- Email: [email protected]
Observation of the disk mode pattern in organic microdisk
~
Solid State Communications, Vol. 105, No. 7, pp. 445-448, 1998 © 1998 Elsevier Science Lid Printed in Great Britain. All fights reserved 0038-1098/98 $19.00+.00
Pergamon
PII: S0038-1098(97) 10169-7
OBSERVATION OF THE DISK MODE PATTERN IN ORGANIC MICRODISKt Yong Lin, a Bei Zhang,a'* Yongchun Xinfl Chaohua Guofl Lun Daifl Dejian Zhou b and Chunhui Huang b aphysics Department and State Key Laboratory of Mesoscopic Physics, Peking University, Beijing, 100871, P.R. China bState Key Laboratory of Rare Earth Material Chemistry and Application, Peking University, Beijing, 100871, P.R. China
(Received 12 October 1997; accepted 20 October 1997 by Z.Z. Gan) A novel microdisk containing organic emitting material rare-earth complex Eu(TTA)2.NOa.2TPPO has been fabricated. The microdisk mode pattern in a microdisk with radius of 9.1/~m is visually observed from fluorescence microscopic image. The observed microdisk mode pattern reflects a combining contribution of Whispering-Gallery Modes and Surface-Emitting Modes. The radial emission intensity profile near the circumference is well consistent with the "Whispering Gallery Mode" approximation. © 1998 Elsevier Science Ltd Keywords: A. thin films, A. nanostructure, D. optical properties, E. luminescence.
Optical microdisks have attracted much attention due to both of its fundamental physics and various applications since McCall et al. demonstrated semiconductor microdisk laser in 1992 [1]. Because of strong optical confinement to the gain region, high spontaneous emission coefficient/3 and high quality factor Q could be achieved in microdisks [2]. Microdisks also have the advantages of structure simplicity for fabrication and analysis. A variety of microdisks made by different material systems have been investigated by different groups [3-8]. In addition to the semiconductor microdisks, the organic microdisks are also attractive. The dye-doped polymer microdisks have been demonstrated by Kuwata and his co-workers [9]. In the view of optical modes in cavities, the predominant resonance modes in microdisks are Whispering-Gallery Modes (WG Modes) [3], which are propagating along the edge of microdisk. To our knowledge, still little observation of the microdisk modes in the microdisk was reported. In this letter, a new kind of organic microdisk is successfully fabricated and the microdisk mode pattern is visually observed from
* To whom all correspondence should be sent. t Supported by National Nature Science Foundation of China (NNSFC) under project of No. 69687007.
the image of fluorescence microscope. The comparison of radial intensity distribution of microdisk between theoretical and experimental results is presented. In our experiments, the organic emitting material used for microdisk is chosen to be rare-earth complex Eu(TTA)2. NO3 • 2TPPO. The molecular structure of Eu(TTA)2. NO3 • 2TPPO is shown in Fig. 1. As the common property in rare-earth compounds, it possesses a narrow fluorescent spectrum with peak at the wavelength of 612 nm. In particular, polyimide is used as the host of emitting rare-earth complex due to its transparent and good film forming property [10]. The polyimide is diluted by N-methyl-2-ketopyrrolidine. The doping concentration of the Eu(TTA) 2 • NO 3 • 2TPPO in diluted polyimide is about 2 - 4 m g m l -l. Thin film of Eu(TTA)2 • NO3 • 2TPPO doped polyimide is firstly prepared on the substrate of glass slides by means of spin coating. The thickness of the film can be regulated by spin rate [10]. The pattern of original microdisk array with different diameters of disks is fabricated by the conventional photolithography. A special technique of "Over-Developing" is used, thus the patterned polyimide is slightly detached by the developer and then falls down onto the glass substrate. In this case, it might exist as a thin air spacer between microdisks and the glass substrate. Consequently, the organic microdisks
445
446
DISK MODE PATTERN IN ORGANIC MICRODISK
O
I P=O 2
O --C \ c r 3
1 2
