摘要
近年來，超短脈衝之兆赫(Terahertz; THz)電磁輻射已形成一個蓬勃發展的領域。就產生此兆赫電磁波的方式而言，其中最簡單的方法乃利用飛秒級(femto-second)雷射脈衝來激發半導體光電開關，以產生暫態的脈衝電流。雖然超導體材料之超快電磁特性較為複雜，且尚未完全被瞭解，但同樣地，我們可預期利用此雷射脈衝來調制超導電流，以激發出兆赫電磁輻射。
於本論文中，我們以超短雷射脈衝來激發一外加電流源之偶極結構YBCO天線，而產生之超快電磁輻射，利用電光取樣法(EO sampling)所觀察之實驗結果，此THz電磁輻射頻率可達1.0THz。
由於以超導體所激發之電磁輻射波形略與傳統半導體不同，並且依據其他研究顯示，所得之超導體輻射其波形亦互不一致，而目前所有的理論探討僅限於THz輻射的強度變化，並未涉及輻射脈衝波形之解釋。亦即目前沒有任何的理論與模型來描述處於非平衡態之超導體暫態載子動力行為。
為了解釋我們所觀察到的超導體輻射波形，並且描述暫態載子行為，於是我們基於古典電磁理論之加速帶電粒子的觀念，來建構一個更完整的模型，而對一個外加定電流之超導天線，我們同時考慮二流體模型中之超流載子(supercarrier)與常態載子(normal carrier)隨時間變化之分佈模式及運動方式，並依Rothwarf and Taylor方程式，我們可以解析出，處於非平衡態超導體\材料之暫態載子行為。
我們經由此模型所計算結果成功地與實驗得之波形來進行擬合(fitting)，可以估計出YBCO超導體內之準粒子再復合速率(quasiparticle recombination rate)與聲子對破壞生存期(phonon pair breaking time)的乘積約為金屬超導體(鉛)的五倍，這顯示YBCO超導體較金屬性超導體，具有更強的電-聲交互作用(electron-phonon interaction);而所得之另一重要擬合參數-常態載子遷移率,則展現YBCO薄膜為雜質支配之特性，而其值可估計為μq = 660 (cm2 / V-s)。
我們也廣泛地藉由量測激發光強度、外加電流與溫度對THz強度的變化來探討YBCO天線之輻射特性。我們觀察到THz輻射強度與激發光強度變化有一飽和的趨勢，而其與外加電流變化則為非線性關係，此飽和趨勢應為局部熱效應表現，然而對電流變化所展現的非線性行為，則顯示出我們的模型應稍加以修正，以期更精確地描述非平衡態超導體內暫態載子之行為，最後我們深入探討此偏離之可能之形成原因，以完成本論文。

The physics of short-pulse terahertz radiation has recently become an active research field, with interest both in fundamental aspects of generation and detection of tera-hertz (THz) radiation and in spectroscopic applications after many pioneering researches done in the past twenty years. Many methods have been exploited to develop different sources of pulsed THz. One simple method to generate THz radiation is to create the ultrafast current transients in a semiconductor switch illuminated with femtosecond laser pulses. It is also expected that the THz radiation should be emitted from superconductors if the supercurrent is modulated at a sufficiently high speed by femtosecond laser pulses. However, the ultrafast electromagnetic properties of radiated THz pulses from superconductors are generally quite complicated and not well understood. This is particularly true when high power of THz is generated at the condition of high bias current or pumping power.
In this dissertation, we observed the ultrashort electromagnetic pulse radiation from a current-biased bow-tie structure of YBa2Cu3O7-δ thin film dipole antenna on MgO substrate by using 100 fs, 750 nm laser pulses. With the scheme of electro-optic detection, we obtained the THz pulses with 1.0 ps full width at half maximum, containing frequency components up to 1.0 THz. The parallel polarization of THz radiation emitted from a current biased superconductive antenna to the direction of the bias current exhibits that the ultrashort pulses were due to a straight current flowing along the bridge, not the current loop at the luminous area of the bridge.
The observed radiation waveforms emitted from a superconductor differ slightly from that radiated by a conventional semiconductor antenna. Moreover, the radiation waveforms for superconductors obtained by other researches are also dissimilar to each other. Almost all other researchers focused on the dependence of THz radiation amplitude for superconductors, they did not address the radiated pulse shape. Namely, no theories or models have been developed to describe the transient carrier dynamics in the nonequilibrium state of superconductors.
In order to explain the shape of radiation waveforms emitted from the superconductor and describe the transient carrier dynamics, first we discuss the experimental results in relation to the radiation pattern, polarization, and capacitor effect to confirm the origin of ultrashort electromagnetic pulses radiated from a superconducting antenna. Then, we construct a more complete model by using the concept of carrier acceleration based on the classical electrodynamics. For a constant-current biased superconducting antenna, we propose that the total constant current density consists of time-varying suppercarriers and normal carriers in the two-fluid model when the superconducting antenna is excited by femtosecond laser pulses. The transient carrier dynamics in this nonequilibrium state can be obtained by using the Rothwarf and Taylor rate equations. We have solved successfully the time transient quasiparticles density in the nonequilibrium state of superconductors and the calculated far-field radiation fits well for the radiation waveforms with some fitting parameters, such as the recombination rate, phonon pair breaking time and the mobility of the normal carriers.
Through the simulated fitting with our observed waveforms, we can estimate that the product of quasipartcle recombination rate and phonon pair breaking time for the YBCO superconductor at low temperatures is five-time larger than the metallic superconductor Pb. It implies that the YBCO superconductor presents a stronger electron-phonon interaction than the metallic superconductor. The effective mobility for normal carriers also obtained from the fitting shows the impurity dominated characteristics of the YBCO thin film and the mobility in real units is estimated to be μq = 660 (cm2 / V-s), comparable to the hole mobility of Si at room temperature.
We also investigated widely the THz emission properties of YBCO antenna by measuring the pumping power, bias current and ambient temperature dependences on the radiation amplitudes. The THz peak amplitude dependence shows the saturation and a nonlinear behavior with a higher excitation pumping power and with the applied bias currents. The saturation on the dependence with the excitation powers exhibits the bolometric heating in nature. However, the measured nonlinear dependence on the applied bias current deviated from our linear simulated results on the effective current density especially at moderate and high pump powers or low temperatures. It indicates that our model should be considered more accurately describing the deviation. Finally, we discussed the possibilities to eliminate the deviation by replacing a nonlinear term in the supercarrier density for our model or taking the screen effects into account with the simulated results.

