Picosecond Third Harmonic Generation in /?-BaB

Picosecond Third Harmonic Generation in /?-BaB

0

and Calcite

A. Penzkofer, P. Qiu *, and F. Ossig

Naturwissenschaftliche Fakultat H-Physik, Universitat Regensburg, D-8400 Regensburg, Fed. Rep, of Germany

*On leave from Shanghai Institute of Optics and Fine Mechanics, Academia Sinica, Shanghai, Peop.Rep.of China

1. I n t r o d u c t i o n

Phase-matched t h i r d harmonic generation has been achieved i n metal vapors [ 1 , 2 ] i n e r t gases [ 3 ] , organic dyes [ 4 - 6 ] , l i q u i d c r y s t a l s [7] and b i r e f r i n g e n t c r y - s t a l s [ 8 - 1 4 ] . T h i r d harmonic l i g h t may be generated by the d i r e c t t h i r d - o r d e r n o n l i n e a r i n t e r a c t i o n , v^L+v^L+v^L+v³, due t o the t h i r d - o r d e r n o n l i n e a r s u s c e p t i b i - l i t y X ^ G * O R I T M A Y B E 9^{e n e r}a t e d by cascading the second harmonic g e n e r a t i o n , v^L+v^L-^v², and the frequency m i x i n g , v²+v^L+v³. The second harmonic g e n e r a t i o n and the frequency mixing are due t o the second-order n o n l i n e a r s u s c e p t i b i l i t i e s XJH G

and X F M • Phase-matching, Ak=0, i s necessary f o r e f f i c i e n t t h i r d harmonic light:

g e n e r a t i o n . In b i r e f r i n g e n t c r y s t a l s i t i s achieved by c r y s t a l o r i e n t a t i o n and angle t u n i n g . In c r y s t a l s w i t h i n v e r s i o n center o n l y d i r e c t t h i r d harmonic gene- r a t i o n i s allowed w h i l e i n c r y s t a l s without i n v e r s i o n c e n t e r cascading and mixed ( d i r e c t and cascading) t h i r d harmonic generation a r e p o s s i b l e . A double phase- matching o f t h e second harmonic generation and the frequency mixing r e q u i r e s two s e p a r a t e l y o r i e n t e d c r y s t a l s i n s e r i e s . The subsequent phase-matched second har- monic g e n e r a t i o n and phase-matched frequency mixing i s most e f f i c i e n t and i s w i d e l y used [15]. The v a r i o u s phase-matching schemes f o r t h i r d harmonic genera- t i o n i n negative u n i a x i a l b i r e f r i n g e n t c r y s t a l s are summarized i n Table 1.

Table 1 S i n g l e and double phase-matched angle-tuned g e n e r a t i o n o f t h i r d - h a r m o n i c l i g h t i n negative u n i a x i a l b i r e f r i n g e n t c r y s t a l s ( n^e< n^o) . D = d i r e c t . C = c a s - cading. D+C = mixed. IC = i n v e r s i o n c e n t e r .

C r y s t a l Process Phase-matching I n t e r a c t i o n C o n t r i b u t i o n s i n g l e c r y s t a l , s i n g l e phase-matched

Y X eff,THG with IC D _{T H G} =0

A kS H G^{= 0}.^{A k}F M *⁰ V type type type

I II I I I

O l O L ° L⁺e³

° L^eL^eL "^e3

Y X eff,THG

without IC C

T H G ⁼0

A kS H G^{= 0}.^{A k}F M *⁰ V type type

I

II ° L ° L *^e2 ^v (2)

* eff,SHG

C type

type type

I II I I I

o²o^L-*e³ o²e L - e³

e2 < V^e3

v ^{( 2 )} X eff,FM

D+C A kT H G^{= A k}S H G^{+ A k}F M^{= 0} type type type

I II I I I

°^L° L⁰L^{> e}3

° L^eL e i + e³

Y (3) ^{+ Y}( 2 )

X eff, THG *eff,cas two c r y s t a l s , double phase-matched

without IC C A ksHG,i =0 and

A k^{r a},² =0 type type

I II

oo+e

oe-»-e 1: Xe1f,^SHG ^{a n d} 2: x ^{( 2 )}

* eff.FM

a) Cascading t h i r d harmonic generation w i t h A k^{S H G} =0 i s l e s s e f f i c i e n t compared to Ak =0 [13].

