High sensitive measurements of absorption coefficient and optical nonlinearities

Optics Communications 261 (2006) 158–162 www.elsevier.com/locate/optcom

High sensitive measurements of absorption coefficient and optical nonlinearities Debabrata Goswami

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Department of Chemistry, Indian Institute of Technology, SL-216, IITK, Kanpur 208016, India Received 21 August 2005; accepted 23 November 2005

Abstract Accurate knowledge of absorption coefficient of a sample is a prerequisite for measuring the third-order optical nonlinearity of materials, which can be a serious limitation for unknown samples. We introduce a method, which measures both the absorption coefficient and the third-order optical nonlinearity of materials with high sensitivity in a single experimental arrangement. We use a dual-beam pump–probe experiment and conventional single-beam z-scan under different conditions to achieve this goal with communication relevant wavelength. We also demonstrate a counterintuitive coupling of the non-interacting probe-beam with the pump-beam in pump– probe z-scan experiment.  2005 Elsevier B.V. All rights reserved. PACS: 42.65.k; 42.65.Jx

1. Introduction Development of high power laser sources has motivated an extensive research in the study of nonlinear optical properties and optical limiting behavior of materials. There exits a continued effort in making sensitive measurements on absorption coefficient and nonlinear coefficients, however, most of the experimental techniques are focused on measuring one or the other of these two important parameters. A variety of interferometric methods [1,2], degenerate four wave mixing [3], nearly degenerate three wave mixing [4] and beam distortion measurement [5], have been used for measuring the nonlinear refractive index. One of the most important techniques to measure nonlinear refractive index was shown by Sheik Bahaei et al. [6] This technique is simple and versatile yet is highly sensitive. However, an accurate knowledge of absorption coefficient (a0) is necessary for the use of this technique, which is a serious limitation for unknown samples. An easy way to measure a0 is to

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0030-4018/$ - see front matter  2005 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2005.11.051

use the Beer’s law [7,8], which operates in the linear absorption regime and has limited sensitivity. More sensitive methods have been developed, of which the technique [9–15] using thermal lens (TL) effect is perhaps the simplest and the most effective. In this method, a lens focuses the laser beam into the sample resulting in a temperature gradient, which in turn produces a spatial gradient in refractive index. The relative change in transmittance of the laser beam can then be measured, after passing through an aperture, with the help of a detector [9–11]. Shen et al. [12–14] introduced a pump–probe laser scheme under mode-mismatched and mode-matched conditions to improve sensitivity of the TL method. More recently, Marcano et al. [15] have used this method to measure the absorption coefficient of water with high accuracy. A single experimental technique to measure both the parameters, however, is yet to emerge, which could be of significance in the study of new materials. In this paper, we introduce a single experimental technique to measure both the parameters. Our aim has been to measure the absorption coefficient (a0) as well as the real and imaginary parts of third-order optical nonlinearity (v(3)) with high sensitivity in a transparent sample using a single

D. Goswami / Optics Communications 261 (2006) 158–162

Our experimental scheme (Fig. 1) involves a sub-100 fs mode-locked Er:doped fiber laser (IMRA Inc.) operating at a repetition rate of 50 MHz and provides the fundamental (1560 nm) and its second-harmonic wavelength (780 nm) simultaneously as a single output. Either we use both the wavelengths from the laser simultaneously or separate the two copropagating beams with the help of a dichroic beamsplitter and use each of them independently. We scan the sample through the focal point of a 75 cm focusing lens and this allows a smooth intensity scan for either/or both of the wavelengths. The laser has a Gaussian beam-waist of 2.77 mm (which is measured by integrating the residual intensity that is measured by translating a knife edge across the beam). This results in the maximum intensity of 0.56 and 2.8 MW/cm2 for the 1560 and 780 nm wavelengths, respectively at the focal point. Care has been taken to make sure that there is no effect of the laser beams on the cuvette alone by conducting an empty cuvette experiment. A silicon photodetector (Thorlab: DET210) is used for the 780 nm beam detection, while an InGaAs photodetector (Acton Research) is used for the 1560 nm beam detection. The sample is double distilled water in a 1.6 mm thick BK7-glass cuvette. To measure the real and imaginary parts of the third-order nonlinear susceptibility in water, we filtered one of the two wavelengths and used each of them independently in the z-scan geometry. We find that the 1560 nm beam produces changes in the relative transmission of the laser beam at different intensities as the sample is scanned through the lens focus depending whether we collect all the light (Fig. 2) or only central 40% of the transmitted light (Fig. 3). However, the 780 nm beam does not produce any effect even at our peak powers at the focal point of the laser as is expected from negligible absorption at 780 nm (Fig. 4). This enables us to use the 780 nm wavelength as the non-interacting probe-beam for the subsequent dual-beam experiments, where we use both the

Fig. 1. Schematic of typical z-scan experimental setup, where a sample (S) is scanned across a laser beam that is being focused through a lens of focal length (L1) and is collected through an aperture (A) and a lens of focal length (L2) into the detector (D).