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[22] P. G. de GENNES, “Superconductivity of Metals and Alloys”, Addison-Wesley Publishing Co., Inc., Ch. 6-5, P. 184, (1989).
[23] Same as [21], Ch. 4.4, P. 123.

Ch.III. References

[1] Y. Cai, I. Brener, J. Lopata, J. Wynn, L. Pfeiffer, J. B. Stark, Q. Wu, X. C. Zhang, J. F. Federici, “Coherent terahertz radiation detection: Direct comparison between free-space electro-optic sampling and antenna detection”, Appl. Phys. Lett. 73, 444 (1998).
[2] S. G. Han, Z. V. Vardeny, K. S. Wong, O. G. Symko, and G. Koren, “Femtosecond optical detection of quasiparticle dynamics in high-Tc YBa2Cu3O7-δ superconducting thin films”, Phys. Rev. Lett. 65, 2708 (1990)
[3] Masayoshi Tonouchi, Masahiko Tani, Zhen Wang, Kiyomi Sakai, Seiji Tomozawa, Masanori Hangyo, Yoshishige Murakami and Shin-ichi Nakashima, “Ultrashort electromagnetic pulse radiation from YBCO thin films excited by femtosecond optical pulse”, Jpn. J. Appl. Phys. Part 1, 35, 2624 (1996).
[4] Masahiko Tani, Masayoshi Tonouchi, Masanori Hangyo, Zhen Wang, Noriaki Onodera and Kiyomi Sakai, “Emission properties of YBa2Cu3O7-δ-film photoswitches as terahertz radiation sources”, Jpn. J. Appl. Phys. 36, 1984 (1997).
[5] Christian Jaekel, Hartmut G. Roskos and Heinrich Kurz , “Ultrafast optoelectronic switches based on high-Tc superconductors”, IEEE Transactions on Applied Superconductivity, 7, 3722 (1997).
[6] Po-Iem Lin, K. H. Wu, J. Y. Juang, J.-Y. Lin, T. M. Uen, and Y. S. Gou, “Free-Space electrooptic sampling of terahertz radiation from optically excited superconducting YBa2Cu3O7-δ thin films”, IEEE Transactions on Applied Superconductivity, 13, 20 (2003).
[7] F. A. Hegmann, J. S. Preston, “Origin of the fast photoresponse of epitaxial YBa2Cu3O7-δ thin films”, Phys. Rev. B 48, 16023 (1993).
[8] C. Jaekel, H. G. Roskos and H. Kurz, “Emission of picosecond electromagnetic pulses from optically excited superconducting bridges”, Phys. Rev. B 54, 6889 (1996).
[9] Masayoshi Tonouchi, Masahiko Tani, Zhen Wang, Kiyomi Sakai, Noboru Wada and Masanori Hangyo, “Terahertz emission study of femtosecond time-transient nonequilibrium state in optically excited YBa2Cu3O7-δ thin films”, Jpn. J. Appl. Phys. Part 2, 35, L1578 (1996).
[10] Michael Tinkham, “Introduction to superconductivity”, McGraw-Hill international Editions, Ch. 11, P. 408. (1996).
[11] S. D. Brorson, A. Kazeroonian, J. S. Moodera, D. W. Face, T. K. Cheng, E. P. Ippen, M. S. Dresselhaus, and G. Dresselhaus, “Femtosecond room-temperature measurement of the electron-phonon coupling constant λ in metallic superconductors”, Phys. Rev. Lett. 64, 2172 (1990).
[12] J. M. Chwalek, C. Uher, J. F. Whitaker, G. A. Mourou, J. Agostinelli and M. Lelental, “Femtosecond optical absorption studies of nonequilibrium electronic processes in high Tc superconductors”, Appl. Phys. Lett. 57, 1696 (1990).
[13] Y. S. Lai, Y. Q. Liu, W. L. Cao, Chi H. Lee, Zhi-Yuan Shen, Philip Pang, Dennis J. Kountz, and William L. Holstein, “Picosecond optical response of Tl2Ba2CaCu2O8 and Tl0.5Pb0.5Sr2(Ca0.8Y0.2)Cu2O7 high Tc superconductor films”, Appl. Phys. Lett. 66, 1135 (1995).
[14] Nathan Bluzer, “Temporal relaxation measurements of photoinduced nonequilibrium in superconductors”, J. Appl. Phys. 71, 1336 (1992).
[15] A. Frenkel, ” Mechanism of nonequilibrium optical response of high-temperature superconductors”, Phys. Rev. B 48, 9717 (1993).

