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Bragg solitons and optical switching in nonlinear periodic structures: an historical perspective
Optics Express, Vol. 3, Issue 11, pp. 385-388 (1998)
http://dx.doi.org/10.1364/OE.3.000385
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Abstract
A brief historical narrative of the study of Bragg solitons and optical switching in nonlinear periodic structures is presented, beginning with the first theoretical predictions in the late 1970’s up to and including several recent experimental demonstrations of optical switching and nonlinear pulse propagation in these structures.
© Optical Society of America
[Optical Society of America ]
1. Introduction.
Optical structures which exhibit a one-dimensional periodicity in the dispersive part of the refractive index have long been known to exhibit narrow regions of high reflectivity; in recent years the parallel between these “gaps” in the transmission spectrum and the energy gaps which appear in the dispersion relation of a single electron in a solid have been examined, with particular attention to the enhancement or suppression of such optical phenomena as spontaneous emission, absorption, and nonlinear optical interactions. It was noted, by Winful, Marburger and Garmire [1], Winful and Cooperman [2], and Winful and Stegeman [3], that the optical response of such structures could include bistability, switching, limiting, and dynamical instabilities in cases where Kerr or Kerr-like nonlinearities are present.
H. G. Winful et. al., “Theory of bistability in nonlinear distributed feedback structures“ Appl. Phys. Lett. 35, 379 (1979). [CrossRef]
H. G. Winful and C. D. Cooperman, “Self-pulsing and chaos in distributed feedback bistable optical devices“ Appl. Phys. Lett. 40, 298 (1982). [CrossRef]
The increase in interest in these structures in recent years can be traced to two observations: (1) The introduction of the concept of “photonic band structure” by Yablonovitch in the late 1980’s [4], and (2) The discovery that periodic structures, when fabricated in a medium with a Kerr-type optical nonlinearity, can exhibit solutions whose envelopes take the form of solitary waves. Chen and Mills [5] and Mills and Trullinger [6] made this observation about infinite periodic structures in the steady-state. Shortly after this, Sipe and Winful [7], de Sterke and Sipe [8], Christodoulides and Joseph [9], and Aceves and Wabnitz [10] published analyses showing that these “gap-solitons” (which now have the somewhat more accurate designation Bragg soliton) are not only fundamental solutions in the weak-field regime but could be detected as propagating solutions in structures of finite length. (One trademark of the Bragg soliton is an effective transit time much greater than the group velocity of the unperturbed medium without the accompanying pulse broadening which occurs in the linear regime.) Sipe and de Sterke examined, in further publications [11–13], the pulse transmission behavior as a function of both pulse energy and detuning from the Bragg resonance.
E. Yablonovitch and T. J. Gmitter, “Photonic band structure: the face-centered-cubic case” Phys. Rev. Lett. , 63, 1950 (1989). [CrossRef] [PubMed]
W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices“ Phys. Rev. Lett. 58, 160 (1987). [CrossRef] [PubMed]
D. L. Mills and S. E. Trullinger, “Gap solitons in nonlinear periodic structures“ Phys. Rev. B 36, 947 (1987). [CrossRef]
J. E. Sipe and H. G. Winful, “Nonlinear Schrodinger solitons in a periodic structure“ Opt. Lett. 13, 132 (1988). [CrossRef] [PubMed]
C. M. de Sterke and J. E. Sipe, “Envelope-function approach for the electrodynamics of nonlinear periodic structures“ Phys. Rev. A , 38, 5149 (1988). [CrossRef] [PubMed]
D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in Nonlinear Periodic Structures” Phys. Rev. Lett. , 62, 1746 (1989). [CrossRef] [PubMed]