Fig. 1. The chemical structure of Eu(TTA)2. NO 3 • 2(TPPO). with stronger optical confinement are produced. Without this procedure of "over-developing", small index difference of refraction between emission medium and the substrate may cause large loss in the disk modes. The fluorescence microscopic image of this Eu-complex doped organic microdisk is performed in an Olympus BX60m system microscope. The pumping source is ultraviolet light in the wavelength range from 330-385 nm which is filtered from a 100 W mercury lamp. Under the excitation, a bright red ring of fluorescence near the edge of microdisk can be observed from the microscope. The image is also acquired and digitized through a write-black 512 X 512 charge-coupler device (CCD) camera system connected with a personal computer. Figure 2 illustrates the typical luminescence image of a microdisk with radius of 9.1 #m. Obviously, the light intensity concentrates on the edge of the microdisk. The dominant Whispering-Gallery Modes in this microdisk are therefore demonstrated. In principle, for the case of an ideal isolated dielectric disc with no free electrical charges and no current
sources, the optical field is the solution to the Helmholtz equation. Since the radial distribution of optical field in the microdisk is the most interesting point for us, if we ignore the stationary component of the vertical direction from the disk plane, the Helmholtz equation could be then reduced into two-dimensions by separation of variables. For a cylindrical coordinate system (r, O,z) with z axis coinciding with the disk symmetrical axis of the microdisk which has thickness of d, radius of R and effective refraction index of ne#, the two dimensional optical field ,it should be the functions of r and Oseparately. It is therefore expressed as 9(r, 0) = R(r)O(O) and satisfies the following equation, respectively, d2
r2 -~R(r) -4- r ff----:(r)+ (k2r2 -M2)R(r) = 0
(1)
and d2
d020(O) +
M20(O)=
O,
(2)
where k = neyfo~lC, C is the light speed in vacuum. M is generally a complex constant with assumed boundary condition '~(R,O)= O, the optical field solution in microdisk is described as
(3)
¢l(r, O) = AM,NJM(rneff6OM,N/C ) eiMO,
where J u are Mth order Bessel functions of integer order, M = 0, - 1 , _+2, ---3..... AM,tO are normalization constants. 0JM~V= XM~vCI(nefR), where XM.Nis the Nth root of JM(r) and N = 1 for Whispering-Gallery Modes [11]. In this situation, the optical field in the radial direction for Whispering-Gallery Modes is in proportion to JM(XM.lr/R) [12]. The effective index of refraction neff could be estimated by the three-layered slab waveguide. The refraction index of the emission medium is close to that of polyimide which is determined by optical ellipsometer and is equal to 1.96. The emission wavelength of our microdisk is fixed at about 610nm corresponding to the optical transition of rare-earth element of Eu. Experimentally, the value of X~t,/vcould be easily found out.
(a) Fig. 2. Microscopic luminescence image of a typical microdisk with radius of 9.1 ttm.
Vol. 105, No. 7
(b)
Fig. 3. Two dimensional luminescence profile of organic microdisk.
Vol. 105, No. 7
447
DISK MODE PATTERN IN ORGANIC MICRODISK
Considering Bessel function JM(XM,Ir/R) with radius r ranging from 0 to R, for a given M, there is only one maximum value of JM near the edge of the disk. So we could define a "characteristic radial value" as rma~ which is corresponding to the maximum value of Ju. Consequently, for a fixed disk radius R, the JM(XM,tr/R) of different order M has different characteristic ratio of rmJR. However, in microdisk the larger M, the greater quality factor Q of Whispering-Gallery Mode. As a result, for a microdisk with a certain radius R and a medium having fixed emitting wavelength, only the Whispering-Gallery Mode of M order with the highest Q factor dominates. In other words, if WG mode really dominates in microdisk, from the experimental intensity profile and the value of rr,,ax/R,the corresponding order M of Bessel function could be then found out. Figure 4 presents the dependence of fluorescence intensity on the r of the same microdisk with R = 9.1/zm as shown in Fig. 2. As a result, the intensity profile peaks at rma~which is very close to the circumference of the disk and equals 8.4 #m. Thus, the experimental characteristic ratio rmo:,/R is 0.923. Comparing with the theoretical rmaJR of Bessel functions with different orders, the M value which corresponding the above rmuxlRis just found to be M = 47. It means that the resonant light modes intensity of Whispering-Gallery Mode IJ47(X47,1r/R)I2 should be the most proximate theoretical profile of radial light field intensity. Figure 5 illustrates the comparison between the curve (dotted) of experimental optical field intensity and curve (solid) of the ideal intensity of Whispering-Gallery Modes. Clearly, these two curves fit satisfactorily especially on the region of disk circumference. It verifies that the observed microdisk mode is dominated by Whispering-Gallery Mode. We could also find out from the curve (dotted) in Fig. 5 that the optical intensity is not zero but a Micro
Disk
....