312 Springer Proceedings in Physics, Vol. 36

Nonlinear Optics of Organics and Semiconductors

Editor T. Kobayashi © Springer-Verlag Berlin, Heidelberg 1989

In t h i s paper the s i n g l e phase-matched t h i r d harmonic generation i n s i n g l e c r y s t a l s of c a l c i t e and e-BaB²0⁴ i s s t u d i e d . C a l c i t e i s a negative u n i a x i a l c r y - s t a l with i n v e r s i o n center ( t r i g o n a l system, space group R3c, point group 3m).

B-BaB²0⁴ i s a newly developed negative u n i a x i a l c r y s t a l without i n v e r s i o n center [16,17] ( t r i g o n a l system, space group R3, point group 3; a higher symmetry o f R3c and 3m i s s t a t e d i n [18]). The l a r g e e f f e c t i v e second harmonic c o e f f i c i e n t s , the wide transparent waveband (190 - 3500 nm), and the high damage t h r e s h o l d make BBO very important f o r second harmonic generation and frequency mixing i n the u l t r a v i o l e t s p e c t r a l region [19-24]. e-BaB²0- was a p p l i e d s u c c e s s f u l l y i n the second harmonic generation o f femtosecond pulses [25,26].

Table 2 gives a l i s t o f c r y s t a l s that have been a p p l i e d t o the phase-matched t h i r d harmonic generation i n a s i n g l e c r y s t a l .

Table 2 Realized phase-matched t h i r d harmonic generation i n s i n g l e c r y s t a l s . A l l c r y s t a l s are negative u n i a x i a l . D = d i r e c t . D+C = mixed.

C r y s t a l Class I n t e r a c t i o n Laser

[nm]

References

C a l c i t e t r i g o n a l , R3c t r i g o n a l , R3c D Q-switched 694.3 8,9 Q-swi tched 1060 11,14 Mode-locked 1054 t h i s work KDP t e t r a g o n a l , 42m D+C Q-switched 1064 11

ADP t e t r a g o n a l , 42m D+C Q-switched 1060 10 Mode-locked 1060 10

6-BaB²0⁴ t r i g o n a l , R3(R3c) D+C Mode-locked 1054 t h i s work

2. Fundamentals

The geometrical arrangement o f phase-matched t h i r d harmonic generation i n a

s i n g l e c r y s t a l i s sketched i n F i g ^ l . The angle 0 between the c r y s t a l f i x e d z - a x i s ( o p t i c a x i s ) and wave-vector ic^L(||ic³) i s adjusted to phase-matching. a^L and a³ are the w a l k - o f f angles between the ray d i r e c t i o n s of e x t r a o r d i n a r y and ordinary p o l a r i z e d l i g h t .

Col l i n e a r phase-matching of mixed o r d i r e c t THG r e q u i r e s

A k = k e 3 - ^k a L - ^k b L - ^k c L ^{= 0} » ^{( 1}>

a,b,c i n d i c a t e the p o l a r i z a t i o n s o o r e o f the fundamental waves. In the case of type-II phase-matching i t i s k3e-2k^OL-k^eL=0. The wave-vectors are r e l a t e d to the r e f r a c t i v e i n d i c e s n by k=27rnv/c⁰ where v i s the frequency and c⁰ i s the vacuum l i g h t v e l o c i t y . The o r d i n a r y r e f r a c t i v e index n⁰ i s independent of c r y - s t a l o r i e n t a t i o n . The e x t r a o r d i n a r y r e f r a c t i v e index depends on the polar angle 0 by

n n

n^p( 0 ) = —y—5— o o 1/2 5 (²)

e ( n^Zc o s^Z0 + n^Zs i n^Z0 )^{1 / z}

n⁰ and n^e are the p r i n c i p a l r e f r a c t i v e i n d i c e s .

lL.eff

F i g . l Schematic geometrical arrangement

The walk-off angle a^L l i m i t s the overlap length o f the o und e pump l a s e r components i n the case o f type-II and t y p e - I l l phase-matching t o

Ad^L

AL^fe f f * 2 S [

where A d^Li s the pump pulse beam diameter. The walk-off angle a³ allows t h i r d harmonic generation over the whole c r y s t a l length but a m p l i f y i n g i n t e r a c t i o n between pump and t h i r d harmonic l i g h t occurs only w i t h i n an e f f e c t i v e length

