- Email: [email protected]
Top-emitting organic light-emitting device with weak viewing angle-dependence
Journal of Luminescence 131 (2011) 2419–2421
Contents lists available at ScienceDirect
Journal of Luminescence journal homepage: www.elsevier.com/locate/jlumin
Top-emitting organic light-emitting device with weak viewing angle-dependence Zhijun Wu n, Jiaxian Wang College of Information Science and Engineering, Huaqiao University, Quanzhou 362011, PR China
a r t i c l e i n f o
abstract
Article history: Received 13 April 2011 Received in revised form 7 June 2011 Accepted 9 June 2011 Available online 15 June 2011
In this study, a top-emitting organic light-emitting device (TEOLED) with high efficiency and near angle-independence was fabricated on silicon substrate. The blue-shift of the resonant wavelength (RW) with increasing view angles was nearly negligible. The theoretical simulation was described by a model based on the Fabry–Perot microcavity structure. The maximum current efficiency of the fabricated device is 11.5 cd/A at 12 V. & 2011 Elsevier B.V. All rights reserved.
Keywords: Microcavity Optical simulation Angle-independence
1. Introduction
2. Experimental details
Top-emitting organic light-emitting devices (TEOLEDs) are demanded for active-matrix organic light-emitting devices (AMOLEDs) fabricated on crystalline silicon substrate owing to the advantages of high-aperture-ratio, high efficiency and high pixel resolution. A typical TEOLED consists of a reflective bottom anode, a semitransparent top cathode and organic layers sandwiched in between. Metals with high reflectance, For example Ag [1], Au [2] and Mo [3], and some semitransparent thin metal films, such as Al/Ag [4], Sm [5] and Ca/Ag [6], are commonly used as anodes and cathodes, respectively, in TEOLEDs. . Top-emitting device with such structure demonstrates relatively strong microcavity effects, which offers various advantages for display applications such as color saturation and efficiency enhancement; however, this structure also suffers large color variation with viewing angles [7]. Quite a few OLED publications had focused on the improvement and optimization of emission characteristics of TEOLEDs [8–10]. More recently, microlens arrays or diffusers have been integrated on the top cathode to optimize the output efficiency and angular dependence [11,12]. however, it complicated the fabrication process. In this paper, a TEOLED with high efficiency, highly saturated color and weak angular dependence is realized without complicating the fabrication process by precisely controlling the resonant wavelength.
The device was built on a 1600-nm-SiO2-coated silicon substrate precoated with 70-nm-thick Ag. Then a thin silver oxide (Ag2O) layer was induced on the surface of Ag by the UV–ozone treatment for 30 s, which enormously enhances the hole-injection from Ag to the organic hole-injection layer [13,14]. The organic multilayer structure was 4,40 ,400 -tris{N,-(3-methylphenyl)-Nphenylamine}triphenylamine (m-MTDATA, 45 nm); N,N0 -bis-(1naphthyl)-N-N0 -diphenyl-1,10 -biphenyl-4,40 -diamine (NPB, 5 nm), tris(8-hydroxyquinoline) aluminum (Alq, 30 nm) doped with 5% 5,6,11,12-tetraphenylnaphthacene (Rubrene) and another undoped Alq (35 nm). Finally, to achieve both desired transmittance and effective electron injection, we applied multiple functional layers consisting of LiF (1 nm)/Al (2 nm)/Ag (20 nm) thermally deposited onto the organic layers as cathode. In the device, Ag /Ag2O, m-MTDATA, NPB, Rubrene: Alq, Alq, and LiF/Al / Ag were employed as anode, hole-injection layer, hole transporting layer, emitting layer, electron transporting layer and cathode, respectively. The active area of the device is 3 3.3 mm2. All films were deposited at pressure below 4 10 6 Torr. The Deposition rate, monitored by quartz oscillating thickness monitor, was 0.2 nm/s. The characteristics of current–voltage–luminance and electroluminescent (EL) spectra were measured using a programmable Keithley model 2400 power supply and a Photo-research PR650 spectrometer in air at room temperature.
3. Results and discussion n
Corresponding author. Tel.: þ86 595 22103983. E-mail address: [email protected] (Z. Wu).
