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Experimental examination of the two-photon XX absorption models by a new type of polarization spectroscopy in CuCl
JOURNAL OF
LUMINESCENCE EJ-SEYIER
Journal
of Luminescence
66&67 (1996) 396-400
Experimental examination of the two-photon XX absorption models by a new type of polarization spectroscopy in CuCl M. Hasuo*, Department
of Physics,School
qf
Science,
H. Kawano, The Uniwrsiiy
N. Nagasawa
qf Tokyo, 7-3-l. Hongo, Bunkyo-ku, Tokyo 113, Japan
Abstract
A new type of nonlinear polarization spectroscopy for precise measurements of the two-photon biexciton (XX) absorption in CuCl in the very weak excitation regime is developed. The spectral width, the two-photon absorption coefficient and the third-order nonlinear susceptibility associated with the two-photon XX resonance are evaluated. Experimental results are consistent with the theoretical ones evaluated from the new model of the two-photon XX absorption developed by Ivanov and Haug.
1. Introduction A biexciton (XX) is a complex of two excitons bound by the Coulomb interaction. It is well known that a biexciton can be directly generated from the crystal ground state by a two-photon absorption process with very high efficiency. This absorption is called the giant two-photon absorption (GTA). About 20 years ago, Hanamura proposed a model of the GTA adopting the concept of the giant oscillator strength [l]. Recently, Ivanov and Haug proposed a new model, including the Coulomb interaction and polariton effects of excitons self-consistently [2]. They also showed that the radiative width rc”, the Lamb shift dxx, the third-order nonlinear susceptibility xc3’ associated with the two-photon XX resonance and corresponding two-photon absorption coefficient ZP’, can be derived from their theory by only giving the biexciton binding energy [3]. They
*Corresponding
author
estimated corresponding rc”, Ax’, xc3) and Kc2’ for the XX in CuCl. In order to check the validity of these models, quantitative measurements of rf”, Ax’, xc3’ and K@’ are necessary. From the experimental point of view however, there have been two serious difficulties: one is the saturation effects of the relevant optical nonlinearity that appear in the very weak excitation regime. The other is the very narrow spectral width of the two-photon XX resonance of 20 ueV, that is narrower than the line width of a conventional pulsed dye laser light. To obtain the true spectrum of the relevant resonance, a deconvolution technique is required but is difficult to apply to the nonlinear spectroscopy, such as nonlinear polarization rotation spectroscopy, that has been used as the most precise method to observe the two-photon XX resonance [4]. In order to overcome these difficulties and to measure the two-photon XX absorption precisely in CuCl, we developed a new type of nonlinear polarization spectroscopy [S]. We obtained values of the spectral width of the two-photon XX resonance
0022-2313/96/$15.00 ,(“ 1996 ~ Elsevier Science B.V. All rights reserved SSDI 0022.2313(95)00177-8
M. Hasuo et al. /Journal
Zxx, K”’ and xc3’ and compared theoretical ones.
of Luminescence
them with the
2. Experiment A schematic illustration of our experimental setup is shown in Fig. 1. Two dye lasers simultaneously pumped by an excimer laser (Lambda Physik 53ESC) were used as the light sources. The polarizations of the pump and the probe light were made linear and circular, respectively. The intensities of the pump and the probe light were Ik = 2 N 10 kW/cm’ and I0 = 0.4 kW/cm’, respectively. The circular polarized probe light can be expressed by a coherent superposition of orthogonal linear polarization components with the same amplitude. According to the polarization selection rule of the two-photon XX absorption, only the component of the probe light whose polarization is parallel to that of the pump light couples to the pump light to produce a modulation of the polarization of the transmitted probe light. Passing the transmitted probe light through a polarized beam splitter, each linear polarized component of the probe light was separately obtained. Then, the corresponding intensities Ii, and II were detected independently by PIN photodiodes (Hamamatsu S3072). The peak intensity of the output of each PIN photodiode was held by an intensity holder with a time window of 1 ns. Because the duration of each laser pulse was 10 ns, the time evolution of the exciting laser light was neglected during the measuring time window. For each laser pulse the