(3)

l3 , e f f * 2£ (4)

3

For femtosecond pulses the temporal overlap o f the o and e pump pulse compo- nents o f t y p e - I I and t y p e - I l l phase-matched c r y s t a l s may be l i m i t e d by the group v e l o c i t y d i s p e r s i o n . The group r e f r a c t i v e index i s

°9 " i v M n 3v

(5)

The time delay between o r d i n a r y and e x t r a o r d i n a r y rays i s given by ( 6 t / 6 j , )^{o L e L} = [ⁿg o L ~ⁿg e L (⁰) ] /^co and the.overlap length i s l i m i t e d t o

At,

o ² (6t/6£) (6)

oLeL

The d u r a t i o n o f the generated t h i r d harmonic pulse i s given approximately by A t³ . + ( « t/ a £ ) 23 o |_ £ f j¹ ^ ; (7)

where i^l i s the s h o r t e r length o f i^Q, and « .^{L f e f f} .

The energy conversion e f f i c i e n c y o f t h i r d harmonic generation i s given by 112,13]

_ 2.2- i ,2 s i n (Ala/2) -,.^A .ⁿ . ^{A t} v

nE ^K O l J^xe f f I ^{U | a} ) ^{2 )}2 f( A d^L, A OL, A v^L, A t^L)

k comprises constant f a c t o r s . The f u n c t i o n f takes care o f the r e d u c t i o n of con- v e r s i o n e f f i c i e n c y due t o the f i n i t e beam diameter Ad^L, the divergence A O^l, the s p e c t r a l width A v^L, and the pulse d u r a t i o n A t^L o f the pump pulse.

3. C r y s t a l data

The d i s p e r s i o n o f the p r i n c i p l e r e f r a c t i v e i n d i c e s n⁰ and n^e o f c a l c i t e [271 and BBO [19] are depicted i n F i g . 2 . The transmissions T are shown i n F i g . 3 . The t y p e - I , I I , and I I I phase-matching angles o f d i r e c t THG i n c a l c i t e and o f mixed THG i n BBO are p l o t t e d i n Fig.4. The corresponding w a l k - o f f angles a ^L and a³ are diagrammed i n F i g . 5 .

The angular dependence n^E(⁰)/n^E(OpM) ^{o f B B 0 i s} shown i n Fig.6a f o r X^L =

1.054 um (A0^L=O, Av^L=0, A d^L= « ) . AG ^{1 / 2} i s the FWHM of the angular detuning curve.

F i g . 2 Fig.3 dashed)

0.5 1 2 3 Q2 0.5

WAVELENGTH x turn] WAVELENGTH X t u r n ] R e f r a c t i v e i n d i c e s o f 6-BaB²0⁴ ( s o l i d ) [19] and c a l c i t e (dashed)[27].

Spectral t r a n s m i s s i o n o f 6-BaB²0⁴ {i = 6 mm, s o l i d ) and c a l c i t e (i - 33 mm,

j i i i i i i i i i i i i

2 3 1 2 3 1 2

WAVELENGTH X^L [um] WAVELENGTH x^L [|im]

Fig.4 Type-I, I I , and I I I phase-matching i n 6-BaB²0⁴ (a) and c a l c i t e (b).

Fig.5 Walk-off angles a^L( a ) and a³( b ) of BBO ( s o l i d and dotted) and c a l c i t e (dashed, only t y p e - I I i s shown).

A 0i / 2 ^{1 S} "inverse p r o p o r t i o n a l t o the c r y s t a l length i. A G^{1 / 2}* versus wavelength i s p l o t t e d i n Fig.7 f o r c a l c i t e and BBO. The i n t e r n a l divergence o f the pump l a s e r r a d i a t i o n , A 0A?L,int > _{_}^T^ f » should be l e s s than A G

r J\/2

able l o s s o f e f f i c i e n c y (external divergence angle

i n order t o avoid remark-

A G ,

no L^{A 0}L , i n t ) -

The frequency dependence n^E( v ) / n^E( v^L) a t a f i x e d angle i s s i m i l a r t o the angular dependence a t a f i x e d wavelength. n^E( v ) / n^E( v^L) o f BBO i s depicted i n

Fig.6b ( A G^l= 0 , A V^l= 0 , A d^L= « ) . Phase-matching i s adjusted t o V~^l = X^L = 1.054 nm.

