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Bragg Solitons
Research Scholar
Center for Nanoscience and Engineering
Indian Institute of Science, Bangalore
Course presentation: Nonlinear Photonics
Ajay Singh
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
Fiber Brag Grating
Optical solitons: From fibers to photonic crystals, “Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003)
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
Fiber Brag Grating
How to write:
Irradiation from UV
Irradiate germanium doped
fiber with argon laser
Holographic technique
kg= 2π/Λ
Λ =~o.5 µm for λ=1.55 µm region
Optical solitons: From fibers to photonic crystals, “Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003)
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
Fiber Brag Grating Coupled-Mode Equations
How to write:
Irradiation from UV
Irradiate germanium doped
fiber with argon laser
Holographic technique
kg= 2π/Λ
Λ =~o.5 µm for λ=1.55 µm region
Optical solitons: From fibers to photonic crystals, “Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003)
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
Fiber Brag Grating Coupled-Mode Equations
How to write:
Irradiation from UV
Irradiate germanium doped
fiber with argon laser
Holographic technique
kg= 2π/Λ
Λ =~o.5 µm for λ=1.55 µm region
Optical solitons: From fibers to photonic crystals, “Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003)
Coupled-Mode Equations and Nonlinear Propagation Equations
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
Optical solitons: From fibers to photonic crystals, “Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003)
Coupled-Mode Equations and Nonlinear Propagation Equations
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
Optical solitons: From fibers to photonic crystals, “Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003)
Coupled-Mode Equations and Nonlinear Propagation Equations
Anomalous
GVD
Normal
GVD
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
Optical solitons: From fibers to photonic crystals, “Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003) Link
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
Introduction
Nonlinearity (SPM)
Dispersion (Material)
Soliton
Nonlinearity (SPM)
Dispersion (Grating)
Soliton Like Pulses
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Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
Effective NLS Equation
Optical solitons: From fibers to photonic crystals, “Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003)
Now introduce the speed reduction factor f:
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
Effective NLS Equation
Fig.. Intensity (solid line) and normalized spatial width (dot-dashed line) of fundamental soliton pulses, [6].
Optical solitons: From fibers to photonic crystals, “Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003)
Now introduce the speed reduction factor f:
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
Effective NLS Equation
Fig.. Intensity (solid line) and normalized spatial width (dot-dashed line) of fundamental soliton pulses, [6].
Fig. Evoluation of (a) |Af|2 and (b) |Ab|2 [6].
Optical solitons: From fibers to photonic crystals, “Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003)
Now introduce the speed reduction factor f:
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
Let us consider different cases of Bragg solitons
1-<v<1
Ψ=π/2: Center of the stop band: Combination of two counter-propogating waves VG = v.νg
If equal amplitude: νg= 0 Stationary gap soliton
|v|=1
Bragg soliton ceases to exist since the grating becomes ineffactive
General solution (coupled mode eqn) of shape preserving solitons: Solition exist in normal
Dispersion region also: Dark solitions
Video: Propagation of a single bragg soliton in a uniform grating [17]
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
B. J. Eggleton, R. E. Slusher (Bell Laboratories, Lucent Technologies, New Jersey 07974) and C.
Martijn de Sterke (University of Sydney): Vol. 16, No. 4/ April 1999/J. Opt. Soc. Am. B [7]
Fig. Schematic of our experimental setup.
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
B. J. Eggleton, R. E. Slusher (Bell Laboratories, Lucent Technologies, New Jersey 07974) and C.
Martijn de Sterke (University of Sydney): Vol. 16, No. 4/ April 1999/J. Opt. Soc. Am. B [7]
Fig. Schematic of our experimental setup.
Link
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
Fig. Schematic of our experimental setup.