~retk~ Expedment 0.0 0.04
Radial Emission Intensity Profile of Microdisk 02 04 06 08 lo |
,
,
0.03
=l
,
,0.04
0.03
002 t 0.02
001
o.o,
W, -to.~
0 O0 0,0 ,,
,
012
i
I 04
i
I 0,6
,
I 0.8
r/R
Fig, 5. Comparison of radial luminescence profile between experimental results and results calculated. Dotted curve, experimental results; solid curve, results calculated. weak even-distribution along the central region of the microdisk. It is reasonable to suggest that it should correspond to some contribution of surface emitting modes existing in the microdisk [13]. The ratio of the peak intensity at rm~xto that of central part is about 7. Although the intensity is weak, they are competing with the Whispering-Gallery Modes. The rough estimation of quality factor Q of Surface-Emitting Modes and Whispering-Gallery Modes in the microdisk could make a comparison for us. In general, the Q value of Surface-Emitting Modes (Qs) approximately equals the Q value of F - P cavity with identical optical length between F - P mirrors, so that Q s = ~ r k l ~g~f ,
k = 2nd X '
(4)
where n and d are the refractive index and the thickness of microdisk respectively, k is the resonant wavelength of the cavity, Rf is the reflectivity. According to Fresnel formula, in the case of normal incidence,
i
(nl --n2) 2
i
60
•
50
'
RT = \ n l + n2} '
40
30
•
-15
,
.110
,
I -5
,
I 0
,
I 5
,
,I 10
i 15
R(um )
Fig. 4. Radial luminescence profile of organic microdisk as shown in Fig. 2.
(5)
where n i and n2 are the refractive indices of two sides. In the case of our microdisk, the reflection interfaces are the upper and lower polyimide surface of microdisk between the surrounding air, so take n2 as 1.96 and nl as 1.00, Rf = 0.10. The thickness of microdisk is measured to be 1.54 #m, k = 612 nm, from equation (4), k = 9.86. Then, the quality factor Q of Surface-Emitting Modes Qs = 11. On the other hand, according to tunneling arguments, the quality factor Q of Whispering-Gallery Modes (Qw)
448
DISK MODE PATI'ERN IN ORGANIC MICRODISK
depends on geometry of disk and the effective index of medium material. It is approximately expected to vary with the order of M exponentially [14], Q = b e2Mr,
(6)
where I is the function of ne~, b is a constant [14]. Theoretically, the Q value of the Whispering-Gallery Mode with M ----47 order is unbelievably large. In fact, the imperfection or roughness of the disk edge would greatly decrease the effective Q value of the WhisperingGallery Modes to be about 1000 as estimated [14-16]. But this is still much greater than the above estimated Q value of Surface-Emitting Modes. Consequently, the microdisk mode intensity profile observed from fluorescence microscopic image in our organic microdisk could be understood as the distribution of the dominant Whispering-Gallery Modes combining with the SurfaceEmitting Modes. The particular intensity ratio relating to the competition of these two kinds of modes is dependent on the configuration and imperfection of microdisk. To make some evidence for our suggestion, some of our experiments with different microdisk configurations have been done to demonstrate the competition. As a matter of fact, the conventional microdisks generally have a pedestal under the disk. Because of the coupling of Whispering-Gallery Modes into substrate via the pedestal, the Q value of conventional microdisk decreases dramatically comparing with that of ideal microdisk without pedestal. We have made some thumbtack like organic microdisks with different size of pedestal. By modifying the diameter of the pedestal in organic microdisks, the Q value of Whispering-Gallery Modes changed. Therefore the change in the intensity ratio of ring peak to that of the central part is obtained. It demonstrates the competition between Surface-Emitting Modes and Whispering-Gallery Modes. The details will be discussed in elsewhere. In conclusion, we have successfully fabricated a remarkable microdisk which consists of the emitting material Eu(TTA)2. NO 3 • 2TPPO. The radial electromagnetic energy distribution of this kind of microdisk is observed by the microscopic fluorescence image. The observed microdisk mode reflects a combining contribution of Whispering-Gallery Modes and SurfaceEmitting Modes. In these microdisks, the radial emission intensity profile near the inner disk circumference is
Vol. 105, No. 7
consistent with the calculated Whispering-Gallery Mode approximation.
