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Theoretical analysis of measured waveform distortion in an HTS sampler
Physica C 392–396 (2003) 1441–1445 www.elsevier.com/locate/physc
Theoretical analysis of measured waveform distortion in an HTS sampler Michitaka Maruyama *, Mutsuo Hidaka, Tetsuro Satoh Fundamental Research Laboratories, NEC Corporation, 34 Miyukigaoka, Tsukuba 305-8501, Japan Received 13 November 2002; accepted 31 January 2003
Abstract The origin of measured waveform distortion observed in a high-resolution current-waveform measurement system based on a high-Tc superconductor sampler was investigated. The observed distortion is well explained by a model that assumes sampling-timing modulation by magnetic field leakage into the sampler circuit. Calculations based on both this model and experimental results indicate that the leakage magnetic field should have an advanced phase of about 70–90 compared to that of an applied magnetic field. The observed waveform distortion apparently originates from AC susceptibility in the YBa2 Cu3 O7x (YBCO) ground plane. 2003 Elsevier B.V. All rights reserved. PACS: 85.25.)j; 06.60.Jn; 75.30.Cr; 74.76.Bz Keywords: HTS sampler; Waveform distortion; AC susceptibility; YBCO thin films
1. Introduction The continuing growth in the operation speed of communication and other electronic systems is creating strong demands for ways to observe the high-speed signal waveforms used in these systems. To meet these demands, we proposed waveform measurement based on a high-Tc superconductor (HTS) sampler [1]. The HTS sampler circuits use
*
Corresponding author. Address: Division of Electric Devices, ISTEC, SRL, 10-13 Shinonome 1-chome, Koto-ku, Tokyo 135-0062, Japan. Tel.: +81-3-3536-5709; fax: +81-33536-5717. E-mail address: [email protected] (M. Maruyama).
single flux quantum (SFQ) pulses, which enable signal detection with a bandwidth of more than 100 GHz, even at an operation temperature of around 40 K. We constructed a prototype highresolution current-waveform measurement system composed of an HTS sampler circuit, semiconductor control units, and a compact single-stage cryocooler [1,2]. The sampler circuit was fabricated based on YBa2 -Cu3 O7x (YBCO) ramp-edge Josephson junction technology [3] and has an upper-layer ground plane structure [4]. A YBCO pickup coil is built into the sampler chip and connected to the sampler circuit. This system enables non-contact current-waveform measurement, an attractive method, especially for analyzing electromagnetic interference (EMI) [5] and so forth.
0921-4534/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0921-4534(03)01044-X
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M. Maruyama et al. / Physica C 392–396 (2003) 1441–1445
We previously demonstrated the operation of the system and used it to observe current signals of up to 20 GHz with the correct periods [1,2]. In our observations, however, the measured sinusoidal waveforms were often distorted. The observed distortion can be roughly classified into two types. One is simple tilting of the waveform. This type of distortion is caused by current leakage due to parasitic inductance in the sampler circuit. Accordingly, it can be eliminated by inserting a buffer into the circuit [6,7]. The other is a little more complex. It is a non-linear change in the waveforms, which cannot be explained by current leakage due to parasitic inductance. In this paper, we describe a model that explains such non-linear waveform distortion. Comparison of the waveforms calculated based on this model with ones measured experimentally showed that the model explains the distortion well.
2. Operation principle of sampler system The operation principle of the system discussed in this paper is illustrated in Figs. 1 and 2. First, a magnetic field generated by a current signal in a device under test (DUT), which is placed outside of a cryochamber, is detected using a superconducting pickup coil as a shielding current ðIcoil Þ. A trigger current ðItr Þ sent to the pulse generator of the sampler circuit with a controlled delay time ðtd Þ switches trigger junction JJ1. This creates a current pulse ðIp Þ that is transmitted to a comparator, which determines the sampling timing. If the sum of Icoil , Ip and DC feedback current ðIf Þ exceeds the critical current of comparator junction JJ3, JJ3 is switched, creating an SFQ pulse, which is detected by a readout superconducting quantum interference device (SQUID) as the voltage output. These processes are repeated with different If values until the minimum value of If at which JJ1 is switched ðIfmin Þ is found. Consequently, the waveform of Icoil is reconstituted by plotting the values of ðIf0 Ifmin ) in a graph of current versus td , where If0 represents the Ifmin value obtained without input signals. Sampler operation is described in more detail elsewhere [2,8].
