Two-wave coupling and self-pumped phase conjugation at near infrared wavelengths in BaTiO3

Optics Communications 88 (1992) 424-430 North-Holland

OPTICS COM MUN ICATIONS

Two-wave coupling and self-pumped phase conjugation at near infrared wavelengths in BaTiO3 H.Y. Zhang, X . H . H e a n d Y . H . Shih Department of Physics, Universityof Maryland at Baltimore County, Baltimore, MD 21228, USA

Received 20 August 1991; revised manuscript received 31 October 1991

Using an undoped BaTiO3crystal,the reflectivitiesof the self-pumpedphase-conjugatemirror operated in total internal-reflection geometry (TIR) at near infrared wavelengths from 706 to 850 nm were measured. The phase conjugation refleetivities Rp~>50% at 706 to 760 nm, R~=40% at 816 rim, and R~=20% at 850 nm were observed. The two-wavecoupling exponential gain coefficientFand the photorefraetiveindex grating formation rate rb-d as a function of wavelengthfrom 706 to 850 nm were studied. The exponentialgain coefficientsF= 11.1 era- l at 706 nm and F= 7.6 cm- t at 850 nm were obtained. It was also found that the absorption coefficienta in the near infrared wavelengthsis much smaller than that in the visible region.

1. Introduction The photorefractive effect and self-pumped phase conjugation (SPPC) in BaTiO3 crystals have been extensively studied in the visible spectral region (mostly at 2 = 4 8 8 a n d 514.5 n m ) . Many different geometries of self-pumped phase conjugation were studied. The most common design has been the total internal reflection geometry ( T I R ) [ 1 ] (usually called cat conjugator) and the self-pumped phase conjugation with an external ring cavity [ 2 ]. Recent interest at near infrared region has been brought by the compact semiconductor diode laser's applications. For laser diodes (LDs), two-wave coupling and phase conjugation may provide a unique beam distortion correction capability that can alleviate beam astigmatism and improve the overall beam quality [3]. Phase conjugation feedback was suggested for use in self-aligned phase locking of LDs and LD arrays [4 ] and the experiment has been successfully performed with two single-element LDs [ 5 ] and two ten-element LD arrays [ 6 ] by using BaTiO3. Besides the applications, the self-pumped phase conjugation of BaTiO3 itself may need much intensive study. To our knowledge, only a few publications have been concerned with the self-pumped phase conjugation in the near infrared region with undoped BaTiO3 and most of the successful experiments [ 7,8 ] were using 424

external ring cavity geometry. Recently, Rytz et al. [9] reported self-pumped phase conjugation with T I R geometry in the dear infrared wavelengths using cobalt-doped BaTiO3. We report here an intensive experimental study of undoped BaTiO3 two-wave coupling and self-pumped phase conjugation with T I R geometry in near infrared wavelengths.

2. Two-wave coupling in BaTiO3 We measured two-wave coupling gain in the BaTiO3 crystal. The internal angle between the " p u m p " beam and the "signal" beam is 20. When two beams interfere inside the crystal, a sinusoidal intensity pattern would be produced with fringe separation As: As=2/2nsinO,

ks=2rc/A s ,

where 2 is the wavelength in free space, n is the refractive index, 0 is the internal half angle between two beams and ks is the magnitude of the grating wave vector. The interference pattern causes migration of charge inside the crystal. The resulting space charge field produces a photorefractive index grating. This index grating couples the two beams with a two-wave coupling gain coefficient F. The gain coefficient F is expected to be

0030-4018/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.

Volume 88, number 4,5,6

F=

co Im(Esc) reff r/c

COS 0

'

OPTICS COMMUNICATIONS

(1)

The photorefractive response time can be simply expressed as [ 11 ] ('L'pR)-- I =

where co is the optical frequency, c is the speed of light, n is the index of refraction corresponding to the polarization of the light, E~ is the magnitude of the space charge electric field inside the crystal and r~ff is the effective electro-optical coefficient. In the absence of any applied or intrinsic electric field, the charge migration is diffusion dominated and purely imaginary. For this case the total space charge electric field E~ induced by the interference pattern of the two coupling beams for extraordinary polarization is given by Im(Esc) = kBT ks cos 20, q 1 + (k./ko) 2

(2)

where kBT is the thermal energy, q is the charge of the mobile charge carriers, kg is the grating wavevector and ko is a constant of the material that depends on the number density N of available mobile charge carriers, 4nn . kg= --~- sm v ,

(3)

( Nq2"~ 1/2 ko = k:--~--o-~aTj ,

(4)

where eo is the permittivity of free space, e is the effective dc dielectric constant in the direction of k v According to eqs. ( 1 ) - (4) both F and E~c reach their maximum when k~= ko [ 101. The exponential gain coefficient F o f the two-wave coupling can be calculated from the experimental data using the following equation [ 11 ]: 1

F= Z

_

1.

I'sIp Idp, ,

(5)

where I~ (Is) is the intensity of transmitted signal beam with (without) two-wave coupling, and I~, (Ip) is the intensity of transmitted p u m p beam with (without) two-wave coupling and L is the interaction length of the two beams. Because I" and Is (I~, and Ip) are both transmitted intensities, they experience the same absorption and Fresnel losses. These losses cancel each other and do not appear i n the above expression.

