微结构中波的动力学及共振现象的研究
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摘要
随着科学技术的不断进步和信息社会的发展，集成光学，大规模集成电子线路和量子电子器件等信息技术已逐步接近和达到微纳尺度，对此领域的研究是21世纪高新技术发展所急需的先导和支撑．本论文围绕着微结构中波的动力学及共振现象这一主题开展研究．作者取得的主要研究成果是：
(1)研究了光学微结构中有限光束的反常侧向位移及其机制．首先，研究了有限光束穿过薄介质板时透射光束存在侧向位移、角偏转、束腰宽度的修正以及焦点的纵向移动四种非几何光学效应，给出了该侧向位移反向时入射角及介质板的厚度所需满足的必要条件，报道了利用微波技术首次在实验上观测到穿过薄介质板时波束的反向位移．其次，研究发现了有限光束穿过左手介质板时共振增强的侧向位移，可以为负，也可以为正．这个结果说明，薄介质板结构中的负侧向位移与负折射率材料无关，是介质板边界效应相互作用的结果．最后，我们利用多个有限光束之间的干涉效应揭示了薄介质板结构中反常侧向位移的物理机制。
(2)研究了二维量子微结构中电子束的空间位移及其调制。研究发现电子束穿过半导体量子势垒的空间位移与电子波的Snell定律预言的结果不同，并且当电子束的入射角小于且接近临界角时透射电子束的空间位移具有共振增强效应。其次，发现在半导体量子势阱结构中透射或反射电子束的空间位移可以为正也可以为负，并且给出了电子束位移为负的必要条件。更重要的是，首次发现了在磁电势垒结构中电子束的正、负位移可以通过外加电场或磁场进行调制．这些新奇现象将为新型量子电子器件提供新的思路。
(3)研究了量子结构中粒子的反常群时延及其物理机制。人们已经在理论和实验上证明了量子势阱中粒子的负群时延。在此基础上，系统地研究了单个非对称量子势垒中反射和透射时延。研究发现，在消逝场和行波场的情况下，反射和透射时延与势垒高度以及势垒外两边势能的相对高度有关，且可正或可负。在消逝场的情况下，即当粒子的入射能量比势垒高度低时，在非透明势垒极限下反射和透射时延与势垒厚度无关，表现出超光速性。在行波场的情况下，即当粒子的入射能量大于势垒高度时，反射与透射时延是势垒厚度的周期函数，具有共振增强效应。最后，从多个波包干涉的角度解释了量子势阱结构中粒子的负群时延，并且进一步揭示了量子势垒结构中Hartman效应的本质。
(4)研究了相对论性粒子在量子结构中的渡越时间。首先，主要讨论了相对论性粒子穿越量子势阱群时延的性质。研究表明，相对论性粒子穿越势阱的时延与非相对论的情况类似具有超光速性，甚至可以为负，并且提出了群时延为负的必要条件。进一步分析发现负群时延与其在共振点处反常依赖于势阱宽度有关。数值比较说明了在相对论量子理论中群时延大于在非相对论量子理论中相应的群时延。此外，进一步推广了在非相对论量子理论中一种不具有超光速的渡越时间——能量转移时间，分别讨论了消逝场和行波场两种情况下相对论性粒子穿过势垒时该渡越时问的亚光速性。研究表明，在消逝场情况下，能量转移时间的特性与非相对论的情况类似，不具有超光速性。同样，在行波场情况下，能量转移时间也不存在超光速的问题。
With the progress of science & technology and the development of information society, information technology such as integrated optics, large-scaled integrated circuits and quantum electronic devices has approached and even reached nanometre scale. Therefore, the research in this field is the forunner and basis for the high technology development in the 21st century. In this Ph. D. dissertation, the investigations of the wave dynamics and its resonance phenomena in the microstructures are presented. The main results given by the author are as follows:
(i) The anomalous lateral displacement and its mechanism in the optics microstructures are investigated. Firstly, it is reported that the finite-sized light beam transmitted through a thin dielectric slab experiences four non-geometric effects, such as lateral displacement, angular deflection, modification of waist width, and longitudinal focal shift. Necessary conditions are advanced for the lateral displacement to be backward. The experimental observations of the backward displacement in the microwave region are reported for the first time. Secondly, I have found that the resonance-enhanced lateral displacement of the light beam transmitted through a left-handed slab can also be negative as well as positive. These show that the negative lateral displacement of the finite-sized light beam transmitted through a thin dielectric slab is the result of the interaction of the boundary effects of the slab, and have nothing to do with the negative refractive index itself. Finally, we have investigated the origin of the anomalous displacements in a thin dielectric slab by the interference between the multiple finite-sized light beam.
(ii) The lateral displacements of the electron beam and their modulation in the two-dimensional quantum microstructures are investigated. It is found that the displacement of the electron beams transmitting through a two-dimensional semiconductor barrier is quite different from the prediction from Snell's law for electron waves. It is shown that the displacement can be greatly enhanced by transmission resonance when the incidence angle is less than but close to the critical angle for total reflection. In addition, the lateral displacement of the transmitted electron beam through a semiconductor quantum well can be negative as well as positive. The necessary condition is obtained for the displacement to be negative. More importantly, the positive and negative displacements of the electron beam in transmission through a two-dimensional electron gas can be modulated by a ferromagnetic (FM) stripe under an applied voltage. These phenomena may lead to novel applications in quantum electronic devices.
(iii) The anomalous group delay in the quantum structures and its mechanism are investigated. The theoretical and experimental researches have demonstrated that the group delay for quantum particles traveling through a potential well can be negative. Accordingly, the reflection and transmission group delay times are systematically investigated in an asymmetric single quantum barrier. It is found that the reflection times in both evanescent and propagating cases can be negative as well as positive, depending on the relative height of the potential energies on the two sides of the barrier. In evanescent case where the energy of incident particles is less than the height of the barrier, the reflection and transmission group delay times in the opaque limit are both independent of the barrier's thickness. In the propagating case where the energy of incident particles is larger than the height of the barrier, the group delay times depend periodically on the barrier's thickness, thus can be greatly enhanced by the transmission resonance. Finally, the physical mechanism of superluminal and even negative group delay in quantum well structure and the nature of Hartman effect in quantum barrier structure are investigated from the viewpoint of interference between multiple finite wave packets, due to the multiple reflections.
(iv) The traversal times for Dirac particles through the quantum microstruc-tures are investigated. Firstly, the properties of group delay for Dirac particles traveling through a quantum potential well are investigated. A necessary condition is put forward for the group delay to be negative. It is shown that this negative group delay is closely related to its anomalous dependence on the width of the potential well around the resonance points. Furthermore, a traversal time that has no problem of superluminality for particles to tunnel through potential barriers in the non-relativistic quantum theory is generalized to Dirac's relativistic quantum theory. Both evanescent and propagating cases are considered. It is shown that the traversal time in the evanescent case has much the same properties as in the non-relativistic quantum theory and thus has no problem of superluminality. It also gets rid of the problem of superluminality in the propagating case. Comparisons with the dwell time, the group delay, and the velocity of monochromatic front are also made.
(1)研究了光学微结构中有限光束的反常侧向位移及其机制．首先，研究了有限光束穿过薄介质板时透射光束存在侧向位移、角偏转、束腰宽度的修正以及焦点的纵向移动四种非几何光学效应，给出了该侧向位移反向时入射角及介质板的厚度所需满足的必要条件，报道了利用微波技术首次在实验上观测到穿过薄介质板时波束的反向位移．其次，研究发现了有限光束穿过左手介质板时共振增强的侧向位移，可以为负，也可以为正．这个结果说明，薄介质板结构中的负侧向位移与负折射率材料无关，是介质板边界效应相互作用的结果．最后，我们利用多个有限光束之间的干涉效应揭示了薄介质板结构中反常侧向位移的物理机制。
(2)研究了二维量子微结构中电子束的空间位移及其调制。研究发现电子束穿过半导体量子势垒的空间位移与电子波的Snell定律预言的结果不同，并且当电子束的入射角小于且接近临界角时透射电子束的空间位移具有共振增强效应。其次，发现在半导体量子势阱结构中透射或反射电子束的空间位移可以为正也可以为负，并且给出了电子束位移为负的必要条件。更重要的是，首次发现了在磁电势垒结构中电子束的正、负位移可以通过外加电场或磁场进行调制．这些新奇现象将为新型量子电子器件提供新的思路。
(3)研究了量子结构中粒子的反常群时延及其物理机制。人们已经在理论和实验上证明了量子势阱中粒子的负群时延。在此基础上，系统地研究了单个非对称量子势垒中反射和透射时延。研究发现，在消逝场和行波场的情况下，反射和透射时延与势垒高度以及势垒外两边势能的相对高度有关，且可正或可负。在消逝场的情况下，即当粒子的入射能量比势垒高度低时，在非透明势垒极限下反射和透射时延与势垒厚度无关，表现出超光速性。在行波场的情况下，即当粒子的入射能量大于势垒高度时，反射与透射时延是势垒厚度的周期函数，具有共振增强效应。最后，从多个波包干涉的角度解释了量子势阱结构中粒子的负群时延，并且进一步揭示了量子势垒结构中Hartman效应的本质。
(4)研究了相对论性粒子在量子结构中的渡越时间。首先，主要讨论了相对论性粒子穿越量子势阱群时延的性质。研究表明，相对论性粒子穿越势阱的时延与非相对论的情况类似具有超光速性，甚至可以为负，并且提出了群时延为负的必要条件。进一步分析发现负群时延与其在共振点处反常依赖于势阱宽度有关。数值比较说明了在相对论量子理论中群时延大于在非相对论量子理论中相应的群时延。此外，进一步推广了在非相对论量子理论中一种不具有超光速的渡越时间——能量转移时间，分别讨论了消逝场和行波场两种情况下相对论性粒子穿过势垒时该渡越时问的亚光速性。研究表明，在消逝场情况下，能量转移时间的特性与非相对论的情况类似，不具有超光速性。同样，在行波场情况下，能量转移时间也不存在超光速的问题。
With the progress of science & technology and the development of information society, information technology such as integrated optics, large-scaled integrated circuits and quantum electronic devices has approached and even reached nanometre scale. Therefore, the research in this field is the forunner and basis for the high technology development in the 21st century. In this Ph. D. dissertation, the investigations of the wave dynamics and its resonance phenomena in the microstructures are presented. The main results given by the author are as follows:
(i) The anomalous lateral displacement and its mechanism in the optics microstructures are investigated. Firstly, it is reported that the finite-sized light beam transmitted through a thin dielectric slab experiences four non-geometric effects, such as lateral displacement, angular deflection, modification of waist width, and longitudinal focal shift. Necessary conditions are advanced for the lateral displacement to be backward. The experimental observations of the backward displacement in the microwave region are reported for the first time. Secondly, I have found that the resonance-enhanced lateral displacement of the light beam transmitted through a left-handed slab can also be negative as well as positive. These show that the negative lateral displacement of the finite-sized light beam transmitted through a thin dielectric slab is the result of the interaction of the boundary effects of the slab, and have nothing to do with the negative refractive index itself. Finally, we have investigated the origin of the anomalous displacements in a thin dielectric slab by the interference between the multiple finite-sized light beam.