A. B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media” Phys. Lett. A , 141, 37 (1989). [CrossRef]
C. M. de Sterke and J. E. Sipe, “Extensions and generalizations of an envelope-function approach for the electrodynamics of nonlinear periodic structures” Phys. Rev. A , 39, 5163 (1989). [CrossRef] [PubMed]
Both limiting phenomena as well as other, rather exotic, pulse propagation effects have been discussed in detail in these publications. Among the contributions of de Sterke, Sipe and others was a rigorous development of coupled-wave and multiple-scales approximations as well as the description of numerical methods [14] suitable for examining the regimes of instability of these structures. In order to better simulate experimental conditions, Broderick, de Sterke and Jackson presented a method of numerically modeling periodic structures having optical nonlinearities with nonzero response time [15]. Still other generalizations have been discussed by Feng and Kneubuhl [16] and by Feng [17]. Other important extensions and generalizations include a series of papers by Aceves and coworkers extending many of these principles to waveguide arrays. [18]
C. M. deSterke, K. R. Jackson, and B. D. Robert, “Nonlinear coupled-mode equations on a finite interval: a numerical procedure” J. Opt. Soc. Am. B , 8, 403 (1991). [CrossRef]
N. G. R. Broderick, C. M. d. Sterke, and K. R. Jackson, “Coupled mode equations with free carrier effects: a numerical solution” Opt. Quantum Electron. 26, S219 (1994). [CrossRef]
J. Feng and F. K. Kneubuhl, “Solitons in a periodic structure with Kerr nonlinearity” IEEE J. Quantum Electronics 29, 590 (1993). [CrossRef]
J. Feng, “Alternative scheme for studying gap solitons in an infinite periodic Kerr medium” Opt. Lett. 18, 1302 (1993). [CrossRef] [PubMed]
A. B. Aceves et al., “Storage and steering of self-trapped discrete solitons in nonlinear waveguide arrays” Opt. Lett. 19, .332 (1994). [CrossRef] [PubMed]
Scalora et. al., in a 1994 paper entitled “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” [19] began the process of recasting many of these principles into the new language of photonic crystals. Since then, a large number of publications have been devoted to the linear and nonlinear properties of photonic crystals, and researchers following the current literature will find the structures described herein under the various terms “Distributed Feedback Structures”, “Nonlinear Periodic Structures”, “Optical Superlattices”, or “X-d photonic crystals”, with ‘X’ designating the dimensionality of the periodic structure. It was in this vein that Radic, George and Agrawal noted the close analogy between nonlinear periodic structures and distributed feedback lasers and suggested the use of λ/4 phase-shifted gratings for use in optical switching. [20] Meanwhile, Russell and Archambault pursued the photonic crystal/Bloch wave approach in order to better understand the propagation characteristics and stability of oblique waves in nonlinear periodic media. [21]
M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer. “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials” Phys. Rev. Lett. . 73, 1368 (1994). [CrossRef] [PubMed]
S. Radic, N. George, and G. P. Agrawal, “Optical switching in λ/4-shifted nonlinear periodic structures” Opt. Lett. 19, 1789 (1994). [CrossRef] [PubMed]
P. St. J. Russell and J.-L. Archambault, “Field microstructure and temporal and spatial instability of photonc Bloch waves in nonlinear periodic structures” J. Phys. III France 4, 2471 (1994). [CrossRef]
2. Experimental Contributions
To our knowledge, it was Larochelle, Hihino, Mizrahi and Stegeman [22] who were the first to report (in 1990) an experimental investigation of the optical response of nonlinear periodic structures. They employed an optical Kerr-effect cross-phase modulation in fiber gratings to achieve switching of a probe beam by a control beam.