Acknowledgements--We would like to acknowledge Prof. Shumin Wang and Dr Zhengxiang Gao for technical assistance and Prof. Changzhi Guo and Dr Ruopeng Wang for helpful discussion. REFERENCES 1. McCall, S.L., Levi, A.F.J., Slusher, R.E., Pearton, S.J. and Logan, R.A.,Appl. Phys. Lett., 60, 1992, 289. 2. Levi, A.F.J., Slusher, R.E., McCall, S.L., Pearton, S.J. and Hobson, W.S., Appl. Phys. Len., 62, 1993, 2021. 3. Chu, D.Y., Chin, M.K., Sauer, N.J., Xu, Z., Chang, T.Y. and Ho, S.T., IEEE Photonics Technology Lett,, 5, 1993, 1353. 4. Hovinen, M., Ding, J. and Nurmikko, A.V., Appl. Phys. Lett., 63, 1993, 3128. 5. Zhang Bei, Wang Ruopeng, Ding Xiaomin, Dai Lun and Wang Shumin, Solid State Commun., 91, 1994, 699. 6. Mohideen, U., Hobson, W.S., Pearton, S.J., Ren, F. and Slusher, R.E., Appl. Phys. Lett., 64, 1994, 1911. 7. Zhang Bei, Wang Ruopeng, Ding Xiaomin, Yang Zhijian, Dai Lun, Cui Xiaoming and Wang Shumin, Chinese J. Infrared & Millimeter Waves (overseas edition), 14, 1995, 253. 8. Chu, D.Y., Ho, S.T., Wang, X.Z., Wessels, B.W., Bi, W.G., Tu, C.W., Espindola, R.P. and Wu, S.L., Appl. Phys. Lett., 66, 1995, 2843. 9. Kuwata-Gonokami, M., Jordan, R.H., Dodabalapur, A., Katz, H.E., Schilling, M.L. and Slusher, R.E., Optics Lett., 20, 1995, 2093. 10. Zhang Bei, Zhuang Lei, Lin Yong, Xia Zhongju, Ma Yong, Ding Xiaomin, Wang Shumin, Zhou Dejian and Huang Chunhui, Solid State Commun., 97, 1996, 445. 11. Fratechi, N.C. and Levi, A.F.J., Appl. Phys. Lett., 66, 1995, 2932. 12. Guo Changzhi and Cben Shuilian, Acta Physica Sinca, 5, 1996, 185. 13. Wang Ruopeng and Maria-Manuela Dumitrescu, J. Appl. Phys., 81, 1997, 3391. 14. Slusher, R.E., Levi, A.F.J., Mohideen, U., McCall, S.L., Pearton, S.J. and Logan, R.A., Appl. Phys. Left., 63, 1993, 1310. 15. Fratechi, N.C. and Levi, A.F.J., J. Appl. Phys., 80, 1996, 644. 16. Levi, A.F.J., Solid State Electronic., 37, 1994, 1297.