(ii) The lateral displacements of the electron beam and their modulation in the two-dimensional quantum microstructures are investigated. It is found that the displacement of the electron beams transmitting through a two-dimensional semiconductor barrier is quite different from the prediction from Snell's law for electron waves. It is shown that the displacement can be greatly enhanced by transmission resonance when the incidence angle is less than but close to the critical angle for total reflection. In addition, the lateral displacement of the transmitted electron beam through a semiconductor quantum well can be negative as well as positive. The necessary condition is obtained for the displacement to be negative. More importantly, the positive and negative displacements of the electron beam in transmission through a two-dimensional electron gas can be modulated by a ferromagnetic (FM) stripe under an applied voltage. These phenomena may lead to novel applications in quantum electronic devices.
(iii) The anomalous group delay in the quantum structures and its mechanism are investigated. The theoretical and experimental researches have demonstrated that the group delay for quantum particles traveling through a potential well can be negative. Accordingly, the reflection and transmission group delay times are systematically investigated in an asymmetric single quantum barrier. It is found that the reflection times in both evanescent and propagating cases can be negative as well as positive, depending on the relative height of the potential energies on the two sides of the barrier. In evanescent case where the energy of incident particles is less than the height of the barrier, the reflection and transmission group delay times in the opaque limit are both independent of the barrier's thickness. In the propagating case where the energy of incident particles is larger than the height of the barrier, the group delay times depend periodically on the barrier's thickness, thus can be greatly enhanced by the transmission resonance. Finally, the physical mechanism of superluminal and even negative group delay in quantum well structure and the nature of Hartman effect in quantum barrier structure are investigated from the viewpoint of interference between multiple finite wave packets, due to the multiple reflections.
(iv) The traversal times for Dirac particles through the quantum microstruc-tures are investigated. Firstly, the properties of group delay for Dirac particles traveling through a quantum potential well are investigated. A necessary condition is put forward for the group delay to be negative. It is shown that this negative group delay is closely related to its anomalous dependence on the width of the potential well around the resonance points. Furthermore, a traversal time that has no problem of superluminality for particles to tunnel through potential barriers in the non-relativistic quantum theory is generalized to Dirac's relativistic quantum theory. Both evanescent and propagating cases are considered. It is shown that the traversal time in the evanescent case has much the same properties as in the non-relativistic quantum theory and thus has no problem of superluminality. It also gets rid of the problem of superluminality in the propagating case. Comparisons with the dwell time, the group delay, and the velocity of monochromatic front are also made.
引文
[1] F. Goos and H. Hanchen, Ein neuer und funamentaler Versuch zur Totalreflexion, Ann. Phys. (Leipzig) 1, 333-346 (1947).
[2] K. V. Artmann, Berechung der seitenversetzung des reflektieren strahles, Ann. Phys. (Leipzig) 2, 87-102 (1948).
[3] H. K. V. Lotsch, Beam displacements at total reflection: The Goos-Hanchen effect, Optik (Stuttgart) 32, 116-137 (1970); 32, 189-204 (1970); 32, 299-319 (1971); 32, 553-569 (1971).
[4] H. M. Lai and S. W. Chan, Large and negative Goos-Hanchen shift near the Brewster dip on reflection from weakly absorbing media, Opt. Lett. 27, 680-682 (2002).
[5] W. J. Wild and C. Lee Giles, Goos-Hanchen shifts from absorbing media, Phys. Rev. A., 25, 2099-2101 (1982).
[6] J. Birman, D. N. Pattanayak, and A. Puri, Prediction of a resonance-enhanced Laser-beam displacement at total internal reflection in semiconductors, Phys. Rev. Lett. 50, 1664-1667 (1983).
[7] E. Pfleghaar, A. Mareseille, and A. Weis, Quantitative investigation of the effect of resonant absorbers on the Goos-Hanchen shift, Phys. Rev. Lett. 70 2281-2284 (1993).
[8] B. A. Anicin, R. Fazlic, and M. Kopric, Theoretical evidence for negative Goos-Hanchen shifts, J. Phys. A, 11, 1657-1662 (1978).
[9] C. K. Carniglia and K. R. Brownstein, Focal shift and ray mode for total internal reflection, J. Opt. Soc. Am. 67, 121-122 (1977).
[10] A. Haibel, G. Nimtz, and A. A. Stahlhofen, Frustrated total reflection: The double-prism revisited, Phys. Rev. E 63, 047601 (2001).
[11] T. Tamir and H. L. Bertoni, Lateral displacement of optical beams at multilayered and periodic structures, J. Opt. Soc. Am. 61, 1397-1413 (1971).
[12] B. R. Horowitz and T. Tamir, Lateral displacement of a light beam at a dielectric interface, J. Opt. Soc. Am. 61, 586-594 (1971).
[13] C. W. Huse and T. Tamir, Lateral displacement and distortion of beams incident upon a transmitting layer configuration, J. Opt. Soc. Am. A 2, 978-987 (1985).
[14] T. Tamir, Nonspecular phenomena in beam fields reflected by multilayered media, J. Opt. Soc. Am. A 3, 558-565 (1986).
[15] R. P. Riesz and R. Simon, Reflection of a Gaussian beam from a dielectric slab, J. Opt. Soc. Am. A 2, 1809-1817 (1985).
[16] C. W. Hsue and T. Tamir, Lateral beam displacements in transmitting layered structures, Opt. Commun. 49, 383-387 (1984).
[17] R. Briers, O. Leroy, and G. Shkerdin, Bounded beam interaction with thin inclusions. Characterization by phase differences at l~yleigh angle incidence, J. Acoust. Soc. Am. 108, 1622-1630 (2000).
[18] O. Emile, T. Galstyan, A. LeFloch, and F. Bretenaker, Measurement of the nonlinear Goos-Hanchen effect for Gaussian optical beams, Phys. Rev. Lett. 75, 1511-1513 (1995).
[19] B. M. Jost, A. A. R. Al-Rashed, and B. E. A. Salch, Observation of the Goos-Hanchen effect in a phase-conjugate mirror, Phys. Rev. Lett. 81, 2233-2235 (1998).
[20] N. J. Harrick, Study of physics and chemistry of surfaces from frustrated total internal reflections, Phys. Rev. Lett. 4, 224-226 (1960).
[21] V. K. Ignatovich, Neutron reflection from condensed matter, the Goos-Hanchen effect and coherence, Phys. Lett. A 322, 36-46 (2004).
[22] X. Chen, C.-F. Li, and Y. Ban, Novel displacement in transmission through a two-dimensional semiconductor barrier, Phys. Lett. A 354, 161-165 (2006).
[23] S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge University Press, New York, (1996) 276.
[24] M. Crespo and S. Datta, Physics Today 74-82, Feb. (1990).
[25] D. W. Wilson and T. K. Gaylord, Electron waveguiding characteristics and ballistic current capacity of semiconductor quantum slabs, IEEE J. Quantum Electron, 29, 1364-1382 (1993).
[26] T. K. Gaylord and K. F. Brennan, Electron wave optics in semiconductors, J. Appl. Phys, 65(2), 814-820 (1988).
[27] T. K. Gaylord, E. N. Glytsis, G. N. Henderson, K. P. Martin, D. B. Walker, D. W. Wilson, and K. F. Brennan, Ballistic electron transport in semiconductor heterostructures and its analogies in electromagnetic propagation in general dielectrics, Proc. IEEE 79, 1643-1659 (1991).
[28] J. Spector, H. L. Stormer, K. W. Baldwin, L. N. Pfeiffer, and K. W. West, Electron focusing in two-dimensional systems by means of an electrostatic lens, Appl. Phys. Lett. 56, 1290-1292 (1990).
[29] J. Spector, H. L. Stormer, K. W. Baldwin, L. N. Pfeiffer, and K. W. West, Refractive switch for two-dimensional electron, Appl. Phys. Lett. 56, 2433-2435 (1990).
[30] K. Furuya, Novel high-speed transistor using electron-wave diffraction, J. Appl. Phys. 62, 1492-1494 (1987).
[31] K. Firiya and K. Kurishima, Theoretical properties of electron wave diffraction due to a transversally periodic structure in semiconductors, IEEE J. Quantum Electron 24, 1652-1658 (1988).
[32] S. Datta, Quantum devices, Superlattices Microstructures 6, 83-89 (1989).