S. Larochelle, V. Mizrahi, and G. Stegeman, “All-optical switching of grating transmission using cross-phase modulation in optical fibres” Electron. Lett. 26, 1459 (1990). [CrossRef]
The first detailed experimental observation of all-optical switching dynamics in a nonlinear periodic structure was reported by Sankey, Prelewitz and Brown in 1992 [23]. The structure used was a corrugated, silicon-on-insulator optical waveguide, and employed a Nd:YAG excitation pulse in order to exploit the near band-edge Kerr-like nonlinearities which are present in such semiconductors. Because thermal transients are always an issue in such observations, a more detailed follow-up study was carried out, in which the dynamics were examined over a wider range of structures [24]. The results showed all-optical switching, true optical hysteresis, and a tendency toward unstable behavior at high intensities and strong coupling. This work was later extended to optically-resonant periodic-electrode (ORPEL) structures and out-of-plane coupling into higher order Bragg resonators. [25,26]
N. D. Sankey, D. F. Prelewitz, and T. G. Brown, “All-optical switching in a nonlinear periodic waveguide structure“ Appl. Phys. Lett. 60, 1427 (1992). [CrossRef]
N. D. Sankey, D. F. Prelewitz, and T. G. Brown, “Optical switching dynamics of the nonlinear Bragg reflector: comparison of theory and experiment“ J. Appl. Phys. 73, 1 (1993). [CrossRef]
Amy E. Bieber et. al., “Optical Switching in a metal-semiconductor-metal waveguide structure“ Appl. Phys. Lett. 66, 3401 (1995). [CrossRef]
Amy E. Bieber and T. G. Brown, “Integral coupler-resonator for silicon-based switching and modulation“ Appl. Phys. Lett. 71, 861 (1995). [CrossRef]
Meanwhile, a set of experiments which demonstrated optical limiting in a three-dimensional periodic structure was reported by Herbert and Malcuit [27]. They employed an ordered colloidal suspension immersed in a Kerr medium, and observed clear evidence of a dynamical shift in the Bragg resonance. Other experimental efforts have also been reported.
C. Herbert and M. Malcuit, Opt. Lett. , 17, 1037 (1992). [CrossRef] [PubMed]
For example, in an effort to broaden the applications to free-space switching and limiting, He and Cada [28] examined the use of both III-V and SiGe multilayers as nonlinear Bragg reflectors.
J. He and M. Cada, “Optical bistability in semiconductor periodic structures“ J. Quantum Electron. 27, 1182 (1991). [CrossRef]
The first direct observations of ultrafast nonlinear optical interactions in periodic media were not carried out until a few years ago. To date, two groups have published experimental evidence of gap-soliton propagation, pulse compression, and switching. An investigation of nonlinear pulse propagation (λ=1064 nm) in uniform fiber gratings was published by Eggleton et. al. in 1996. [29] This was followed by further reports from the same group, which both refined the experimental technique and broadened the experimental understanding of the dynamics of pulse propagation in periodic structures. [30] The Southhampton group [31] first demonstrated switching at the important optical communication wavelength of λ=1550 nm, and in doing so have confirmed certain key aspects of the physics of pulse propagation in nonlinear periodic structures.
B. J. Eggleton, R. E. Slusher, C. M. deSterke, P. A. Krug, and J. E. Sipe, “Modulational instability and tunable multiple soliton generation in apodized fiber gratings” Opt. Commun. 149, 267 (1998). [CrossRef]
N. G. R. Broderick, D. Taverner, D. J. Richardson, M. Ibsen, and R. I. Laming, “Experimental Observation of nonlinear pulse compression in nonuniform Bragg gratings“ Opt. Lett. 22, 1837 (1997). [CrossRef]
What do we currently know about nonlinear interactions in periodic media in general, and the physics of Bragg soliton propagation in particular? The theorists have taught us that many of these problems can be mapped on to propagation problems in equivalent, uniform media and have described how impedance mismatches can effectively be handled by adiabatic tapers, a practical issue which let to the first unambiguous experimental observations of Bragg-soliton propagation. We now understand that a Bragg soliton need not be centered near the Bragg resonance╌indeed, some very interesting propagation effects occur rather far from the band edge. We understand much of the physics governing nanosecond-scale switching dynamics in semiconductor Bragg reflectors, but have not yet extended those studies to the picosecond time scale. There is clearly much yet to do.