66&67 (1996) 396-400
397
outputs of the intensity holders were AD converted and recorded by a personal computer during the 100 ms time interval between pulses. As explained in Ref. [S], the two-photon XX coefficient in the measurements, absorption lV’(W()) wk), can be evaluated by the equation
zP2’(o,, Ok) z
ln(z~(%)/zli(oO~ wk)) ~(zk(wk))
(1) ’
where (Zk(Wk)) is the spatially averaged intensity of the pump light in the sample: 1 (zkbk))
=
exp(
-
&hk)l)
(2)
Ik(Wk) %bk)l
Here, o0 and Lc)k are the photon energy of the probe and pump light, respectively. @r(wk) and 1 are the linear absorption coefficient at wk and the sample thickness, respectively. This method allows extraction of the two-photon XX absorption from the linear absorption while avoiding the influence of fluctuations of I0 automatically, by carrying out the calculation of Z,/Z,, in Eq. (1) for every laser pulse [6]. In the experiments, the photon energy of the pump light was scanned to obtain Kc2’(~,, ok). The intensity of the transmitted pump light was also measured by a PIN photodiode and an intensity holder in order to monitor the intensity of the pump light and to confirm that the two-photon absorption of the pump light caused by the combination with the probe light is negligible. A single crystal platelet of CuCl prepared from a vapor phase was used as a sample. The thickness was
Fig. 1. Schematic diagram of the experimental set-up for new polarization PBS: polarized beam splitter, PD: photodiode, IH: intensity holder.
spectroscopy.
P: polarizer,
Q: quarter
wave
plate,
15 urn. The sample was held in an immersion-type cryostat at 2 K.
x5 k = 5.5 x105
cm”
0
t
Oo(d) wo=3.2173
t
ev
3. Results and discussion Fig. 2 shows an example of the spectra of I, (a), II (b) and K”‘(wO, wk) (c) at w0 = 3.1863 eV obtained under a very weak excitation condition. As can be seen in the figure, the two-photon XX absorption was not observed clearly in Fig. 2(a) as it was masked by the large fluctuation of IO. However, a clear spectrum of E2’(q, (ok) is obtained in Fig. 2(c). This clearly shows the remarkable effects of the cancellation of the fluctuation of I,, in our new method. Fig. 3 shows examples of the spectra of R’2’(~0, ~0~) at several wO. The solid curves in the figure are the results of Lorentzian fits. The spectral shapes are well reproduced giving a spectral width of w 80 ueV. Under a condition where xNLl < 1,
0
I
I
1
I
I
I
1
I
‘I
-0.5
Q,, - (%+%)
I
0.5
(meV)
Fig. 3. Examples of the spectra of K”‘(cu,, (1~~)for several (u,~. The solid curve in each spectrum is a Lorentzian fit. k shown on the right side of each spectrum is the wave number of the XX.
CuCl 2K w"=3.1863
the absorbed intensity of the probe light is approximately proportional to (xNLIO= K’2’I,Z,, where Kc2’ is the true two-photon XX absorption coefficient. Therefore, the relation between K’2’(q, wk) and ZQ2’ is given as
eV
IP’(c0,,
cc)k)=
(b) 1L(~o)
K’2’(W 1W2).fb(%
o-)1 1
/s x,/&k,
02)
dwldw2,
(3)
where,fb(cJlo, w’) and,fj(ok, 02) are the normalized spectral shapes of the probe and pump light, respectively. In Ivanov’s model, Kc2’(~r, (u2) can be expressed as P2’(o 111
I 3.185"
Photon
I 3.1855
t
I
1, (02) l- xx
I
3.1860
Energy of Pump Light (eV)
Fig. 2. Examples of the spectra of I (Q, ~9~) (a), I,(~IJ,,. (1~~)(b) and R’*‘(U),,, (I)~) (c) at CO,,= 3.1863 eV. The intensities of the pump and the probe light were 3 and 0.4 kW/cm’. respectively.