Fig. 1. Photographs (a) and schematic diagram (b) of highresolution current-waveform measurement system. Inset in (a) shows sampler chip in which HTS sampler circuit and pickup coil are fabricated.
Fig. 2. Equivalent circuit of HTS sampler with pickup coil.
M. Maruyama et al. / Physica C 392–396 (2003) 1441–1445
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3. Leakage magnetic field model In the sampler chip, the pickup coil is connected to the sampler circuit. The separation between them (100 lm) is much smaller than that between the DUT and the coil (2 mm). This means that not only the pickup coil but also the sampler-circuit area is exposed to the signal magnetic field. The circuit itself is nominally shielded from the magnetic field by a YBCO ground plane. In our model, we assume that some of the signal magnetic field penetrates into the sampler circuit through the ground plane as magnetic field leakage for a reason that will be discussed in the next section. Shielding currents are thus generated in the sampler circuit because the circuit is composed of superconducting loops (Fig. 2). The shielding currents in the pulse generator of the circuit change the switch timing of trigger junction JJ1, resulting in modulation of the sampling timing. 0 The shielding current flowing through JJ1 ðIsd Þ can be defined using the shielding current in Loop1 0 0 ðIsd1 Þ and that in Loop2 ðIsd2 Þ as 0 0 0 Isd Isd1 Isd2 ;
ð1Þ
0 0 where the amplitudes of Isd1 and Isd2 are determined by the inductances and by the sizes and flux densities, respectively, in Loop1 and Loop2. If we consider a sinusoidal wave to be the input signal, 0 Isd can be expressed as a sine function: 0 Isd ðtÞ ¼ b sinð2pftÞ;
ð2Þ
0 where t is time, b is the amplitude of Isd , and f is the signal frequency. Thus, the total current 0 flowing into JJ1 is the sum of Itr and Isd (Fig. 3). For simplification, we regard Itr as a linearly increasing current that rises to the critical current of JJ1 ðIc1 Þ within time str . Since the amount of modulation of the switch timing of JJ1 (Dt1 ) depends on both the magnitude 0 of Isd at the moment of switching and the steepness in the rise of Itr it is described using Eq. (2): 0 Dt1 ¼ Isd ðt1 Þ=ðIc1 =str Þ
¼ ðbstr =Ic1 Þ sinð2pft1 Þ;
ð3Þ
Fig. 3. Time sequence of trigger current Itr , shielding current 0 due to magnetic field leakage ðIsd Þ (solid lines), and total current flowing into junction JJ1 (broken line).
where t1 is the time of switching of JJ1. From Fig. 3 and Eq. (3), t1 can be described using a cyclic equation: t1 ¼ td þ t0 þ str þ Dt1 ¼ td þ t0 þ str þ ðbstr =Ic1 Þ sinð2pft1 Þ;
ð4Þ
where t0 corresponds to the difference in timing 0 between Isd and Itr , and td is the delay time of Itr which is controlled by a variable delay line and used as the time scale in the graphs of the measured waveforms. The signals measured using the sampler ðIs Þ are described using t1 : Is ¼ a sinð2pft1 dÞ;
ð5Þ
where a is the amplitude of Is and d is a fitting parameter representing the phase difference be0 tween Icoil and Isd . Substituting Eq. (4) into Eq. (5), we can calculate the measured signals and plot them in the graphs of Is versus td . Typical waveforms measured using the sampler for sinusoidal signals show non-linear distortion with sharp and rounded peaks (Fig. 4). The waveforms calculated using Eqs. (4) and (5), which are also shown in this figure, coincide well with the measured ones. Similar results were obtained for many other sinusoidal waveforms measured using
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M. Maruyama et al. / Physica C 392–396 (2003) 1441–1445
Fig. 4. Waveforms measured using sampler system (open circles), and ones calculated based on leakage magnetic field model (solid lines).
the sampler. These results suggest that the measured waveform distortion is caused by magnetic field leaking into the sampler circuit.
Fig. 5. Calculated phase difference ðdÞ between leakage magnetic field and applied magnetic field, taking effect of AC susceptibility in both the layers of ground plane and circuit loops into account.
which correspond to the ratio of the imaginary part v00 to the real part v0 according to Eq. (6).