0022-2313/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jlumin.2011.06.014
Optically, a TEOLED could be considered as the Fabry — Perot cavity embedded with a source. The resonant wavelength can be
2420
Z. Wu, J. Wang / Journal of Luminescence 131 (2011) 2419–2421
determined by the following equation [15]: P 4p ni di jtop jbot ¼ 2mp
l
where l is the resonant wavelength; ni and di are the refractive index and the thickness of each organic layer, respectively; ftop and fbot are the wavelength dependent phase changes on reflection from the top and the bottom electrodes, respectively; m is an integer that defines the mode number. Fig. 1 shows the calculated P 4pni di round-trip phase changes (i.e.j1 ¼ l ) between two reflective electrodes and phase changes (i.e.j2 ¼ jtop þ jbot) on two reflective electrodes. The incidence medium is Alq for cathode and m-MTDATA for anode. The intersection of f1 and f2 in Fig. 1 is 564 nm, which is the theoretical RW of the device. Fig. 2 illustrates the normal direction emission spectrum of the fabricated TEOLED. The resonant wavelength of the measured device is 560 nm. The theoretical RW in Fig. 1 is close to the experimental result in Fig. 2 but there is still some discrepancy between simulated and experimental RW for the reason that the thicknesses of the organic layers and electrodes used for simulation cannot be exactly the same as those of the actual device. For comparison, the spectrum of a bottom-emission device (BEOLED) with the same structure is also displayed in Fig. 2. Owing to the
microcavity effect, TEOLED demonstrates narrower spectrum and more saturated color. Obviously, The vibronic spectrum of the rubrene molecule, which appears in the BEOLED, is missing in the TEOLED, as resulted from the microcavity. In comparison to the BEOLED,the microcavity in TEOLED changes the relative EL intensity of emitter, resulting in the remarkable change in spectrum shape.The Inset in Fig. 2 compares the spectrum of a fabricated TEOLED with the calculated spectrum [16]. The simulated spectrum agrees well with the experimental data, confirming the validity of the optical model used [15,16] and the accuracy of optical simulation. Top-emission device also demonstrates negligible color variation. Fig. 3 depicts the spectra of the TEOLED at the viewing angles 01, 451, 601 and 751 off the normal direction. The spectral peak shift of the TEOLED is only 8 nm when viewing angle moves from normal direction to 751 off the normal direction. With the increase of the viewing angles the RW shifts to shorter wavelengths, while the rapid fall-off of the intrinsic emission intensity at RWs strongly suppresses the blue-shift caused by the microcavity effects. As a result, at large viewing angles, the spectrum shift is barely perceptible and the emission intensity undergoes a sharp drop, which is shown in Fig. 3. Measured and simulated spectra at different viewing angles, 451, 601 and 751 off the normal direction of a TEOLED, are
phase changes on two electrodes) round-trip phase change
6.5
1.8 1.6
6.0
(75)
1.4
0
5.5 564nm
Intensity (a.u)
Phase change on reflection (rad)
7.0
5.0 4.5 4.0
1.2
(45)
1.0
(60)
0.8 0.6 0.4
3.5 3.0 350
0.2
400
450
500 550 600 650 Wavelength (nm)
700
750
0.0
800
-0.2 300
400
Fig. 1. Calculated round-trip phase changes between two electrodes and phase changes on two electrodes.
500 600 Wavelength (nm)
700
800
Fig. 3. Spectra characteristics of TEOLED at different viewing angles.
1.0 TEOLED Calculated
0.6
400
0.2
60, calculated 60, measured
0.5 0.5
0.0
0.4
75,calculated 75,measured 1.0
1.0
0.5
600 Wavelength (nm)
800
Intensity (a.u)
Intensity (a.u)
TEOLED BEOLED
Intensity (a.u)
1.0
0.8
2.0
1.5
0.0
600 800 400 Wavelength (nm)
1.0
0.5
0.0 400
600 800 Wavelength (nm)
45,calculated 45,measured
0.0 300
400
500
600 700 800 900 1000 1100 1200 Wavelength(nm)
Fig. 2. Spectra characteristics of TEOLED and BEOLED. Inset shows a comparison of experimental and calculated spectra on normal direction.
0.0
400
600 800 Wavelength (nm)
1000
1200
Fig. 4. Normalized, measured and simulated EL spectra of the TEOLED at viewing angles of 451, 601 and 751off normal direction.