B. J. Eggleton, R. E. Slusher (Bell Laboratories, Lucent Technologies, New Jersey 07974) and C.
Martijn de Sterke (University of Sydney): Vol. 16, No. 4/ April 1999/J. Opt. Soc. Am. B [7]
Link
818 m-1
3612 m-1
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
B. J. Eggleton, R. E. Slusher (Bell Laboratories, Lucent Technologies, New Jersey 07974) and C.
Martijn de Sterke (University of Sydney): Vol. 16, No. 4/ April 1999/J. Opt. Soc. Am. B [7]
Link
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
B. J. Eggleton, R. E. Slusher (Bell Laboratories, Lucent Technologies, New Jersey 07974) and C.
Martijn de Sterke (University of Sydney): Vol. 16, No. 4/ April 1999/J. Opt. Soc. Am. B [7]
Fig. 16. transmitted pulse for incoming pulse energies of 0.66 µJ Left experimental results; right follow numerical calculation.(solid curves) The values of the detuning are 876 m-
1 [traces (a) and (b)], 994 m-1 [traces (c) and (d)], 1318 m-1 [traces (e) and (f )], and 1847 m-1 [traces (g) and (h)].
Inte
nsi
ty (
a.u
.)
Link
Link
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
B. J. Eggleton, R. E. Slusher (Bell Laboratories, Lucent Technologies, New Jersey 07974) and C.
Martijn de Sterke (University of Sydney): Vol. 16, No. 4/ April 1999/J. Opt. Soc. Am. B [7]
Link
Mathematical Analysis…..
• All-optical switching [5,8,9],
• Pulse compression [10,11,25],
• Pulse Limiting [12],
• Logic operations [13],
• Promising for the fiber-sensing technology [14],
• Optical communication systems [15,16],
• All optical buffers and storing devices can be based on such fibers [18],
• Pulse source for the soliton transmission system [19,20 ],
• All-optical modulation and demultiplexing systems [23],
• Tunable optical pulse source [24, 26],
• A possible way to trap a zero-velocity soliton is to use an attractive
finite-size or Local defect in BG [22] ,
• THz pulse generation !!!
• Suppercontinuum generation !!!
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
Applications of Bragg Solitons…..
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Applications
References:
[1] K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, Appl. Phys. Lett., Vol. 32, pp. 647, 1978. [2] E. Yablonovitch and T. J. Gmitter, Phys. Rev. Lett., Vol. 63, pp. 1950, 1989. [3] A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg and Y. Silberberg, IEEE J. Quantum Electron, Vol. 39, pp. 31, 2003. [4] W. Chen and D. L. Mills, Phys. Rev. Lett., Vol. 58, pp. 160, 1987. [5] S. Larochelle, V. Mizrahi, and G. Stegeman, Electron. Lett., Vol. 26, pp. 1459, 1990. [6] A. B. Aceves and S. Wabnitz, Phys. Lett. A, Vol. 141, pp. 37, 1989. [7] B. J. Eggleton, C. M. de, Sterke, and R. E. Slusher, J. Opt. Soc. Am. B, Vol. 16, pp. 587, 1999. [8] N. G. R. Broderick, D. Taverner, and D. J. Richardson, Opt. Express, Vol. 3, pp. 447, 1998. [9] Amer Kotb and Kyriakos, Optical Engineering (SPIE), Optical Engineering , Vol. 55(8), pp. 087109 (1-7), 2016. [10] N. G. R. Broderick, D. Taverner, D. J. Richardson, M. Ibsen and R. I. Laming, Opt. Lett. Vol. 22, pp. 1837, 1997. [11] N. G. R. Broderick, D. Taverner, D. J. Richardson, M. Ibsen and R. I. Laming, Phys. Rev. Lett.,Vol.79, pp. 4566, 1997. [12] D. E. Pelinovsky, L. Brzozowski, and