Three - University of Arkansas Physics Department

More documents

Recommendations

Info

Experimental observation of chirped continuous pulse-tr ain soliton solutions to the Maxwell- Bloch equations Shihadeh M. Saadeh, John L. Shultz, and Gregory J. Salamo Department of Physics, University of Arkansas, Fayetteville, Arkansas, USA Abstract: A frequency chirped continuous wave laser beam incident upon a resonant, two-level atomic absorber is seen to evolve into a Jacobi ellipticpulsetrain solution to the Maxwell-Bloch equations. Experimental pulse-train envelopes are found in good agreement with numerical and analytical predictions. 02000 Optical Society of America OCIS codes: (190.5530) Pulse propagation and solitons, (190.5940) Self-action effects References and links I. S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183,457-485 (1969). 2. J. H. Eberly, "Optical pulse and pulse-train propagation in a resonant medium," Phys. Rev. Lett. 22, 760-762 (1969). 3. M. D. Crisp, "Distortionless propagation of light through an optical medium," Phys. Rev. Lett. 22, 820-823 (1969). 4. D. Dialetis, "Propagation of electromagnetic radiation through a resonant medium," Phys. Rev. A 2, 1065.1075 (1970). 5. L. Matulic and J. H. Eberly, "Analytic study of pulse chirping in self-induced transparency," Phys. Rev. A 6, 822-836 (1972). 6. M. A. Newbold and G. J. Salamo, "Effects of relaxation on coherent continuous-pulse-train propagation," Phys. Rev. Lett. 42, 887-890 (1979). 7. J. L. Shultz and G. J. Salamo, "Experimental observation of the continuous pulse-train soliton solution to the Maxwell-Bloch equations," Phys. Rev. Lett. 78, 855-858 (1997). 8. N. Akhmediev and J. M. Soto-Crespo, "Dynamics of solitonlike pulse propagation in birefringent optical fibers," Phys. Rev. E 49,5742-5754 (1994). Coherent propagation of trains of optical pulses through atwo-level absorber has beeninvestigated, from a theoretical viewpoint, by many researchers. These investigations have been based on the self-induced transparency (SIT) equations [I], both with [2-51, and without [6], the assumption of zero relaxation. Recently, theoretical predictions have been supported by experimental observations of the Jacobi elliptic dn solution [7]. In particular, experiments demonstrated the evolution of an arbitrarily shaped input optical pulse train into the analytic shape-preserving Jacobi elliptic pulse train solution to the Maxwell-Bloch equations [8]. A special feature of the observed solution was that the chirp in the optical frequency of the pulse train was zero. In this paper we report the experimental and numerical demonstration of the evolution of a continuous wave laser beam into an analytic shape-preserving pulse train solution. In this case, the analytic solution to the Maxwell-Bloch equations is a Jacobi elliptic function with a nonzero frequency chirp. The interaction of a plane-wave optical field with an inhomogeneously broadened two-level absorber can be described by two sets of equations. The Bloch equations describe the effect of the optical field on the atom while the reduced Maxwell equations describe the effect of the atom on the optical field. For significant absorption, self-consistent solutions to both equations describe the propagation of the optical field through the two-level absorber. Together, the two sets of equations are known as the reduced Maxwell-Bloch equations. For circularly polarized light traveling in the z-direction, the electric field at the position of the #29439 - $15.00 US (C) 200 1 OSA Received November 22,2000; Revised January 10,2001 15 January 2001 1 Vol. 8, No. 2 1 OPTICS EXPRESS 153
October 15, 2001 / Vol. 26, No. 20 / OPTICS LETTERS 1547 . Theory of self-focusing in photorefractive InP Raam Uzdin and Mordechai Segev Technion-Israel Institute of Technology, Haifa 32000, Israel Gregory J. Salamo University of Arkansas, Fayetteville. Arkansas 72701 Received August 1. 2001 . > We present a theory of self-focusing and solitons in photorefractive InP, including the previously unexplained intensity resonance and the resonant enhancement of the spacecharge field. O 2001 Optical Society of America OCIS codes: 190.5530, 190.5330. Self-trapping of optical beams in photorefractive (PR) InP was observed in 1996.1a2 Self-trapping of beams in such PR semicondudors offers attractive features: operation at communications wavelengths, fast response times (microseconds), and low power level micro watt^).'