Light-climbing effect in LiNbO3:Fe crystal

Liu Simin, Xu Jingjun, Zhang Guangyin, and Wu Yuanqing

The light-climbing effect in a LiNbO3:Fe crystal sheet was experimentally studied, and the mechanism forlight climbing proposed was proved to be correct. The relevant optical properties were investigated.

1. Introduction

The light-climbing effect' in a LiNbO3:Fe crystalsheet was first observed by us in 1987. We foundthat when an e-polarized He-Ne laser light beam wasincident normal to a LiNbO3:Fe crystal sheet with alarge diameter, D, light spot on it, the scattered lightclimbed up and down along the ferroelectric polaraxis, C, of the crystal, and 90'-scattered light at boththe positive and negative ends of the C-axis outsidethe sheet was strengthened gradually. The mecha-nism for light climbing was proposed by us as follows:when the diameter, D, of the light spot on the sheetwas approximately equivalent to or larger than thecrystal sheet thickness, d, scattered light, which metthe requirement of the internal total reflection, wouldbe amplified in the region of beam coupling and climbin the sheet. Climbing light also caused the photore-fractive effect, which made the climbing scatteredlight deviate from its original direction. As a result,the deviated light went out from the crystal asapproximate 90'-scattered light, the power of whichdepended greatly on that of climbing light. We alsoproved that climbing light was responsible for anadditional energy loss of unknown origin that wasobserved in Ref. 2.

At that time we thought that only under thecondition of D/d > 4 did the light-climbing effectexist; recently, however, we observed this phenom-enon under the condition of D d 2 mm, andwhite-black, equidistant fringes could been seen inthe region of light climbing in the crystal. Thereflection angle calculated from the spacing betweenthe fringes fit well with the internal total calculatedfrom the refraction theory. The experiment directly

The authors are with the Department of Physics, NankaiUniversity, Tianjin 300071, China.

Received 3 September 1992; revision received 10 June 1993.0003-6935/94/060997-03$06.00/0.© 1994 Optical Society of America.

proved the mechanism of the light-climbing effect putforward by us in Ref. 1.

Through observations of the light-climbing effectin crystals of different thicknesses with differentdiameters of incident light spots on them, we foundthat under different conditions the outcome of thecompetition between light climbing and forward scat-tering was obviously different, and the transmittedlight of the incident beam was limited to differentextents. The experimental results illustrated thatthe angle distribution of scattered light might bedetermined by the ratio of D/d.

2. Experiment and Results

A. Reflection Angle of Climbing Light

The experimental equipment is shown in Fig. 1, inwhich e-polarized light was incident upon an X- orY-cut LiNbO3:Fe sheet S; the lens M was used tochange the diameter, D, of the incident light spotupon the crystal ( = 632.8 nm). When D = 2 mmand the sheet thickness d = 2 mm, the spacingbetween fringes in the crystal was equal to 1.88 mm,as shown in Fig. 2, so we found that the reflectionangle a. = arctan(Al/2d) 25.20, which fit well withthe internal total reflection angle i = arcsin(n'/n) 25.9, where n' = 1 and n = 2.286.

In Ref. 3, we proposed a modified model combiningthe steady-state two-wave coupling theory and themoving grating mechanism and concluded that be-cause of the pulsation of the intensities of the scat-tered beams from the crystal, which is caused by themoving gratings relating to the trap-recharging waves,light-induced scattering with an unwanted side ef-fect4 in the LiNbO3:Fe crystal, which is different fromscattering with the fanning effect in BaTiO3, SBN,etc., is determined by the absolute value of thesteady-state two-wave coupling coefficient IF I of scat-tering light intensity per unit solid angle in a specificdirection with the incident light intensity; and is

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I C. 60I

J"S

Fig. 1. Experimental arrangement: L, He-Ne laser beam; M,lens; S, sheet sample; P, power meter. C, C-axis.

expressed as

2 ,rrreff kBT KnX cos(/2) e + (KK cos ()

for the extraordinary polarization, where the effectiveelectro-optic coefficient, reff, is given as

reff = no2ne2 r5l sin(0/2)sin 0 + n 4r33 cos(0/2)cos 0 (2)

for the incident light normal to the direction of theC-axis of the crystal; 0 is the angle between thescattered light beam and the incident light beam; andkBT/e is the thermal energy per charge; the Debyewave number, K0, is given by

Ko = e(NC/eEokBT)1/2 (3)

and depends on the photorefractive charge density,Ne, along with the dc dielectric constant EEO[E = Ellsin2(0/2) + E3 3 cos2(0/2)] in the direction of the grat-ing wave vector, K [K = (4irn/X)sin(0/2)]; n is theeffective refractive index.

Here we calculated the absolute value of the steady-state two-wave coupling coefficient I F I in our samplefrom Eqs. (1)-(3) and the calculated result for thee-polarized light incident normal to the direction ofthe C-axis of the crystal was shown in Fig. 3, in whichwe know that large coupling coefficients lie within therange of ±23° 350; they are larger than 5 cm-'.So scattered light that met the requirement of theinternal reflection could be amplified effectively andclimbed in the sheet.

(a) (b)

Fig. 2. (a) Light climbing in the z-x plane, as shown in Fig. 1, (b)photograph of light climbing in the crystal in the y-z plane whenD = 2 mm and d = 2 mm.