E. H. Sargent. Phys. Rev. E, Vol. 62, pp. 4536, 2000. [13]. L. Brzozowski and E. H. Sargent, IEEE J. Quantum Electron, Vol. 36, pp. 550, 2000. [14] W. C. K. Mak, B. A. Malomed, and P. L. Chu, J. Opt. Soc. Am. B, Vol. 20, pp. 725, 2003. [15] R. H. Goodman, R. E. Slusher, and M. I. Weinstein, J. Opt. Soc. Am. B, Vol. 19, pp. 1635, 2002. [16] G. P. Agrawal, Nonlinear Fiber Optics. (New York: Academic), 1989. [17]. https://www.youtube.com/watch?v=GxmjYNuaoSE [18]. Xiaolu Li, Yuesong Jiang, and Lijun Xu, Communication and Network, Vol. 2, pp. 44, 2010 [19] N. Dogru and M. S. Ozyazici, LFNM. September 2004, pp. 115. [20]. N. Dogru, 2005, IEEE NUSOD’05, September 2005, pp.89. [21] C. M. de Sterke, B. J. Eggleton, and P. A. Krug, J. Lightwave Technol, Vol. 15, pp. 1494, 1997. [22] K. T. Mc-Donald, Am. J. Phys., Vol. 68, pp. 293, 2000. [23]. J. H. Lee, L. Katsuo, K. S. Berg, A. T. Clausen, D. J. Richardson, and P. Jeppesen, J. Lightwave Technol, Vol. 21, pp. 2518, 2003. [24]. J. H. Lee, Y. M. Chang, Y. G. Han, S. H. Kim, H. Chung,and S. B. Lee, IEEE Photon. Technol. Lett., Vol. 17, pp. 34, 2005. [25]. G. Lenz and B. J. Eggleton, J. Opt. Soc. Am. B, Vol. 15, pp. 2980, 1998. [26] Norihiko Nishizawa, Yoshimichi Andou, Emiko Omoda, Hiromichi Kataura, and Youichi Sakakibara, Opt. Exp. 23403, Vol. 24, 2016.
!
1553.2 nm Q-switching of the laser at a repetition rate of 500 Hz. train of pulses, each with a duration of approximately 80 ps. To avoid thermal effects, an electro-optic pulse selector was used to select one pulse in each train. fast photodiode with a response time of 9 ps The net time resolution, including trigger jitter and oscilloscope resolution, was approximately 20 ps. 75-mm-long unchirped, apodized fiber grating
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Historical prospective.…
Schematic illustration of a fiber grating. Dark and light shaded regions withi n the fiber core show periodic variations of the refractive index.
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
First photo-induced optical fiber Bragg gratings
by Hill and coworkers in 1978 [1]
Photonic band structure” concept: Yablonovitch
in the late 1980’s [2]
Light interaction with nonlinear periodic media
yields a diversity of fascinating phenomenan:
discrete (or lattice) solitons and gap (or Bragg)
solitons [11-12]
Larochelle, Hihino, Mizrahi and Stegeman (in
1990): experimental investigation of the optical
response of nonlinear periodic structures.
investigation of nonlinear pulse propagation in
uniform fiber gratings: the Bragg solitons easily
generated in the laboratory travel at 60–80% of
veocity of light in fiber absence of grating [5]
Fiber Brag Grating
How to write:
Irradiation from UV
Irradiate germanium
doped fiber with argon
laser
Holographic technique
kg= 2π/Λ
Λ =~o.5 µm for λ=1.55 µm
region
Optical solitons: From fibers to photonic crystals, “Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003)
Optical solitons: From fibers to photonic crystals, “Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003)
Coupled-Mode Equations
And here dispersion comes into play…..
Figure : Dispersion curves showing variation of 6 with q and the existence of the photonic bandgap for a fiber grating.
