Abstract
An intense investigation of electromagnetic wave propagation phenomena at optical frequencies in periodic structures has occurred over the past two decades. Usually referred to as photonic band gap (PBG) crystals [1], the essential property of these structures is the existence of allowed and forbidden frequency bands and gaps, in analogy to energy bands and gaps of semiconductors. An early paper by Armstrong and co-workers [2] and a second by Bloembergen and Sievers [3] outlined the advantage of periodic dielectric structures to achieve phase matching. The further advantage of band edge enhancement and group velocity changes had not been worked out at that time.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
P. Yeh, Optical Waves in Layered Media John (Wiley & Sons, New York Chichester 1988); E. Yablonovitch: Phys. Rev. Lett. 58, 2059 (1987); S. John: Phys. Rev. Lett. 58, 2486 (1987); J. Maddox: Nature 348 481 (1990); E. Yablonovitch and K.M. Leung: Nature 351, 278 (1991); J. Martorell and N.M. Lawandy: Phys. Rev. Lett. 65, 1877 (1990); Development and Applications of Materials Exhibiting Photonic Band Gaps, edited by C.M. Bowden, J.P. Dowling, and H.O. Everitt, special issue of J. Opt. Soc. Am. B 10, 279 (1993); J. Mod. Opt. 41, 171 (1994), special issue on photonic band gaps, edited by G. Kurizki and J.W. Haus; J.D. Joannopoulos, R.D. Mead, and J.N. Winn, Photonic Crystals ( Princeton University Press, Princeton 1994 )
J.A. Armstrong, N. Bloembergen, J. Ducuing, and P.S. Pershan: Phys. Rev. 127, 1918 (1962)
N. Bloembergen and A.J. Sievers: Appl. Phys. Rev. Lett. 17, 483 (1970)
M. Scalora, J.P. Dowling, C.M. Bowden, and M.J. Bloemer: Phys. Rev. Lett. 73, 1368 (1994)
M. Scalora, J.P. Dowling, M.J. Bloemer, and C.M. Bowden: J. Appl. Phys. 76, 2023 (1994)
J.P. Dowling, M. Scalora, M.J. Bloemer, and C.M. Bowden: J. Appl. Phys. 75, 1896 (1994)
M. Scalora, R.J. Flynn, S.B. Reinhardt, R.L. Fork, M.D. Tocci, M.J. Bloemer, C.M. Bowden, H.S. Ledbetter, J.M. Bendickson, J.P. Dowling, and R.P. Leavitt: Phys. Rev. E 54, 1078 (1996)
M. Scalora, M.J. Bloemer, A.S. Manka, J.P. Dowling, C.M. Bowden, R. Viswanathan, and J.W. Haus: Phys. Rev. A 56, 3166 (1997)
M. Scalora, M.J. Bloemer, A.S Pethel, J.P. Dowling, C.M. Bowden, and A.S. Manka: J. of Appl. Phys. 83, 2377 (1998)
G. D’Aguanno, E. Angelillo, C. Sibilia, M. Scalora, and M. Bertolotti: J. Opt. Soc. Am. B 17, 1188 (2000)
J.C. Knight, T.A. Birkes, P.S. Russell, and J.P. De Sandro: J. Opt. Soc. Am. A 15, 748 (1998)
E. Yablonovitch: Microwave Journal VI, 66 (1999)
J. Martorell, R. Vilaseca, and R. Corbalan: Appl. Phys. Lett. 70, 702 (1997); J. Martorell, R. Vilaseca, and R. Corbalan: Phys. Rev. A 55, 4520 (1997); J. Martorell, R. Vilaseca, and R. Corbalan: J. Opt. Soc. Am. B 15, 2581 (1998)
C. Simonneau, J.P. Debray, J.C. Harmand, P. Vidakovic, D.J. Lovering, and J.A. Levenson: Opt. Lett. 23, 1775 (1997)
A.V. Balakin, D. Boucher, V.A. Bushey, N.I. Koroteev, B.I. Mantsyzov, P. Masselin, I.A. Ozheredov, and A.P. Shurinov: Opt. Lett. 24, 793 (1999)