1 April 1992

O"d

+el~ZRaI/hv,

(6)

*o~ where ad is the dark conductivity,/tZR is the product of mobility and recombination time, h v is the photon energy and ot is the absorption coefficient which corresponds to the photorefractive effect. A cw tunable Ti:sapphire laser was used as the p u m p source. A telescope was used for reducing the laser beam size to about 0.5 m m at the surface of the crystal, which was defined as where the intensity reduced to e - 2 of its center value. The laser beam was split into two beams, i.e. " p u m p " and "signal", by a beam splitter. With the help of an N D filter the ratio of the pump beam intensity to the signal beam intensity was chosen to be r = 1000. The incident angles of the signal and pump beam were 19 o and 51.2 °, respectively. The angle between the two beams was therefore about 32.2 °. It was calculated that the angle between the grating wave vector and the c-axis of the crystal was 13.4 ° and the grating period for 2 = 8 0 0 nm was Ag= 1.7 ~tm. This particular orientation was used to utilize the large electro-optical coefficient r42 of the BaTiO3. The size of the crystal was 5.87 × 4.64 × 3.86 m m 3. The interaction length L of two beams was about 4.64 mm. The exponential gain coefficient F for different wavelengths is reported in fig. 1. F decreases from 11.1 cm -~ at 706 nm to 7.62 cm -~ at 850 nm. The calculated ratio F(706 n m ) / F ( 8 5 0 rim) ~ 1.46. This indicated that F is approximately proportional to 1/22. According to eq. ( 1 ) F is proportional to the product of oJ and E~, while E~ is roughly proportional to l / 2 in the optimized experimental condition, which can be estimated from eqs. (2), (3) and (4). The pump power dependence of F was studied at 2 = 7 9 0 nm. The results are shown in fig. 2. It was found that F did not increase significantly, when the pump power was increased from 2.6 to 150 mW. The response time ZpR of the two-wave coupling at different wavelengths of pump power Po = 66 mW was measured. ZpR was defined to be the time for the amplified beam in two-wave coupling to reach l - e of its steady-state value, and zb-~ to be the photorefractive grating formation rate. The response time 425

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12

i

[

720

740

i

I

1 April 1992

]

i

i

800

820

11 10 E ~ 9 .E 8

7

m

~8 0

5

w 4 3

2 700

I

,

760

I

I

780

,

840

860

Wavelength (nm) Fig. 1. Two-wave coupling exponential gain Fversus wavelength in BaTiO3 in the near infrared region.

11

I

I

10 A

e" m

~ m tO

c

0 Q. X W

8

7

6

L

5

0

I

20

i

40

I

60

I

I

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120

I

140

60

Power (row) Fig. 2. Two-wave coupling exponential gain Fversus the pump power in BaTiO3 at 790 nm.

426

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increased from 4.8 s at 2 = 706 nm to 19.2 s at 2 = 850 nm. Fig. 3 reports the photorefractive grating formation rate z~-d versus wavelength. According to eq. (6) zFd is approximately proportional to a I / h v, the absorbed photon number density, ot was measured to be 0.048 cm -1 at 850 nm and 0.157 cm - I at 706 nm, which was increased 3.3 times from 850 to 706 nm (the measurement of ot is reported in the next section). From fig. 3 we found that T~-R t increased about 4 times when 2 changed from 850 to 706 nm. The experimental results were close to the prediction by eq. (6). After the correction for Fresnel reflections and scattering losses the absorption coefficient ot of the crystal is plotted in fig. 4, which is in the range of 0.05 to 0.15 c m - t. Compared to the absorption coefficient a in the visible region, 1.5 to 0.5 cm -~, this is a rather small value.

1April 1992

periment shown in fig. 5. The laser beam size was reduced by a telescope and then divided into the "reflected beam" with power P~ and the "transmitted beam" with power Pin by a beam splitter. The beam diameter at the input surface of BaTiO3 crystal was about 0.5 mm, which was defined as where the intensity reduced to e -2 of its center value. The transmitted beam was used as the input pump beam of self-pumped phase conjugation. The phase conjugate wave P ~ was reflected by the same beam splitter. The power of the reflected phase conjugate wave t P ~ equals Ppc = rPpc, where r is the reflectivity of the beam splitter and P~ is the power of the phase conjugate wave. The net phase conjugate reflectivity Rp~ is then given by

=P~/Pi. =P'pc/P'o(1 - r )

R~

.

(7)

The power P ~ and P3 were measured by two power meters simultaneously. Both power meters were calibrated carefully before the measurement. The orientation of the crystal was optimized with respect to the direction of incident beam at 706 nm. Both the position of the incident spot on the entrance face and the angle between the incident beam and the normal

3. Self-pump phase conjugation The same BaTiO3 crystal and Ti:sapphire laser were used for the self-pumped phase conjugation ex-

30 25

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740

760

780

800

820

.