Anomalous
GVD
Normal
GVD
o β2 changes its sign on the
two sides of the stop band
centered at the Bragg
wavelength, whose
location is easily
controlled and can be in
any region of the optical
spectrum.
o β2 is anomalous on the
shorter-wavelength side
of the stop band, unlike
for wavelengths longer
than the zero dispersion
wave-length in the fibers
o The magnitude of β2 >
100ps2/cm
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
o the negative sign appearing in front of the ∂Ab/∂Z term: because of backward propagation of Ab and
o the presence of linear coupling between the counter propagating waves governed by the parameter k
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Fig. 13. Comparison between the estimated pulse energy in the fiber and the deduced value of the peak intensity. The result, which is consistent with the expected proportionality between the two quantities, leads to a proportionality constant of 47 GW/cm2 µJ-1.
Fig. 8. Intensity versus time after propagation through the grating at a pulse energy of approximately 0.66 µJ, for a detuning close to the edge of the gap (solid curve) and far from the edge of the gap (dashed curve). The pulse tuned close to the edge of the gap is delayed by approximately 310 ps, corresponding to an average velocity of approximately 0.50V.
Fig. 7. Intensity versus time after propagation through the grating at a peak input intensity of 11 GW/cm2, for seven different values of the detuning (solid curve, 729 m-1; dotted curve, 788 m-1; short-dashed curve, 847 m-1; long-dashed curve, 935 m-1; short-dashed–dotted curve, 1053 m-1; long-dashed–dotted curve, 1406 m-1; long–short-dashed curve, 3612 m-1)
Fig. 6. Delay of the transmitted pulses versus detuning at low intensity. Experimental results are indicated by dots, numerical results by the solid curve.
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
B. J. Eggleton, R. E. Slusher (Bell Laboratories, Lucent Technologies, New Jersey 07974) and C.
Martijn de Sterke (University of Sydney): Vol. 16, No. 4/ April 1999/J. Opt. Soc. Am. B
Back
Fig. 16. transmitted pulse for incoming pulse energies of 0.66 µJ at 4 different detunings. Left figures are experimental results; right follow from solving Eq. (1) numerically and convolving the result with the estimated response of the detection system (solid curves) and from the NLSE followed by a convolution (dashed curves). The values of the detuning are 876 m-1 [traces (a) and (b)], 994 m-1 [traces (c) and (d)], 1318 m-1 [traces (e) and (f )], and 1847 m-1 [traces (g) and (h)].
Fig. 9. FWHM of the transmitted pulses versus detuning at an estimated pulse energy of 0.06 µJ. Experimental results are indicated by dots, numerical results obtained by solving Eq. (1) are indicated by the solid curve, and numerical obtained by solving q. (10) are indicated by the dashed curve; in both sets of numerical results the peak intensity of the incoming pulse is taken to be 3 GW/cm2.
Fig. 15. Solid curve: Estimated peak power of the fundamental soliton versus detuning with the parameters from the text. Dots: Similar results, but deduced from the experiments, with the criterion that the width does not change upon propagation.
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
B. J. Eggleton, R. E. Slusher (Bell Laboratories, Lucent Technologies, New Jersey 07974) and C.
Martijn de Sterke (University of Sydney): Vol. 16, No. 4/ April 1999/J. Opt. Soc. Am. B
Back
Fig. 5. Full-width at half-maximum (FWHM) of the transmitted pulses versus detuning at low intensity. Experimental results are indicated by dots, numerical results by the solid curve.
Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications
Fig. Schematic of our experimental setup.
B. J. Eggleton, R. E. Slusher (Bell Laboratories, Lucent Technologies, New Jersey 07974) and C.
Martijn de Sterke (University of Sydney): Vol. 16, No. 4/ April 1999/J. Opt. Soc. Am. B [7]
Fig. Intensity versus time after propagation through the grating at low intensity, for seven different values of the detuning (solid curve, 818 m-1; dotted curve, 847 m-1; short-dashed curve, 906 m-1; long-dashed curve, 965 m-1; short-dashed– dotted curve, 1023 m-1; long-dashed–dotted curve, 1171 m-1; long–short-dashed curve, 3612 m-
1).
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