Solid State Communications, Vol. 105, No. 7, pp. 445-448, 1998 © 1998 Elsevier Science Lid Printed in Great Britain. All fights reserved 0038-1098/98 $19.00+.00
Pergamon
PII: S0038-1098(97) 10169-7
OBSERVATION OF THE DISK MODE PATTERN IN ORGANIC MICRODISKt Yong Lin, a Bei Zhang,a'* Yongchun Xinfl Chaohua Guofl Lun Daifl Dejian Zhou b and Chunhui Huang b aphysics Department and State Key Laboratory of Mesoscopic Physics, Peking University, Beijing, 100871, P.R. China bState Key Laboratory of Rare Earth Material Chemistry and Application, Peking University, Beijing, 100871, P.R. China
(Received 12 October 1997; accepted 20 October 1997 by Z.Z. Gan) A novel microdisk containing organic emitting material rare-earth complex Eu(TTA)2.NOa.2TPPO has been fabricated. The microdisk mode pattern in a microdisk with radius of 9.1/~m is visually observed from fluorescence microscopic image. The observed microdisk mode pattern reflects a combining contribution of Whispering-Gallery Modes and Surface-Emitting Modes. The radial emission intensity profile near the circumference is well consistent with the "Whispering Gallery Mode" approximation. © 1998 Elsevier Science Ltd Keywords: A. thin films, A. nanostructure, D. optical properties, E. luminescence.
Optical microdisks have attracted much attention due to both of its fundamental physics and various applications since McCall et al. demonstrated semiconductor microdisk laser in 1992 [1]. Because of strong optical confinement to the gain region, high spontaneous emission coefficient/3 and high quality factor Q could be achieved in microdisks [2]. Microdisks also have the advantages of structure simplicity for fabrication and analysis. A variety of microdisks made by different material systems have been investigated by different groups [3-8]. In addition to the semiconductor microdisks, the organic microdisks are also attractive. The dye-doped polymer microdisks have been demonstrated by Kuwata and his co-workers [9]. In the view of optical modes in cavities, the predominant resonance modes in microdisks are Whispering-Gallery Modes (WG Modes) [3], which are propagating along the edge of microdisk. To our knowledge, still little observation of the microdisk modes in the microdisk was reported. In this letter, a new kind of organic microdisk is successfully fabricated and the microdisk mode pattern is visually observed from
* To whom all correspondence should be sent. t Supported by National Nature Science Foundation of China (NNSFC) under project of No. 69687007.
the image of fluorescence microscope. The comparison of radial intensity distribution of microdisk between theoretical and experimental results is presented. In our experiments, the organic emitting material used for microdisk is chosen to be rare-earth complex Eu(TTA)2. NO3 • 2TPPO. The molecular structure of Eu(TTA)2. NO3 • 2TPPO is shown in Fig. 1. As the common property in rare-earth compounds, it possesses a narrow fluorescent spectrum with peak at the wavelength of 612 nm. In particular, polyimide is used as the host of emitting rare-earth complex due to its transparent and good film forming property [10]. The polyimide is diluted by N-methyl-2-ketopyrrolidine. The doping concentration of the Eu(TTA) 2 • NO 3 • 2TPPO in diluted polyimide is about 2 - 4 m g m l -l. Thin film of Eu(TTA)2 • NO3 • 2TPPO doped polyimide is firstly prepared on the substrate of glass slides by means of spin coating. The thickness of the film can be regulated by spin rate [10]. The pattern of original microdisk array with different diameters of disks is fabricated by the conventional photolithography. A special technique of "Over-Developing" is used, thus the patterned polyimide is slightly detached by the developer and then falls down onto the glass substrate. In this case, it might exist as a thin air spacer between microdisks and the glass substrate. Consequently, the organic microdisks
445
446
DISK MODE PATTERN IN ORGANIC MICRODISK
O
I P=O 2
O --C \ c r 3
1 2
Fig. 1. The chemical structure of Eu(TTA)2. NO 3 • 2(TPPO). with stronger optical confinement are produced. Without this procedure of "over-developing", small index difference of refraction between emission medium and the substrate may cause large loss in the disk modes. The fluorescence microscopic image of this Eu-complex doped organic microdisk is performed in an Olympus BX60m system microscope. The pumping source is ultraviolet light in the wavelength range from 330-385 nm which is filtered from a 100 W mercury lamp. Under the excitation, a bright red ring of fluorescence near the edge of microdisk can be observed from the microscope. The image is also acquired and digitized through a write-black 512 X 512 charge-coupler device (CCD) camera system connected with a personal computer. Figure 2 illustrates the typical luminescence image of a microdisk with radius of 9.1 #m. Obviously, the light intensity concentrates on the edge of the microdisk. The dominant Whispering-Gallery Modes in this microdisk are therefore demonstrated. In principle, for the case of an ideal isolated dielectric disc with no free electrical charges and no current