50

, 40rI

f 30

" 20

10

0-90-60-30 0 30 60 90

0 (deg)Fig. 3. Absolute value of the steady-state two-wave couplingcoefficient I versus the angle 0 between the weak scattered lightbeam and the incident light beam, which is normal to the crystal,where Ne 1016 cm- 3 ; r 5 l and r3 3 are 28 and 30.8 pm/V,respectively; no and ne are 2.286 and 2.196, respectively; and E

and e33 are 44 and 29, respectively.

These results supported the light-climbing mecha-nism put forward by us in Ref. 1.

B. Competition between Light Climbing and ForwardSmall-Angle Scattering

We obtained different results of the competitionbetween light climbing and forward small-angle scat-tering under conditions of different ratios of D/d atthe constant incident light power. The results weredivided into four categories:

1. When D d < 10 pum, no light climbing, 900scattering, and forward small-angle scattering tookplace.

2. When D > d> 0.1 mm, light climbing and 900scattering were dominant; forward small-angle scat-tering was hardly observed.

3. When D > d > 0.5 mm, light climbing, 900scattering, and forward small-angle scattering alloccurred, and they competed with each other strongly.

4. When D < d > 0.5 mm, forward small-anglescattering was dominant; light climbing and 90°scattering were hardly observed.

C. Limiting the Transmitted Light Power of theIncident Beam

Light climbing and 90° scattering became stronger,and the transmitted light power of the incident beamwas limited more seriously, when the incident lightpower I, became bigger and the diameter D of lightspots on the crystal became larger, as shown in Fig. 4.

3. Discussion

Noise phase gratings in the crystal, through whichscattered light is amplified by the incident light, playan important role in the formation of light climbing,90° scattering, and forward small-angle scattering, so

998 APPLIED OPTICS / Vol. 33, No. 6 / 20 February 1994

It(mW)L 1

18

9

0

18lt(M'V)

9

0

D 10

(a)

0 10(b)

Fig. 4. (a) Time dependence of the tramdifferent incident powers (spot diameter D =3, and 4, respectively, correspond to incidenand 1 mW. (b) Time dependence of the tr,several different spot diameters (incidentcurves 1-3 correspond to D = 0.8 mm, D =respectively.

d, because it goes many times between the front andback crystal faces in the beam-coupling region, solight climbing is absolutely dominant among all thescattering light. When d 2 0.5 mm, the two-wavecoupling length of the forward-scattered light withthe incident light increases with an increase of thecrystal thickness, so the strong forward small-anglescattered light at the front face is easy to amplify withthe long coupling length L, and a rather large fraction

20 t(m*n) of incident light energy is brought away by forwardsmall-angle scattered light to make the preponder-ance of light climbing less obvious. When D isreduced to less than d, the coupling length of theclimbing light with the incident light is less than thecoupling length of forward small-angle scattered light

____________1 with the incident light. So light scattered in thedirection satisfying the internal total reflection, which

2 is very weak at crystal front face, is very difficult to2___ amplify. In this case, forward small-angle scattered3 light is in a dominant position.

If the incident light power is so small that most of______________ , the light energy is absorbed by the sample itself or D

20 t(min) is so small that climbing light cannot be amplifiedenough, the light cannot climb for a long distance in

,mitted power, It, for the crystal. Therefore the transmitted light power= 3 mm). Curves 1, 2, of the incident beam obviously will not be limited.t powers of 32, 22, 11, Only when incident light power is large enough, D >>msmitted power It for d, and samples are much thinner than 0.5 mm, canpower is 32 mW), the incident light energy be converted to climbing light1.5 mm, D = 3.0 mm, and be limited effectively.

all these effects must satisfy the same requirement ofthe light-scattering specklon size effect.5 That is tosay the diameter, D, of the incident light spots on thecrystal must be larger than the fringe spacing, A, ofthe noise phase grating (A 101 [um). If this sizeeffect is not satisfied, none of light climbing, 900scattering, and forward small-angle scattering willoccur, as the experimental result in Subsection 2.B,category 1, shows.

When the size effect is satisfied, as in Subsection2.B, categories 2-4, scattered light in the direction inwhich F is the largest and its path through theilluminated region is longest will be amplified mosteffectively. When D > d 2 0.1 mm, the light beamsatisfying the condition of total reflection travels for alonger distance in the two-wave coupling region thanthe forward small-angle scattered light, and the lightbeam will travel much longer, especially when D >>

This work was supported by a grant for a keyresearch project in the Climbing Program from theState Science and Technology Commission of China.

References

1. G. Zhang, Y. Wu, S. Liu, and J. Wang, "Light-climbing effect inthin LiNbO3:Fe wafers," Chin. Phys. Lasers 14, 606-609(1987).

2. P. A. Augustov, M. J. Reinfelde, and K. K. Shvarts, "Photorefrac-tion and anisotropic light scattering in LiNbO3:Fe crystals,"Appl. Phys. A 29, 169-172 (1982).

3. Y. Wu, J. Xu, S. Liu, and G. Zhang, "The model for the spatialdistribution of light-induced scattering in LiNbO3:Fe crystal,"submitted to J. Opt. Soc. Am. B.

4. J. Marotz, K. H. Ringhofer, R. A. Rupp, and S. Treichel,"Light-induced scattering in photorefractive crystals," IEEE J.Quantum Electron. QE-22, 1376-1382 (1986).

5. G. Zhang, Q.-X. Li, P.-P. Ho, S. Liu, Z. K. Wu, and R. R. Alfano,"Dependence of specklon size on the laser beam size viaphoto-induced light scattering in LiNbO3:Fe," Appl. Opt. 25,2955-2959 (1986).

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