Z. Wu, J. Wang / Journal of Luminescence 131 (2011) 2419–2421
of the organic layers and electrodes between experiment and calculation. The luminance–current density characteristics and the dependence of current efficiency on voltage are plotted in Figs. 5 and 6. The maximum current efficiency can be achieved at 12 V with the value of 11.5 cd/A. The efficiency of TEOLED at 10 V is 11 cd/A, which is higher than that of the bottom-emission device (3.5 cd/A) reported in reference at the same bias [18]. The improvement on current efficiency can be attributed to the microcavity effect.
100000
Luminance (cd/m2)
2421
80000 60000 40000 20000
4. Conclusion:
0 200 400 600 800 Current Density (mA/cm2)
0
1000
Fig. 5. L–J characteristics of TEOLED.
In summary, by controlling the cavity mode and resonance wavelength, high efficiency top-emitting organic light-emitting device with narrow emissive spectrum and negligible color variation has been demonstrated. In comparison with the results reported in literatures [8, 9], our works has suggested a simpler way to make a TEOLED with near angle-independence without complicating the fabrication process.
Current Efficiency (cd/A)
12
Acknowledgement
10
This work was supported by the National Natural Science Foundation of China under Grant no60838003, and Research Foundation of Huaqiao University Grant no07BS108.
8 6
References 4 2 0 4
6
8
10
12
14
Voltage (V) Fig. 6. Current efficiency–voltage characteristic of the device.
illustrated in Fig. 4 to elucidate the angular-characteristics of TEOLED. The emission spectra at different angles were calculated according to the microcavity theory [17]. The measured spectra are in excellent agreement with calculated ones, confirming the accuracy of the simulation and the reasonable explanation to the angular-characteristics of TEOLED. The slight distinctions between them might be due to the small thickness discrepancy
[1] W.F. Xie, S.F. Chen, L.T. Zhang, S.Y. Liu, J. Phys. D: 40 (2007) 5888. [2] W.F. Xie, H.Y. Sun, C.W. Law, C.S. Lee, S.T. Lee, S.Y. Liu, Appl. Phys. A: Mater. Sci. Process 85 (2006) 95. [3] C.J. Yang, C.L. Lin, T.H. Chen, Appl. Phys. Lett. 87 (2005) 143507. [4] W.Y. Ji, L.T. Zhang, T.Y. Zhang, W.F. Xie, Opt. Lett. 34 (2009) 2703. [5] Z.Y. Xie, L.S. Huang, F.R. Zhu, Chem. Phys. Lett. 381 (2003) 691. [6] R.B. Pode, C.J. Lee, D.G. Moon, J.I. Han, Appl. Phys. Lett. 84 (2004) 4614. [7] J. Ma, X.C. Piao, J. Liu, W.F. Xie, H.N. Cui, Org. Electron. 12 (2011) 923. [8] C.C. Wu, C.L Lin, P.Y. Hsieh, H.H. Chiang, Appl. Phys. Lett. 84 (2004) 3966. [9] C.J. Yang, T.Y. Cho, C.L Lin, C.C. Wu, Appl. Phys. Lett. 90 (2007) 173507. [10] C.C. Wu, C.W. Chen, C.L Lin, C.J. Yang, IEEE. J. Disp. Technol. 1 (2005) 248. [11] C.J. Yang, S.H. Liu, C.C. Wu, Appl. Phys. Lett. 91 (2007) 253508. [12] C.C. Liu, S.H. Liu, K.C. Tien, C.C. Wu, Appl. Phys. Lett. 94 (2009) 103302. [13] C.W. Chen, P.Y. Hsieh, H.H. Chiang, C.L Lin, H.M. Wu, C.C. Wu, Appl. Phys. Lett. 83 (2003) 5127. [14] S.F. Chen, W.F. Xie, S.Y. Liu, J. Appl. Phys. 103 (2008) 054506. [15] B. Djuriˇsic´, A.D. Rakic´, Appl. Opt. 41 (2002) 7650. [16] T. Shiga, H. Fujikawa, Y Taga, J. Appl. Phys. 93 (2003) 19. [17] P. Royo, R.P. Stanley, M. Ilegems, IEEE J. Sel. Top. Quant Electron. 8 (2002) 207. [18] W.B. Gao, J.X. Sun, S.Y. Liu, Opt. Quantum Electron. 35 (2003) 1149.