sources, the optical field is the solution to the Helmholtz equation. Since the radial distribution of optical field in the microdisk is the most interesting point for us, if we ignore the stationary component of the vertical direction from the disk plane, the Helmholtz equation could be then reduced into two-dimensions by separation of variables. For a cylindrical coordinate system (r, O,z) with z axis coinciding with the disk symmetrical axis of the microdisk which has thickness of d, radius of R and effective refraction index of ne#, the two dimensional optical field ,it should be the functions of r and Oseparately. It is therefore expressed as 9(r, 0) = R(r)O(O) and satisfies the following equation, respectively, d2
r2 -~R(r) -4- r ff----:(r)+ (k2r2 -M2)R(r) = 0
(1)
and d2
d020(O) +
M20(O)=
O,
(2)
where k = neyfo~lC, C is the light speed in vacuum. M is generally a complex constant with assumed boundary condition '~(R,O)= O, the optical field solution in microdisk is described as
(3)
¢l(r, O) = AM,NJM(rneff6OM,N/C ) eiMO,
where J u are Mth order Bessel functions of integer order, M = 0, - 1 , _+2, ---3..... AM,tO are normalization constants. 0JM~V= XM~vCI(nefR), where XM.Nis the Nth root of JM(r) and N = 1 for Whispering-Gallery Modes [11]. In this situation, the optical field in the radial direction for Whispering-Gallery Modes is in proportion to JM(XM.lr/R) [12]. The effective index of refraction neff could be estimated by the three-layered slab waveguide. The refraction index of the emission medium is close to that of polyimide which is determined by optical ellipsometer and is equal to 1.96. The emission wavelength of our microdisk is fixed at about 610nm corresponding to the optical transition of rare-earth element of Eu. Experimentally, the value of X~t,/vcould be easily found out.
(a) Fig. 2. Microscopic luminescence image of a typical microdisk with radius of 9.1 ttm.
Vol. 105, No. 7
(b)
Fig. 3. Two dimensional luminescence profile of organic microdisk.
Vol. 105, No. 7
447
DISK MODE PATTERN IN ORGANIC MICRODISK
Considering Bessel function JM(XM,Ir/R) with radius r ranging from 0 to R, for a given M, there is only one maximum value of JM near the edge of the disk. So we could define a "characteristic radial value" as rma~ which is corresponding to the maximum value of Ju. Consequently, for a fixed disk radius R, the JM(XM,tr/R) of different order M has different characteristic ratio of rmJR. However, in microdisk the larger M, the greater quality factor Q of Whispering-Gallery Mode. As a result, for a microdisk with a certain radius R and a medium having fixed emitting wavelength, only the Whispering-Gallery Mode of M order with the highest Q factor dominates. In other words, if WG mode really dominates in microdisk, from the experimental intensity profile and the value of rr,,ax/R,the corresponding order M of Bessel function could be then found out. Figure 4 presents the dependence of fluorescence intensity on the r of the same microdisk with R = 9.1/zm as shown in Fig. 2. As a result, the intensity profile peaks at rma~which is very close to the circumference of the disk and equals 8.4 #m. Thus, the experimental characteristic ratio rmo:,/R is 0.923. Comparing with the theoretical rmaJR of Bessel functions with different orders, the M value which corresponding the above rmuxlRis just found to be M = 47. It means that the resonant light modes intensity of Whispering-Gallery Mode IJ47(X47,1r/R)I2 should be the most proximate theoretical profile of radial light field intensity. Figure 5 illustrates the comparison between the curve (dotted) of experimental optical field intensity and curve (solid) of the ideal intensity of Whispering-Gallery Modes. Clearly, these two curves fit satisfactorily especially on the region of disk circumference. It verifies that the observed microdisk mode is dominated by Whispering-Gallery Mode. We could also find out from the curve (dotted) in Fig. 5 that the optical intensity is not zero but a Micro
Disk
....
