Jan 15, 1996 - A. Marcano O. Centro de Fisica, Instituto Venezolano de Investigaciones Cientificas, Apartado 21827, Caracas 1020 A, Venezuela. H. Maillotte ...
January 15, 1996 / Vol. 21, No. 2 / OPTICS LETTERS
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Picosecond nonlinear refraction measurement in single-beam open Z scan by charge-coupled device image processing A. Marcano O. Centro de Fisica, Instituto Venezolano de Investigaciones Cientificas, Apartado 21827, Caracas 1020 A, Venezuela
H. Maillotte, D. Gindre, and D. M´etin Laboratoire d’ Optique P. M. Duffieux, Unite´ de Recheche Associ´ee Centre National de la Recherche Scientifique 214, Universite´ de Franche-Comte, ´ 16 route de Gray, 25030 Besan¸ con Cedex, France Received April 24, 1995 We propose a picosecond single-beam open Z-scan experiment in which the usual apertured detection scheme is replaced by a two-dimensional single-shot CCD camera. This enables us to extract the two-dimensional transverse modifications of the whole far-f ield pattern that are due to nonlinear refraction as well as to measure the induced nonlinear phase shift with increased sensitivity compared with that of the conventional Z scan. 1996 Optical Society of America
The Z-scan method1,2 is a highly sensitive, simple, and versatile technique for measuring the sign and the magnitude of light-induced variations of the refractive index of any type of material and of other x s3d nonlinearities (e.g., two-photon absorption). The technique relies on the conversion of phase distortion of a beam focused in a nonlinear sample into amplitude variations in the far field as the sample is scanned axially around the focal region. The sensitivity of the method,2 typically ly300, is restricted mainly by the irradiance f luctuations of the low-repetition-rate laser systems that are generally used. However, some attempts have been made to enhance this sensitivity.3,4 The recent demonstration of the so-called eclipsing Z scan5 has afforded spectacular improvement of the sensitivity, namely, ly10,000. We present another extension of the Z-scan technique in which the usual circular- or annularapertured far-f ield detection scheme is replaced by a two-dimensional single-shot CCD camera. As a first step and to calibrate the method, we studied pure refractive nonlinearity [Re x s3d fi 0 and Im x s3d > 0] by choosing a good lossless Kerr medium, namely, carbon disulf ide (CS2). We performed an open single-beam Z scan, which is usually useless for measuring pure nonlinear refractions. However, here one can extract the two-dimensional transverse modif ications of the whole far-f ield pattern that is due to the Kerr-induced nonlinear lens by processing all the pixels of the camera. For a given position of the cell the induced nonlinear phase shift DfNL 2pgLI yl is then measured with an increased sensitivity compared with that of the conventional Z scan, where g is the nonlinear coeff icient of the refractive index, L is the length of the nonlinear sample, I is the pulse intensity, and l is the radiation wavelength in vacuum. The principles of the single-beam Z-scan method have been described in Refs. 1 and 2. A schematic of our experiment is shown in Fig. 1. The linearly polarized TEM00 laser beam at l 1.06 mm comes 0146-9592/96/020101-03$6.00/0
from a mode-locked Nd:YAG laser. The Gaussian pulse duration (50 ps FWHM) is the reciprocal of its spectral bandwidth. The beam energy is properly adjusted by a half-wave plate and a Glan polarizer. Then the beam is focused by lens L 1 of focal distance f 250 mm. The waist radius at the focal plane (z 0) is v0 65 mm, corresponding to a Rayleigh range z0 pv0 2 yl ø 12.5 mm. The CS2 cell of good optical quality, movable along the z axis of the focused beam, is 2 mm thick, i.e., approximately one sixth of the Rayleigh range. The incident energy is measured immediately before the cell by a calibrated energy meter. A two-dimensional CCD camera (512 3 512 pixels) operating in single-shot mode detects the farfield pattern. Lens L2 between the CS2 cell and the camera serves for adjusting the size of the pattern to the size of the sensor (8.7 mm 3 5.6 mm) while respecting the far-f ield approximation (d ,, D and v0 2 ylD ,, 1). The pattern is coded on 8 bits (256 gray levels) for further processing. For every z position of the CS2 cell this detection setup is therefore aimed at measuring the Kerr-induced variations of the far-f ield intensity in a systematic way, i.e., one measurement for one pulse issued from the laser. Also, a statistical treatment is performed to account for the pulse-to-pulse energy f luctuations. For this purpose a
Fig. 1. Experimental setup: ly2, half-wave plate; P, Glan polarizer; M’s, mirrors; B.S., beam-splitter; L 1, L 2, converging lenses; O.D., neutral-density filter. 1996 Optical Society of America