= C(w,,
w2) (CF
-
co1
- 02)2 + (PX)2
(4)
where Qxx is the XX energy. C(wI, 02) is a proportional factor and is almost constant at the vicinity of the two-photon XX resonance [3]. Therefore,
M. Hasuo et al. iJournal
Table 1 Comparison
between
experimental
and theoretical
~f’Luminescence
66&67
(IY96)
396-400
399
values
F
This work - 28 PeV
New model” 27.4 PeV
GOS model” I60 PeV
j(‘.l’((~~O = 3.1863 eV) K”‘(tu,, = 3.1863 eV) K”‘(tu,, = 3.1986 eV) K”‘(cf~,,, = 3.2094 eV) K”‘(to,, = 3.2173 eV)
3.8 x IO-‘esu 0.33 cm,!W 1.20 cm/W 0.41 cm,‘W 0.05 cm: W
1.05 x IO-‘esu 0.091 cm/W 0.45 cmiW 0.22 cm;W 0.020 cm/W
0.18 x lO_‘esu 0.016 cm/W 0.12 cm/W 0. I I cm/W 0.016 cm!W
’ Evaluated hObtained
for the k = 0 biexciton resonance using the giant oscillator strength
[3]. model [I] by Ref. [3].
C(ctii, LUG)can be replaced by C(u,,, wk) and taken outside the integration of Eq. (3). In the experiment, the spectral shapes of the laser light could be approximated by Lorentzian shapes with the widths of To = 20 peV and rk = 32 ueV for the probe and pump light, respectively. In this case, the integration in Eq. (3) can be easily carried out in the same manner as convolution in linear spectroscopy:
rxx
x(QXX
_
(Ok)’+ (rxx +
('Jo -
To +
ra)’
(5)
Therefore, one can obtain a true fxx by subtracting To and rk from the measured spectral width, and a true value of the maximum of K”‘(wo, ok), K’2’((ti0), from the relation p2’(w,)
(
=
(YXX
+
To
(rxx)2
+
r/A2
-(2) K
(OJO).
From the analysis by the procedure mentioned above, true values of Yxx and Kc2’(oo) at w. = 3.1863 eV were obtained to be + 28 ueV and 0.33 cm/W, respectively. The corresponding x’~‘(~~) at the resonance was obtained from K”‘(wo) to be 3.8 x 10e4 esu. These values are compared with the theoretical ones in Table 1 and a good quantitative coincidence with the values estimated from the new model was found. Before concluding, we wish to comment on the radiative renormalization effects of biexcitons. Ivanov and Haug calculated rtX and dxx as a function of the wave number k, of XX [3,6]. In our measurement, the wave number of the XX
excited is in the range 5 x 105-10x lo5 cm-‘, as shown in the right side of each spectrum in Fig. 3, that comes from the combination of the photon energies (momenta) of the pump and probe light. From these data, we can determine Yxx and in principle, compare the results to the theoretical values. Unfortunately, however, we could not observe the explicit change of the spectral width within the experimental error. An increase in the precision is needed in order to discriminate the change of the l’g” of the order of ueV that is predicted by their model [3, 63. Nevertheless, the measurement of dxx seems quite difficult in the present experimental configuration because the absolute value of the two-photon XX resonance energy would need to be measured with the accuracy of ueV for this purpose.
4. Conclusion The two-photon XX absorption in CuCl was measured precisely by applying a new type of nonlinear polarization spectroscopy in the very weak excitation regime. Yxx, Kc2’(~,) and I’m’ at i coo = 3.1863 eV were measured to be _ 28 ueV, 0.33 cm/W and 3.8 x 10 4 esu, respectively. Our results are consistent with the theoretical values obtained by Ivanov and Haug.
Acknowledgements
The authors would like to thank Dr. A.L. Ivanov for valuable discussions about the two-photon XX absorption. This work was partially supported by
400
M. Hasuo et al. /Journal
of Luminescence
The Grant-in-Aid for Scientific Research from The Ministry of Education, Science and Culture.
References [l] E. Hanamura, Solid State Commun. 12 (1973) 951. [2] A.L. Ivanov and H. Haug, Phys. Rev. B 48 (1993) 1490.
66&67 (3996) 396-400
[3] A.L. Ivanov, M. Hasuo, N. Nagasawa and H. Haug, Phys. Rev. B, accepted. [4] N. Nagasawa, M. Kuwata, E. Hanamura, T. ltoh and A. Mysyrowicz, Appl. Phys. Lett. 55 (1989) 1999. [S] M. Hasuo, H. Kawano and N. Nagasawa, Phys. Stat. Sol. (B) 188 (1995) 77. [6] A.L. Ivanov and H. Haug, Phys. Rev. Lett. 74 (1995) 438.