References
H. G. Winful et. al., “Theory of bistability in nonlinear distributed feedback structures“ Appl. Phys. Lett. 35, 379 (1979). [CrossRef] | |
H. G. Winful and G. I. Stegeman, “Applications of nonlinear periodic structures in guided wave optics“ Proc. SPIE 517, 214 (1984). | |
H. G. Winful and C. D. Cooperman, “Self-pulsing and chaos in distributed feedback bistable optical devices“ Appl. Phys. Lett. 40, 298 (1982). [CrossRef] | |
E. Yablonovitch and T. J. Gmitter, “Photonic band structure: the face-centered-cubic case” Phys. Rev. Lett. , 63, 1950 (1989). [CrossRef] [PubMed] | |
W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices“ Phys. Rev. Lett. 58, 160 (1987). [CrossRef] [PubMed] | |
D. L. Mills and S. E. Trullinger, “Gap solitons in nonlinear periodic structures“ Phys. Rev. B 36, 947 (1987). [CrossRef] | |
J. E. Sipe and H. G. Winful, “Nonlinear Schrodinger solitons in a periodic structure“ Opt. Lett. 13, 132 (1988). [CrossRef] [PubMed] | |
C. M. de Sterke and J. E. Sipe, “Envelope-function approach for the electrodynamics of nonlinear periodic structures“ Phys. Rev. A , 38, 5149 (1988). [CrossRef] [PubMed] | |
D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in Nonlinear Periodic Structures” Phys. Rev. Lett. , 62, 1746 (1989). [CrossRef] [PubMed] | |
A. B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media” Phys. Lett. A , 141, 37 (1989). [CrossRef] | |
C. M. de Sterke and J. E. Sipe, “Extensions and generalizations of an envelope-function approach for the electrodynamics of nonlinear periodic structures” Phys. Rev. A , 39, 5163 (1989). [CrossRef] [PubMed] | |
C. M. de Sterke and J. E. Sipe, “Coupled modes and the nonlinear Schrodinger equation“ Phys. Rev. A 42, 550 (1990). [CrossRef] | |
C. M. de Sterke and J. E. Sipe, “Switching dynamics of finite periodic nonlinear media: a numerical study“ Phys. Rev. A 42, 2858 (1990). [CrossRef] [PubMed] | |
C. M. deSterke, K. R. Jackson, and B. D. Robert, “Nonlinear coupled-mode equations on a finite interval: a numerical procedure” J. Opt. Soc. Am. B , 8, 403 (1991). [CrossRef] | |
N. G. R. Broderick, C. M. d. Sterke, and K. R. Jackson, “Coupled mode equations with free carrier effects: a numerical solution” Opt. Quantum Electron. 26, S219 (1994). [CrossRef] | |
J. Feng and F. K. Kneubuhl, “Solitons in a periodic structure with Kerr nonlinearity” IEEE J. Quantum Electronics 29, 590 (1993). [CrossRef] | |
J. Feng, “Alternative scheme for studying gap solitons in an infinite periodic Kerr medium” Opt. Lett. 18, 1302 (1993). [CrossRef] [PubMed] | |
A. B. Aceves et al., “Storage and steering of self-trapped discrete solitons in nonlinear waveguide arrays” Opt. Lett. 19, .332 (1994). [CrossRef] [PubMed] | |
M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer. “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials” Phys. Rev. Lett. . 73, 1368 (1994). [CrossRef] [PubMed] | |
S. Radic, N. George, and G. P. Agrawal, “Optical switching in λ/4-shifted nonlinear periodic structures” Opt. Lett. 19, 1789 (1994). [CrossRef] [PubMed] | |
P. St. J. Russell and J.-L. Archambault, “Field microstructure and temporal and spatial instability of photonc Bloch waves in nonlinear periodic structures” J. Phys. III France 4, 2471 (1994). [CrossRef] | |
S. Larochelle, V. Mizrahi, and G. Stegeman, “All-optical switching of grating transmission using cross-phase modulation in optical fibres” Electron. Lett. 26, 1459 (1990). [CrossRef] | |