Contents lists available at ScienceDirect
Journal of Luminescence journal homepage: www.elsevier.com/locate/jlumin
Top-emitting organic light-emitting device with weak viewing angle-dependence Zhijun Wu n, Jiaxian Wang College of Information Science and Engineering, Huaqiao University, Quanzhou 362011, PR China
a r t i c l e i n f o
abstract
Article history: Received 13 April 2011 Received in revised form 7 June 2011 Accepted 9 June 2011 Available online 15 June 2011
In this study, a top-emitting organic light-emitting device (TEOLED) with high efficiency and near angle-independence was fabricated on silicon substrate. The blue-shift of the resonant wavelength (RW) with increasing view angles was nearly negligible. The theoretical simulation was described by a model based on the Fabry–Perot microcavity structure. The maximum current efficiency of the fabricated device is 11.5 cd/A at 12 V. & 2011 Elsevier B.V. All rights reserved.
Keywords: Microcavity Optical simulation Angle-independence
1. Introduction
2. Experimental details
Top-emitting organic light-emitting devices (TEOLEDs) are demanded for active-matrix organic light-emitting devices (AMOLEDs) fabricated on crystalline silicon substrate owing to the advantages of high-aperture-ratio, high efficiency and high pixel resolution. A typical TEOLED consists of a reflective bottom anode, a semitransparent top cathode and organic layers sandwiched in between. Metals with high reflectance, For example Ag [1], Au [2] and Mo [3], and some semitransparent thin metal films, such as Al/Ag [4], Sm [5] and Ca/Ag [6], are commonly used as anodes and cathodes, respectively, in TEOLEDs. . Top-emitting device with such structure demonstrates relatively strong microcavity effects, which offers various advantages for display applications such as color saturation and efficiency enhancement; however, this structure also suffers large color variation with viewing angles [7]. Quite a few OLED publications had focused on the improvement and optimization of emission characteristics of TEOLEDs [8–10]. More recently, microlens arrays or diffusers have been integrated on the top cathode to optimize the output efficiency and angular dependence [11,12]. however, it complicated the fabrication process. In this paper, a TEOLED with high efficiency, highly saturated color and weak angular dependence is realized without complicating the fabrication process by precisely controlling the resonant wavelength.
The device was built on a 1600-nm-SiO2-coated silicon substrate precoated with 70-nm-thick Ag. Then a thin silver oxide (Ag2O) layer was induced on the surface of Ag by the UV–ozone treatment for 30 s, which enormously enhances the hole-injection from Ag to the organic hole-injection layer [13,14]. The organic multilayer structure was 4,40 ,400 -tris{N,-(3-methylphenyl)-Nphenylamine}triphenylamine (m-MTDATA, 45 nm); N,N0 -bis-(1naphthyl)-N-N0 -diphenyl-1,10 -biphenyl-4,40 -diamine (NPB, 5 nm), tris(8-hydroxyquinoline) aluminum (Alq, 30 nm) doped with 5% 5,6,11,12-tetraphenylnaphthacene (Rubrene) and another undoped Alq (35 nm). Finally, to achieve both desired transmittance and effective electron injection, we applied multiple functional layers consisting of LiF (1 nm)/Al (2 nm)/Ag (20 nm) thermally deposited onto the organic layers as cathode. In the device, Ag /Ag2O, m-MTDATA, NPB, Rubrene: Alq, Alq, and LiF/Al / Ag were employed as anode, hole-injection layer, hole transporting layer, emitting layer, electron transporting layer and cathode, respectively. The active area of the device is 3 3.3 mm2. All films were deposited at pressure below 4 10 6 Torr. The Deposition rate, monitored by quartz oscillating thickness monitor, was 0.2 nm/s. The characteristics of current–voltage–luminance and electroluminescent (EL) spectra were measured using a programmable Keithley model 2400 power supply and a Photo-research PR650 spectrometer in air at room temperature.
3. Results and discussion n
Corresponding author. Tel.: þ86 595 22103983. E-mail address: [email protected] (Z. Wu).
