 nm, 40% and 480 nm, respectively. The side faces of glass substrate were assumed as (a) light-absorbed surfaces and (b) transparent surfaces, respectively.

parameters were as listed in Table 2. The simulated results show that when the side faces of glass substrate are equivalent to lightabsorbed surfaces, the luminous intensity distribution is close to Lambertian distribution, as shown in Fig. 12(a). Such case may occur when the OLED sample is installed into a package frame and the result agrees with the measurement in the literature [40]. On the other hand, when these sides are bare, equivalent to transparent surfaces, the light coupling out from these sides enhances the luminous intensities in the angles larger than the critical angle, leading to a broadened distribution in polar coordinates, as shown in Fig. 12(b).

5. Conclusions In conclusion, an OLED modeling technique has been proposed in this paper by means of the combination of rigorous coupled wave analysis (RCWA) and Monte Carlo ray- tracing techniques to

[1] C.W. Tang, S.A. VanSlyke, Appl. Phys. Lett. 51 (1987) 913. [2] L.-Y. Chen, S.-H. Chen, C.-T. Kuo, H.-C. Wang, Org. Electron. 15 (2014) 2194. [3] G.J. Zhou, Q. Wang, C.L. Ho, W.Y. Wong, D.G. Ma, L.X. Wang, Chem. Commun. (2009) 3574. [4] G.J. Zhou, Q. Wang, X.Z. Wang, C.L. Ho, W.Y. Wong, D.G. Ma, L.X. Wang, Z.Y. Lin, J. Mater. Chem. 20 (2010) 7472. [5] B.H. Zhang, G.P. Tan, C.S. Lam, B. Yao, C.L. Ho, L.H. Liu, Z.Y. Xie, W.Y. Wong, J. Q. Ding, L.X. Wang, Adv. Mater. 24 (2012) 1873. [6] M. Flämmich, M.C. Gather, N. Danz, D. Michaelis, A.H. Bräuer, K. Meerholz, A. Tünnermann, Org. Electron. 11 (2010) 1039. [7] S. Nowy, B.C. Krummacher, J. Frischeisen, N.A. Reinke, W. Brütting, J. Appl. Phys. 104 (2008) 123109. [8] B. Ruhstaller, T. Flatz, M. Moos, G. Sartoris, M. Kiy, T. Beierlein, R. Kern, C. Winnewisser, R. Pretot, N. Chebotareva, P. Schaaf, SID Symposium Digest of Technical Papers 38, 2007, pp. 1686. [9] M.-H. Lu, J.C. Sturm, J. Appl. Phys. 91 (2002) 595. [10] H. Riel, S. Karg, T. Beierlein, W. Rieß, K. Neyts, J. Appl. Phys. 94 (2003) 5290. [11] W.L. Barnes, J. Mod. Opt. 45 (1998) 661. [12] H. Benisty, R. Stanley, M. Mayer, J. Opt. Soc. Am. A 15 (1998) 1192. [13] W. Lukosz, J. Opt. Soc. Am. 71 (1981) 774. [14] R.R. Chance, A.H. Miller, A. Prock, R. Silbey, J. Chem. Phys. 63 (1975) 1589. [15] C.C. Katsidis, D.I. Siapkas, Appl. Opt. 41 (2002) 3978. [16] B. Ruhstaller, T. Beierlein, H. Riel, S. Karg, J.C. Scott, W. Riess, IEEE J. Sel. Top. Quantum Electron. 9 (2003) 723. [17] M. Bahl, G.R. Zhoub, E. Hellera, W. Cassarlyb, M. Jianga, R. Scarmozzinoa, G. G. Gregory, Proc. SPIE 9190 (2014) 919009. [18] G.L. Fillmore, R.F. Tynan, J. Opt. Soc. Am. 61 (1971) 199. [19] X.D. Hoa, M. Tabrizian, A.G. Kirk, J. Sensors 2009 (2009) 713641. [20] W. Lee, D. Kim, J. Opt. Soc. Am. A 29 (2012) 1367. [21] K.H. Yoon, M.L. Shuler, S.J. Kim, Opt. Express 14 (2006) 4842. [22] Y.-S. Chen, C.-Yi Lin, C.-M. Yeh, C.-T. Kuo, C.-W. Hsu, H.-C. Wang, Opt. Express 22 (2014) 5183. [23] H.-C. Wang, Y.-T. Chiang, C.-Y. Lin, M.-Y. Lu, M.K. Lee, S.-W. Feng, C.-T. Kuo, Opt. Express 24 (2016) 4411. [24] C.H. Tsuei, J.W. Pen, W.S. Sun, Opt. Express 16 (2008) 18692. [25] Y.C. Lo, J.Y. Cai, M.S. Tasi, Z.Y. Tasi, C.C. Sun, Opt. Express 22 (2014) A365. [26] X.H. Lee, I. Moreno, C.C. Sun, Opt. Express 21 (2013) 10612. [27] L.H. Smith, J.A.E. Wasey, W.L. Barnes, Appl. Phys. Lett. 84 (2004) 2986. [28] G.R. Fowles, Introduction to Modern Optics, Dover Publications, New York 1989, pp. 38–46. [29] Z. Huang, C.C. Lin, D.G. Deppe, IEEE J. Quantum Electron. 29 (1993) 2940. [30] M. Flämmich, J. Frischeisen, D.S. Setz, D. Michaelis, B.C. Krummacher, T. D. Schmidt, W. Brütting, N. Danz, Org. Electron. 12 (2011) 1663. [31] T.D. Schmidt, D.S. Setz, M. Flämmich, J. Frischeisen, D. Michaelis, B.

400

A.-C. Wei, J.-R. Sze / Optics Communications 380 (2016) 394–400

C. Krummacher, N. Danz, W. Brütting, Appl. Phys. Lett. 99 (2011) 163302. [32] W. Song, I. Lee, J.Y. Lee, Adv. Mater. 27 (2015) 4358. [33] J. Zhang, D. Ding, Y. Wei, H. Xu, Chem. Sci. 7 (2016) 2870. [34] X.L. Li, X. Ouyang, M. Liu, Z. Ge, J. Peng, Y. Caoa, S.J. Su, J. Mater. Chem. C 3 (2015) 9233. [35] Y.H. Lee, B.K. Ju, W.S. Jeon, J.H. Kwon, O.O. Park, J.W. Yu, B.D. Chin, Synth. Met. 159 (2009) 325. [36] Y. Bai, J. Feng, Y.F. Liu, J.F. Song, J. Simonen, Y. Jin, Q.D. Chen, J. Zi, H.B. Sun, Org. Electron. 12 (2011) 1927.

[37] T. Schwab, C. Fuchs, R. Scholz, A. Zakhidov, K. Leo, M.C. Gather, Opt. Express 22 (2014) 7524. [38] Y. Bai, Y. Fan, Q. Lu, X. Wang, M. Chu, X. Liu, Appl. Phys. Express 8 (2015) 022102. [39] Y.G. Bi, J. Feng, Y.F. Li, X.L. Zhang, Y.F. Liu, Y. Jin, H.B. Sun, Adv. Mater. 25 (2013) 6969. [40] Y.-F. Liu, J. Feng, Y.-G. Bi, J.-F. Song, Y. Jin, Y. Bai, Q.-D. Chen, H.-B. Sun, Opt. Lett. 37 (2012) 124.