W. Chen and D.L. Mills: Phys. Rev. Lett. 58, 160 (1987); J.E. Sipe and H.G. Winful: Opt. Lett. 13, 132 (1988); S. John and N. Akozbek: Phys. Rev. Lett. 71, 1168 (1993); C.M. de Sterke, D.G. Salinas and J.E. Sipe: Phys. Rev. E 54, 1969 (1996); B.J. Eggleton, R.E. Slusher, C.M de Sterke, P.A. Krug, and J.E. Sipe: Phys. Rev. Lett. 76, 160 (1996)
C. Conti, S. Trillo, and G. Assanto: Phys. Rev. Lett. 78, 2341 (1997)
G. D’Aguanno, M. Centini, C. Sibilia, M. Bertolotti, M.Scalora, M. Bloemer, and C.M. Bowden: Opt. Lett. 24, 1663 (1999)
M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. Bloemer, C.M. Bowden, and I. Nefedov: Phys. Rev. E 60, 4891 (1999)
A.E. Siegman: Phys. Rev. A 39, 1253 (1989); P.T. Leung, W.M. Suen, C.P. Sun, and K. Young: Phys. Rev. E 57, 6101 (1998)
D. Bohm Quantum Theory (Dover Publications, 1989) pp. 283–295; ibid. pp. 910; ibid. pp. 97–98
J.M. Bendickson, J.P Dowling, and M. Scalora: Phys. Rev E 53, 4107 (1996); C. Sibilia, I. Nefedov, M. Bertolotti; and M. Scalora: J. Opt. Soc. Am. B 1947 (1998)
A.M. Steinberg, P.G. Kwiat, and R.T. Chiao: Phys. Rev. Lett. 71, 708 (1993)
L. Brillouin, Wave Propagation and Group Velocity ( Academic Press, New York 1960 )
R. Loudon: J. Phys. A 3, 283 (1970)
C.G.B. Garret and D.E. McCumber: Phys. Rev. A 1, 305 (1970)
S. Chu and S. Wong: Phys. Rev. Lett. 48, 738 (1982)
J. Peatross, S.A. Glasgow, and M. Ware: Phys. Rev. Lett. 84, 2370 (2000)
L.J. Wang, A. Kuzmich, and A. Dogariu: Nature 406, 277 (2000)
A. Yariv and P. Yeh, Optical Waves in Crystals ( Wiley & Sons, New York Chichester 1984 )
P.S.J. Russell: J. Mod. Optics 38, 1599 (1991); C.M. De Sterke and J.E. Sipe: J. Opt. Soc. Am B 6, 1722 (1989)
For a review article on the definition of tunneling times see: E.H. Hauge and J.A. Stoevneng: Rev. Mod. Phys 61, 917 (1989); see also R.T. Chiao and A.M. Steinberg, Progress in Optics, edited by E. Wolf, Vol. XXXVII, (1997) p. 345
J.W. Haus, R. Viswanathan, M. Scalora, A.G. Kalocsai, J.D. Cole, and J. Theimer: Phys. Rev. A. 57 2120 (1998) (and references therein)
C.M. de Sterke and J.E. Sipe: Phys. Rev. A 38 5149 (1988); A. Arraf and C.M. de Sterke: Phys. Rev. E 58 7951 (1998) (and references therein)
Y. Dumeige et al., to appear in Applied Physics Lett.
V. Balakin, V.A. Bushuev, B.I. Mantsyzov, P Masselin, I.A. Ozheredov, and A.P. Shkurinov: JETP Letters 70, 725 (1999)
M. Born and E. Wolf, Principles of Optics,5th Edn., (Oxford, Pergamon Press)
M. Scalora and M.E. Crenshaw: Opt. Commun 108, 191 (1994)
S.A. Akhmanov and R.V. Khokhlovnce, (Gordon and Breach, New York 1972 ). Translated from the original Russian edition: Problemy Nelineinoi Optiki, Academy of Sciences of the USSR, 1964
R. Loudon, The Quantum Theory Of Light, 2nd Ed., (Oxford University Press, 1984 )
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
D’Aguanno, G. et al. (2003). Photonic Band Edge Effects in Finite Structures and Applications to χ(2) Interactions. In: Slusher, R.E., Eggleton, B.J. (eds) Nonlinear Photonic Crystals. Springer Series in Photonics, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05144-3_6
Download citation
DOI: https://doi.org/10.1007/978-3-662-05144-3_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07867-5
Online ISBN: 978-3-662-05144-3
eBook Packages: Springer Book Archive