cascaded nonlinear optical processes presented by s. saltiel univ. sofia, bulgaria part i i i...
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CASCADED NONLINEAR OPTICAL CASCADED NONLINEAR OPTICAL
PROCESSESPROCESSES
CASCADED NONLINEAR OPTICAL CASCADED NONLINEAR OPTICAL
PROCESSESPROCESSES
presented by S. Saltiel Univ. Sofia, Bulgaria
PART I I I
September, 2002
CASCADED NONLINEAR OPTICAL PROCESSES
Cascading with two simultaneously phase matched (DPM) interactions
Part II
Part III
in out
Methods for achieving DPM.
cascading with 2D nonlinear photonic crystals
Methods for double phase matching
DPM with uniform QPM
DPM with nonuniform QPM
DPM in 2D nonlinear photonic crystals
DPM in 1D PC
QPM - the revolution in optical frequency conversion. D. Hanna.
QPM - quasi phase matching - is an artificial reversal of the sign of second order nonlinearity with the aim to PM nonlinear processes l1
l2 D= l2/l1
d d
Gm
ziGgdzd mm
mo exp)(
0
,....,,, 3212 mmm G
set of reciprocal grating vectors with amplitude
)sin( mDmgm 2
Factor that express the reduction of nonlinear coefficient - the price: the
smaller is m - the higher is
For PM of single process (e.g. 3 = 1 + 2) we compensate the wave vector mismatch with one of the reciprocal gratings Gm
0123 mkkkk Gk3
Gm
k1 k2
Methods for double phase matching - uniform QPM
2
4
QPM media
Example: if m = 1 then
SHG
HG
k
kn 4
SHGk
2
Method of two commensurable periods
1.0 1.5 2.0 2.5 3.0 3.5 4.00
5
10
15
20
25
30
35
40
G
ratin
g Pe
riod
s (
m)
LiNbO3
I order FHG III order FHG V order FHG VII order FHG I order SHG
1(m)
- fundamental wavelengths good for DPM
Works only for discrete wavelengths
Ref. e. g. Pfister et al OL’97
02 12 mSHG Gkkk
02 244 nHG Gkkk
mGm 2
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
Input waves
angle of noncollinearity
Gm
k1
212 kGk m
321 kGkk n
k1
k1Gmk2
k3
Gn
Example: THG
Ref. Saltiel,Kivshar, BulgJPhys’2000
Phase Matching with Noncollinear QPM for third-harmonic MSC in LTN
0
1
2
3
4
5
6
1 1.5 2 2.5 3fundamental wavelength, m
70
80
90
100
m =n =1
period, m)(degr)
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)]
Q
ph
,,....,,,
,)(
321
ml
egdzd ziGlmo
lm
mlGphQ
lm
22
Now we have two dimentional set of reciprocal vectors {Glm} and flexibility to PM several processes is much bigger
Phase-reversed Phase-reversed QPM struturesQPM strutures
2112
2112
2112
2112
2
2
klkl
mlml
kmkm
mlml
Ph
Q
1k 2k
I st. II st.
11mlG
22mlG
kn
own
Methods for DPM - non-uniform QPM structures
Another type non-uniform QPM grating - QPM structure with periodical change of the period O.Bang et al OL’99]
,,....,,,
,)(
321
ml
egdzd ziGlmo
lm
2112
2112
2112
2112
2
2
klkl
mlml
kmkm
mlml
ch
Q
1k 2k
11mlG
22mlG
Periodically chirped Periodically chirped QPM struturesQPM strutures
choQ z 2cosch
Periods for MSC THG in LTN with periodically chirped QPM structure
0
25
50
75
100
0.5 1 1.5 2 2.5 3
fundamental wavelength, m
, m
11
13
22
11
lm
lm
,
,ph
Q
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
Liu et al PRA(1998)
23% efficiency in THG is reported:Zhu, Science (1997)
27% efficiency in THG is reported:Zhang, OL (2001)
Two of {K m,n} are used to PM the two processes:
22
11
2
1
nm
nm
Kk
Kk
This system allows to find D and
ziKgdzd nm
nmnmo ,
,, exp)(
DnmK nm 2,
AB LLD
Methods for DPM - 1D photonoc band gap
n1 n2
Methods for DPM - 1D photonoc band gap
Example: THG
N-1 N-2 N-3resonance:
Condition for DPM are
23
2
where the Bloch phases are
33
22
1
3
2
NN
NN
NN
2D NONLINEAR PHOTONIC CRYSTALS
This drawing is valid for nonlinear photonic
crystals too. They are proposed by
Berger, PRL’98QPM
1D NPC 2D NPC 3D NPC
We will consider these types of NPC for which: Linear properties remain unchanged and there is modulation of nonlinear properties.