~retk~ Expedment 0.0 0.04
Radial Emission Intensity Profile of Microdisk 02 04 06 08 lo |
,
,
0.03
=l
,
,0.04
0.03
002 t 0.02
001
o.o,
W, -to.~
0 O0 0,0 ,,
,
012
i
I 04
i
I 0,6
,
I 0.8
r/R
Fig, 5. Comparison of radial luminescence profile between experimental results and results calculated. Dotted curve, experimental results; solid curve, results calculated. weak even-distribution along the central region of the microdisk. It is reasonable to suggest that it should correspond to some contribution of surface emitting modes existing in the microdisk [13]. The ratio of the peak intensity at rm~xto that of central part is about 7. Although the intensity is weak, they are competing with the Whispering-Gallery Modes. The rough estimation of quality factor Q of Surface-Emitting Modes and Whispering-Gallery Modes in the microdisk could make a comparison for us. In general, the Q value of Surface-Emitting Modes (Qs) approximately equals the Q value of F - P cavity with identical optical length between F - P mirrors, so that Q s = ~ r k l ~g~f ,
k = 2nd X '
(4)
where n and d are the refractive index and the thickness of microdisk respectively, k is the resonant wavelength of the cavity, Rf is the reflectivity. According to Fresnel formula, in the case of normal incidence,
i
(nl --n2) 2
i
60
•
50
'
RT = \ n l + n2} '
40
30
•
-15
,
.110
,
I -5
,
I 0
,
I 5
,
,I 10
i 15
R(um )
Fig. 4. Radial luminescence profile of organic microdisk as shown in Fig. 2.
(5)
where n i and n2 are the refractive indices of two sides. In the case of our microdisk, the reflection interfaces are the upper and lower polyimide surface of microdisk between the surrounding air, so take n2 as 1.96 and nl as 1.00, Rf = 0.10. The thickness of microdisk is measured to be 1.54 #m, k = 612 nm, from equation (4), k = 9.86. Then, the quality factor Q of Surface-Emitting Modes Qs = 11. On the other hand, according to tunneling arguments, the quality factor Q of Whispering-Gallery Modes (Qw)
448
DISK MODE PATI'ERN IN ORGANIC MICRODISK
depends on geometry of disk and the effective index of medium material. It is approximately expected to vary with the order of M exponentially [14], Q = b e2Mr,
(6)
where I is the function of ne~, b is a constant [14]. Theoretically, the Q value of the Whispering-Gallery Mode with M ----47 order is unbelievably large. In fact, the imperfection or roughness of the disk edge would greatly decrease the effective Q value of the WhisperingGallery Modes to be about 1000 as estimated [14-16]. But this is still much greater than the above estimated Q value of Surface-Emitting Modes. Consequently, the microdisk mode intensity profile observed from fluorescence microscopic image in our organic microdisk could be understood as the distribution of the dominant Whispering-Gallery Modes combining with the SurfaceEmitting Modes. The particular intensity ratio relating to the competition of these two kinds of modes is dependent on the configuration and imperfection of microdisk. To make some evidence for our suggestion, some of our experiments with different microdisk configurations have been done to demonstrate the competition. As a matter of fact, the conventional microdisks generally have a pedestal under the disk. Because of the coupling of Whispering-Gallery Modes into substrate via the pedestal, the Q value of conventional microdisk decreases dramatically comparing with that of ideal microdisk without pedestal. We have made some thumbtack like organic microdisks with different size of pedestal. By modifying the diameter of the pedestal in organic microdisks, the Q value of Whispering-Gallery Modes changed. Therefore the change in the intensity ratio of ring peak to that of the central part is obtained. It demonstrates the competition between Surface-Emitting Modes and Whispering-Gallery Modes. The details will be discussed in elsewhere. In conclusion, we have successfully fabricated a remarkable microdisk which consists of the emitting material Eu(TTA)2. NO 3 • 2TPPO. The radial electromagnetic energy distribution of this kind of microdisk is observed by the microscopic fluorescence image. The observed microdisk mode reflects a combining contribution of Whispering-Gallery Modes and SurfaceEmitting Modes. In these microdisks, the radial emission intensity profile near the inner disk circumference is
Vol. 105, No. 7
consistent with the calculated Whispering-Gallery Mode approximation.
