Goos-H（？）nchen位移增强效应及Fabry-Perot振荡场传感器研究
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摘要
古斯-汉欣(Goos-Hanchen,简称GH)位移指的是反射光的实际反射点和入射点(也即几何光学反射点)有一段距离的偏移的现象。这是由于入射光中不同的单色平面波分量具有不同的反射相移所造成的。研究Goos-H?nchen位移有多种方法,本文采用Artmann发展的静态位相(stationary phase)方法和高斯光束下的数值计算方法,主要研究了导波共振和表面等离子波共振时GH位移增强效应。
在普通的两层介质的界面上,GH位移大小为波长量级。因此对光波单次反射所产生的GH位移在实验上难以直接观察。因此,长期以来,一方面,人们在实验上较多地采用微波波段进行实验,另一方面,很多人在理论上研究不同条件下的GH位移增强效应以获得较大的GH位移,到目前为止已经发现了许多种GH位移增强效应。其中,由表面等离子波共振引起的GH位移增强效应早在上世纪八十年代就开始被人注意到。但直到2004年,Yin Xiaobo等人在实验上才首次证实了表面等离子波共振引起的GH位移增强效应的存在。同时他们在实验上还发现了一个在理论上以前从未有过的新现象:如果金属层的厚度超过零反射率下的最佳金属层厚度,GH位移为负,反之为正,并且还发现金属层的厚度越接近零反射率下的最佳厚度,GH位移就越大,反之就越小。本文则在理论上把这个结果进行了推广,得出了一
Goos-H?nchen shift refers to the lateral shift of a totally reflected beam from the position predicted by geometrical optics. It is because each plane wave component of the incident beam undergoes a slight different phase change after total internal reflection. Many representation approaches to the Goos-H?nchen shift have been developed. In this paper, we examine theoretically the GH shift under the conditions of guided wave resonance and surface plasmon resonance by using the stationary phase method and numerical calculation method with an incident beam of the Gaussian shape.
At a single dielectric interface, the GH shift is of the order of wavelength. The smallness of the shift for optical wavelengths had impeded its direct observation in a single reflection. Therefore, on the one hand, the wavelengths in the microwave range are selected to perform experiments. On the other hand, the enhancement effects of GH shift under different conditions were analyzed in many papers. Up to now, many kinds of enhancement effects of GH shift were reported. The enhancement effect of GH shift due to the surface plasmon resonance was discussed in 1980s. In 2004, Xiaobo Yin et al. firstly reported the
在普通的两层介质的界面上,GH位移大小为波长量级。因此对光波单次反射所产生的GH位移在实验上难以直接观察。因此,长期以来,一方面,人们在实验上较多地采用微波波段进行实验,另一方面,很多人在理论上研究不同条件下的GH位移增强效应以获得较大的GH位移,到目前为止已经发现了许多种GH位移增强效应。其中,由表面等离子波共振引起的GH位移增强效应早在上世纪八十年代就开始被人注意到。但直到2004年,Yin Xiaobo等人在实验上才首次证实了表面等离子波共振引起的GH位移增强效应的存在。同时他们在实验上还发现了一个在理论上以前从未有过的新现象:如果金属层的厚度超过零反射率下的最佳金属层厚度,GH位移为负,反之为正,并且还发现金属层的厚度越接近零反射率下的最佳厚度,GH位移就越大,反之就越小。本文则在理论上把这个结果进行了推广,得出了一
Goos-H?nchen shift refers to the lateral shift of a totally reflected beam from the position predicted by geometrical optics. It is because each plane wave component of the incident beam undergoes a slight different phase change after total internal reflection. Many representation approaches to the Goos-H?nchen shift have been developed. In this paper, we examine theoretically the GH shift under the conditions of guided wave resonance and surface plasmon resonance by using the stationary phase method and numerical calculation method with an incident beam of the Gaussian shape.
At a single dielectric interface, the GH shift is of the order of wavelength. The smallness of the shift for optical wavelengths had impeded its direct observation in a single reflection. Therefore, on the one hand, the wavelengths in the microwave range are selected to perform experiments. On the other hand, the enhancement effects of GH shift under different conditions were analyzed in many papers. Up to now, many kinds of enhancement effects of GH shift were reported. The enhancement effect of GH shift due to the surface plasmon resonance was discussed in 1980s. In 2004, Xiaobo Yin et al. firstly reported the
引文
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[6]. J. B. Pendry, “Negative refraction makes a perfect lens”, Phys. Rev. Lett., (2000), 85, 3966.
[7]. D. Schurig and D. R. Smith, “Spatial filtering using media with indefinite permittivity and permeability tensors”, Appl. Phys. Lett., (2003), 82, 2215.