^^ These properties suggest exciting applications, such as reconfigurable switches, interconnects, and self-induced waveguides. Unfortunately, PR semicondudors tend to have tiny electrogptic coefficients (1.5 pm/V), and thus a conventional screening soliton in such materials would require applied fields of 50 kV/cm and higher,3 too large for most applications. Fortunately, Fedoped InP crystals offer an exception to this rule. When the photoexcitation rate of holes is comparable with the thermal excitation rate of electrons, the spacecharge field is resonantly enhanced by more than tenfold. That is, the internal photoinduced field exceeds 50 kV/cm when the applied field is 5 kV/cm. This enhancement, and other peculiar phenomena, appears only in the vicinity of a particular intensity of the beam.',' These features cannot be explained by the theory of screening soliton^,^-^ as that theory does not show a resonance of any sort. Furthermore, despite the experimental ob~ervations,'.~ thus far there is no proof that self-trapped beams exhibiting stationary propagation can form in this nonlinearity. Experimentally, when a beam is launched into an W:Fe crystal under various applied fields Eo and intensity conditions, the main features observed are the following1: nance at which the spacecharge field is enhanced. Slightly below resonance, self-focusing occurs at Eo < 0. The first and second features inlply that self-focusing occurs at both field polarities (at different intensity regimes), whereas in other PR media the sign of the nonlinearity is determined by the polarity of Eo and does not depend on I,,,. The second and third features suggest that this nonlinearity not only saturates but also decreases with intensity as I,,, exceeds I,,. Here we present a theory describing resonant selffocusing effects in PR semiconductors. We explain the main features of the theory, extract new predictions, and show that, in at least one parameter regime, stationary self-trapped beams (spatial solitons) do exist in such media. The theory is based on a moc;e16 with two levels of dopants, one deep Fe-trap level and conduction of both electrons and holes. " :. ~rlode; ,> successful in explaining two-wave mixi~ig bu~ :i Lartnot explain self-focusing, because it relies on a periodic grating at low visibility. Even a superposition of gratings cannot be used to treat localized beams. Yet the assumptions about the rate equations hold fq a localized beam and serve as a starting polnt. We start with the standard set of equations6 in temporal steady state: the continuity equations for electrons and holes, the rate equation for the Fe traps, the trane-, port equations, and Gauss's law: 1. For Eo < 0 and I,., - I,,. (the resonance intensity), self-focusing occurs, and the peak of the intensity structure, I,,,, is shifted from the center (of the normally diffracted beam at Eo = 0). 2. For EO > 0 and I,., < I,., the beam selffocuses, but at the resonance itself (I,, = I,,,) the beam breaks up. 3. Irrespective of the polarity of Eo, for high enough intensity, I,,, >> I,,,, the beam goes through the crystal almost unaffected, that is, diffracting normally as if Eo = 0. The first feature highlights the unique property of this nonlinearity: the pronounced intensity reso- 0146.9592/01/201547-03$15.0010 63 2001 Optical Society of America ., :
Page 1 and 2: CLEO '02. Technical Digest. pp. 225
Page 3 and 4: APPLlED PllYSlCS LETTERS VOLUME XI,
Page 5 and 6: JOURNAL OF APPLIED PHYSICS VOLUME 9
Page 7: ASEE Annual Conference Proceedings,
Page 11 and 12: JOURPU'AL OF APPLIED PHYSICS VOLUME
Page 13 and 14: Reflection-second-harmonic generati
Page 15 and 16: APPLIED PHYS1C:S LETTERS VOLUME 79.
Page 17 and 18: APPLIED PHYSICS LETTERS VOLUME 79,
Page 19 and 20: JOURNAL OF APPLIED PHYSICS VOLUME 8
Page 23 and 24: IMAPS - EUROPE PRAGUE 2000 - Prague
Page 25 and 26: 50th Electronic Components and Tech
Page 27 and 28: ' CLEO '99. Conference on Lasers an
Page 29 and 30: The Portable Holographic Interferom
Page 31 and 32: Journal of Electronic Materials, Vo
Page 33 and 34: --- CLE0'98. Conference on Lasers a
Page 35 and 36: SHOP NOTES These are "how to do it"
Page 37 and 38: 3TA DEL NUOVO CIMENTO VOL. 21, N. 6
Page 39 and 40: VOLUME 78, NUMBER 5 PHYSICAL REVIEW
Page 41 and 42: Three-dimensional image reconstruct
Page 43 and 44: . ( :, ... ... j 2 $8 y Journal of
Page 45 and 46: Materials Research Society Symposiu
Page 47 and 48: 476 / CLE0'99 / THURSDAY AFTERNOON
Page 49 and 50: January 15,1999 1 Vol. 24, No. 2 /
Page 51 and 52: SHOP NOTES These are "how to do it"
Page 55 and 56: CLE0'97. Conference on Lasers and E
Page 57 and 58: Proceedings of the SPIE , v 3134, p
Page 59 and 60:
Fabrication techniques and electric
Page 61 and 62:
220 / QELS'96 / THURSDAY ACTERN( IO
Page 63 and 64:
Magnetic field and temperature depe
Page 65 and 66:
Optically induced birefringence in
Page 67 and 68:
324 OPTICS LETTERS / Vol. 21, No. 5
Page 69:
PHYSICAL REVIEW E VOLUME 53, NUMBER
show all

Three - University of Arkansas Physics Department

Create successful ePaper yourself

Delete template?

Save as template?