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OPTICS LETTERS / Vol. 21, No. 2 / January 15, 1996
small part E0 of the incident energy is sampled by a beam splitter and directed toward the camera, which illuminates a small area of the CCD sensor without interfering with the previous far-field pattern. Figure 2 (displayed without this energy sample) illustrates the processing. The top-left photograph (marked Ref.) is an acquisition of the far-f ield pattern of the reference beam, i.e., when the CS2 cell is far away from the beam waist so that nonlinear refraction is negligible, whatever the intensity. This image is chosen after a straightforward statistical estimation of the energy f luctuations, so it actually can act as the reference for the Z scan. Then a signal image is chosen for every z position only if its calculated energy E0 exp lies within a small range (namely 1– 5%) around the energy E0 ref of the reference, with the background noise f luctuations on the CCD sensor also taken into account. The top-right photograph (Signal) in Fig. 2 is an example of the far-f ield pattern when the CS2 cell is after (z . 0) but close to the beam waist so that nonlinear refraction is induced. This image exhibits, but with very little contrast, a radially patterning effect that is due to nonlinear refraction. The bottom-left photograph (d1) of Fig. 2 has an intensity distribution given by Ii, j
d1
Maxs0; Ii, j
ref
2 Ii, j d , s
Ii, j Ii, j
exp
(2)
The superscripts ref , s, and exp refer to the reference, corrected signal, and actual signal images, respectively, and Ii, j is the brightness of the jth pixel of line i. The bottom-right photograph (d2) has an intensity distribution given by Ii, j d2 Maxs0; Ii, j s 2 Ii, j ref d .
(3)
The shapes of d1 and d2 evolve during the Z scan, as shown in Fig. 3(a). Photographs 1–4 correspond to successive positions of the cell as it gets nearer the beam waist (z , 0), whereas the cell moves away from the waist in photographs 6–8 (z . 0). Their main qualitative features can easily be explained by the schematic drawing of Fig. 3(b), assuming an aberrationless focusing thin lens. For z , 0 the stronger focusing by the Kerr-induced lens gives rise hereafter to a signal-beam divergence higher than the reference one. The subtraction (d1) is of circular shape, whereas d2 exhibits a ring structure. For z . 0 the focusing action of the Kerr lens concentrates the signal beam with respect to the reference beam. The subtraction (d1) is a ring of smaller diameter and higher brightness than the one mentioned above, and d2 exhibits a smaller and brighter circle plus a weak ring. We attribute this ring, more easily observable when the beam concentrates (z . 0), to aberrations owing to the difference between a perfect parabolic imaging lens and the actual Kerr lens created by a Gaussian prof ile.6,7 The strongest nonlinear refraction occurs when the CS2 cell is located at the beam waist (z 0). Photograph 5 of Fig. 3(a) corresponds approxi-
i, j
X∑
∏
Ii, j s szd
i, j
X∑
∏
Ii, j szlin d s
i, j
3 X∑
∏
Ii, j szlin d 1 Ii, j szlin d d1
d2
i, j
XÇ
ref
E0 . 3 E0 exp
Sszd
(1)
where we applied the correction factor s
mately to this situation. The accurate description of the mechanism for this position is diff icult because the intensity and hence the aberrations are the highest. Moreover, photograph 5 shows a maximum energy for the subtraction (d1), whereas d2 exhibits almost nothing but the aberrant ring mentioned above. These features clearly indicate that the beam energy diminishes after the beam crosses the CS2 cell. Further observations revealed effectively a self-focusing of the beam for z > 0. Starting from the d1 and d2 subtractions, we then def ined a total signal that can express the Kerrinduced phase shift and hence the nonlinear coeff icient g of the refractive index. For each z position this total normalized signal Sszd is def ined by ∏ X∑ Ii, j d1 szd 1 Ii, j d2 szd
i, j
Ii, j s szd 2 Ii, j ref X∑
Ii, j s szd
∏
i, j
≥ ¥∏ Ii, j s zlin
Ç
X∑ XÇ
i, j
Ii, j s szlin d 2 Ii, j ref
Ç.
i, j
(4) The second factor in each term of Eq. (4) is a normalization factor that we added to have Sszd 1 for a negligible nonlinearity, i.e., when the position zlin of the cell is far away from the beam waist. Figure 4 shows the experimental data computed during the Z scan with a beam energy of 9 mJ , resulting in a peak intensity of ,5 GWycm2 in the focus. The stars give the signal Sszd, calculated from Eq. (4). The signal increases as the cell gets near z 0 and reaches maximum values around this position. To study the evolution of Sszd versus the nonlinear phase shift we measured the experimental beam
Fig. 2. Far-f ield acquistions by the CCD camera. Top left, reference far-field pattern; top right, signal far-field pattern; bottom left, first subtraction (d1 Ref. 2 Signal); bottom right, second subtraction (d2 Signal 2 Ref.).