[33] F. Sols, M. Macucci, U. Ravaioli, and K. Hess, On the possibility of transistor action based on quantum interference phenomena, Appl. Phys. Lett. 54, 350-352 (1989).
[34] F. Sols, M. Macucci, U. Ravaioli, and K. Hess, Theory for a quantum modulated transistor, J. Appl. Phys. 66, 3892-3906 (1989).
[35] S. Subramaniam, S. Bandyopadhyay, and W. Porod, Analysis of the device performance of quantum interference transistors utilizing ultrasmall semiconductor T structures, J. Appl. Phys. 68, 4861-4870 (1991).
[36] C. C. Eugster and J. A. del Alamo, Tunneling spectroscopy of an electron waveguide, Phys. Rev. Lett. 67, 3586-3589 (1991).
[37] J. A. del Alamo and C. C. Eugster, Quantum field-effect directional coupler, Apph Phys. Lett. 56, 78-80 (1990).
[38] N. Tsukada, A. D. Wieck and K. Ploog, Proposal of novel electron wave coupled devices, Appl. Phys. Lett. 56, 2527-2529 (1990).
[39] R. Q. Yang and J. M. Xu, Analysis of guided electron waves in coupled quantum wells, Phys. Rev. B 43, 1699-1706 (1991).
[40] R. Q. Yang and J. M. Xu, Energy-dependent electron wave coupling between two asymmetric quantum well waveguides, Appl. Phys. Lett. 59, 315-317 (1991).
[41] J. Q. Wang, $. Q. Yuan, B. Y. Gu and G. Z. Yang, Guided electron waves in coupled deep quantum wells, Phys. Rev. B 44, 13618-13625 (1991).
[42] L. Thylen and Q. Sahen, Switch energy analysis of quantum interference directional couplers, IEEE J. Qunantum Electron 28, 31-33 (1992).
[43] R. H. Renard, Total reflection: a new evaluation of the Goos-Hanchen shift, J. Opt. Soc. Am. 54, 1190-1197 (1964).
[44] J. L. Carter and H. Hora, Total reflection of matter waves: The Goos-Hanchen effect for grazing incidence, J. Opt. Soc. Am. 61, 1640-1645 (1971).
[45] S. C. Miller, Jr., and N. Ashby, Shifts of electron beam position due to total reflection at a barrier, Phys. Rev. Lett. 29, 740-743 (1972);
[46] D. M. Fradkin and R. J. Kashuba, Spatial displacement of electrons due to multiple total reflections, Phys. Rev. D 9, 2775-2788 (1974);
[47] D. M. Fradkin and R. J. Kashuba, Position-operator method for evaluating the shift of a totally reflected electron, Phys. Rev. D 10, 1137-1145 (1974).
[48] L. Arthur, A. Read, and G. E. Reesor, Displacement of a microwave beam upon transmission through a dielectric slab, Can. J. Phys. 57, 1409-1413 (1979).
[49] L. Arthur, A. Read, Wong Man, and G. E. Reesor, Displacement of an electromagnetic beam upon reflection from a dielectric slab, J. Opt. Soc. Am. A 68, 319-322 (1978).
[50] C.-F. Li, Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects, Phys. Rev. Lett. 91, 133903 (2003).
[51] X.-H. Huang and C.-F. Li, Novel light beam propagation through optical "potential well", Europhys. Lett. 63, 28-34 (2003).
[52] C.-F. Li and Q. Wang, Prediction of simultaneously large and opposite generalized Goos-Hiinchen shifts for TE and TM light beams in an asymmetric double-prism configuration, Phys. Rev. E 69, 055601(R) (2004).
[53] C.-F. Li and X.-Y. Yang, Thin-film enhanced Goos-Hanchen shift in total internal reflection, Chin. Phys. Lett. 21,485-488 (2004).
[54] 朱绮彪，李春芳，陈玺，双棱镜结构中的透射光束的Goos-Hanchen位移，光学学报5，673-675(2005)．
[55] X.-B. Liu, Cao Z.-Q., Zhu P.-F., Shen Q.-S., and Liu X.-M., Large positive and negative lateral optical beam shift in prism-waveguide coupling system, Phys. Rev. E. 73, 056617 (2006).
[56] X.-B. Liu, Cao Z.-Q., Zhu P.-F., Shen Q.-S., and Liu X.-M., Simultaneously large and opposite lateral beam shifts for TE and TM modes on a double metal-cladding slab, Chin. Phys. Lett. 23(S), 2077-2079 (2006).
[57] L.-G. Wang, H. Chert, and S.-Y. Zhu, Large negative Goos-Hanchen shift from a weakly absorbing dielectric slab, Opt. Lett. 30, 2936-2938 (2005).
[58] L.-G. Wang and S.-Y. Zhu, Large positive and negative Goos-Hanchen shifts from a weakly absorbing left-handed slab, J. Appl. Phys. 98, 043522 (2005).
[59] L.-G. Wang, and S.-Y. Zhu, Gaint lateral shift of a light beam at the defect mode in one-dimensional photonic crystals, Opt. Lett. 31, 101-103 (2006).
[60] A. Ranfagni, D. Mugnai, P. Fabeni, and G. P. Pazzi, Delay-time measurements in narrowed waveguides as a test of tunneling, Appl. Phys. Lett. 58, 774-776 (1991).
[61] A. Enders and G. Nimtz, Zero-time tunneling of evanescent mode packets, J. Phys. I (France) 3, 1089-1092 (1993).
[62] A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, Measurement of the single-photon tunneling time, Phys. Rev. Lett. 71(5), 708-711 (1993).
[63] Ch. Spielmann, R. Szipocs, A. Stingl, and F. Krausz, Tunneling time of optical pulses through photonic band gaps, Phys. Rev. Lett. 73, 2308-2311 (1994).
[64] Ph. Balcou and L. Dutriaux, Dual optical tunneling time in frustrated total internal reflection, Phys. Rev. Lett. 78, 851-854 (1997).
[65] A. Haibel and G. Nimtz, Universal relationship of time and frequency in photonic tunneling, Ann. Phys. (Leipzig) 9, 1-5 (2001).
[66] A. M. Steinberg and R. Y. Chiao, Tunneling delay times in one and two dimensions, Phys. Rev. A 49, 3283-3295 (1994).
[67] R. Landauer, Light faster than light?, Nature (London) 341, 567-568 (1989).
[68] L. A. MacColl, Note on the transmission and reflection of wave packets by potential barriers, Phys. Rev. 40, 621-626 (1932).
[69] E. P. Wigner, Lower limit for the energy derivative of the scattering phase shift, Phys. Rev. 98, 145-150 (1955).
[70] T. E. Hartman, Tunneling of a wave packet, J. Appl. Phys. 33, 3427-3433 (1962).
[71] M. Büttiker and R. Landauer, Traversal time for tunneling, Phys. Rev. Lett. 49, 1739-1742 (1982).
[72] M. Büttiker, Larmor precession and the traversal time for tunneling, Phys. Rev. B 27, 6178-6184 (1983).
[73] E. H. Hauge and J. A. Stovneng, Tunneling times: a critical review, Rev. Mod. Phys. 61, 917-924 (1989).
[74] R. Landauer and Th. Martin, Barrier interaction time in tunneling, Rev. Mod. Phys. 66, 217-228 (1994).
[75] G. Nimtz and W. Heitmann, Superluminal photonic tunneling and quantum electron- ics, Prog. Quant. Electron. 21, 81-108 (1997).
[76] R.Y. Chiao and A. M. Steinberg, Tunneling Times and Superluminality, Ed. E. Wolf, Progress in Optics Vol. ⅩⅩⅩⅦ (Elsevier B.V. Science, Amsterdam, 1997), p. 345.
[77] Time in Quantum Mechanics, edited by J. G. Muga, R. Sala Mayato, and I. L. Egusquiza (Springer, Berlin, 2002).
[78] G. Nimtz, On superluminal tunneling, Prog. Quantum Electron. 27, 417-450 (2003).
[79] C. R. Learvens and G. C. Aers, Dwell time and phase time for transmission and reflection, Phys. Rev. B 39, 1202-1206 (1989).
[80] E. H. Hauge, J. P. Falck, and T. A. Fjeldly, Transmission and reflection times for scattering of wave packets off tunneling barriers, Phys. Rev. B 36, 4203-4214 (1987).
[81] Th. Martin and R. Landauer, Time delay of evanescent electromagnetic waves and the analogy to particle tunneling, Phys. Rev. A 45, 2611-2617 (1992).
[82] B. Lee, Electron tunneling time through a heterostructure, Superlatt. Microstruct. 14, 295-298 (1993).
[83] V. V. Paranjape, Transmission coefficient and stationary-phase tunneling time of an electron through a heterosture, Phys. Rev. B 52, 10740-10743 (1995).
[84] Y. Japha and G. Kurizki, Superluminal delays of coherent pulses in nondissipative media: A universal mechanism, Phys. Rev. A 53(1), 586-590 (1996).
[85] V. M. de Aquino, V. C. Aguilera-Navarro, M. Goto, and H. Iwamoto, Tunneling time through a rectangular barrier, Phys. Rev. A 58, 4359-4367 (1998).
[86] Ph. Grossel, F. Depasse, and J.-M. Vigoureux, Reflection and transmission behaviour of a particle in a resonant tunnelling barrier, J. Phys. A: Math. Gen. 35, 9787-9800 (2002).
[87] J. Co Martinez and E. Polatdemir, Transit and reflection times for a non-symmetric barrier and a symmetric double barrier, Physica Scripta. 68, 108-114 (2003).
[88] M. Goto, H. Iwamoto, V. M de Aquino, V. C. V. Navarro and D. H. Kobe, Relationship between dwell, transmission and reflection tunnelling times, J. Phys. A: Math. Gen. 37, 3599-3603 (2004).