0022-2313/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jlumin.2011.06.014
Optically, a TEOLED could be considered as the Fabry — Perot cavity embedded with a source. The resonant wavelength can be
2420
Z. Wu, J. Wang / Journal of Luminescence 131 (2011) 2419–2421
determined by the following equation [15]: P 4p ni di jtop jbot ¼ 2mp
l
where l is the resonant wavelength; ni and di are the refractive index and the thickness of each organic layer, respectively; ftop and fbot are the wavelength dependent phase changes on reflection from the top and the bottom electrodes, respectively; m is an integer that defines the mode number. Fig. 1 shows the calculated P 4pni di round-trip phase changes (i.e.j1 ¼ l ) between two reflective electrodes and phase changes (i.e.j2 ¼ jtop þ jbot) on two reflective electrodes. The incidence medium is Alq for cathode and m-MTDATA for anode. The intersection of f1 and f2 in Fig. 1 is 564 nm, which is the theoretical RW of the device. Fig. 2 illustrates the normal direction emission spectrum of the fabricated TEOLED. The resonant wavelength of the measured device is 560 nm. The theoretical RW in Fig. 1 is close to the experimental result in Fig. 2 but there is still some discrepancy between simulated and experimental RW for the reason that the thicknesses of the organic layers and electrodes used for simulation cannot be exactly the same as those of the actual device. For comparison, the spectrum of a bottom-emission device (BEOLED) with the same structure is also displayed in Fig. 2. Owing to the
microcavity effect, TEOLED demonstrates narrower spectrum and more saturated color. Obviously, The vibronic spectrum of the rubrene molecule, which appears in the BEOLED, is missing in the TEOLED, as resulted from the microcavity. In comparison to the BEOLED,the microcavity in TEOLED changes the relative EL intensity of emitter, resulting in the remarkable change in spectrum shape.The Inset in Fig. 2 compares the spectrum of a fabricated TEOLED with the calculated spectrum [16]. The simulated spectrum agrees well with the experimental data, confirming the validity of the optical model used [15,16] and the accuracy of optical simulation. Top-emission device also demonstrates negligible color variation. Fig. 3 depicts the spectra of the TEOLED at the viewing angles 01, 451, 601 and 751 off the normal direction. The spectral peak shift of the TEOLED is only 8 nm when viewing angle moves from normal direction to 751 off the normal direction. With the increase of the viewing angles the RW shifts to shorter wavelengths, while the rapid fall-off of the intrinsic emission intensity at RWs strongly suppresses the blue-shift caused by the microcavity effects. As a result, at large viewing angles, the spectrum shift is barely perceptible and the emission intensity undergoes a sharp drop, which is shown in Fig. 3. Measured and simulated spectra at different viewing angles, 451, 601 and 751 off the normal direction of a TEOLED, are
phase changes on two electrodes) round-trip phase change
6.5
1.8 1.6
6.0
(75)
1.4
0
5.5 564nm
Intensity (a.u)
Phase change on reflection (rad)
7.0
5.0 4.5 4.0
1.2
(45)
1.0
(60)
0.8 0.6 0.4
3.5 3.0 350
0.2
400
450
500 550 600 650 Wavelength (nm)
700
750
0.0
800
-0.2 300
400
Fig. 1. Calculated round-trip phase changes between two electrodes and phase changes on two electrodes.
500 600 Wavelength (nm)
700
800
Fig. 3. Spectra characteristics of TEOLED at different viewing angles.
1.0 TEOLED Calculated
0.6
400
0.2
60, calculated 60, measured
0.5 0.5
0.0
0.4
75,calculated 75,measured 1.0
1.0
0.5
600 Wavelength (nm)
800
Intensity (a.u)
Intensity (a.u)
TEOLED BEOLED
Intensity (a.u)
1.0
0.8
2.0
1.5
0.0
600 800 400 Wavelength (nm)
1.0
0.5
0.0 400
600 800 Wavelength (nm)
45,calculated 45,measured
0.0 300
400
500
600 700 800 900 1000 1100 1200 Wavelength(nm)
Fig. 2. Spectra characteristics of TEOLED and BEOLED. Inset shows a comparison of experimental and calculated spectra on normal direction.
0.0
400
600 800 Wavelength (nm)
1000
1200
Fig. 4. Normalized, measured and simulated EL spectra of the TEOLED at viewing angles of 451, 601 and 751off normal direction.
