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CASCADED NONLINEAR OPTICAL CASCADED NONLINEAR OPTICAL PROCESSES PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002
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Page 1: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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

Page 2: CASCADED NONLINEAR OPTICAL PROCESSES 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

Page 3: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

Methods for double phase matching

DPM with uniform QPM

DPM with nonuniform QPM

DPM in 2D nonlinear photonic crystals

DPM in 1D PC

Page 4: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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

Page 5: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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

Page 6: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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)

Page 7: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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

Page 8: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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

Page 9: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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

Page 10: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

Methods for DPM - 1D photonoc band gap

n1 n2

Page 11: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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

Page 12: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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)

Page 13: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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

Page 14: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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

Page 15: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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)

Page 16: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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

Page 17: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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

Page 18: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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

Page 19: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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)

Page 20: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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!

Page 21: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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

Page 22: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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

Page 23: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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

Page 24: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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%

Page 25: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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

Page 26: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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

Page 27: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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

Page 28: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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

Page 29: CASCADED NONLINEAR OPTICAL PROCESSES presented by S. Saltiel Univ. Sofia, Bulgaria PART I I I September, 2002.

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


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