[8]. I. V. Shadrivov, A. A. Sukhorukov and Y. S. Kivshar, “Beam shaping by a periodic structure with negative refraction”, Appl. Phys. Lett., (2003), 82, 3820.
[9]. P. R. Berman, “Goos-H?nchen shift in negatively refractive media”, Phys. Rev. E, (2002), 66, 067603.
[10]. D.-K. Qing and G. Chen, “Goos-H?nchen shifts at the interfaces between left- and right-handed media,” Opt. Lett., (2004), 29, 872.
[11]. X. Chen and C. F. Li, “Lateral shift of the transmitted light beam through a left-handed slab,” Phys. Rev. E, (2004), 69, 066617.
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[14]. I. Shadrivov, R. Ziolkowski, A. Zharov and Y. Kivshar, “ Excitation of guided waves in layered structures with negative refraction,” Opt. Express, (2005), 13, 481.
[15]. H. Lai and S. Chan, “Large and negative Goos-H?nchen shift near the Brewster dip on reflection from weakly absorbing media,” Opt. Lett., (2002), 27, 680.
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[17]. L. Wang, H. Chen, and S. Zhou, “Large negative Goos-H?nchen shift from a weakly absorbing dielectric slab,” Opt. Lett., (2005), 30, 2936.
[18]. C. F. Li and X. Y Yang, “Thin-Film Enhanced Goos–H?nchen Shift in Total Internal Reflection,” Chin. Phys. Lett., (2004), 21, 485.
[1]. T. Tamir and H. L. Bertoni, “Lateral Displacement of Optical Beams at Multilayered and Periodic Structures,” J. Opt. Soc. Am., (1971), 61, 1397.
[2]. V. Shah and T. Tamir, “Absorption and lateral shift of beams incident upon lossy multilayered media,” J. Opt. Soc. Am. A, (1983), 73, 37.
[3]. P. Mazur, and B. Djafari-Rouhani, “Effect of surface polaritons on the lateral displacement of a light beam at a dielectric interface,” Phys. Rev. B. (1984), 30, 6759.
[4]. S. L. Chuang, “Lateral shift of an optical beam due to leaky surface-plasmon excitations,” J. Opt. Soc. Am. A. (1986), 3, 593.
[5]. G. Abbate, P. Maddalena, and E. Santamato, P. Mormile, and G. Pierattini, “Observation of lateral displacement of an optical beam enhanced by surface plasmon excitation,” J. Mod. Opt., (1988), 35, 1257.
[6]. X. Yin, L. Hesselink, Z. Liu, et al. “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett., (2004), 85, 372.
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[8]. X. Liu, Z. Cao, P. Zhu, Q. Shen and X. Liu, “Large positive and negative lateral optical beam shift in prism-waveguide coupling system,” Phys. Rev. E, (2006), 73, 056617.
[9]. T. Okamoto, M. Yamamoto, and I. Yamaguchi, “Optical waveguide absorption sensor using a single coupling prism,” J. Opt. Soc. Am. A, (2000), 17, 1880.
[10]. K. Artmann, “Berechnung der Seitenversetzung des totalreflektieren Strahles,” Ann. Phys., (1948), 2, 87.
[11]. T. Okamoto and I. Yamaguchi, “Absorption measurement using a leaky waveguide mode,” Opt. Rev., (1997), 4, 354.
[12]. C. F. Li, Q. Wang, “Prediction of simultaneously large and opposite generalized Goos-H?nchen shifts for TE and TM light beams in an asymmetric double-prism configuration,” Phys. Rev. E, (2004), 69, 055601(R).
[13]. C.-W. Hsue and T. Tamir, “Lateral displacement and distortion of beams incident upon a transmitting-layer configuration,” J. Opt. Soc. Am. A, (1985), 2, 978.
[14]. I. Shadrivov, R. Ziolkowski, A. Zharov and Y. Kivshar, “ Excitation of guided waves in layered structures with negative refraction,” Opt. Express, (2005), 13, 481.
[15]. W. P. Chen, J. M. Chen, “Use of surface plasma waves for determination of the thickness and optical constants of thin metallic films,” J. Opt. Soc. Am., (1981), 71, 189.
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[1]. H. Lai and S. Chan, “Large and negative Goos-H?nchen shift near the Brewster dip on reflection from weakly absorbing media,” Opt. Lett., (2002), 27, 680.
[2]. X. Yin, L. Hesselink, Z. Liu, et al. “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett., (2004), 85, 372.