Acknowledgements--We would like to acknowledge Prof. Shumin Wang and Dr Zhengxiang Gao for technical assistance and Prof. Changzhi Guo and Dr Ruopeng Wang for helpful discussion. REFERENCES 1. McCall, S.L., Levi, A.F.J., Slusher, R.E., Pearton, S.J. and Logan, R.A.,Appl. Phys. Lett., 60, 1992, 289. 2. Levi, A.F.J., Slusher, R.E., McCall, S.L., Pearton, S.J. and Hobson, W.S., Appl. Phys. Len., 62, 1993, 2021. 3. Chu, D.Y., Chin, M.K., Sauer, N.J., Xu, Z., Chang, T.Y. and Ho, S.T., IEEE Photonics Technology Lett,, 5, 1993, 1353. 4. Hovinen, M., Ding, J. and Nurmikko, A.V., Appl. Phys. Lett., 63, 1993, 3128. 5. Zhang Bei, Wang Ruopeng, Ding Xiaomin, Dai Lun and Wang Shumin, Solid State Commun., 91, 1994, 699. 6. Mohideen, U., Hobson, W.S., Pearton, S.J., Ren, F. and Slusher, R.E., Appl. Phys. Lett., 64, 1994, 1911. 7. Zhang Bei, Wang Ruopeng, Ding Xiaomin, Yang Zhijian, Dai Lun, Cui Xiaoming and Wang Shumin, Chinese J. Infrared & Millimeter Waves (overseas edition), 14, 1995, 253. 8. Chu, D.Y., Ho, S.T., Wang, X.Z., Wessels, B.W., Bi, W.G., Tu, C.W., Espindola, R.P. and Wu, S.L., Appl. Phys. Lett., 66, 1995, 2843. 9. Kuwata-Gonokami, M., Jordan, R.H., Dodabalapur, A., Katz, H.E., Schilling, M.L. and Slusher, R.E., Optics Lett., 20, 1995, 2093. 10. Zhang Bei, Zhuang Lei, Lin Yong, Xia Zhongju, Ma Yong, Ding Xiaomin, Wang Shumin, Zhou Dejian and Huang Chunhui, Solid State Commun., 97, 1996, 445. 11. Fratechi, N.C. and Levi, A.F.J., Appl. Phys. Lett., 66, 1995, 2932. 12. Guo Changzhi and Cben Shuilian, Acta Physica Sinca, 5, 1996, 185. 13. Wang Ruopeng and Maria-Manuela Dumitrescu, J. Appl. Phys., 81, 1997, 3391. 14. Slusher, R.E., Levi, A.F.J., Mohideen, U., McCall, S.L., Pearton, S.J. and Logan, R.A., Appl. Phys. Left., 63, 1993, 1310. 15. Fratechi, N.C. and Levi, A.F.J., J. Appl. Phys., 80, 1996, 644. 16. Levi, A.F.J., Solid State Electronic., 37, 1994, 1297.