4. Origin of magnetic field leakage
jv00 =v0 j ¼ tan h
Typical values of parameter d obtained by fitting many measured waveforms were about 70– 0 90, indicating that Isd (the shielding current in the circuit loops created by the leakage magnetic field) has an advanced phase of Icoil (the shielding current in the pickup coil created by the signal magnetic field). Note that the observed non-linear distortion with sharp and rounded peaks as shown in Fig. 4 is not obtained if one assumed jdj 90 in Eq. (5). This suggests that the origin of the magnetic field leakage (and the resultant waveform distortion) is AC susceptibility ðvac ¼ v0 þ jv00 Þ in the YBCO ground plane because the imaginary part of vac should cause a phase shift in the shielding magnetic field, resulting in magnetic field leakage with an advanced phase. Fig. 5 shows the calculated phase difference ðdÞ between the leakage magnetic field and applied magnetic field based on the above discussion, considering both the superconducting layers of the ground plane and circuit loops. Parameters hgp and hc represent the phases of vac in the layers of the ground plane and the circuit loops, respectively,
In the calculation of Fig. 5, we assumed size-effect parameter s to be 0.8. Details of the calculation were described in Ref. [9]. Fig. 5 shows that when both hgp and hc are zero, which means that susceptibility has no imaginary part, d is also zero. (In that case, there is of course no magnetic field leakage.) A small value of hgp , however, causes magnetic field leakage, resulting in a finite value of d close to 90. Larger hgp or hc values cause leakage with a larger amplitude but a smaller d. It is estimated that a hgp (and hc ) of less than about 2 causes a d of about 70–90. This indicates that the existence of a small imaginary part in AC susceptibility ðjv00 =v0 j K 0:04Þ of the ground plane could cause the leakage magnetic field into the circuit loops with an advanced phase of about 70–90. Though these results suggest that the waveform distortion originates from an essential matter, we should be able to reduce it by
ð0 6 h 6 p=2Þ:
ð6Þ
• sandwiching the circuit between two ground planes,
M. Maruyama et al. / Physica C 392–396 (2003) 1441–1445
• moving the circuit away from the pickup coil, and • using ground plane material with a smaller imaginary part in AC susceptibility.
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Acknowledgements
Additionally, directly coupled type method of signal input instead of magnetically coupled type one would free the system from this problem [1].
We thank J.S. Tsai and W. Hattori for their helpful discussions. This work was supported by the New Energy and Industrial Technology Development Organization through ISTEC as Collaborative Research and Development of Fundamental Technologies for Superconductivity Applications.
5. Summary
References
The origin of measured waveform distortion observed in a high-resolution current-waveform measurement system based on a high-Tc superconductor sampler was theoretically investigated. The observed distortion is well explained by a model that assumes modulation of sampling timing caused by the shielding currents in the circuit loops due to magnetic field leakage. Numerical calculation showed that a small imaginary part in AC susceptibility of the YBCO ground plane could cause leakage magnetic field into the circuit loops with an advanced phase close to 90 compared to that of applied magnetic field, which coincides with the results calculated based on our model.
[1] M. Hidaka, T. Satoh, N. Ando, M. Kimishima, M. Takayama, S. Tahara, Physica C 357–360 (2001) 1521. [2] M. Hidaka, N. Ando, T. Satoh, S. Tahara, IEEE Trans. Appl. Supercond. 11 (2001) 986. [3] T. Satoh, M. Hidaka, S. Tahara, IEEE Trans. Appl. Supercond. 9 (1999) 3141. [4] H. Terai, M. Hidaka, T. Satoh, S. Tahara, Appl. Phys. Lett. 70 (1997) 2690. [5] S. Yoshida, H. Tohya, in: IEEE Int. Symp. Electromagnetic Compatibility Record, August 1998, p. 641. [6] M. Hidaka, M. Maruyama, T. Satoh, Physica C 378–381 (2002) 1435. [7] M. Maruyama, M. Hidaka, T. Satoh, IEEE Trans. Appl. Supercond., in press. [8] M. Hidaka, T. Satoh, H. Terai, S. Tahara, in: Proc. 10th Int. Symp. Supercond., Gifu, 1997, p. 1191. [9] M. Maruyama, M. Hidaka, T. Satoh, Appl. Phys. Lett. 82 (2003) 2868.