A vi / 2 ^{i s t h} e F W H M o f t h e sP^{e c t r a} l detuning curve. Av w^? i s i n v e r s e p r o p o r t i o n a l to the c r y s t a l length i. A $^{1 / 2}£ , versus wavelength i s d i s p l a y e d i n Fig.8. The s p e c t r a l width o f the pump l a s e r A v^L should be l e s s than A v^{1 / 2} i n order t o avoid remarkable l o s s o f e f f i c i e n c y .

The group v e l o c i t y d i s p e r s i o n l i m i t s the temporal overlap (Eqs.6 and 7 ) . The curves o f (&t/6i)^oLeL and (<$t/<5£)^e3oL are depicted i n Fig.9a and 9b, r e - s p e c t i v e l y .

UJ

F c

a

Z 10 -1 z

jOL

ui

1

A '

| 1 1 ' • ' " • T V | V I 1—» 1 |

- (a)

: /

•

" , A i

li

1 -10 10

0 - 0

Cmrad]

f o r

9 - \ [cm"

]

.6 Angular (a) and s p e c t r a l (b) detuning curves o f 3-BaB²0. a t x.

type-II phase-matched mixed THG (i = 0.72 mm). 1.054 um

0»-—I 1 1 1 1 1 I I I I I I L

1 2 3 WAVELENGTH x^L d m ]

Fig.7 Halfwidth o f angular tuning curves f o r BBO ( s o l i d ) and c a l c i t e (dashed, only t y p e - I I ) . Mixed THG.

WAVELENGTH x, [|tin]

Fiq.8 Halfwidth o f s p e c t r a l tuning curves f o r BBO ( s o l i d and dotted) and c a l - c i t e (dashed, o n l y type-II i s shown). Mixed THG.

£ -Si

£

-I 41

mmm

+-*

«o

8

o

-f> 0

S 0 I V

\\\ (b)

• w

-

mm,

' - ^ ^ ^ -

i

"

_JL-——

1 1 — J J 1 1 1 1 ' ¹ » ' ' ' 1

WAVELENGTH x

l^ml

Fig.9 Time delays (&t/6i)^oLqL (a) and ( 6 t / 6 £ )^{e 3 o L} (b) f o r mixed THG i n BBO ( s o l i d ) and d i r e c t THG i n c a l c i t e (only type-II i s shown).

4. Experimental

The experimental setup i s shown i n Fig.10. S i n g l e picosecond l i g h t pulses o f a p a s s i v e l y mode-locked Nd-phosphate g l a s s l a s e r ( A t^L - 5 ps, A ^L = 1.054 Mm) are used as pump p u l s e s . The energy conversion e f f i c i e n c y o f t h i r d harmonic l i g h t versus input pump pulse peak i n t e n s i t y i s measured and the angular detuning curves are determined. The c a l c i t e c r y s t a l i s 2 cm long and the length o f the B-BaB²0⁴ c r y s t a l i s i = 7.2 mm. In some c a l c i t e measurements a c y l i n d r i c a l lens i s i n s e r t e d t o generate a l i n e - f o c u s which increases the l i g h t i n t e n s i t y a t the c r y s t a l without i n c r e a s i n g the r e l e v a n t l a s e r divergence A G^l i n the plane span- ned by the o p t i c a x i s and the l i g h t propagation d i r e c t i o n .

M.L.LASER 1 — | SWITCH [ - HAMPLIFIERI \

PM

\ — '* /

F CR i i

cjn SA

[J ]PD2 6 ^PD1

Fig.10 Experimental setup. PD1, PD2, photodetectors. SA, s a t u r a b l e absorber (Kodak No.9860) f o r peak i n t e n s i t y d e t e c t i o n [28]. CR, c r y s t a l . F, f i l t e r . PM, p h o t o m u l t i p l i e r .

5. R e s u l t s

Type-II phase-matched mixed (BBO) and d i r e c t ( c a l c i t e ) THG are i n v e s t i g a t e d . The angular detuning curves n^E( o ) / n^E( O p^M) of BBO and c a l c i t e are shown i n Fig.11.