[89] N. Yamada, Unified derivation of tunneling times from decoherence functionals, Phys. Rev. Lett. 93, 170401 (20(}4).
[90] S. K. Sekatskii and V. S. Letokhov, Electron tunneling time measurement by fieldemission microscopy, Phys. Rev. B 64, 233311 (2001).
[91] S. Longhi, Superluminal pulse reflection in asymmetric one-dimensional photonic band gaps, Phys. Rev. E. 64, 037601 (2001).
[92] D. Dragoman and M. Dragoman, Single-chip device for tunneling time measurements, J. Appl. Phys. 93, 6133-6136 (2003).
[93] J. C. Martinez and E. Polatdemir, Measurement of tunneling time via electron interferometry, Appl. Phys. Lett. 84, 1320-1322 (2004).
[94] F. Zhai, Y. Guo, and B.-L. Gu, Tunneling time in magnetic barrier structures, Eur. Phys. J. B 29, 147-152 (2002).
[95] X.-H. Wang, B.-Y. Gu, and G. Z. Yang, Influence of magneto-coupling between the longitudinal motion component and transverse Landau orbits of an electron on transmission features in single quantum barrier, Eur. Phys. J. B 2, 121-129 (1998).
[96] S. Bandopadhyay, R. Krishnan, and A. M. Jayannavar, Hartman effect in presence of Aharanov-Bohm flux, Solid State Commun. 131, 447-451 (2004).
[97] S. Bandopadhyay and A. M. Jayannavar, Hartman effect and nonlocality in quantum networks, Phys. Lett. A 335, 266-273 (2005).
[98] B. Wang, Y. Guo, and B.-L. Gu, Tunneling time of spin-polarized electrons in ferromagnetic insulator (semiconductor) double junctions under an applied electric field, J. Appl. Phys. 91, 1318-1323 (2002).
[99] Y. Guo, C.-E. Shang, and X.-Y. Chen, Spin-dependent delay time and the Hartman effect in tunneling through diluted-magnetic-semiconductor/semiconductor heterostructures, Phys. Rev. B, 72, 045356 (2005).
[100] C.-F. Li and Q. Wang, Negative phase time for particles passing through a potential well, Phys. Lett. A 275, 287-262 (2000).
[101] X. Chen and C.-F. Li, Negative group delay for Dirac particles traveling through a potential well, Phys. Rev. A 68, 052105 (2003).
[102] R.-M. Vetter, A. Haibel, and G. Nimtz, Negative phase time for scattering at quantum wells: A microwave analogy experiment, Phys. Rev. E 63, 046701 (2001).
[103] X. Chen and C.-F. Li, The reflection and transmission group delay times in an asymmetric single quantum barrier, Eur. Phys. J. B 46, 433-440 (2005).
[104] C.-F. Li and H. Spieker, Resonance-enhanced group delay times in an asymmetric single quantum barrier, Opt. Comm. 259, 158-163 (2006).
[105] M. Biittiker and S. Washburn, Ado about nothing much, Nature (London) 422, 271 (2003).
[106] H. G. Winful, Mechanism for 'superluminal' tunnelling, Nature (London) 424, 638 (2003).
[107] H. G. Winful, The nature of 'superluminal' barrier tunneling, Phys. Rev. Lett. 90, 023901 (2003).
[108] H. G. Winful, Delay time and the Hartman effect in quantum tunneling, Phys. Rev. Lett. 91, 260401 (2003).
[109] H. G. Winful, Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox, Phys. Rep. 436, 1-69 (2006).
[110] J. C. Martinez and E. Polatdemir, Original of Hartman effect, Phys. Lett. A 351, 31-36 (2006).
[111] J. C. Martinez, E. Polatdemir, and M. Taufik, Interference and dispersion effects on tunneling time, Eur. Phys. J. D 41, 49-54 (2007).
[112] D. Solli, R. Y. Chiao, and J. M. Hickmann, Superluminal effects and negative group delays in electronics, and their applications, Phys. Rev. E 66, 056601 (2002).
[113] C.-F. Li, Q.-B. Zhu, G. Nimtz, X. Chen, and Y. Zhang, Observation of backward longitudinal shifts for microwave beams transmitting through dielectric slab, Opt. Comm. 259, 470-473 (2006).
[114] V. G. Veselago, The electrodynamics of substances with simultaneously negative values of ε and μ, Sov. Phys. Usp. 10, 509-514 (1968).
[115] D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Compos- ite medium with simultaneously negative permeability and permittivity, Phys. Rev. Lett. 84(18), 4184-4187 (2000).
[116] D. R. Smith and N. Kroll, Negative refractive index in left-handed materials, Phys. Rev. Lett. 85, 2933-2936 (2000).
[117] R. A. Shelby, D. R. Smith, and S. Schultz, Experimental verification of a negative index of refraction, Science 292, 77 (2001).
[118] C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, Experimental verification and simulation of negative index of refraction using Shell's law, Phys. Rev. Lett. 90, 107401 (2003).
[119] J. B. Pendry, Negative refraction makes a perfect lens, Phys. Rev. Lett. 85, 3966-3969 (2000).
[120] P. M. Valanju, R. M. Walser, and A. P. Valanju, Wave refraction in negative-index media: always positive and very inhomogeneous, Phys. Rev. Lett. 88, 187401 (2002).
[121] N. Garcia and M. Nieto-Vesperinas, Left-handed materials do not make a perfect lens, Phys. Rev. Lett. 88, 207403 (2002).
[122] Z. M. Zhang and C. J. Fu, Unusual photon tunneling in the presence of a layer with a negative refractive index, Appl. Phys. Lett. 80, 1097-1097 (2002).
[123] P. R. Berman, Goos-Hanchen shift in negatively refractive media, Phys. Rev. E 66, 067603 (2002).
[124] A. Lakhtakia, Positive and negative Goos-Hanchen shifts and negative phase-velocity mediums (alias left-handed materials), Int. J. Electron. Commun., 28, 229-231 (2004).
[125] D. K. Qing and G. Chen, Goos-Hanchen at the interfaces between left- and right-handed media, Opt. Lett. 29, 872-874 (2004).
[126] I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, Gaint Goos-Hanchen effect at the reflection from left-handed metamaterial, Appl. Phys. Lett. 83 2713-2715 (2003).
[127] J. A. Kong, B.-L. Wu and Y. Zhang, Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability, Appl. Phys.Lett. 80, 2084-2086 (2002).
[128] J. A. Kong, B.-L. Wu and Y. Zhang, A unique lateral displacement of a Gaussian beam transmitted through a slab with negative permittivity and permeability, Microw. Opt. Techn. Lett. 33(2), 136-139 (2002).
[129] X. Chen and C.-F. Li, Lateral shift of the transmitted beam through a left-handed slab, Phy. Rev. E 69, 066617 (2004).
[130] Y. Yan, X. Chen, and C.-F. Li, Large and negative lateral displacement in an active dielectric slab configuration, Phys. Lett. A 361, 178-181 (2007).
[131] X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, Large postive and negative lateral optical beam displacement due to surface plasmon resonance, Appl. Phys. Lett. 85, 372-374 (2004).
[132] F. Pillon, H. Gilles, S. Girard, and M. Laroche, Goos-Hanchen and Imbert-Fedorov shift in total internal reflection, J. Opt. Soc. Am. B 22, 1290-1299 (2005).
[133] J. J. Chen, T. M. Grzegorczyk, B.-L. Wu, and J. A. Kong, Role of evanescent waves in the positive and negative Goos-Hanchen shifts with left-handed material slabs, J. Appl. Phys. 98, 094905 (2005).
[134] H.-L. Zhou, X. Chen, and C.-F. Li, Lateral displacement and its mechanism in asymmetric layered configuration J. Mod. Opt. 53(15), 2153-2165 (2006).
[135] M. Born and E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1980), Chap. 7, p.323.
[136] D. Dragoman and M. Dragoman, Optical analogue structures to mesoscopic devices, Progress in Quantum Electronics 23(4-5), 131-188 (1999).
[137] W. Liang, M. Bockrath, D. Bozovic, J. H. Hafner, M. Tinkham, and H. Park, Fabry Perot interference in a nanotube electron wavegnide, Nature (London) 411, 665-669 (2001).
[138] C. T. White and T. N. Todorov, Nanotubes go ballistic, Nature (London) 411, 649-651 (2001).
[139] Y. Ji, Y. Chung, D. Sprinzak, M. Heiblum, D. Mahalu, and H. Shtrikman, An electronic Mach-Zehnder interferometer, Nature (London) 422, 415-418 (2003).
[140] D. Bohm, Quantum Theory, New York: Prentice-Hall, (1951) 257-261.
[141] F. M. Peeters and A. Matulis, Quantum structures created by nonhomogeneous magnetic fields, Phys. Rev. B 48, 15166-15174 (1993).
[142] A. Matulis, F. M. Peeters, and Vasilopoulos, Wave-vector-dependent tunneling through magnetic barrier, Phys. Rev. Lett. 72, 1518-1520 (1994).
[143] Y. Guo, H. Wang, B. L. Gu, and Y. Kawazoe, Electric-field effects on electronic tunneling transport in magnetic barrier structures, Phys. Rev. B 61, 1728-1731 (2000).
[144] A. Majumdar, Effects of intrinsic spin on electronic transport through magnetic barrier, Phys. Rev. B 54, 11911-11913 (1996).
[145] M.-W. Lu, L.-D. Zhang, and X.-H. Yan, Spin polarization of electrons tunneling through magnetic-barrier nanostructures, Phys. Rev. B 66 224412 (2002).
[146] G. Papp and F. M. Peeters, Spin filtering in a magnetic-electric barrier structure, Appl. Phys. Lett. 78, 2184-2186 (2001); Erratum: "Spin filtering in a magneticelectric barrier structure". 79, 3198 (2001).