[3]. C. F. Li, Q. Wang, “Prediction of simultaneously large and opposite generalized Goos-H?nchen shifts for TE and TM light beams in an asymmetricdouble-prism configuration,” Phys. Rev. E, (2004), 69, 055601(R).
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[1]. 曹庄琪,《导波光学中的转移矩阵方法》,上海交通大学出版社,2000。
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[7]. D. Schurig and D. R. Smith, “Spatial filtering using media with indefinite permittivity and permeability tensors”, Appl. Phys. Lett., (2003), 82, 2215.
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[1]. T. Tamir and H. L. Bertoni, “Lateral Displacement of Optical Beams at Multilayered and Periodic Structures,” J. Opt. Soc. Am., (1971), 61, 1397.
[2]. V. Shah and T. Tamir, “Absorption and lateral shift of beams incident upon lossy multilayered media,” J. Opt. Soc. Am. A, (1983), 73, 37.
[3]. P. Mazur, and B. Djafari-Rouhani, “Effect of surface polaritons on the lateral displacement of a light beam at a dielectric interface,” Phys. Rev. B. (1984), 30, 6759.
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[5]. G. Abbate, P. Maddalena, and E. Santamato, P. Mormile, and G. Pierattini, “Observation of lateral displacement of an optical beam enhanced by surface plasmon excitation,” J. Mod. Opt., (1988), 35, 1257.
[6]. X. Yin, L. Hesselink, Z. Liu, et al. “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett., (2004), 85, 372.
[7]. F. Schreier, M. Schmitz, O. Bryngdahl, “Beam displacement at diffractive structures under resonance conditions,” Opt. Lett. (1998), 23, 576.
[8]. X. Liu, Z. Cao, P. Zhu, Q. Shen and X. Liu, “Large positive and negative lateral optical beam shift in prism-waveguide coupling system,” Phys. Rev. E, (2006), 73, 056617.
[9]. T. Okamoto, M. Yamamoto, and I. Yamaguchi, “Optical waveguide absorption sensor using a single coupling prism,” J. Opt. Soc. Am. A, (2000), 17, 1880.
[10]. K. Artmann, “Berechnung der Seitenversetzung des totalreflektieren Strahles,” Ann. Phys., (1948), 2, 87.
[11]. T. Okamoto and I. Yamaguchi, “Absorption measurement using a leaky waveguide mode,” Opt. Rev., (1997), 4, 354.
[12]. C. F. Li, Q. Wang, “Prediction of simultaneously large and opposite generalized Goos-H?nchen shifts for TE and TM light beams in an asymmetric double-prism configuration,” Phys. Rev. E, (2004), 69, 055601(R).
[13]. C.-W. Hsue and T. Tamir, “Lateral displacement and distortion of beams incident upon a transmitting-layer configuration,” J. Opt. Soc. Am. A, (1985), 2, 978.
[14]. I. Shadrivov, R. Ziolkowski, A. Zharov and Y. Kivshar, “ Excitation of guided waves in layered structures with negative refraction,” Opt. Express, (2005), 13, 481.
[15]. W. P. Chen, J. M. Chen, “Use of surface plasma waves for determination of the thickness and optical constants of thin metallic films,” J. Opt. Soc. Am., (1981), 71, 189.
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[1]. H. Lai and S. Chan, “Large and negative Goos-H?nchen shift near the Brewster dip on reflection from weakly absorbing media,” Opt. Lett., (2002), 27, 680.
[2]. X. Yin, L. Hesselink, Z. Liu, et al. “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett., (2004), 85, 372.
[3]. C. F. Li, Q. Wang, “Prediction of simultaneously large and opposite generalized Goos-H?nchen shifts for TE and TM light beams in an asymmetricdouble-prism configuration,” Phys. Rev. E, (2004), 69, 055601(R).
[4]. H. Li, Z. Cao, H. Lu, and Q. Shen, “Free-space coupling of a light beam into a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett., (2003), 83, 2757.
[5]. H. Lu, Z. Cao, H. Li, et al, “Polarization-independent and tunable comb filter based on a free-space coupling technique,” Opt. Lett., (2006), 31, 386.
[6]. H. Lu, Z. Cao, H. Li, et al., “Study of ultrahigh-order modes in a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett., (2004), 85, 4579.
[7]. R. Ulrich, “Theroy of Prism-Film Coupler by Plane-Wave Analysis,” J. Opt. Soc. Am., (1970), 60, 1337.
[8]. T. Tamir and S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys., (1977), 14, 235.
[9]. W. P. Chen and J. M. Chen, “Use of surface plasma waves fore determination of the thickness and optical constants of thin metallic films,” J. Opt. Soc. Am., (1981), 71, 189
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