LUMINESCENCE EJ-SEYIER
Journal
of Luminescence
66&67 (1996) 396-400
Experimental examination of the two-photon XX absorption models by a new type of polarization spectroscopy in CuCl M. Hasuo*, Department
of Physics,School
qf
Science,
H. Kawano, The Uniwrsiiy
N. Nagasawa
qf Tokyo, 7-3-l. Hongo, Bunkyo-ku, Tokyo 113, Japan
Abstract
A new type of nonlinear polarization spectroscopy for precise measurements of the two-photon biexciton (XX) absorption in CuCl in the very weak excitation regime is developed. The spectral width, the two-photon absorption coefficient and the third-order nonlinear susceptibility associated with the two-photon XX resonance are evaluated. Experimental results are consistent with the theoretical ones evaluated from the new model of the two-photon XX absorption developed by Ivanov and Haug.
1. Introduction A biexciton (XX) is a complex of two excitons bound by the Coulomb interaction. It is well known that a biexciton can be directly generated from the crystal ground state by a two-photon absorption process with very high efficiency. This absorption is called the giant two-photon absorption (GTA). About 20 years ago, Hanamura proposed a model of the GTA adopting the concept of the giant oscillator strength [l]. Recently, Ivanov and Haug proposed a new model, including the Coulomb interaction and polariton effects of excitons self-consistently [2]. They also showed that the radiative width rc”, the Lamb shift dxx, the third-order nonlinear susceptibility xc3’ associated with the two-photon XX resonance and corresponding two-photon absorption coefficient ZP’, can be derived from their theory by only giving the biexciton binding energy [3]. They
*Corresponding
author
estimated corresponding rc”, Ax’, xc3) and Kc2’ for the XX in CuCl. In order to check the validity of these models, quantitative measurements of rf”, Ax’, xc3’ and K@’ are necessary. From the experimental point of view however, there have been two serious difficulties: one is the saturation effects of the relevant optical nonlinearity that appear in the very weak excitation regime. The other is the very narrow spectral width of the two-photon XX resonance of 20 ueV, that is narrower than the line width of a conventional pulsed dye laser light. To obtain the true spectrum of the relevant resonance, a deconvolution technique is required but is difficult to apply to the nonlinear spectroscopy, such as nonlinear polarization rotation spectroscopy, that has been used as the most precise method to observe the two-photon XX resonance [4]. In order to overcome these difficulties and to measure the two-photon XX absorption precisely in CuCl, we developed a new type of nonlinear polarization spectroscopy [S]. We obtained values of the spectral width of the two-photon XX resonance
0022-2313/96/$15.00 ,(“ 1996 ~ Elsevier Science B.V. All rights reserved SSDI 0022.2313(95)00177-8
M. Hasuo et al. /Journal
Zxx, K”’ and xc3’ and compared theoretical ones.
of Luminescence
them with the
2. Experiment A schematic illustration of our experimental setup is shown in Fig. 1. Two dye lasers simultaneously pumped by an excimer laser (Lambda Physik 53ESC) were used as the light sources. The polarizations of the pump and the probe light were made linear and circular, respectively. The intensities of the pump and the probe light were Ik = 2 N 10 kW/cm’ and I0 = 0.4 kW/cm’, respectively. The circular polarized probe light can be expressed by a coherent superposition of orthogonal linear polarization components with the same amplitude. According to the polarization selection rule of the two-photon XX absorption, only the component of the probe light whose polarization is parallel to that of the pump light couples to the pump light to produce a modulation of the polarization of the transmitted probe light. Passing the transmitted probe light through a polarized beam splitter, each linear polarized component of the probe light was separately obtained. Then, the corresponding intensities Ii, and II were detected independently by PIN photodiodes (Hamamatsu S3072). The peak intensity of the output of each PIN photodiode was held by an intensity holder with a time window of 1 ns. Because the duration of each laser pulse was 10 ns, the time evolution of the exciting laser light was neglected during the measuring time window. For each laser pulse the