N. D. Sankey, D. F. Prelewitz, and T. G. Brown, “All-optical switching in a nonlinear periodic waveguide structure“ Appl. Phys. Lett. 60, 1427 (1992). [CrossRef] | |
N. D. Sankey, D. F. Prelewitz, and T. G. Brown, “Optical switching dynamics of the nonlinear Bragg reflector: comparison of theory and experiment“ J. Appl. Phys. 73, 1 (1993). [CrossRef] | |
Amy E. Bieber et. al., “Optical Switching in a metal-semiconductor-metal waveguide structure“ Appl. Phys. Lett. 66, 3401 (1995). [CrossRef] | |
Amy E. Bieber and T. G. Brown, “Integral coupler-resonator for silicon-based switching and modulation“ Appl. Phys. Lett. 71, 861 (1995). [CrossRef] | |
C. Herbert and M. Malcuit, Opt. Lett. , 17, 1037 (1992). [CrossRef] [PubMed] | |
J. He and M. Cada, “Optical bistability in semiconductor periodic structures“ J. Quantum Electron. 27, 1182 (1991). [CrossRef] | |
B. J. Eggleton, R. E. Slusher, C. M. deSterke, P. A. Krug, and J. E. Sipe “Bragg grating solitons“ Phys. Rev. Lett. 76, 627 (1996). | |
B. J. Eggleton, R. E. Slusher, C. M. deSterke, P. A. Krug, and J. E. Sipe, “Modulational instability and tunable multiple soliton generation in apodized fiber gratings” Opt. Commun. 149, 267 (1998). [CrossRef] | |
N. G. R. Broderick, D. Taverner, D. J. Richardson, M. Ibsen, and R. I. Laming, “Experimental Observation of nonlinear pulse compression in nonuniform Bragg gratings“ Opt. Lett. 22, 1837 (1997). [CrossRef] |
OCIS Codes
(060.1810) Fiber optics and optical communications : Buffers, couplers, routers, switches, and multiplexers
(190.5970) Nonlinear optics : Semiconductor nonlinear optics including MQW
(230.1150) Optical devices : All-optical devices
ToC Category:
Focus Issue: Bragg solitons and nonlinear optics of periodic structures
History
Original Manuscript: November 19, 1998
Published: November 23, 1998
Citation
Thomas Brown and Benjamin Eggleton, "Bragg solitons and optical switching in nonlinear periodic structures: an historical perspective," Opt. Express 3, 385-388 (1998)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-3-11-385
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References
- H. G. Winful et. al., "Theory of bistability in nonlinear distributed feedback structures" Appl. Phys. Lett. 35, 379 (1979). [CrossRef]
- H. G. Winful and G. I. Stegeman, "Applications of nonlinear periodic structures in guided wave optics" Proc. SPIE 517, 214 (1984).
- H. G. Winful and C. D. Cooperman, "Self-pulsing and chaos in distributed feedback bistable optical devices" Appl. Phys. Lett. 40, 298 (1982). [CrossRef]
- E. Yablonovitch, T. J. Gmitter, "Photonic band structure: the face-centered-cubic case" Phys. Rev. Lett., 63, 1950 (1989). [CrossRef] [PubMed]
- W. Chen and D. L. Mills, "Gap solitons and the nonlinear optical response of superlattices" Phys. Rev. Lett. 58, 160 (1987). [CrossRef] [PubMed]
- D. L. Mills and S. E. Trullinger, "Gap solitons in nonlinear periodic structures" Phys. Rev. B 36, 947 (1987). [CrossRef]
- J. E. Sipe and H. G. Winful, "Nonlinear Schrodinger solitons in a periodic structure" Opt. Lett. 13, 132 (1988). [CrossRef] [PubMed]
- C. M. de Sterke and J. E. Sipe, "Envelope-function approach for the electrodynamics of nonlinear periodic structures" Phys. Rev. A 38, 5149 (1988). [CrossRef] [PubMed]
- D. N. Christodoulides and R. I. Joseph, "Slow Bragg solitons in Nonlinear Periodic Structures" Phys. Rev. Lett. 62, 1746 (1989). [CrossRef] [PubMed]
- A. B. Aceves and S. Wabnitz, "Self-induced transparency solitons in nonlinear refractive periodic media" Phys. Lett. A 141, 37 (1989). [CrossRef]