January 15, 1996 / Vol. 21, No. 2 / OPTICS LETTERS
Fig. 3. (a) Evolution of d1 and d2 versus z during the Z scan. ( b) Qualitative interpretation assuming an aberrationless transformation of the beam profile.
Fig. 4. Experimental Z-scan-normalized data (left scale): stars, total signal Sszd; crosses, apertured-Z-scan curve with linear transmittance equal to 0.035; dashed curve, energy Eszd; solid curve (right scale), plot of 1yr 2 versus z.
radius r (FWHM) versus z. The plot of the experimental (1yr 2 ) values versus z is shown as a solid curve in Fig. 4. The good overall proportionality between Sszd and s1yr 2 dszd is clearly exhibited, and a least-squares fit gives Sszd 77 3 10210 s1yr 2 dszd for these plots, with 1yr 2 in inverse square meters. This shows that Sszd varies linearly with the intensity of the beam and hence with the nonlinear phase shift DfNL . This result is consistent with preliminary calculations performed with the Gaussian decomposition method. Assuming that the laser pulse is spatially and temporally Gaussian and using the commonly adopted value of g 3.5 3 10218 m2 yW for CS2, we found, for 9 mJ , Sszd > 3DfNL szd. The proportionality still holds for different beam energies. The proposed method also gives all the information needed for performing a normal or an eclipsing Z scan. For
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this purpose we numerically def ined circular or annular apertures of various diameters and widths on the reference and signal far-f ield patterns. The crosses in Fig. 4 show an example of an apertured Z-scan curve processed from the same far-f ield patterns as for curve Sszd. In the usual Z scan,2 the peak nonlinear phase shift DfNL s0d is given by the difference between peak and valley transmittances, according to the relation DTpv 0.406s1 2 ST d0.25 3 DfNL s0d, ST being the linear transmittance.2 The numerical diaphragm is a circle for which ST 0.035. The shape of the curve is typical of a positive g. We found DTpv 0.89, giving DfNL s0d 2.21 rad. We carefully compared the signal-to-noise ratios for both techniques. For this purpose we measured the Z-scan signal by the procedure def ined by Eq. (4) but performing the summation only over the pixels of the aperture. We found that the sensitivity of the present measurement Sszd with respect to the nonlinear phase shift is 7–8 times larger than that of the usual Z-scan performed with the numerical aperture. The dashed curve in Fig. 4 is a plot of the normalized energy Eszd of the signal far-field pattern. This curve shows how the statistical treatment smooths the energy f luctuations. It also exhibits the energy decrease near the waist discussed above. Thus the proposed processing can easily detect self-focusing thresholds. As the described procedure gives a calibration of the proposed method by studying nonlinear refraction in a good standard material such as CS2, it henceforth can be used to yield measurements of the nonlinear coeff icient g of other materials. The higher sensitivity could allow appropriately for measurement of the nonlinear susceptibility of thin films. However, the technique still remains to be validated in the presence of nonlinear absorption. Furthermore, if we wish to take full advantage of the method a further step would consist in a precise analysis of the nonlinear far-f ield prof ile variations to determine the susceptibility accurately. The authors thank the Consejo Nacional Tecnologicas de Investigaciones Cientif icas y Technicas, Venezuela, and the Centre National de la Recherche Scientif iqueyDirection des Relations Internationales, France, for financial support. References 1. M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, Opt. Lett. 14, 955 (1989). 2. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990). 3. J. A. Hermann and P. B. Chapple, J. Mod. Opt. 38, 1035 (1991). 4. W. Zhao and P. Palffy-Muhoray, Appl. Phys. Lett. 63, 1613 (1993). 5. T. Xia, D. J. Hagan, M. Sheik-Bahae, and E. W. Van Stryland, Opt. Lett. 19, 317 (1994). 6. A. Marcano O., G. Da Costa, and J. A. Castillo, Opt. Eng. 32, 1125 (1993). 7. A. Marcano O. and J. Castillo, Pure Appl. Opt. 3, 339 (1994).