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)
2D NONLINEAR PHOTONIC CRYSTALS
How it works:
Real structure. The circles
mark the regions with “ ”.
da
a
a
bb b cbcc
a
d
c
We have many gratings characterized by
grating vectors pq .with p,q = 1, 2,
3... All of them can be expressed by two fundamental vectors a and c that
form the reciprocal lattice (a).
a) Reciprocal lattice
ac
32
(a)
acpq qp KKK
aaK
2
ccK
2
b) SHG PM tringle
y
x
k2
2k1
pq
(b)
pq
212 kKk pq
Any reciprocal lattice vector pq can be used to PM the
nonlinear process. Disadvantage: noncollinear interaction, but angles - not big
2D NONLINEAR PHOTONIC CRYSTALS
Real structure. The circles
mark the regions with “ ”.
d a
a
a
bb b cbcc
a
d
c
Note three parameters
dcharacterize
the 2D NPC
Methods for DPM - 2D NPC
Principe for DPM is the same as for the most of other methods. We have pool of vectors {pq}. One of the process we PM with ij
and the other with mn .From the PM conditions we find the parameters of the 2D NPC structure: d and and .
DPM for SHG + 4HG
x
y k4
2k1
pq
ij
k2
Kmn
2
y
k3
2k1
pq
ij
k1 Kmn
DPM for SHG + THG
pqfd
mn
ij
Kk
Kk
2
1
Since we have three parameters to define:
d three processes can be simultaneously PM e.g SHG + THG + 4HG Ref. Saltiel,Kivshar OL(2000)
Nonlinear cascaded processes in 2D NPC
p 772.5 nm, 325 mW
1 1535 nm, 500 mW
2 1555 nm, 500 mW
Noncollinearity in this case is working for us !!!!!!
The output beams are automatically separated
The two processes are simultaneously PM according
following PM conditions:
mnp
ijp
Kkkk
Kkkk
12
21
'
'
12
21
p
p
Experimental demonstration of 1535–1555-nm simultaneous optical wavelength interchange with a nonlinear photonic crystal
September 1, 2001 / Vol. 26, No. 17 / OPTICS LETTERS 1353
A. Chowdhury, Ch. Staus, B. Boland, Th. Kuech and L. McCaughan
Reciprocal lattice
a
c
kp
kp
y
x
ij
mn
1'k
2'k
pk
2k1k
DFM phase-matchings
1
2 2
2D NPC
1
mnp
ijp
Kkkk
Kkkk
12
21
'
'
12
21
p
p
Nonlinear optical wavelength interchange in 2D NPC
Nonlinear optical wavelength interchange in 2D NPC
mnp
ijp
Kkkk
Kkkk
12
21
'
'1
2 2
2D NPC
1
12
21
p
p
Simple theoretical analysis (not in the ref.) gives not only wavelength routing with interchange of the information, but also AMPLIFICATION !!!