[147] H. Z. Xu and Y. Okada, Does a magnetic barrier or a magnetic-electric barrier structure possess any spin polarization and spin filtering under zero bias?, Appl. Phys. Lett. 79, 3119-3121 (2001).
[148] F. Zhal, H. Q. Xu, and Y. Guo, Tunable spin polarization in a two-dimensional electron gas modulated by a ferromagnetic metal stripe and a Schottky metal stripe, Phys. Rev. B 70, 085308 (2004).
[149] G. Papp, P. Vasilopoulos, and F. M. Peeters, Spin polarization in a two-dimensional electron gas modulated periodically by ferromagnetic and Schottky metal stripes, Phys. Rev. B 72, 115315 (2005).
[150] A. M. Kan'an and A. Puri, Transmission of an obliquely electron wave through GaAs-AlGaAs structures: Application to an electron wave filter, J. Appl. Phys. 74, 370-374 (1994).
[151] A. M. Kan'an and A. Puri, The generalized transmission matrix for electron-wave-optics through biased heterostructures: quantum device applications, J. Appl. Phys. 75, 351-356 (1994).
[152] B. Wang, Y. Guo, X.-Y. Chen, and B.-L. Gu, Spin polarization induced by an external electric field in a hybrid magnetic-electric barrier, J. Appl. Phys. 92(7), 4138-4140 (2002).
[153] V. Gasparian, T. Christen, and M. Biittiker, Partial densities of states scattering matrices, and Green's functions, Phys. Rev. A 54, 4022-4031 (1996).
[154] J. G. Muga, I. L. Egusquiza, J. A. Damborenea, F. Delgado, Bounds and enhancements for negative scattering time delays, Phys. Rev. A 66, 042115 (2002).
[155] M. Biittiker, in Electronic Properties of Multilayers and Low-Dimensional Semiconductors Structures, edited by J. M. Chamberlain, L. Eaves, and J. C. Portal (Plenum Press, New York, 1990), p.297
[156] C.-F. Li, Comment on "Photonic tunneling time in frustrated total internal reflection", Phys. Rev. A 65, 066101 (2002).
[157] H. Luo, N. Dai, F. C. Zhang, N. Smarth, M. Dobrowdska, J. K. Furdyna, C. Parks, and A. K. Radams, Observation of quasibound states in semiconductor single quantum barriers, Phys. Rev. Lett. 70, 1307-1310 (1993).
[158] G. Garcia-Calderon and A. Rubio, Properties of the dwell time and the transmission and reflection times for resonant tunneling, Solid State Commun. 71, 237-241 (1989).
[159] Y.-P. Wang and D.-L. Zhang, Reshaping, path uncertainty, and superluminal travelling, Phys. Rev. A 52, 2597-2600 (1995).
[160] A. Dogariu, A. Kuzmich, and L. J. Wang, Transparent anomalous dispersion and superluminal light-pulse propagation at a negative group velocity, Phys. Rev. A 63, 053806 (2001).
[161] L. G. Wang, N.-H. Liu, Q. Lin, and S.-Y. Zhu, Superluminal propagation of light pulses: A result of interference, Phys. Rev. E 68, 066606 (2003).
[162] W. Guo, Understanding subluminal and superluminal propagation through superposition of frequency components, Phys. Rev. E 73, 016605 (2006).
[163] Y. Aharonov, N. Erez, and B. Reznik, Superluminal tunnelling times as weak values, J. Mod. Opt. 50(6-7), 1139-1149 (2003).
[164] D. Sokolovski, A. Z. Msezane, and V. R. Shaginyan, "Superluminal" tunneling as a weak measurement effect, Phys. Rev. A 71, 064103 (2005).
[165] C. G. B. Garrett and D. E. McCumber, Propagation of a Gaussian light pulse through an anomalous dispersion medium, Phys. Rev. A 1, 305 (1970).
[166] S. Chu and S. Wong, Linear pulse propagation in an absorbing medium, Phys. Rev. Lett. 48, 738-741 (1982).
[167] B. Segard and B. Macke, Observation of negative velocity pulse propagation, Phys. Lett. A 109, 213-216 (1985).
[168] L. J. Wang, A. Kuzmich, and A. Dogariu, Gain-assisted superluminal light propagation, Nature (London) 406, 277-279 (2000).
[169] C.-F. Li and X. Chert, Traversal time for Dirac particles through a potential barrier, Ann. Phys. (Leipzig) 11(12), 916-925 (2002).
[170] P. Krekora, Q. Su, and R. Grobe, Effects of relativity on the time-resolved tunneling of electron wave packets, Phys. Rev. A 63, 032107 (2001).
[171] V. Petrillo and D. Janner, Relativistic analysis of a wave packet interacting with a quantum-mechanical barrier, Phys. Rev. A 67, 012110 (2003).
[172] C.-F. Li and Q. Wang, A traversal time for tunneling particles through a potential barrier, Physica B 296, 356-360 (2001).
[173] C. R. Leavens and G. C. Aers, Larmor-clock transmission times for resonant double barriers, Phys. Rev. B 40, 5387-5400 (1989).
[174] C.-F. Li and Q. Wang, Duration of tunneling photons in a frustrated-total-internal-reflection structure, J. Opt. Soc. Am. B 18, 1174-1179 (2001).
[175] M. Buttiker and H. Thomas, Front propagation in evanescent media, Superlattices and Microstructures 23(314), 781-794 (1998).
[176] M. Biittiker and H. Thomas, Front propagation in evanescent media, Ann. Phys. (Leipzig) 7, 602-617 (1998).
[177] See, for example, the detailed discussions in L. Brillouin, Wave Propagation and Group velocity, Academic Press, New York 1960.
[178] A. Calogeracos and N. Dombey, History and physics of the klein paradox, Contemp. Phys. 40(5), 313-321 (1999).
[179] A. Calogeracos and N. Dombey, Klein tunnelling and the klein paradox, Int. J. Mod. Phys. A 14(4), 631-643 (1999).
[180] N. S. Todorov, Extended particles Part II on klein's paradox, Ann. Fond. Louis Broglie 25(2) 209-222 (2000).
[181] M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Tunable refraction and reflection of self-confined light beam, Nature Phys. 2, 737-742 (2006).
[182] Y. Ban, X. Chen, and C.-F. Li, Controllable negative and positive group delay in transmission through a single quantum well at finite magnetic fields, Phys. Lett. A 364, 76-80 (2007).
[183] M. Onoda, S. Murakami, and N. Nagaosa, Hall effect of light, Phys. Rev. Lett. 93, 083901 (2004).
[184] K. Yu. Bliokh and Yu. P. Bliokh, Conservation of Angular Momentum, Transverse Shift, and Spin Hall Effect in Reflection and Refraction of an Electromagnetic Wave Packet, Phys. Rev. Lett. 96, 073903 (2004).
[185] M. Onoda, S. Murakami, and N. Nagaosa, Geometric aspects in optical wavepacket dynamics, Phys. Rev. E 74, 066610 (2004).
[2] K. V. Artmann, Berechung der seitenversetzung des reflektieren strahles, Ann. Phys. (Leipzig) 2, 87-102 (1948).
[3] H. K. V. Lotsch, Beam displacements at total reflection: The Goos-Hanchen effect, Optik (Stuttgart) 32, 116-137 (1970); 32, 189-204 (1970); 32, 299-319 (1971); 32, 553-569 (1971).
[4] H. M. Lai and S. W. Chan, Large and negative Goos-Hanchen shift near the Brewster dip on reflection from weakly absorbing media, Opt. Lett. 27, 680-682 (2002).
[5] W. J. Wild and C. Lee Giles, Goos-Hanchen shifts from absorbing media, Phys. Rev. A., 25, 2099-2101 (1982).
[6] J. Birman, D. N. Pattanayak, and A. Puri, Prediction of a resonance-enhanced Laser-beam displacement at total internal reflection in semiconductors, Phys. Rev. Lett. 50, 1664-1667 (1983).
[7] E. Pfleghaar, A. Mareseille, and A. Weis, Quantitative investigation of the effect of resonant absorbers on the Goos-Hanchen shift, Phys. Rev. Lett. 70 2281-2284 (1993).
[8] B. A. Anicin, R. Fazlic, and M. Kopric, Theoretical evidence for negative Goos-Hanchen shifts, J. Phys. A, 11, 1657-1662 (1978).
[9] C. K. Carniglia and K. R. Brownstein, Focal shift and ray mode for total internal reflection, J. Opt. Soc. Am. 67, 121-122 (1977).
[10] A. Haibel, G. Nimtz, and A. A. Stahlhofen, Frustrated total reflection: The double-prism revisited, Phys. Rev. E 63, 047601 (2001).
[11] T. Tamir and H. L. Bertoni, Lateral displacement of optical beams at multilayered and periodic structures, J. Opt. Soc. Am. 61, 1397-1413 (1971).
[12] B. R. Horowitz and T. Tamir, Lateral displacement of a light beam at a dielectric interface, J. Opt. Soc. Am. 61, 586-594 (1971).
[13] C. W. Huse and T. Tamir, Lateral displacement and distortion of beams incident upon a transmitting layer configuration, J. Opt. Soc. Am. A 2, 978-987 (1985).
[14] T. Tamir, Nonspecular phenomena in beam fields reflected by multilayered media, J. Opt. Soc. Am. A 3, 558-565 (1986).
[15] R. P. Riesz and R. Simon, Reflection of a Gaussian beam from a dielectric slab, J. Opt. Soc. Am. A 2, 1809-1817 (1985).
[16] C. W. Hsue and T. Tamir, Lateral beam displacements in transmitting layered structures, Opt. Commun. 49, 383-387 (1984).
[17] R. Briers, O. Leroy, and G. Shkerdin, Bounded beam interaction with thin inclusions. Characterization by phase differences at l~yleigh angle incidence, J. Acoust. Soc. Am. 108, 1622-1630 (2000).