Theoretical analysis of measured waveform distortion in an HTS sampler Michitaka Maruyama *, Mutsuo Hidaka, Tetsuro Satoh Fundamental Research Laboratories, NEC Corporation, 34 Miyukigaoka, Tsukuba 305-8501, Japan Received 13 November 2002; accepted 31 January 2003
Abstract The origin of measured waveform distortion observed in a high-resolution current-waveform measurement system based on a high-Tc superconductor sampler was investigated. The observed distortion is well explained by a model that assumes sampling-timing modulation by magnetic field leakage into the sampler circuit. Calculations based on both this model and experimental results indicate that the leakage magnetic field should have an advanced phase of about 70–90 compared to that of an applied magnetic field. The observed waveform distortion apparently originates from AC susceptibility in the YBa2 Cu3 O7x (YBCO) ground plane. 2003 Elsevier B.V. All rights reserved. PACS: 85.25.)j; 06.60.Jn; 75.30.Cr; 74.76.Bz Keywords: HTS sampler; Waveform distortion; AC susceptibility; YBCO thin films
1. Introduction The continuing growth in the operation speed of communication and other electronic systems is creating strong demands for ways to observe the high-speed signal waveforms used in these systems. To meet these demands, we proposed waveform measurement based on a high-Tc superconductor (HTS) sampler [1]. The HTS sampler circuits use
*
Corresponding author. Address: Division of Electric Devices, ISTEC, SRL, 10-13 Shinonome 1-chome, Koto-ku, Tokyo 135-0062, Japan. Tel.: +81-3-3536-5709; fax: +81-33536-5717. E-mail address: [email protected] (M. Maruyama).
single flux quantum (SFQ) pulses, which enable signal detection with a bandwidth of more than 100 GHz, even at an operation temperature of around 40 K. We constructed a prototype highresolution current-waveform measurement system composed of an HTS sampler circuit, semiconductor control units, and a compact single-stage cryocooler [1,2]. The sampler circuit was fabricated based on YBa2 -Cu3 O7x (YBCO) ramp-edge Josephson junction technology [3] and has an upper-layer ground plane structure [4]. A YBCO pickup coil is built into the sampler chip and connected to the sampler circuit. This system enables non-contact current-waveform measurement, an attractive method, especially for analyzing electromagnetic interference (EMI) [5] and so forth.
0921-4534/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0921-4534(03)01044-X
1442
M. Maruyama et al. / Physica C 392–396 (2003) 1441–1445
We previously demonstrated the operation of the system and used it to observe current signals of up to 20 GHz with the correct periods [1,2]. In our observations, however, the measured sinusoidal waveforms were often distorted. The observed distortion can be roughly classified into two types. One is simple tilting of the waveform. This type of distortion is caused by current leakage due to parasitic inductance in the sampler circuit. Accordingly, it can be eliminated by inserting a buffer into the circuit [6,7]. The other is a little more complex. It is a non-linear change in the waveforms, which cannot be explained by current leakage due to parasitic inductance. In this paper, we describe a model that explains such non-linear waveform distortion. Comparison of the waveforms calculated based on this model with ones measured experimentally showed that the model explains the distortion well.
2. Operation principle of sampler system The operation principle of the system discussed in this paper is illustrated in Figs. 1 and 2. First, a magnetic field generated by a current signal in a device under test (DUT), which is placed outside of a cryochamber, is detected using a superconducting pickup coil as a shielding current ðIcoil Þ. A trigger current ðItr Þ sent to the pulse generator of the sampler circuit with a controlled delay time ðtd Þ switches trigger junction JJ1. This creates a current pulse ðIp Þ that is transmitted to a comparator, which determines the sampling timing. If the sum of Icoil , Ip and DC feedback current ðIf Þ exceeds the critical current of comparator junction JJ3, JJ3 is switched, creating an SFQ pulse, which is detected by a readout superconducting quantum interference device (SQUID) as the voltage output. These processes are repeated with different If values until the minimum value of If at which JJ1 is switched ðIfmin Þ is found. Consequently, the waveform of Icoil is reconstituted by plotting the values of ðIf0 Ifmin ) in a graph of current versus td , where If0 represents the Ifmin value obtained without input signals. Sampler operation is described in more detail elsewhere [2,8].
