Vladimir Kalashnikov, Evgeni Sorokin and Irina T. Sorokinainfo.tuwien.ac.at/kalashnikov/2D.pdf · Vladimir Kalashnikov, Evgeni Sorokin and Irina T. Sorokina. Institüt für Photonik,
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Spatial-time dynamics of supercontinua in multimode fibers Vladimir Kalashnikov, Evgeni Sorokin and Irina T. Sorokina Institüt für Photonik, TU Wien, Gusshausstr. 27/387, A-1040 Vienna, Austria
Spatial-time dynamics of supercontinua in multimode
fibers
Vladimir Kalashnikov,Evgeni Sorokin and Irina T. Sorokina
Institüt für Photonik, TU Wien, Gusshausstr. 27/387, A-1040 Vienna, Austria
Presenter
Presentation Notes
Dear colleagues, I would like to present you the talk “Spatial-time dynamics of supercontinua in multimode fibers”. This work has been carried out in Photonics Institute, Viennese Technical University. My co-authors are Evgeni Sorokin and Irina Sorokina.
an operation in the vicinity of the zero-dispersion wavelength*
of a highly-nonlinear fiber
Motivation and problem definition• Sources of coherent spectral continuum within 1-3 µm range are interesting for a
number of applications:– Measurement and testing– Optical coherence tomography (OCT)– Metrology (frequency combs)
reduced nonlinearity (as μ1/3) and gain of IR pump laser
large size of the fiber core in IR
nonlinear co-propagation of several transverse modes
AIM OF THIS STUDY: Analyze the spatial-time dynamics and the structure of the IR- supercontinuum
*J. Herrmann, et al., Phys. Rev Lett., 88, 173901 (2002).
Presenter
Presentation Notes
Main motivation of the work is an intense interest in the spectral continuum within near- and mid-IR spectral range. Such a continuum can be used in measurements, metrology, optical coherence tomography etc. Main problem in generation of such a continuum is the decrease of effective nonlinearity with wavelength. This results from both the mode area growth and the wave number decrease. The situation can be rectified by operation in the vicinity of the zero-dispersion wavelength of a highly-nonlinear fiber. However, this condition requires a large fiber core size and, as a result, leads to a nonlinear co-propagation of the several transverse fiber modes. Hence, spatial-time dynamics of the supercontinuum formation requires careful consideration.
Soft glass PCF structures for IR- supercontinua
SF6Core dia. 4.5 µmAeff 9.4 µm2
1,0 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2,0-250
-200
-150
-100
-50
0
50
100
150
SF57, r=2.3 m
SF57, r=2.25 m
SF6, r=2.6 m
GV
D, p
s/(k
m n
m)
, m
SF6, r=2.25 m
GDD of high-n2 fibers
SF6 and SF57 PCFs provide near-zero GDD at 1.5 m wavelength. SPM coefficients are: 0.088 cm/GW (SF6) and 0.17 cm/GW (SF57). Another glasses (e.g. SF10) require larger radii ( lower effective nonlinearity) and produce higher third-order dispersion ( spectrum fragmentation).
Presenter
Presentation Notes
The analyzed nonlinear structure is soft-glass PCF. SF6 and SF57 glass fibers provide near-zero GDD at 1.5 micrometers wavelength that allows the pump by a femtosecond Cr:YAG all-solid-state oscillator. Simultaneously, these glasses provide ten- and forty-fold growth of the effective nonlinearity, respectively. Another fibers of this kind need larger core sizes for maintenance of the near-zero GDD at 1.5 micrometers and introduce a larger third-order dispersion.
Model of spatial-time dynamics
2
2 2
2 1
( ) (, 12 (
, ) 12
,!!
,)
mm
mm
n nn
n
N
na t x y z i a ii
n tka a
aFm t
n xkz
y
One has to take into account: Group-delay dispersion; Diffraction; Self-phase modulation; Raman self-frequency shift; Profile of the refractive index
Our numerical analysis has been based on the full-dimensional generalized nonlinear Schroedinger equation taking into account GDD of a real fiber, diffraction in the fiber core, self-phase modulation, Raman self-scattering and real profile of the fiber refractive index. We used two solution methods. First one is an usual split-step method, which treats nonlinear factors in time domain while dispersion, diffraction and refraction are considered in frequency domain. To increase the simulation efficiency, a slab of the frequency-dependent Crank-Nicolson matrixes was used.
Model of spatial-time dynamics (continue)
1
0 0 0 0
1 1 11 12 ( ) 2 2
i ik k t k t
Approximation:
Approximated time-domain representation of the master equation (cylindrical symmetry):
0
2
22 30
2
20 0
2
0
2 0
3
20 0
0
3
0
340 0
, ,2
12
(
3
) 1
2c aa r
t n
ic i n i an r in a a
c arn r t r r
i c aa
c
a r t zz
ar
r
ac tn r
rr
t n r
r
r
r
r r
Waveguide-induced group-delay; waveguide-modified second-order GDD; waveguide-modified third-order GDD; diffraction; profile of the refractive index; SPM
Solution method: FEM in time-domaingrid: 213 x 150
Presenter
Presentation Notes
An alternative method was based on the finite-element method in time-domain. As the diffraction is frequency-dependent, that is the key factor in our case, we approximate this dependence by the expansion in time-domain. Hence, we obtain the approximated version of the master equation. In this case, one can see explicit contribution of waveguide-induced group-delay, waveguide-modified GDD, diffraction, fiber refraction and self-phase modulation.