[18] O. Emile, T. Galstyan, A. LeFloch, and F. Bretenaker, Measurement of the nonlinear Goos-Hanchen effect for Gaussian optical beams, Phys. Rev. Lett. 75, 1511-1513 (1995).
[19] B. M. Jost, A. A. R. Al-Rashed, and B. E. A. Salch, Observation of the Goos-Hanchen effect in a phase-conjugate mirror, Phys. Rev. Lett. 81, 2233-2235 (1998).
[20] N. J. Harrick, Study of physics and chemistry of surfaces from frustrated total internal reflections, Phys. Rev. Lett. 4, 224-226 (1960).
[21] V. K. Ignatovich, Neutron reflection from condensed matter, the Goos-Hanchen effect and coherence, Phys. Lett. A 322, 36-46 (2004).
[22] X. Chen, C.-F. Li, and Y. Ban, Novel displacement in transmission through a two-dimensional semiconductor barrier, Phys. Lett. A 354, 161-165 (2006).
[23] S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge University Press, New York, (1996) 276.
[24] M. Crespo and S. Datta, Physics Today 74-82, Feb. (1990).
[25] D. W. Wilson and T. K. Gaylord, Electron waveguiding characteristics and ballistic current capacity of semiconductor quantum slabs, IEEE J. Quantum Electron, 29, 1364-1382 (1993).
[26] T. K. Gaylord and K. F. Brennan, Electron wave optics in semiconductors, J. Appl. Phys, 65(2), 814-820 (1988).
[27] T. K. Gaylord, E. N. Glytsis, G. N. Henderson, K. P. Martin, D. B. Walker, D. W. Wilson, and K. F. Brennan, Ballistic electron transport in semiconductor heterostructures and its analogies in electromagnetic propagation in general dielectrics, Proc. IEEE 79, 1643-1659 (1991).
[28] J. Spector, H. L. Stormer, K. W. Baldwin, L. N. Pfeiffer, and K. W. West, Electron focusing in two-dimensional systems by means of an electrostatic lens, Appl. Phys. Lett. 56, 1290-1292 (1990).
[29] J. Spector, H. L. Stormer, K. W. Baldwin, L. N. Pfeiffer, and K. W. West, Refractive switch for two-dimensional electron, Appl. Phys. Lett. 56, 2433-2435 (1990).
[30] K. Furuya, Novel high-speed transistor using electron-wave diffraction, J. Appl. Phys. 62, 1492-1494 (1987).
[31] K. Firiya and K. Kurishima, Theoretical properties of electron wave diffraction due to a transversally periodic structure in semiconductors, IEEE J. Quantum Electron 24, 1652-1658 (1988).
[32] S. Datta, Quantum devices, Superlattices Microstructures 6, 83-89 (1989).
[33] F. Sols, M. Macucci, U. Ravaioli, and K. Hess, On the possibility of transistor action based on quantum interference phenomena, Appl. Phys. Lett. 54, 350-352 (1989).
[34] F. Sols, M. Macucci, U. Ravaioli, and K. Hess, Theory for a quantum modulated transistor, J. Appl. Phys. 66, 3892-3906 (1989).
[35] S. Subramaniam, S. Bandyopadhyay, and W. Porod, Analysis of the device performance of quantum interference transistors utilizing ultrasmall semiconductor T structures, J. Appl. Phys. 68, 4861-4870 (1991).
[36] C. C. Eugster and J. A. del Alamo, Tunneling spectroscopy of an electron waveguide, Phys. Rev. Lett. 67, 3586-3589 (1991).
[37] J. A. del Alamo and C. C. Eugster, Quantum field-effect directional coupler, Apph Phys. Lett. 56, 78-80 (1990).
[38] N. Tsukada, A. D. Wieck and K. Ploog, Proposal of novel electron wave coupled devices, Appl. Phys. Lett. 56, 2527-2529 (1990).
[39] R. Q. Yang and J. M. Xu, Analysis of guided electron waves in coupled quantum wells, Phys. Rev. B 43, 1699-1706 (1991).
[40] R. Q. Yang and J. M. Xu, Energy-dependent electron wave coupling between two asymmetric quantum well waveguides, Appl. Phys. Lett. 59, 315-317 (1991).
[41] J. Q. Wang, $. Q. Yuan, B. Y. Gu and G. Z. Yang, Guided electron waves in coupled deep quantum wells, Phys. Rev. B 44, 13618-13625 (1991).
[42] L. Thylen and Q. Sahen, Switch energy analysis of quantum interference directional couplers, IEEE J. Qunantum Electron 28, 31-33 (1992).
[43] R. H. Renard, Total reflection: a new evaluation of the Goos-Hanchen shift, J. Opt. Soc. Am. 54, 1190-1197 (1964).
[44] J. L. Carter and H. Hora, Total reflection of matter waves: The Goos-Hanchen effect for grazing incidence, J. Opt. Soc. Am. 61, 1640-1645 (1971).
[45] S. C. Miller, Jr., and N. Ashby, Shifts of electron beam position due to total reflection at a barrier, Phys. Rev. Lett. 29, 740-743 (1972);
[46] D. M. Fradkin and R. J. Kashuba, Spatial displacement of electrons due to multiple total reflections, Phys. Rev. D 9, 2775-2788 (1974);
[47] D. M. Fradkin and R. J. Kashuba, Position-operator method for evaluating the shift of a totally reflected electron, Phys. Rev. D 10, 1137-1145 (1974).
[48] L. Arthur, A. Read, and G. E. Reesor, Displacement of a microwave beam upon transmission through a dielectric slab, Can. J. Phys. 57, 1409-1413 (1979).
[49] L. Arthur, A. Read, Wong Man, and G. E. Reesor, Displacement of an electromagnetic beam upon reflection from a dielectric slab, J. Opt. Soc. Am. A 68, 319-322 (1978).
[50] C.-F. Li, Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects, Phys. Rev. Lett. 91, 133903 (2003).
[51] X.-H. Huang and C.-F. Li, Novel light beam propagation through optical "potential well", Europhys. Lett. 63, 28-34 (2003).
[52] C.-F. Li and Q. Wang, Prediction of simultaneously large and opposite generalized Goos-Hiinchen shifts for TE and TM light beams in an asymmetric double-prism configuration, Phys. Rev. E 69, 055601(R) (2004).
[53] C.-F. Li and X.-Y. Yang, Thin-film enhanced Goos-Hanchen shift in total internal reflection, Chin. Phys. Lett. 21,485-488 (2004).
[54] 朱绮彪，李春芳，陈玺，双棱镜结构中的透射光束的Goos-Hanchen位移，光学学报5，673-675(2005)．
[55] X.-B. Liu, Cao Z.-Q., Zhu P.-F., Shen Q.-S., and Liu X.-M., Large positive and negative lateral optical beam shift in prism-waveguide coupling system, Phys. Rev. E. 73, 056617 (2006).
[56] X.-B. Liu, Cao Z.-Q., Zhu P.-F., Shen Q.-S., and Liu X.-M., Simultaneously large and opposite lateral beam shifts for TE and TM modes on a double metal-cladding slab, Chin. Phys. Lett. 23(S), 2077-2079 (2006).
[57] L.-G. Wang, H. Chert, and S.-Y. Zhu, Large negative Goos-Hanchen shift from a weakly absorbing dielectric slab, Opt. Lett. 30, 2936-2938 (2005).
[58] L.-G. Wang and S.-Y. Zhu, Large positive and negative Goos-Hanchen shifts from a weakly absorbing left-handed slab, J. Appl. Phys. 98, 043522 (2005).
[59] L.-G. Wang, and S.-Y. Zhu, Gaint lateral shift of a light beam at the defect mode in one-dimensional photonic crystals, Opt. Lett. 31, 101-103 (2006).
[60] A. Ranfagni, D. Mugnai, P. Fabeni, and G. P. Pazzi, Delay-time measurements in narrowed waveguides as a test of tunneling, Appl. Phys. Lett. 58, 774-776 (1991).
[61] A. Enders and G. Nimtz, Zero-time tunneling of evanescent mode packets, J. Phys. I (France) 3, 1089-1092 (1993).
[62] A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, Measurement of the single-photon tunneling time, Phys. Rev. Lett. 71(5), 708-711 (1993).
[63] Ch. Spielmann, R. Szipocs, A. Stingl, and F. Krausz, Tunneling time of optical pulses through photonic band gaps, Phys. Rev. Lett. 73, 2308-2311 (1994).
[64] Ph. Balcou and L. Dutriaux, Dual optical tunneling time in frustrated total internal reflection, Phys. Rev. Lett. 78, 851-854 (1997).
[65] A. Haibel and G. Nimtz, Universal relationship of time and frequency in photonic tunneling, Ann. Phys. (Leipzig) 9, 1-5 (2001).
[66] A. M. Steinberg and R. Y. Chiao, Tunneling delay times in one and two dimensions, Phys. Rev. A 49, 3283-3295 (1994).
[67] R. Landauer, Light faster than light?, Nature (London) 341, 567-568 (1989).
[68] L. A. MacColl, Note on the transmission and reflection of wave packets by potential barriers, Phys. Rev. 40, 621-626 (1932).
[69] E. P. Wigner, Lower limit for the energy derivative of the scattering phase shift, Phys. Rev. 98, 145-150 (1955).
[70] T. E. Hartman, Tunneling of a wave packet, J. Appl. Phys. 33, 3427-3433 (1962).
[71] M. Büttiker and R. Landauer, Traversal time for tunneling, Phys. Rev. Lett. 49, 1739-1742 (1982).
[72] M. Büttiker, Larmor precession and the traversal time for tunneling, Phys. Rev. B 27, 6178-6184 (1983).
