Bragg solitons

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)

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

Fiber Brag Grating Coupled-Mode Equations
How to write:
Irradiation from UV
Irradiate germanium doped
fiber with argon laser
kg= 2π/Λ
Λ =~o.5 µm for λ=1.55 µm region

Coupled-Mode Equations and Nonlinear Propagation Equations

Coupled-Mode Equations and Nonlinear Propagation Equations
Anomalous
GVD
Normal
GVD
Link

Introduction
Nonlinearity
(SPM)
Dispersion
(Material)
Soliton
Nonlinearity
(SPM)
Dispersion
(Grating)
Soliton Like
Pulses
https://en.wikipedia.org/wiki/Soliton_(optics)
Instantaneous
Frequencychirp

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:

Fig.. Intensity (solid
line) and normalized
spatial width (dot-
dashed line) of
fundamental soliton
pulses, [6].
f:

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].
f:

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]

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

Link
818 m-1
3612 m-1

Link

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)].
Intensity(a.u.)
Link
Link
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 !!!
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. Yablonovitchand 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. QuantumElectron, 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. QuantumElectron, 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, Communicationand 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, IEEEPhoton. 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
Back

Schematic illustration of a fiber grating. Dark and light shaded regions
withi n the fiber core show periodic variations of the refractive index.
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
kg= 2π/Λ
Λ =~o.5 µm for λ=1.55 µm
region

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
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
Back

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
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
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.
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.
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.
Fig. Intensity versus
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
dashed curve, 965 m-1;
short-dashed– dotted
dashed–dotted curve,
1171 m-1; long–short-
dashed curve, 3612 m-
1).
Back

Bragg solitons

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