Static spatial modes of PCF
E1,2y
E1,1y E1,1
x E1,2x
E2,1y E2,1
x
Presenter
Presentation Notes
These pictures show the profiles of static modes of real PCF. Only three types of the lower modes with different polarizations are presented.
Spectra corresponding to low-order modes
1,0 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2,0
-200
-150
-100
-50
0
50
100
Ey1,2
Ex1,2
Ex1,1
GD
D, p
s2 /km
, m
bulk SF6
Ey1,1
Ey1,1-mode of PCF with 4.5 m core
Pump, mW10 20 30 40 50
, n
m
750
1000
1250
1500
1750
2000
2250
2500
Ey1,2 -mode of PCF with 4.5 m core
Pump, mW10 20 30 40 50
, n
m
750
1000
1250
1500
1750
2000
Presenter
Presentation Notes
Different modes have different GDDs, zero-wavelengths and areas. As a result, the continuum structure and width depend strongly on the spatial structure of propagating field. As a rule, redistribution between the modes decreases the spectral width but can provide a more smooth spectrum.
Inter-mode beatings for the rectangular core
Presenter
Presentation Notes
An additional factor affecting the continuum is the inter-mode coupling. Such a coupling results in the inter-mode beatings, which are visible here (spatial profile of the power is shown)
Inter-mode beatings for the rectangular core (wider input beam)
Presenter
Presentation Notes
Nature of such beating depends on the beam size. Wider input beam results in more complicate spatial structure of the propagating beam.
Inter-mode beatings for the circular core
Presenter
Presentation Notes
The fiber core possessing a higher symmetry provides a more simple spatial structure. But inter-mode beatings exist in this case, as well.
Experimental observation of mode-beatings
1300 1400 1500 1600 17000
10000
20000
30000
40000
50000
60000
12 mm
spec
tral p
ower
, a.u
.
, nm
input
1200 1300 1400 1500 1600 17000
10000
20000
30000
input
40 mm
spec
tral p
ower
, a.u
.
, nm
1200 1300 1400 1500 1600 17000
10000
20000
30000
40000
50000
60000
55 mm
spec
tral p
ower
, a.u
.
, nm
Presenter
Presentation Notes
Modification of the spectrum due to inter-mode beatings is clearly visible in experiment. On the small propagation distance, interference between the different modes causes the strong spectrum fragmentation. Such a fragmentation decreases with the propagation distance in parallel with the spectrum broadening. This results from the mode-decoupling due to different group-delays of the different modes. However, the mode-coupling does not disappear completely even on the comparatively large propagation distances, when the continuum is already formed.
Spectral-spatial profiles vs. input beam size. I
200 pJ pulses with 60 fs width. 2.6 m core radius of SF6 fiber
Presenter
Presentation Notes
Spatial-spectral structure of the field from 20 cm section of SF6 PCF with cylindrical core of 2.6 micrometers radius is shown in these pictures. The fiber was radiated by the pulses with 60 fs duration and approximately 200 pJ energy. The beam size varies. When the beam size is too small, the spatial structure is simple. Only few lower modes exist, but the spectral components are distributed between modes non-uniformly. The spectrum is comparatively narrow due to redistribution of the radiation between different modes on the initial stage of propagation. The beam size growth makes the spectrum more uniform and smooth.
Spectral-spatial profiles vs. input beam size. II
Presenter
Presentation Notes
Decoupling of the modes during propagation increases the spectrum width as the field is concentrated within only lowest mode. In fact, here we excited only the fundamental mode of a fiber.
Spectral-spatial profiles vs. input beam size. III
Presenter
Presentation Notes
During further beam size growth, spectral fragmentation increases, as well.
Spectral-spatial profiles vs. input beam size. IV
Presenter
Presentation Notes
And, at last, we have very complicate spatial-spectral structure, which can not be described by superposition of static modes. The spectral width can be maximum due to strong focusing of the field caused by the inter-mode beatings on the initial propagation stage. Further beam size growth reduces the spectrum due to radiation out of a fiber.
Conclusions
Division of the input beam into multiple modes reduces the beam power into the lowest mode, where GDD is close to zero. As a result, the spectrum can become narrow
However, inter-mode beatings can increase the effective nonlinearity and, thereby reduce the threshold of supercontinuum generation due to strong focusing of the field
As a result of the nonlinear propagation, the spatial structure of a supercontinuum is not always a superposition of the static fiber modes
Manipulations with the input beam size allow controlling the supercontinuum structure and its width
Acknowledgement: this work was supported by the Austrian national scientific Fund (FWF, project P17973)
Presenter
Presentation Notes
In conclusion. Division of the input beam into multiple modes reduces the beam power into lowest mode, where GDD is close to zero. As a result, the spectrum can become narrow. However, inter-mode beatings can increase the effective nonlinearity and, thereby reduce the threshold of supercontinuum generation due to strong focusing of the field during the mode coupling. As a result of the nonlinear propagation, the spatial structure of a supercontinuum is not always a superposition of the static fiber modes. Manipulations with the input beam size allow controlling the supercontinuum structure and its width.