For BBO the s p e c t r a l width o f the pumg l a s e r i s A v^L = 10 cm"¹. In the case o f c a l c i t e two curves are depicted f o r Av^L = 10 cm" and A V L = 40 cm" ( s e l f - p h a s e modulated p u l s e s ) .

The phase-matched THG energy conversion e f f i c i e n c y versus pump pulse peak i n - t e n s i t y i s depicted i n Fig.12. A t the highest i n t e n s i t i e s a p p l i e d conversion e f f i c i e n c i e s o f n^E » 0.01 ( I^{0 L} = 5 x l 0^{1 0} W/cm²)-and n^E * 8 x l 0 "⁵ ( I ^{0 L} = 1 0^{1 1} W/cm²) have been obtained f o r BBO and c a l c i t e , r e s p e c t i v e l y . The damage t h r e s h o l d o f c a l c i t e i s I^th,c > 10 W/cm² and the damage t h r e s h o l d o f BBO i s Ith,B" 10 W/cm² [18,22] f o r s i n g l e pulses o f 5 ps d u r a t i o n . A t pump pulse i n t e n s i t i e s s l i g h t l y below the damage t h r e s h o l d very high conversion e f f i c i e n c i e s are expected i n both c r y s t a l s .

The e f f e c t i v e n o n l i n e a r s u s c e p t i b i l i t i e s xlW are determined by comparison o f the measured energy conversion e f f i c i e n c i e s n^E w i t h c a l c u l a t i o n s (Eq.5). The ob- tained values are l i s t e d i n Table 3 together with other c r y s t a l parameters. A

4 3 2 1 o 1 2

INTERNAL DETUNING ANGLE 0-e

[mrad]

Fig.11 THG conversion e f f i c i e n c y versus detuning angle f o r BBO o f 0.72 cm length (a) and c a l c i t e o f 2 cm length ( b ) . A0L =5x10 r a d . ( l , o ) , Av^L = 10 cm"¹. ( 2 ,A) , A V^l = 40 cm"¹. Type-II phase-matching.

d e t a i l e d a n a l y s i s o f the e f f e c t i v e s u s c e p t i b i l i t i e s i n d i c a t e s t h a t x⁽!L ™,^r

x ⁽²> are o f the same order o f magnitude f o r BBO [ 1 3 ] . ^e" '

6 £ f fCclS

and

z 10

o

V)

QC

HI > 10

o z u

UJ LLt

10

~ i — i i 11— r — _{i i | i y\ 11} ^{i \ \\y\\}

/ 1 / 1

2 / Ith.C '

—

- y

-

4 _

-

6

-

i i i i t i i i i i i i i 11 1 I i f f 1

10* 10* 10" 10" 10°

INPUT PEAK INTENSITY I^0L TW/cm²]

Fig*12 Energy conversion e f f i c i e n c y o f BBO (curve 1, 0 ; i = 7.2 mm) and c a l c i t e (curve 2,A; % • 2 cm). Type-II phase-matching. A0^L = 10"⁴ r a d . A\>L = 20 c n r¹. The damage thresholds I^{t h / B} (BBO) and I ^{t h f C} ( c a l c i t e ) are i n d i c a t e d .

Table 3 Phase-matched t h i r d harmonic generation o f picosecond pulses o f a Nd-phosphate g l a s s l a s e r i n c a l c i t e U = 2 cm) and 6-BaBpO- (i = 7.2 mm).

A t^L = 5 ps, X^L = 1.054 nm.

Parameter C a l c i t e 6-BaB²0⁴

System Point group Space group Process

Phase-matching

0PM

A°l/2 *

A v^{1 / 2} £

[rad cm]

(6t/6£) _e3oL [°]

[°]

[ps cm'¹]

<^{5 t}/ 6 A )^{o L e L} [ps cm"¹] [ m²V^{- 2}] [ m²V -²] [ m²V -²]

[W cm"²]

x eff,THG

Y (2)

* eff,cas

Y (3)

* eff

^ E n(I

t r i g o n a l 3m R3c D

type-II (ooe+e) 35.96

2.3x10 ^{_ 4} 8.8 6.75 5.85 1.7 2.2 3x10 "2 4

3x10-24 (2.1x10-16 esu) 8 x l 0^{- 5 a )}

> 10 ^{1 3}

* 1

t r i g o n a l 3 (3m) R3 (R3c)

D + C

type-II (ooe+e) 47.4

3.4xl0^{- 4} 3.7 4.45 4.05 2.0 2.1 6 . 4 x l 0^{- 2 3} 6 . 6 x l 0^{- 2 3}

1.3x10-22 (9.2x10 "^{1 S} esu)

0.01 ^{b )}

- 1 01 2

+ 1

a: I _OL 1 0^{1 1} W/cm². b: I _OL 5x10^{1 0} W/cm².