Fig. 1. Photographs (a) and schematic diagram (b) of highresolution current-waveform measurement system. Inset in (a) shows sampler chip in which HTS sampler circuit and pickup coil are fabricated.
Fig. 2. Equivalent circuit of HTS sampler with pickup coil.
M. Maruyama et al. / Physica C 392–396 (2003) 1441–1445
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3. Leakage magnetic field model In the sampler chip, the pickup coil is connected to the sampler circuit. The separation between them (100 lm) is much smaller than that between the DUT and the coil (2 mm). This means that not only the pickup coil but also the sampler-circuit area is exposed to the signal magnetic field. The circuit itself is nominally shielded from the magnetic field by a YBCO ground plane. In our model, we assume that some of the signal magnetic field penetrates into the sampler circuit through the ground plane as magnetic field leakage for a reason that will be discussed in the next section. Shielding currents are thus generated in the sampler circuit because the circuit is composed of superconducting loops (Fig. 2). The shielding currents in the pulse generator of the circuit change the switch timing of trigger junction JJ1, resulting in modulation of the sampling timing. 0 The shielding current flowing through JJ1 ðIsd Þ can be defined using the shielding current in Loop1 0 0 ðIsd1 Þ and that in Loop2 ðIsd2 Þ as 0 0 0 Isd Isd1 Isd2 ;
ð1Þ
0 0 where the amplitudes of Isd1 and Isd2 are determined by the inductances and by the sizes and flux densities, respectively, in Loop1 and Loop2. If we consider a sinusoidal wave to be the input signal, 0 Isd can be expressed as a sine function: 0 Isd ðtÞ ¼ b sinð2pftÞ;
ð2Þ
0 where t is time, b is the amplitude of Isd , and f is the signal frequency. Thus, the total current 0 flowing into JJ1 is the sum of Itr and Isd (Fig. 3). For simplification, we regard Itr as a linearly increasing current that rises to the critical current of JJ1 ðIc1 Þ within time str . Since the amount of modulation of the switch timing of JJ1 (Dt1 ) depends on both the magnitude 0 of Isd at the moment of switching and the steepness in the rise of Itr it is described using Eq. (2): 0 Dt1 ¼ Isd ðt1 Þ=ðIc1 =str Þ
¼ ðbstr =Ic1 Þ sinð2pft1 Þ;
ð3Þ
Fig. 3. Time sequence of trigger current Itr , shielding current 0 due to magnetic field leakage ðIsd Þ (solid lines), and total current flowing into junction JJ1 (broken line).
where t1 is the time of switching of JJ1. From Fig. 3 and Eq. (3), t1 can be described using a cyclic equation: t1 ¼ td þ t0 þ str þ Dt1 ¼ td þ t0 þ str þ ðbstr =Ic1 Þ sinð2pft1 Þ;
ð4Þ
where t0 corresponds to the difference in timing 0 between Isd and Itr , and td is the delay time of Itr which is controlled by a variable delay line and used as the time scale in the graphs of the measured waveforms. The signals measured using the sampler ðIs Þ are described using t1 : Is ¼ a sinð2pft1 dÞ;
ð5Þ
where a is the amplitude of Is and d is a fitting parameter representing the phase difference be0 tween Icoil and Isd . Substituting Eq. (4) into Eq. (5), we can calculate the measured signals and plot them in the graphs of Is versus td . Typical waveforms measured using the sampler for sinusoidal signals show non-linear distortion with sharp and rounded peaks (Fig. 4). The waveforms calculated using Eqs. (4) and (5), which are also shown in this figure, coincide well with the measured ones. Similar results were obtained for many other sinusoidal waveforms measured using
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M. Maruyama et al. / Physica C 392–396 (2003) 1441–1445
Fig. 4. Waveforms measured using sampler system (open circles), and ones calculated based on leakage magnetic field model (solid lines).
the sampler. These results suggest that the measured waveform distortion is caused by magnetic field leaking into the sampler circuit.
Fig. 5. Calculated phase difference ðdÞ between leakage magnetic field and applied magnetic field, taking effect of AC susceptibility in both the layers of ground plane and circuit loops into account.
which correspond to the ratio of the imaginary part v00 to the real part v0 according to Eq. (6).