Ch. IV. References

[1] David K. Cheng, “Field and wave electromagnetics”, Addison-Wesley 2nd, Ch. 11, P. 607, (1989).
[2] David J. Griffiths, “Introduction to electrodynamics”, Prentice Hall International, Inc. 3rd, Ch. 3.4 and Ch11.1.4, (1999).
[3] Masayoshi Tonouchi, Masahiko Tani, Zhen Wang, Kiyomi Sakai, Seiji Tomozawa, Masanori Hangyo, Yoshishige Murakami and Shin-ichi Nakashima, “Ultrashort electromagnetic pulse radiation from YBCO thin films excited by femtosecond optical pulse”, Jpn. J. Appl. Phys. Part 1, 35, 2624 (1996).

Ch. V. References

[1] Cheng-Chung John Chi, “Microwave response of nonequilibrium superconductors”, Ph. D. dissertation submitted at University of Pennsylvania, P.139, (1976).
[2] Charles Kittel, “Introduction to solid state physics”, John Wiley & Sons, Inc., 7th, Ch. 12, P. 354, (1996).
[3] Charles P. Poole, Jr., Timir Datta, and Horacio A. Farach, “Copper oxide superconductors”, John Wiley & Sons, Inc., Ch. VIII, P. 150, (1988).
[4] Masahiko Tani, Masayoshi Tonouchi, Masanori Hangyo, Zhen Wang, Noriaki Onodera and Kiyomi Sakai, “Emission properties of YBa2Cu3O7-δ-film photoswitches as terahertz radiation sources”, Jpn. J. Appl. Phys. 36, 1984 (1997).
[5] Masayoshi Tonouchi, Masahiko Tani, Zhen Wang, Kiyomi Sakai, Seiji Tomozawa, Masanori Hangyo, Yoshishige Murakami and Shin-ichi Nakashima, “Ultrashort electromagnetic pulse radiation from YBCO thin films excited by femtosecond optical pulse”, Jpn. J. Appl. Phys. Part 1, 35, 2624 (1996).

Appendix A. References

[1] Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams”, Appl. Phys. Lett. 67, 3523 (1995).
[2] Q. Wu, M. Litz and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors”, Appl. Phys. Lett. 68, 2924 (1996).
[3] A. Nahata, D. H. Auston, T. F. Heinz and C. Wu, “Coherent detection of freely propagating terahertz radiation by electro-optic sampling”, Appl. Phys. Lett. 68, 150 (1996).
[4] A. Nahata, A. S. Weling and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electrooptic sampling”, Appl. Phys. Lett. 69, 2321 (1996).
[5] Amnon Yariv and Pochi Yeh, “Optical Waves in Crystals: Propagation and Control of Laser Radiation”, John Wiley & Sons, New York, Ch. 4 (1984).
[6] Same as [5], Ch. 7.
[7] Robert W. Boyd, “Nonlinear Optics”, Academic Press, Inc. Ch. 10, P. 403 (1992).
[8] Same as [5], Ch. 7.
[9] Same as [5], Ch. 7, Table 7.1, Table 7.2, Table 7.3.
[10] Same as [5], Ch. 5, P. 129.
[11] Eugene Hecht, “Optics”, Addison Wesley, 4th ed., Ch. 8, P. 378 (2002).