References

1. J.F. R e i n t j e s : In Laser Handbook, ed. by M. Bass and M.L. S t i t c h , Vol.5 (North-Holland, Amsterdam, 1985) C h . l .

2. C R . V i d a l : In Tunable Lasers, ed. by F.L. Mollenauer and J.C. White ( S p r i n - ger, B e r l i n , Heidelberg, 1987) p. 57.

3. A.H. Kung, J.F. Young, S.E. H a r r i s : Appl. Phys. L e t t . 22, 301 (1973).

4. P.P. Bey, J.F. G u i l i a n i , H. Rabin: IEEE J . Quant. E l e c t r o n . g E j 7 , 86 (1971).

5. J.C. D i e l s , F.P. SchSfer: Appl. Phys. 5, 197 (1974).

6. A. Penzkofer, W. Leupacher: Opt. Quant. E l e c t r o n . 20, 222 (1988).

7. J.W. S h e l t o n , Y.R. Shen, Phys. Rev. L e t t . 26, 538 TT971).

8. R.W. Terhune, P.O. Maker, C M . Savage: Appl. Phys. L e t t . 2, 54 (1963).

9. P.D. Maker, R.W. Terhune: Phys. Rev. 137, A801 (1965).

10. C.C. Wang, E.L. Baardsen: Appl. Phys. L e t t . 15, 396 (1969).

11. S.A. Akhmanov, L.B. Meisner, S.T. Parinov, S.M. Sal t i e ! , V.6. Tunkin: Sov.

Phys. JETP 46, 898 (1977).

12. A. Penzkofer, F. O s s i g , P. Qiu: Appl. Phys. B, t o be p u b l i s h e d . 13. P. Q i u , A. Penzkofer: Appl. Phys. B45, 225 (1988).

14. A.P. Sukhorukov, I.V. Tomov, Sov. Phys. JETP 31, 872 (1970).

15. D. E i m e r l , IEEE J . Quant. E l e c t r o n . QE-23, 575 (1987).

16. C. Chen, B. Wu, A. J i a n g , G. You: S c i . S i n i c a (Ser.B) 28, 235 (1985).

17. A. J i a n g , F. Cheng, Q. L i n , C Chen, Y. Zheng: J . C r y s t . Growth 79, 963 (1986).

18. D. E i m e r l , L. Davis, S. Velsko, E.K. Graham, A. Z a l k i n : J . A p p l . Phys. 62, 1968 (1987).

19. K. Kato, IEEE J . Quant. E l e c t r o n . QE-22, 1013 (1986).

20. K. M i y a r z a k i , H. S a k a i , T. Sato: Opt. L e t t . 11, 797 (1986).

21. P. L o k a i , B. Burghardt, D. B a s t i n g , W. Miickenheim, Laser und O p t o e l e k t r o n i k 19, 296 (1987).

22. H. Schmidt, R. W a l l e n s t e i n : Laser und O p t o e l e k t r o n i k 19, 302 (1987).

23. R.S. Adhav, S.R. Adhav, J.M. P e l a p r a t : Laser Focus 23/9, 88 (1987).

24. J.T. L i n , C. Chen, Laser Focus 23/11, 59 (1987).

25. Y. I s h i d a , T. Yajima: Opt. Commun. 62, 197 (1987).

26. K.L. Cheng, W. Bosenberg, F.W. Wise, I.A. Walmsley, C L . Tang: Appl. Phys.

L e t t . 52, 519 (1988).

27. American I n s t i t u t e o f Physics Handbook, 3rd ed., ed. by D.E. Gray (McGraw- H i l l , New York, 1972) p. 6-20.

28. A. Penzkofer, D. von der Linde, and A. Laubereau, Opt. Commun. 4, 377 (1972).