I 1,ou
t/I1,
in ;
I2,
out/I
2,in
2LAI pp
4pI2pI
1pI
Multi-channel harmonics generation in 2D NPC
qp,qp, KK
Symmetrical reciprocal lattice
b
a
2k1
Kp,-q Kp,q
1
2D NPC
2
1
2 2
Multiple phase-matchings
2k1
Broderick et al, PRL(2000)
Multi-channel harmonic generation in 2D NPC - 4HG
pq
nm
nm
Kkkk
Kkk
Kkk
224
12
12
2
2
"'
"
'
,
,
Efficient collinear fourth-harmonic generation by two-channel multistep cascading in a single two-dimensional nonlinear photonic crystal
April 15, 2001 / Vol. 26, No. 8 / OPTICS LETTERS 539
Martijn de Sterke, Solomon M. Saltiel and Yuri S. Kivshar
xnm,K
nm ,K
2'k
2"kI stepx
pqK2'k 2"k
4kII step
422
2
2D NPC
Fourth harmonic beam II Fundamental beam!
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.
0 1 2 3 4 5
1
2
3
4
1 = 2
2ch
,
1ch
2ch
/1c
h
I1 = (1AoL)2
0.0
0.2
0.4
0.6
0.8
1.0
SH efficiency is twice higher
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
nm
nm
,
,
"
'
Kkk
Kkk
12
12
2
2
qp
qp
qp
,224
,224
,224
''
""
''
Kkkk
Kkkk
Kkkk
I st.
II st.
The expected efficiency will be 16 !! times the efficiency of the conventional bulk or 1D QPM single crystal schemes
Ref. Norton&de Sterke NLGW-Italy(2002) + OL (submitted)
x
pqK2'k 2"k
4kII step ch1
x4kqp ,K
qp,K
2k2k
2k2k
II step ch2,3
Multi-channel harmonic generation in 2D NPC -THG
nm
nm
,
,
"
'
Kkk
Kkk
12
12
2
2
qp
qp
,
,
'
"
Kkkk
Kkkk
124
124
I st.
II st.Ref. Karaulanov&Saltiel IQEC(2002)
2D NPC
xpqK
2k'
2k"
3k
II step
qp ,K
1k
xnm,K
nm ,K
2k'
2k"I step1k
2333 "', EEI out
THG
Deflection and Splitting in 2D NPC
All-optical deflection and splitting by second-order cascading
June 1, 2002 / Vol. 27, No. 11 / OPTICS LETTERS, 921
Solomon M. Saltiel and Yuri S. Kivshar
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
Signal will be modulated with the information carried by the pumpsignal
pump
ТS
DS1
DS2SH pump
2D NPC polarizer
signal
pump
ТS
DS
SH pump
Can be realized in 1D QPM structure too
Output deflected signals can be generated with efficiency > 100%
Deflection and Splitting in 2D NPC
PHASE MATCHING CONDITIONS
I st.
K b
2kp
K ak2
k2ks
ks’
II st.
2kp Kb
k2
Kc
Ka
ks’
ks
I st.
II st.
'; sspppp yyzzzz 112211
zy
p
ss
s’
'; sspppp zzzzyy 112211
zy
s’
ss
p
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%.
2
111
2
1
2
4
1
)cosh()(sech pp' LALAss step II
step I
2
1
S
S
D""
T""
0.0 0.5 1.0 1.5 2.00
2
4
6
8
100.0 3.0 6.0 9.0 12.0
transmitted signal
deflected signal
transmitted signal
deflected signal
1AoL
effic
ienc
y
1AoL
61
2
611
2
Today
Several examples of cascaded processes in 2D NPC
We considered methods for double phase matching in NO
1. With uniform QPM gratings 2. With non-uniform QPM gratings 3. With 2D NPC
1. Multi channel generation of second, third and forth harmonics2. Pump induced nonlinear optical wavelength interchange 3. Pump indused deflection and splitting of signal beam
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
CASCADED NONLINEAR OPTICAL PROCESSES III
Cascaded nonlinear optical processes play important role
ACKNOWLEDGEMENTS
University of Sofia, BulgariaKALOIAN 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