- C. M. de Sterke and J. E. Sipe, "Extensions and generalizations of an envelope-function approach for the electrodynamics of nonlinear periodic structures" Phys. Rev. A, 39, 5163 (1989). [CrossRef] [PubMed]
- C. M. de Sterke and J. E. Sipe, "Coupled modes and the nonlinear Schrodinger equation" Phys. Rev. A 42, 550 (1990). [CrossRef]
- C. M. de Sterke and J. E. Sipe, "Switching dynamics of finite periodic nonlinear media: a numerical study" Phys. Rev. A 42, 2858 (1990). [CrossRef] [PubMed]
- C. M. deSterke, K. R. Jackson and B. D. Robert, "Nonlinear coupled-mode equations on a finite interval: a numerical procedure" J. Opt. Soc. Am. B 8, 403 (1991). [CrossRef]
- N. G. R. Broderick, C. M. d. Sterke and K. R. Jackson, "Coupled mode equations with free carrier effects: a numerical solution" Opt. Quantum Electron. 26, S219 (1994). [CrossRef]
- J. Feng and F. K. Kneubuhl, "Solitons in a periodic structure with Kerr nonlinearity" IEEE J. Quantum Electronics 29, 590 (1993). [CrossRef]
- J. Feng, "Alternative scheme for studying gap solitons in an infinite periodic Kerr medium" Opt. Lett. 18, 1302 (1993). [CrossRef] [PubMed]
- A. B. Aceves et al., "Storage and steering of self-trapped discrete solitons in nonlinear waveguide arrays" Opt. Lett. 19, 332 (1994). [CrossRef] [PubMed]
- M. Scalora, J. P. Dowling, C. M. Bowden, M. J. Bloemer. "Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials" Phys. Rev. Lett. 73, 1368 (1994). [CrossRef] [PubMed]
- S. Radic, N. George, G. P. Agrawal, "Optical switching in l/4-shifted nonlinear periodic structures" Opt. Lett. 19, 1789 (1994). [CrossRef] [PubMed]
- P. St. J. Russell and J.-L. Archambault, "Field microstructure and temporal and spatial instability of photonc Bloch waves in nonlinear periodic structures" J. Phys. III France 4, 2471 (1994). [CrossRef]
- S. Larochelle, V. Mizrahi and G. Stegeman, "All-optical switching of grating transmission using cross-phase modulation in optical fibres" Electron. Lett. 26, 1459 (1990). [CrossRef]
- N. D. Sankey, D. F. Prelewitz and T. G. Brown, "All-optical switching in a nonlinear periodic waveguide structure" Appl. Phys. Lett. 60, 1427 (1992). [CrossRef]
- N. D. Sankey, D. F. Prelewitz and T. G. Brown, "Optical switching dynamics of the nonlinear Bragg reflector: comparison of theory and experiment" J. Appl. Phys. 73, 1 (1993). [CrossRef]
- Amy E. Bieber et. al., "Optical Switching in a metal-semiconductor-metal waveguide structure" Appl. Phys. Lett. 66, 3401 (1995). [CrossRef]
- Amy E. Bieber and T. G. Brown, "Integral coupler-resonator for silicon-based switching and modulation" Appl. Phys. Lett. 71, 861 (1995). [CrossRef]
- C. Herbert and M. Malcuit, Opt. Lett. 17, 1037 (1992). [CrossRef] [PubMed]
- J. He and M. Cada, "Optical bistability in semiconductor periodic structures" J. Quantum Electron. 27, 1182 (1991). [CrossRef]
- B. J. Eggleton, R. E. Slusher, C. M. deSterke, P. A. Krug, and J. E. Sipe "Bragg grating solitons" Phys. Rev. Lett. 76, 627 (1996).
- B. J. Eggleton, R. E. Slusher, C. M. deSterke, P. A. Krug, and J. E. Sipe, "Modulational instability and tunable multiple soliton generation in apodized fiber gratings" Opt. Commun. 149, 267 (1998). [CrossRef]
- N. G. R. Broderick, D. Taverner, D. J. Richardson, M. Ibsen and R. I. Laming, "Experimental Observation of nonlinear pulse compression in nonuniform Bragg gratings" Opt. Lett. 22, 1837 (1997). [CrossRef]
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