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We apply the ABCD formalism to a gradient negative index medium (NIM) and investigate the propagation and transformation properties of Gaussian beams in this medium. First, we derive the ABCD formalism in a positive gradient NIM and obtain the propagation model. Spatial soliton and the spatial breather propagation in this medium are revealed. Our research suggests that the gradient coefficient has a significant effect on the focusing ability of slab. When the gradient coefficient increases, the quasi-lense effect becomes more prominent and notable. As a result, the focusing ability improves and the beam waist in the focal point shrinks. Second, when Gaussian beams propagate in the negative gradient NIM, the beam waist enlarges as the distance increases. There is neither spatial soliton phenomenon nor breather transmission phenomenon, which is completely different from the propagation characteristics in the positive gradient NIM.
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Keywords:
- Gaussian beam /
- gradient negative index media /
- ABCD law /
- propagation property
[1] Shelby R A, Smith D R, Schultz S 2001 Science 292 77
[2] Yao J, Liu Z W, Liu Y M, Wang Y, Sun C, Bartal G, Stacy A M, Zhang X 2008 Science 321 930
[3] Alú A, Engheta N 2008 Phys. Rev. Lett. 100 043901
[4] Zhou J H, Luo H L, Wen S C, Fang A L, Zhuang B X 2009 Acta Phys. Sin. 58 1765 (in Chinese)[周建华, 罗海陆, 文双春, 方安乐, 庄彬先 2009 58 1765]
[5] Tang M, Zhou X X, Luo H L, Wen S C 2012 Chin. Phys. B 21 124201
[6] Wang G D, Liu M H, Hu X W, Kong L H, Cheng L L, Chen Z Q 2014 Chin. Phys. B 23 017802
[7] Moore D T 1980 Appl. Opt. 19 1035
[8] Smith D R, Mock J J, Starr A F, Schurig D 2005 Phys. Rev. E 71 036609
[9] Driscoll T, Basov D N, Starr A F, Rye P M, Nemat-Nasser S, Schurig D, Smith D R 2006 Appl. Phys. Lett. 88 081101
[10] Greegor R B, Parazzoli C G, Nielsen J A, Thompson M A, Tanielian M H, Smith D R 2005 Appl. Phys. Lett. 87 091114
[11] Ramakrishna S A, Pendry J B, Schurig D, Smith D R, Schultz S 2002 J. Mod. Opt. 49 1747
[12] Pinchuk A O, Schatz G C 2007 J. Opt. Soc. Am. A 24 A39
[13] Pinchuk A O, Schatz G C 2007 Solid State Electron. 51 1381
[14] Xi C, Xu H S, Yang X M 2009 Appl. Phys. Lett. 95 094107
[15] Nguyen V, Larouche S, Landy N, Lee J S, Smith D R 2012 J. Opt. Soc. Am. A 29 2479
[16] Born M, Wolf E 1999 Principle Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (7th Ed.) (Cambridge: Cambridge University Press) pp58-74
[17] Yarcv A 1975 Quantum Electronics (2nd Ed.) (NewYork: Wiley & Sons) pp67-81
[18] Zhou J H, Luo H L, Wen S C, Zeng Y S 2009 Opt. Commun. 282 2670
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[1] Shelby R A, Smith D R, Schultz S 2001 Science 292 77
[2] Yao J, Liu Z W, Liu Y M, Wang Y, Sun C, Bartal G, Stacy A M, Zhang X 2008 Science 321 930
[3] Alú A, Engheta N 2008 Phys. Rev. Lett. 100 043901
[4] Zhou J H, Luo H L, Wen S C, Fang A L, Zhuang B X 2009 Acta Phys. Sin. 58 1765 (in Chinese)[周建华, 罗海陆, 文双春, 方安乐, 庄彬先 2009 58 1765]
[5] Tang M, Zhou X X, Luo H L, Wen S C 2012 Chin. Phys. B 21 124201
[6] Wang G D, Liu M H, Hu X W, Kong L H, Cheng L L, Chen Z Q 2014 Chin. Phys. B 23 017802
[7] Moore D T 1980 Appl. Opt. 19 1035
[8] Smith D R, Mock J J, Starr A F, Schurig D 2005 Phys. Rev. E 71 036609
[9] Driscoll T, Basov D N, Starr A F, Rye P M, Nemat-Nasser S, Schurig D, Smith D R 2006 Appl. Phys. Lett. 88 081101
[10] Greegor R B, Parazzoli C G, Nielsen J A, Thompson M A, Tanielian M H, Smith D R 2005 Appl. Phys. Lett. 87 091114
[11] Ramakrishna S A, Pendry J B, Schurig D, Smith D R, Schultz S 2002 J. Mod. Opt. 49 1747
[12] Pinchuk A O, Schatz G C 2007 J. Opt. Soc. Am. A 24 A39
[13] Pinchuk A O, Schatz G C 2007 Solid State Electron. 51 1381
[14] Xi C, Xu H S, Yang X M 2009 Appl. Phys. Lett. 95 094107
[15] Nguyen V, Larouche S, Landy N, Lee J S, Smith D R 2012 J. Opt. Soc. Am. A 29 2479
[16] Born M, Wolf E 1999 Principle Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (7th Ed.) (Cambridge: Cambridge University Press) pp58-74
[17] Yarcv A 1975 Quantum Electronics (2nd Ed.) (NewYork: Wiley & Sons) pp67-81
[18] Zhou J H, Luo H L, Wen S C, Zeng Y S 2009 Opt. Commun. 282 2670
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