[73] E. H. Hauge and J. A. Stovneng, Tunneling times: a critical review, Rev. Mod. Phys. 61, 917-924 (1989).
[74] R. Landauer and Th. Martin, Barrier interaction time in tunneling, Rev. Mod. Phys. 66, 217-228 (1994).
[75] G. Nimtz and W. Heitmann, Superluminal photonic tunneling and quantum electron- ics, Prog. Quant. Electron. 21, 81-108 (1997).
[76] R.Y. Chiao and A. M. Steinberg, Tunneling Times and Superluminality, Ed. E. Wolf, Progress in Optics Vol. ⅩⅩⅩⅦ (Elsevier B.V. Science, Amsterdam, 1997), p. 345.
[77] Time in Quantum Mechanics, edited by J. G. Muga, R. Sala Mayato, and I. L. Egusquiza (Springer, Berlin, 2002).
[78] G. Nimtz, On superluminal tunneling, Prog. Quantum Electron. 27, 417-450 (2003).
[79] C. R. Learvens and G. C. Aers, Dwell time and phase time for transmission and reflection, Phys. Rev. B 39, 1202-1206 (1989).
[80] E. H. Hauge, J. P. Falck, and T. A. Fjeldly, Transmission and reflection times for scattering of wave packets off tunneling barriers, Phys. Rev. B 36, 4203-4214 (1987).
[81] Th. Martin and R. Landauer, Time delay of evanescent electromagnetic waves and the analogy to particle tunneling, Phys. Rev. A 45, 2611-2617 (1992).
[82] B. Lee, Electron tunneling time through a heterostructure, Superlatt. Microstruct. 14, 295-298 (1993).
[83] V. V. Paranjape, Transmission coefficient and stationary-phase tunneling time of an electron through a heterosture, Phys. Rev. B 52, 10740-10743 (1995).
[84] Y. Japha and G. Kurizki, Superluminal delays of coherent pulses in nondissipative media: A universal mechanism, Phys. Rev. A 53(1), 586-590 (1996).
[85] V. M. de Aquino, V. C. Aguilera-Navarro, M. Goto, and H. Iwamoto, Tunneling time through a rectangular barrier, Phys. Rev. A 58, 4359-4367 (1998).
[86] Ph. Grossel, F. Depasse, and J.-M. Vigoureux, Reflection and transmission behaviour of a particle in a resonant tunnelling barrier, J. Phys. A: Math. Gen. 35, 9787-9800 (2002).
[87] J. Co Martinez and E. Polatdemir, Transit and reflection times for a non-symmetric barrier and a symmetric double barrier, Physica Scripta. 68, 108-114 (2003).
[88] M. Goto, H. Iwamoto, V. M de Aquino, V. C. V. Navarro and D. H. Kobe, Relationship between dwell, transmission and reflection tunnelling times, J. Phys. A: Math. Gen. 37, 3599-3603 (2004).
[89] N. Yamada, Unified derivation of tunneling times from decoherence functionals, Phys. Rev. Lett. 93, 170401 (20(}4).
[90] S. K. Sekatskii and V. S. Letokhov, Electron tunneling time measurement by fieldemission microscopy, Phys. Rev. B 64, 233311 (2001).
[91] S. Longhi, Superluminal pulse reflection in asymmetric one-dimensional photonic band gaps, Phys. Rev. E. 64, 037601 (2001).
[92] D. Dragoman and M. Dragoman, Single-chip device for tunneling time measurements, J. Appl. Phys. 93, 6133-6136 (2003).
[93] J. C. Martinez and E. Polatdemir, Measurement of tunneling time via electron interferometry, Appl. Phys. Lett. 84, 1320-1322 (2004).
[94] F. Zhai, Y. Guo, and B.-L. Gu, Tunneling time in magnetic barrier structures, Eur. Phys. J. B 29, 147-152 (2002).
[95] X.-H. Wang, B.-Y. Gu, and G. Z. Yang, Influence of magneto-coupling between the longitudinal motion component and transverse Landau orbits of an electron on transmission features in single quantum barrier, Eur. Phys. J. B 2, 121-129 (1998).
[96] S. Bandopadhyay, R. Krishnan, and A. M. Jayannavar, Hartman effect in presence of Aharanov-Bohm flux, Solid State Commun. 131, 447-451 (2004).
[97] S. Bandopadhyay and A. M. Jayannavar, Hartman effect and nonlocality in quantum networks, Phys. Lett. A 335, 266-273 (2005).
[98] B. Wang, Y. Guo, and B.-L. Gu, Tunneling time of spin-polarized electrons in ferromagnetic insulator (semiconductor) double junctions under an applied electric field, J. Appl. Phys. 91, 1318-1323 (2002).
[99] Y. Guo, C.-E. Shang, and X.-Y. Chen, Spin-dependent delay time and the Hartman effect in tunneling through diluted-magnetic-semiconductor/semiconductor heterostructures, Phys. Rev. B, 72, 045356 (2005).
[100] C.-F. Li and Q. Wang, Negative phase time for particles passing through a potential well, Phys. Lett. A 275, 287-262 (2000).
[101] X. Chen and C.-F. Li, Negative group delay for Dirac particles traveling through a potential well, Phys. Rev. A 68, 052105 (2003).
[102] R.-M. Vetter, A. Haibel, and G. Nimtz, Negative phase time for scattering at quantum wells: A microwave analogy experiment, Phys. Rev. E 63, 046701 (2001).
[103] X. Chen and C.-F. Li, The reflection and transmission group delay times in an asymmetric single quantum barrier, Eur. Phys. J. B 46, 433-440 (2005).
[104] C.-F. Li and H. Spieker, Resonance-enhanced group delay times in an asymmetric single quantum barrier, Opt. Comm. 259, 158-163 (2006).
[105] M. Biittiker and S. Washburn, Ado about nothing much, Nature (London) 422, 271 (2003).
[106] H. G. Winful, Mechanism for 'superluminal' tunnelling, Nature (London) 424, 638 (2003).
[107] H. G. Winful, The nature of 'superluminal' barrier tunneling, Phys. Rev. Lett. 90, 023901 (2003).
[108] H. G. Winful, Delay time and the Hartman effect in quantum tunneling, Phys. Rev. Lett. 91, 260401 (2003).
[109] H. G. Winful, Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox, Phys. Rep. 436, 1-69 (2006).
[110] J. C. Martinez and E. Polatdemir, Original of Hartman effect, Phys. Lett. A 351, 31-36 (2006).
[111] J. C. Martinez, E. Polatdemir, and M. Taufik, Interference and dispersion effects on tunneling time, Eur. Phys. J. D 41, 49-54 (2007).
[112] D. Solli, R. Y. Chiao, and J. M. Hickmann, Superluminal effects and negative group delays in electronics, and their applications, Phys. Rev. E 66, 056601 (2002).
[113] C.-F. Li, Q.-B. Zhu, G. Nimtz, X. Chen, and Y. Zhang, Observation of backward longitudinal shifts for microwave beams transmitting through dielectric slab, Opt. Comm. 259, 470-473 (2006).
[114] V. G. Veselago, The electrodynamics of substances with simultaneously negative values of ε and μ, Sov. Phys. Usp. 10, 509-514 (1968).
[115] D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Compos- ite medium with simultaneously negative permeability and permittivity, Phys. Rev. Lett. 84(18), 4184-4187 (2000).
[116] D. R. Smith and N. Kroll, Negative refractive index in left-handed materials, Phys. Rev. Lett. 85, 2933-2936 (2000).
[117] R. A. Shelby, D. R. Smith, and S. Schultz, Experimental verification of a negative index of refraction, Science 292, 77 (2001).
[118] C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, Experimental verification and simulation of negative index of refraction using Shell's law, Phys. Rev. Lett. 90, 107401 (2003).
[119] J. B. Pendry, Negative refraction makes a perfect lens, Phys. Rev. Lett. 85, 3966-3969 (2000).
[120] P. M. Valanju, R. M. Walser, and A. P. Valanju, Wave refraction in negative-index media: always positive and very inhomogeneous, Phys. Rev. Lett. 88, 187401 (2002).
[121] N. Garcia and M. Nieto-Vesperinas, Left-handed materials do not make a perfect lens, Phys. Rev. Lett. 88, 207403 (2002).
[122] Z. M. Zhang and C. J. Fu, Unusual photon tunneling in the presence of a layer with a negative refractive index, Appl. Phys. Lett. 80, 1097-1097 (2002).
[123] P. R. Berman, Goos-Hanchen shift in negatively refractive media, Phys. Rev. E 66, 067603 (2002).
[124] A. Lakhtakia, Positive and negative Goos-Hanchen shifts and negative phase-velocity mediums (alias left-handed materials), Int. J. Electron. Commun., 28, 229-231 (2004).
[125] D. K. Qing and G. Chen, Goos-Hanchen at the interfaces between left- and right-handed media, Opt. Lett. 29, 872-874 (2004).
[126] I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, Gaint Goos-Hanchen effect at the reflection from left-handed metamaterial, Appl. Phys. Lett. 83 2713-2715 (2003).
[127] J. A. Kong, B.-L. Wu and Y. Zhang, Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability, Appl. Phys.Lett. 80, 2084-2086 (2002).
[128] J. A. Kong, B.-L. Wu and Y. Zhang, A unique lateral displacement of a Gaussian beam transmitted through a slab with negative permittivity and permeability, Microw. Opt. Techn. Lett. 33(2), 136-139 (2002).
[129] X. Chen and C.-F. Li, Lateral shift of the transmitted beam through a left-handed slab, Phy. Rev. E 69, 066617 (2004).
[130] Y. Yan, X. Chen, and C.-F. Li, Large and negative lateral displacement in an active dielectric slab configuration, Phys. Lett. A 361, 178-181 (2007).