66&67 (1996) 396-400
397
outputs of the intensity holders were AD converted and recorded by a personal computer during the 100 ms time interval between pulses. As explained in Ref. [S], the two-photon XX coefficient in the measurements, absorption lV’(W()) wk), can be evaluated by the equation
zP2’(o,, Ok) z
ln(z~(%)/zli(oO~ wk)) ~(zk(wk))
(1) ’
where (Zk(Wk)) is the spatially averaged intensity of the pump light in the sample: 1 (zkbk))
=
exp(
-
&hk)l)
(2)
Ik(Wk) %bk)l
Here, o0 and Lc)k are the photon energy of the probe and pump light, respectively. @r(wk) and 1 are the linear absorption coefficient at wk and the sample thickness, respectively. This method allows extraction of the two-photon XX absorption from the linear absorption while avoiding the influence of fluctuations of I0 automatically, by carrying out the calculation of Z,/Z,, in Eq. (1) for every laser pulse [6]. In the experiments, the photon energy of the pump light was scanned to obtain Kc2’(~,, ok). The intensity of the transmitted pump light was also measured by a PIN photodiode and an intensity holder in order to monitor the intensity of the pump light and to confirm that the two-photon absorption of the pump light caused by the combination with the probe light is negligible. A single crystal platelet of CuCl prepared from a vapor phase was used as a sample. The thickness was
Fig. 1. Schematic diagram of the experimental set-up for new polarization PBS: polarized beam splitter, PD: photodiode, IH: intensity holder.
spectroscopy.
P: polarizer,
Q: quarter
wave
plate,
15 urn. The sample was held in an immersion-type cryostat at 2 K.
x5 k = 5.5 x105
cm”
0
t
Oo(d) wo=3.2173
t
ev
3. Results and discussion Fig. 2 shows an example of the spectra of I, (a), II (b) and K”‘(wO, wk) (c) at w0 = 3.1863 eV obtained under a very weak excitation condition. As can be seen in the figure, the two-photon XX absorption was not observed clearly in Fig. 2(a) as it was masked by the large fluctuation of IO. However, a clear spectrum of E2’(q, (ok) is obtained in Fig. 2(c). This clearly shows the remarkable effects of the cancellation of the fluctuation of I,, in our new method. Fig. 3 shows examples of the spectra of R’2’(~0, ~0~) at several wO. The solid curves in the figure are the results of Lorentzian fits. The spectral shapes are well reproduced giving a spectral width of w 80 ueV. Under a condition where xNLl < 1,
0
I
I
1
I
I
I
1
I
‘I
-0.5
Q,, - (%+%)
I
0.5
(meV)
Fig. 3. Examples of the spectra of K”‘(cu,, (1~~)for several (u,~. The solid curve in each spectrum is a Lorentzian fit. k shown on the right side of each spectrum is the wave number of the XX.
CuCl 2K w"=3.1863
the absorbed intensity of the probe light is approximately proportional to (xNLIO= K’2’I,Z,, where Kc2’ is the true two-photon XX absorption coefficient. Therefore, the relation between K’2’(q, wk) and ZQ2’ is given as
eV
IP’(c0,,
cc)k)=
(b) 1L(~o)
K’2’(W 1W2).fb(%
o-)1 1
/s x,/&k,
02)
dwldw2,
(3)
where,fb(cJlo, w’) and,fj(ok, 02) are the normalized spectral shapes of the probe and pump light, respectively. In Ivanov’s model, Kc2’(~r, (u2) can be expressed as P2’(o 111
I 3.185"
Photon
I 3.1855
t
I
1, (02) l- xx
I
3.1860
Energy of Pump Light (eV)
Fig. 2. Examples of the spectra of I (Q, ~9~) (a), I,(~IJ,,. (1~~)(b) and R’*‘(U),,, (I)~) (c) at CO,,= 3.1863 eV. The intensities of the pump and the probe light were 3 and 0.4 kW/cm’. respectively.