4. Origin of magnetic field leakage
jv00 =v0 j ¼ tan h
Typical values of parameter d obtained by fitting many measured waveforms were about 70– 0 90, indicating that Isd (the shielding current in the circuit loops created by the leakage magnetic field) has an advanced phase of Icoil (the shielding current in the pickup coil created by the signal magnetic field). Note that the observed non-linear distortion with sharp and rounded peaks as shown in Fig. 4 is not obtained if one assumed jdj 90 in Eq. (5). This suggests that the origin of the magnetic field leakage (and the resultant waveform distortion) is AC susceptibility ðvac ¼ v0 þ jv00 Þ in the YBCO ground plane because the imaginary part of vac should cause a phase shift in the shielding magnetic field, resulting in magnetic field leakage with an advanced phase. Fig. 5 shows the calculated phase difference ðdÞ between the leakage magnetic field and applied magnetic field based on the above discussion, considering both the superconducting layers of the ground plane and circuit loops. Parameters hgp and hc represent the phases of vac in the layers of the ground plane and the circuit loops, respectively,
In the calculation of Fig. 5, we assumed size-effect parameter s to be 0.8. Details of the calculation were described in Ref. [9]. Fig. 5 shows that when both hgp and hc are zero, which means that susceptibility has no imaginary part, d is also zero. (In that case, there is of course no magnetic field leakage.) A small value of hgp , however, causes magnetic field leakage, resulting in a finite value of d close to 90. Larger hgp or hc values cause leakage with a larger amplitude but a smaller d. It is estimated that a hgp (and hc ) of less than about 2 causes a d of about 70–90. This indicates that the existence of a small imaginary part in AC susceptibility ðjv00 =v0 j K 0:04Þ of the ground plane could cause the leakage magnetic field into the circuit loops with an advanced phase of about 70–90. Though these results suggest that the waveform distortion originates from an essential matter, we should be able to reduce it by
ð0 6 h 6 p=2Þ:
ð6Þ
• sandwiching the circuit between two ground planes,
M. Maruyama et al. / Physica C 392–396 (2003) 1441–1445
• moving the circuit away from the pickup coil, and • using ground plane material with a smaller imaginary part in AC susceptibility.
1445
Acknowledgements
Additionally, directly coupled type method of signal input instead of magnetically coupled type one would free the system from this problem [1].
We thank J.S. Tsai and W. Hattori for their helpful discussions. This work was supported by the New Energy and Industrial Technology Development Organization through ISTEC as Collaborative Research and Development of Fundamental Technologies for Superconductivity Applications.
5. Summary
References
The origin of measured waveform distortion observed in a high-resolution current-waveform measurement system based on a high-Tc superconductor sampler was theoretically investigated. The observed distortion is well explained by a model that assumes modulation of sampling timing caused by the shielding currents in the circuit loops due to magnetic field leakage. Numerical calculation showed that a small imaginary part in AC susceptibility of the YBCO ground plane could cause leakage magnetic field into the circuit loops with an advanced phase close to 90 compared to that of applied magnetic field, which coincides with the results calculated based on our model.
[1] M. Hidaka, T. Satoh, N. Ando, M. Kimishima, M. Takayama, S. Tahara, Physica C 357–360 (2001) 1521. [2] M. Hidaka, N. Ando, T. Satoh, S. Tahara, IEEE Trans. Appl. Supercond. 11 (2001) 986. [3] T. Satoh, M. Hidaka, S. Tahara, IEEE Trans. Appl. Supercond. 9 (1999) 3141. [4] H. Terai, M. Hidaka, T. Satoh, S. Tahara, Appl. Phys. Lett. 70 (1997) 2690. [5] S. Yoshida, H. Tohya, in: IEEE Int. Symp. Electromagnetic Compatibility Record, August 1998, p. 641. [6] M. Hidaka, M. Maruyama, T. Satoh, Physica C 378–381 (2002) 1435. [7] M. Maruyama, M. Hidaka, T. Satoh, IEEE Trans. Appl. Supercond., in press. [8] M. Hidaka, T. Satoh, H. Terai, S. Tahara, in: Proc. 10th Int. Symp. Supercond., Gifu, 1997, p. 1191. [9] M. Maruyama, M. Hidaka, T. Satoh, Appl. Phys. Lett. 82 (2003) 2868.