[131] X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, Large postive and negative lateral optical beam displacement due to surface plasmon resonance, Appl. Phys. Lett. 85, 372-374 (2004).
[132] F. Pillon, H. Gilles, S. Girard, and M. Laroche, Goos-Hanchen and Imbert-Fedorov shift in total internal reflection, J. Opt. Soc. Am. B 22, 1290-1299 (2005).
[133] J. J. Chen, T. M. Grzegorczyk, B.-L. Wu, and J. A. Kong, Role of evanescent waves in the positive and negative Goos-Hanchen shifts with left-handed material slabs, J. Appl. Phys. 98, 094905 (2005).
[134] H.-L. Zhou, X. Chen, and C.-F. Li, Lateral displacement and its mechanism in asymmetric layered configuration J. Mod. Opt. 53(15), 2153-2165 (2006).
[135] M. Born and E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1980), Chap. 7, p.323.
[136] D. Dragoman and M. Dragoman, Optical analogue structures to mesoscopic devices, Progress in Quantum Electronics 23(4-5), 131-188 (1999).
[137] W. Liang, M. Bockrath, D. Bozovic, J. H. Hafner, M. Tinkham, and H. Park, Fabry Perot interference in a nanotube electron wavegnide, Nature (London) 411, 665-669 (2001).
[138] C. T. White and T. N. Todorov, Nanotubes go ballistic, Nature (London) 411, 649-651 (2001).
[139] Y. Ji, Y. Chung, D. Sprinzak, M. Heiblum, D. Mahalu, and H. Shtrikman, An electronic Mach-Zehnder interferometer, Nature (London) 422, 415-418 (2003).
[140] D. Bohm, Quantum Theory, New York: Prentice-Hall, (1951) 257-261.
[141] F. M. Peeters and A. Matulis, Quantum structures created by nonhomogeneous magnetic fields, Phys. Rev. B 48, 15166-15174 (1993).
[142] A. Matulis, F. M. Peeters, and Vasilopoulos, Wave-vector-dependent tunneling through magnetic barrier, Phys. Rev. Lett. 72, 1518-1520 (1994).
[143] Y. Guo, H. Wang, B. L. Gu, and Y. Kawazoe, Electric-field effects on electronic tunneling transport in magnetic barrier structures, Phys. Rev. B 61, 1728-1731 (2000).
[144] A. Majumdar, Effects of intrinsic spin on electronic transport through magnetic barrier, Phys. Rev. B 54, 11911-11913 (1996).
[145] M.-W. Lu, L.-D. Zhang, and X.-H. Yan, Spin polarization of electrons tunneling through magnetic-barrier nanostructures, Phys. Rev. B 66 224412 (2002).
[146] G. Papp and F. M. Peeters, Spin filtering in a magnetic-electric barrier structure, Appl. Phys. Lett. 78, 2184-2186 (2001); Erratum: "Spin filtering in a magneticelectric barrier structure". 79, 3198 (2001).
[147] H. Z. Xu and Y. Okada, Does a magnetic barrier or a magnetic-electric barrier structure possess any spin polarization and spin filtering under zero bias?, Appl. Phys. Lett. 79, 3119-3121 (2001).
[148] F. Zhal, H. Q. Xu, and Y. Guo, Tunable spin polarization in a two-dimensional electron gas modulated by a ferromagnetic metal stripe and a Schottky metal stripe, Phys. Rev. B 70, 085308 (2004).
[149] G. Papp, P. Vasilopoulos, and F. M. Peeters, Spin polarization in a two-dimensional electron gas modulated periodically by ferromagnetic and Schottky metal stripes, Phys. Rev. B 72, 115315 (2005).
[150] A. M. Kan'an and A. Puri, Transmission of an obliquely electron wave through GaAs-AlGaAs structures: Application to an electron wave filter, J. Appl. Phys. 74, 370-374 (1994).
[151] A. M. Kan'an and A. Puri, The generalized transmission matrix for electron-wave-optics through biased heterostructures: quantum device applications, J. Appl. Phys. 75, 351-356 (1994).
[152] B. Wang, Y. Guo, X.-Y. Chen, and B.-L. Gu, Spin polarization induced by an external electric field in a hybrid magnetic-electric barrier, J. Appl. Phys. 92(7), 4138-4140 (2002).
[153] V. Gasparian, T. Christen, and M. Biittiker, Partial densities of states scattering matrices, and Green's functions, Phys. Rev. A 54, 4022-4031 (1996).
[154] J. G. Muga, I. L. Egusquiza, J. A. Damborenea, F. Delgado, Bounds and enhancements for negative scattering time delays, Phys. Rev. A 66, 042115 (2002).
[155] M. Biittiker, in Electronic Properties of Multilayers and Low-Dimensional Semiconductors Structures, edited by J. M. Chamberlain, L. Eaves, and J. C. Portal (Plenum Press, New York, 1990), p.297
[156] C.-F. Li, Comment on "Photonic tunneling time in frustrated total internal reflection", Phys. Rev. A 65, 066101 (2002).
[157] H. Luo, N. Dai, F. C. Zhang, N. Smarth, M. Dobrowdska, J. K. Furdyna, C. Parks, and A. K. Radams, Observation of quasibound states in semiconductor single quantum barriers, Phys. Rev. Lett. 70, 1307-1310 (1993).
[158] G. Garcia-Calderon and A. Rubio, Properties of the dwell time and the transmission and reflection times for resonant tunneling, Solid State Commun. 71, 237-241 (1989).
[159] Y.-P. Wang and D.-L. Zhang, Reshaping, path uncertainty, and superluminal travelling, Phys. Rev. A 52, 2597-2600 (1995).
[160] A. Dogariu, A. Kuzmich, and L. J. Wang, Transparent anomalous dispersion and superluminal light-pulse propagation at a negative group velocity, Phys. Rev. A 63, 053806 (2001).
[161] L. G. Wang, N.-H. Liu, Q. Lin, and S.-Y. Zhu, Superluminal propagation of light pulses: A result of interference, Phys. Rev. E 68, 066606 (2003).
[162] W. Guo, Understanding subluminal and superluminal propagation through superposition of frequency components, Phys. Rev. E 73, 016605 (2006).
[163] Y. Aharonov, N. Erez, and B. Reznik, Superluminal tunnelling times as weak values, J. Mod. Opt. 50(6-7), 1139-1149 (2003).
[164] D. Sokolovski, A. Z. Msezane, and V. R. Shaginyan, "Superluminal" tunneling as a weak measurement effect, Phys. Rev. A 71, 064103 (2005).
[165] C. G. B. Garrett and D. E. McCumber, Propagation of a Gaussian light pulse through an anomalous dispersion medium, Phys. Rev. A 1, 305 (1970).
[166] S. Chu and S. Wong, Linear pulse propagation in an absorbing medium, Phys. Rev. Lett. 48, 738-741 (1982).
[167] B. Segard and B. Macke, Observation of negative velocity pulse propagation, Phys. Lett. A 109, 213-216 (1985).
[168] L. J. Wang, A. Kuzmich, and A. Dogariu, Gain-assisted superluminal light propagation, Nature (London) 406, 277-279 (2000).
[169] C.-F. Li and X. Chert, Traversal time for Dirac particles through a potential barrier, Ann. Phys. (Leipzig) 11(12), 916-925 (2002).
[170] P. Krekora, Q. Su, and R. Grobe, Effects of relativity on the time-resolved tunneling of electron wave packets, Phys. Rev. A 63, 032107 (2001).
[171] V. Petrillo and D. Janner, Relativistic analysis of a wave packet interacting with a quantum-mechanical barrier, Phys. Rev. A 67, 012110 (2003).
[172] C.-F. Li and Q. Wang, A traversal time for tunneling particles through a potential barrier, Physica B 296, 356-360 (2001).
[173] C. R. Leavens and G. C. Aers, Larmor-clock transmission times for resonant double barriers, Phys. Rev. B 40, 5387-5400 (1989).
[174] C.-F. Li and Q. Wang, Duration of tunneling photons in a frustrated-total-internal-reflection structure, J. Opt. Soc. Am. B 18, 1174-1179 (2001).
[175] M. Buttiker and H. Thomas, Front propagation in evanescent media, Superlattices and Microstructures 23(314), 781-794 (1998).
[176] M. Biittiker and H. Thomas, Front propagation in evanescent media, Ann. Phys. (Leipzig) 7, 602-617 (1998).
[177] See, for example, the detailed discussions in L. Brillouin, Wave Propagation and Group velocity, Academic Press, New York 1960.
[178] A. Calogeracos and N. Dombey, History and physics of the klein paradox, Contemp. Phys. 40(5), 313-321 (1999).
[179] A. Calogeracos and N. Dombey, Klein tunnelling and the klein paradox, Int. J. Mod. Phys. A 14(4), 631-643 (1999).
[180] N. S. Todorov, Extended particles Part II on klein's paradox, Ann. Fond. Louis Broglie 25(2) 209-222 (2000).
[181] M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Tunable refraction and reflection of self-confined light beam, Nature Phys. 2, 737-742 (2006).
[182] Y. Ban, X. Chen, and C.-F. Li, Controllable negative and positive group delay in transmission through a single quantum well at finite magnetic fields, Phys. Lett. A 364, 76-80 (2007).
[183] M. Onoda, S. Murakami, and N. Nagaosa, Hall effect of light, Phys. Rev. Lett. 93, 083901 (2004).
[184] K. Yu. Bliokh and Yu. P. Bliokh, Conservation of Angular Momentum, Transverse Shift, and Spin Hall Effect in Reflection and Refraction of an Electromagnetic Wave Packet, Phys. Rev. Lett. 96, 073903 (2004).
[185] M. Onoda, S. Murakami, and N. Nagaosa, Geometric aspects in optical wavepacket dynamics, Phys. Rev. E 74, 066610 (2004).