840

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Fig. 3. The photorefraetivegrating formationrate ~m 0ftwo-wavecouplingversus wavelengthsfor BaTiO3at P= 66 mW. zPRwas defined to be the lime for the amplified beam in two-wave.couplingto reach 1- e- mof its steady-statevalue. 427

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0.40 0.36 0.32

"" 0.28

-Q ® 0.24

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Wavelength (nrn)

Fig. 4. Absorptioncoefficientot versuswavelengthsin BaTiOscrystalin the near infrared region.

Ti : Sapphlre Laser

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Po ~

Pin

Po

p

BTO

pc

C D1

Set up of p u m p e d p h a s e conjugation with T I R g e o m e t r y in B T O crystal

Fig. 5. Schematic diagram of the self-pumpedphase conjugation experiment. of the entrance face of the crystal were adjusted very carefully. The adjustment was very critical. The refracted beam had to be very close to the TIR comer, otherwise the phase conjugate signal decreased significantly. The self-pumped phase conjugate wave could be observed when the incident angle in air was varied from 65 ° to 77 °, or 25 ° to 13 ° from the caxis of the crystal. Most data of phase conjugate reflectivities R ~ were taken around 16 ° from c-axis. 428

Phase conjugate reflectivity R ~ at different pump power for different wavelengths is shown in fig. 6. Rvc> 50% when the pump wavelength is shorter than 760 nm. R~ > 40% when the pump wavelength is 816 nm and pump power is above 30 mW. The phase conjugate wave can be built up at a lower pump power level (about 5 to 15 mW). The build-up time z of the phase conjugate wave for different wavelengths at about 38 mW pump power is shown in fig. 7. z is defined to be the time interval elapsed between 10% and 90% of the steadystate value. The build-up time of the phase conjugate wave is much longer at longer wavelengths. At 2 = 706 nm, z = 13 s and at 2 = 850 nm, z = 158 s, it increased 12 times. Similar results have been observed by other authors [ 7,12 ]. The wavelength dependence of buildup time has not been well understood.

4. Conclusion Two-wave coupling gain F for BaTiO3 in the near infrared region (706 to 850 nm) was studied. It was found that the gain F increased at shorter wave-

Volume 88, number 4,5,6

OPTICS COMMUNICATIONS

60

o

1 April 1992

I

I

50

n.-

S

J,

j.

0

~: 3o m

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•

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70

80

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Power (row) Fig. 6. Self-pumped phase conjugate reflectivity Rp~ versus pump power in BaTiO3 at 760, 816, and 850 nm.

180 1 60

..................

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Wavelength (nm) Fig. 7. The build-up time T of phase conjugate wave versus wavelengths in BaTiO3 at P-- 38 mW. The build-up time r of phase conjugate wave was defined to be the time interval elapsed between the 10% and 90% levels of the saturated phase-conjugate signal. 429

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OPTICS COMMUNICATIONS

lengths from 7.6 c m -~ at 850 n m to 11.1 c m - I at 706 nm. The index grating f o r m a t i o n rate increased 4 times when 2 changed from 850 to 706 nm, comparable to the 3.3 times increase o f a b s o r p t i o n coefficient a . Self-pumped phase conjugation for an u n d o p e d BaTiO3 with T I R geometry was s t u d i e d in the near infrared region (706 to 850 n m ) . T h e phase conjugate reflectivity Rp~> 50% at 2 < 760 nm, R ~ > 40% at 2 < 8 1 6 nm, a n d R p c > 2 0 % at 850 n m were obtained. These measurements suggested that the phase conjugator is useful for i m p r o v i n g the b e a m quality o f s e m i c o n d u c t o r lasers.

References [ 1 ] J. Feinherg, Optics Lett. 7 ( 1982 ) 486.

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[2] M. Cronin-Golomb, B. Fischer, J.O. White and A. Yariv, Appl. Phys. Lett. 42 (1983) 919, [3] A,E. Chiou and P. Yeh, Optics Lett. 11 (1986) 461. [4 ] J. Feinberg and G.D. Bather, Appl. Phys. Lett. 48 (1986 ) 570. [ 5 ] M. Cronin-Goiomb, A. Yariv and I. Ury, Appl. Phys. Lett. 48 (1986) 1240. [6] M. Segev, S. Weiss and B. Fischer, Appl. Phys. Lett. 50 (1987) 1397. [7] M. Cronin-Golomb, K.Y. Lau and A. Yariv, Appi. Phys. Lett. 47 (1985) 567. [8] P.H. Beckwith and W.R. Christian, Optics Leu. 14 (1989) 642. [9] D. Rytz, R.R. Stephens, B.A. Weehsler, M.S. Keirstead and T.M. Baer, Optics Lett. 15 (1990) 1279. [10] R.A. Fisher, ed., Optical phase conjugation (Academic Press, New York, 1983 ) p. 425. [11] M.D. Ewbank, R.R. Neurgaonkar, W.K. Cory and J. Feinberg, J. Appl. Phys. 62 (1987) 374. [ 12 ] B.T. Anderson, P.R. Forman and F.C. Jahoda, Optics Left. 10 (1985) 627.