Z. Wu, J. Wang / Journal of Luminescence 131 (2011) 2419–2421
of the organic layers and electrodes between experiment and calculation. The luminance–current density characteristics and the dependence of current efficiency on voltage are plotted in Figs. 5 and 6. The maximum current efficiency can be achieved at 12 V with the value of 11.5 cd/A. The efficiency of TEOLED at 10 V is 11 cd/A, which is higher than that of the bottom-emission device (3.5 cd/A) reported in reference at the same bias [18]. The improvement on current efficiency can be attributed to the microcavity effect.
100000
Luminance (cd/m2)
2421
80000 60000 40000 20000
4. Conclusion:
0 200 400 600 800 Current Density (mA/cm2)
0
1000
Fig. 5. L–J characteristics of TEOLED.
In summary, by controlling the cavity mode and resonance wavelength, high efficiency top-emitting organic light-emitting device with narrow emissive spectrum and negligible color variation has been demonstrated. In comparison with the results reported in literatures [8, 9], our works has suggested a simpler way to make a TEOLED with near angle-independence without complicating the fabrication process.
Current Efficiency (cd/A)
12
Acknowledgement
10
This work was supported by the National Natural Science Foundation of China under Grant no60838003, and Research Foundation of Huaqiao University Grant no07BS108.
8 6
References 4 2 0 4
6
8
10
12
14
Voltage (V) Fig. 6. Current efficiency–voltage characteristic of the device.
illustrated in Fig. 4 to elucidate the angular-characteristics of TEOLED. The emission spectra at different angles were calculated according to the microcavity theory [17]. The measured spectra are in excellent agreement with calculated ones, confirming the accuracy of the simulation and the reasonable explanation to the angular-characteristics of TEOLED. The slight distinctions between them might be due to the small thickness discrepancy
[1] W.F. Xie, S.F. Chen, L.T. Zhang, S.Y. Liu, J. Phys. D: 40 (2007) 5888. [2] W.F. Xie, H.Y. Sun, C.W. Law, C.S. Lee, S.T. Lee, S.Y. Liu, Appl. Phys. A: Mater. Sci. Process 85 (2006) 95. [3] C.J. Yang, C.L. Lin, T.H. Chen, Appl. Phys. Lett. 87 (2005) 143507. [4] W.Y. Ji, L.T. Zhang, T.Y. Zhang, W.F. Xie, Opt. Lett. 34 (2009) 2703. [5] Z.Y. Xie, L.S. Huang, F.R. Zhu, Chem. Phys. Lett. 381 (2003) 691. [6] R.B. Pode, C.J. Lee, D.G. Moon, J.I. Han, Appl. Phys. Lett. 84 (2004) 4614. [7] J. Ma, X.C. Piao, J. Liu, W.F. Xie, H.N. Cui, Org. Electron. 12 (2011) 923. [8] C.C. Wu, C.L Lin, P.Y. Hsieh, H.H. Chiang, Appl. Phys. Lett. 84 (2004) 3966. [9] C.J. Yang, T.Y. Cho, C.L Lin, C.C. Wu, Appl. Phys. Lett. 90 (2007) 173507. [10] C.C. Wu, C.W. Chen, C.L Lin, C.J. Yang, IEEE. J. Disp. Technol. 1 (2005) 248. [11] C.J. Yang, S.H. Liu, C.C. Wu, Appl. Phys. Lett. 91 (2007) 253508. [12] C.C. Liu, S.H. Liu, K.C. Tien, C.C. Wu, Appl. Phys. Lett. 94 (2009) 103302. [13] C.W. Chen, P.Y. Hsieh, H.H. Chiang, C.L Lin, H.M. Wu, C.C. Wu, Appl. Phys. Lett. 83 (2003) 5127. [14] S.F. Chen, W.F. Xie, S.Y. Liu, J. Appl. Phys. 103 (2008) 054506. [15] B. Djuriˇsic´, A.D. Rakic´, Appl. Opt. 41 (2002) 7650. [16] T. Shiga, H. Fujikawa, Y Taga, J. Appl. Phys. 93 (2003) 19. [17] P. Royo, R.P. Stanley, M. Ilegems, IEEE J. Sel. Top. Quant Electron. 8 (2002) 207. [18] W.B. Gao, J.X. Sun, S.Y. Liu, Opt. Quantum Electron. 35 (2003) 1149.