= C(w,,
w2) (CF
-
co1
- 02)2 + (PX)2
(4)
where Qxx is the XX energy. C(wI, 02) is a proportional factor and is almost constant at the vicinity of the two-photon XX resonance [3]. Therefore,
M. Hasuo et al. iJournal
Table 1 Comparison
between
experimental
and theoretical
~f’Luminescence
66&67
(IY96)
396-400
399
values
F
This work - 28 PeV
New model” 27.4 PeV
GOS model” I60 PeV
j(‘.l’((~~O = 3.1863 eV) K”‘(tu,, = 3.1863 eV) K”‘(tu,, = 3.1986 eV) K”‘(cf~,,, = 3.2094 eV) K”‘(to,, = 3.2173 eV)
3.8 x IO-‘esu 0.33 cm,!W 1.20 cm/W 0.41 cm,‘W 0.05 cm: W
1.05 x IO-‘esu 0.091 cm/W 0.45 cmiW 0.22 cm;W 0.020 cm/W
0.18 x lO_‘esu 0.016 cm/W 0.12 cm/W 0. I I cm/W 0.016 cm!W
’ Evaluated hObtained
for the k = 0 biexciton resonance using the giant oscillator strength
[3]. model [I] by Ref. [3].
C(ctii, LUG)can be replaced by C(u,,, wk) and taken outside the integration of Eq. (3). In the experiment, the spectral shapes of the laser light could be approximated by Lorentzian shapes with the widths of To = 20 peV and rk = 32 ueV for the probe and pump light, respectively. In this case, the integration in Eq. (3) can be easily carried out in the same manner as convolution in linear spectroscopy:
rxx
x(QXX
_
(Ok)’+ (rxx +
('Jo -
To +
ra)’
(5)
Therefore, one can obtain a true fxx by subtracting To and rk from the measured spectral width, and a true value of the maximum of K”‘(wo, ok), K’2’((ti0), from the relation p2’(w,)
(
=
(YXX
+
To
(rxx)2
+
r/A2
-(2) K
(OJO).
From the analysis by the procedure mentioned above, true values of Yxx and Kc2’(oo) at w. = 3.1863 eV were obtained to be + 28 ueV and 0.33 cm/W, respectively. The corresponding x’~‘(~~) at the resonance was obtained from K”‘(wo) to be 3.8 x 10e4 esu. These values are compared with the theoretical ones in Table 1 and a good quantitative coincidence with the values estimated from the new model was found. Before concluding, we wish to comment on the radiative renormalization effects of biexcitons. Ivanov and Haug calculated rtX and dxx as a function of the wave number k, of XX [3,6]. In our measurement, the wave number of the XX
excited is in the range 5 x 105-10x lo5 cm-‘, as shown in the right side of each spectrum in Fig. 3, that comes from the combination of the photon energies (momenta) of the pump and probe light. From these data, we can determine Yxx and in principle, compare the results to the theoretical values. Unfortunately, however, we could not observe the explicit change of the spectral width within the experimental error. An increase in the precision is needed in order to discriminate the change of the l’g” of the order of ueV that is predicted by their model [3, 63. Nevertheless, the measurement of dxx seems quite difficult in the present experimental configuration because the absolute value of the two-photon XX resonance energy would need to be measured with the accuracy of ueV for this purpose.
4. Conclusion The two-photon XX absorption in CuCl was measured precisely by applying a new type of nonlinear polarization spectroscopy in the very weak excitation regime. Yxx, Kc2’(~,) and I’m’ at i coo = 3.1863 eV were measured to be _ 28 ueV, 0.33 cm/W and 3.8 x 10 4 esu, respectively. Our results are consistent with the theoretical values obtained by Ivanov and Haug.
Acknowledgements
The authors would like to thank Dr. A.L. Ivanov for valuable discussions about the two-photon XX absorption. This work was partially supported by
400
M. Hasuo et al. /Journal
of Luminescence
The Grant-in-Aid for Scientific Research from The Ministry of Education, Science and Culture.
References [l] E. Hanamura, Solid State Commun. 12 (1973) 951. [2] A.L. Ivanov and H. Haug, Phys. Rev. B 48 (1993) 1490.
66&67 (3996) 396-400
[3] A.L. Ivanov, M. Hasuo, N. Nagasawa and H. Haug, Phys. Rev. B, accepted. [4] N. Nagasawa, M. Kuwata, E. Hanamura, T. ltoh and A. Mysyrowicz, Appl. Phys. Lett. 55 (1989) 1999. [S] M. Hasuo, H. Kawano and N. Nagasawa, Phys. Stat. Sol. (B) 188 (1995) 77. [6] A.L. Ivanov and H. Haug, Phys. Rev. Lett. 74 (1995) 438.