Microsoft PowerPoint Tutorial

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PART I I I
CASCADED NONLINEAR OPTICAL PROCESSES
presented by S. Saltiel Univ. Sofia, Bulgaria
September, 2002
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CASCADED NONLINEAR OPTICAL PROCESSES
Part II
Cascading with two simultaneously phase matched
(DPM) interactions
? Methods for achieving DPM. ? c(2) c(2)
cascading with 2D nonlinear photonic crystals
Part III
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Methods for double phase matching
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QPM - the revolution in optical frequency
conversion. D. Hanna.
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Methods for double phase matching - uniform QPM
Method of two commensurable periods
Works only for discrete wavelengths
Ref. e. g. Pfister et al OL97
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Methods for DPM - noncollinear QPM structures
Non-collinear interaction with uniform QPM grating

• Advantages
• DPM in broad spectral range
• Small m , n can be used

Ref. Saltiel,Kivshar, BulgJPhys2000
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Methods for DPM - non-uniform QPM structures
Non-uniform QPM grating in the form of
consequence of pieces uniform gratings with
reversed phase Chou et al OL(1999)
Phase-reversed QPM strutures
Now we have two dimentional set of reciprocal
vectors Glm and flexibility to PM several
processes is much bigger
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Methods for DPM - non-uniform QPM structures
Another type non-uniform QPM grating - QPM
structure with periodical change of the period L
O.Bang et al OL99
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Methods for DPM - QPOS
Another type non-uniform QPM gratings, suitable
for DPM, are quasi periodic optical superlattices
QPOS, incl. Fibonacci and generalised Fibonacci
structures
23 efficiency in THG is reportedZhu, Science
(1997) 27 efficiency in THG is
reportedZhang, OL (2001)
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Methods for DPM - 1D photonoc band gap
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Methods for DPM - 1D photonoc band gap
Example THG
w w 2w w 2w 3w
Condition for DPM are
where the Bloch phases are
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2D NONLINEAR PHOTONIC CRYSTALS
This drawing is valid for nonlinear photonic
crystals too. They are proposed by
Berger, PRL98
QPM
It was experimently observed simultaneaous
generation of several harmonics and wavelength
interchange of two signals.
Broderick et al, PRL(2000), Broderick et al,
JOSAB(2002), Chowdhury et al, OL(2000,01)
We will consider these types of NPC for which

Linear properties remain unchanged
and there is modulation of nonlinear properties.
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2D NONLINEAR PHOTONIC CRYSTALS
How it works
We have many gratings characterized by grating
vectors Kpq .with p,q ?1, ?2, ?3... All of them
can be expressed by two fundamental vectors Ka
and Kc that form the reciprocal lattice (a).
Any reciprocal lattice vector Kpq can be used to
PM the nonlinear process. Disadvantage
noncollinear interaction, but angles - not big
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2D NONLINEAR PHOTONIC CRYSTALS
Note three parameters d, d, e characterize
the 2D NPC
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Methods for DPM - 2D NPC
Principe for DPM is the same as for the most of
other methods. We have pool of vectors Kpq.
One of the process we PM with Kij and the
other - with Kmn .From the PM conditions we find
the parameters of the 2D NPC structure d and d
and e .
Ref. Saltiel,Kivshar OL(2000)
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Nonlinear cascaded processes in 2D NPC
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Nonlinear optical wavelength interchange in 2D
NPC
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Nonlinear optical wavelength interchange in 2D
NPC
Simple theoretical analysis (not in the ref.)
gives not only wavelength routing with
interchange of the information, but also
AMPLIFICATION !!!
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Multi-channel harmonics generation in 2D NPC
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Multi-channel harmonic generation in 2D NPC - 4HG
Fourth harmonic beam II Fundamental beam!
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Multi-channel harmonic generation in 2D NPC - 4HG
Then 4HG is more efficient than conventional
single crystal schemes by a factor that reaches
four at low intensities.
SH efficiency is twice higher
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Multi-channel harmonic generation in 2D NPC - 4HG
It is also possible not only first step to be
two-channel, but also II STEP for 4HG to be with
three-channels
The expected efficiency will be 16 !! times the
efficiency of the conventional bulk or 1D QPM
single crystal schemes
Ref. Nortonde Sterke NLGW-Italy(2002)
OL (submitted)
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Multi-channel harmonic generation in 2D NPC -THG
Ref. KaraulanovSaltiel IQEC(2002)
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Deflection and Splitting in 2D NPC
First work that consider vectorial nonlinear
optical interactions in 2D NPC
Pump and signal are at the same wavelength
Pump and signal are cross-polarized
Output deflected signals can be generated with
efficiency gt 100
Signal will be modulated with the information
carried by the pump
Can be realized in 1D QPM structure too
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Deflection and Splitting in 2D NPC
PHASE MATCHING CONDITIONS
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Deflection and Splitting in 2D NPC
Simple theoretical analysis in approximation of
nondepleted pump gives that output deflected
signals can be generated with efficiency bigger
than 100.
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Today
We considered methods for double phase matching
in NO
1. With uniform QPM gratings 2. With non-uniform
QPM gratings 3. With 2D NPC
Several examples of cascaded processes in 2D NPC
1. Multi channel generation of second, third and
forth harmonics 2. Pump induced nonlinear optical
wavelength interchange 3. Pump indused
deflection and splitting of signal beam
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CASCADED NONLINEAR OPTICAL PROCESSES III
Conclusion
Cascaded nonlinear optical processes play
important role

• in frequency conversion processes
• in optical communications for routing,
  switching, information interchange, correction of
  dispersion effects
• for studying fundamental constants of the
  materials
• for mode-locking and pulse compression

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ACKNOWLEDGEMENTS
University of Sofia, Bulgaria KALOIAN KOYNOV,
GEORGI PETROV, NIKOLAY MINKOVSKI, IVAN
BUCHVAROV, YANA DEYANOVA , STOIAN
TANEV Australian National University YURI S.
KIVSHAR, ANDREY A. SUKHORUKOV TRISTRAM J.
ALEXANDER ENSTA, Ecole Politecnique, France JEAN
ETCHEPARE, OLIVIER ALBERT University of Sydney C
MARTIJN DE STERKE University of Salford ALAN
BOARDMAN