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Normalized Transmittance

2. Experiment

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z (cm) Fig. 2. Measured z-scan of a 16 mm thick double distilled water using 95 fs pulses at k = 1560 nm (diamond) and theoretical fit (solid line) for fully open aperture (experimentally measured transmittance is normalized to unity).

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experimental setup. We also show how mid-IR absorption in water (at 1560 nm) manifests itself as a minute nonlinear absorption change in the near-IR transmission window (at 780 nm). Such high sensitive experiments have become possible due to the ultrahigh sensitivity provided by a stable ultrafast laser operating at both the above wavelengths.

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z (cm) Fig. 3. Measured z-scan of a 16 mm thick double distilled water using 95 fs pulses at k = 1560 nm (diamond) and theoretical fit (solid line) for 40% closed aperture (experimentally measured transmittance is normalized to unity).

wavelengths from the laser simultaneously to measure a0 (Fig. 5). Since our 75 cm lens focuses the 780 nm probebeam to its minimal spot size position 0.4 mm ahead of the pump-beam of 1560 nm, this is a mode-mismatched pump–probe experiment. However, the focal spot size of 9 lm for 780 nm is 15 lm smaller than the corresponding 1560 nm spot size at its own focus and the Rayleigh range for 780 nm is 0.32 mm and for 1560 mm it is 1.15 mm. Thus, the 780 nm laser volume is always confined within the 1560 nm laser beam volume when both the beams are used simultaneously from the laser and can act as an effective probe. Our extremely sensitive experimental measure-

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D. Goswami / Optics Communications 261 (2006) 158–162 0.0008 0.07

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Wavelength (nm) Fig. 4. Water spectra covering the 780 and 1560 nm range of wavelengths as a semi-log plot that shows the absorption differences between the two marked wavelengths.

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z (cm) Fig. 5. Measured z-scan transmittance of 80 fs pulses of k = 780 nm as a probe through a 16 mm thick double distilled water being irradiated with 95 fs of k = 1560 nm as pump (diamond) and theoretical fit (solid line) in 40% closed aperture (experimentally measured transmittance is normalized to unity).

ment schemes show that we are able to detect the minute effects of the pump-beam on the probe-beam when they co-propagate in the medium (Fig. 6). 3. Results and discussion For nonlinear materials, the index of refraction n is expressed in terms of nonlinear n2 or c through the relation 2 [16]: n ¼ n0 þ n22 jEj ¼ n0 þ cI, where n0 is the linear index of refraction, E is the peak electric field (cgs) and I (MKS) is the intensity of the laser beam inside the sample. n2 and c are related to each other as: n2 ðesuÞ

Fig. 6. Measured z-scan transmittance of 80 fs pulses of k = 780 nm as a probe through a 16 mm thick double distilled water being irradiated with 95 fs of k = 1560 nm as pump (raw transmittance data is presented to illustrate sensitivity of our measurements). We replot the open aperture data for 1560 nm alone from Fig. 2 on this same plot to show that both essentially have same features except their two orders of magnitude difference in their signal levels and hence the same fit would suffice.

cn0 c ðm2 =W Þ, where c (m/s) is the speed of light in vac¼ 40p uum. The third-order optical susceptibility is considered ð3Þ ð3Þ to be a complex quantity: vð3Þ ¼ vR þ vI . The real and imaginary parts are related to the c and b, respectively [17], where b is the nonlinear absorption coefficient and is defined as a(I) = a0 + bI. The typical z-scan data with fully open aperture is insensitive to nonlinear refraction; therefore, the data is expected to be symmetric with respect to focus. For materials with multiphoton absorption, there is a minimum transmittance in focus (valley) and for saturable absorber samples, there is maximum transmittance in the focus (peak) [6]. Multiphoton absorption suppress the peak and enhance the valley, while saturation produce the opposite effect [6,9]. Our sample shows a peak in the open aperture data (Fig. 2) due to saturation in absorption at 1560 nm. Saturation leads to thermal lensing as is seen in the pump–probe data of Fig. 5 with 40% closed aperture collection of 780 nm probe-beam. Fig. 5 represents the thermal lens effect of the pump-beam resulting in a temperature gradient, which in turn produces a spatial gradient in refractive index which is depicted in the relative change in transmittance of the probe-beam. Such thermal lensing (TL) effect can be used to determine the absorption coefficient (a0) of the sample at the pump wavelength very accurately [15]. We use saturation absorption relations to calculate the unknown parameters as discussed below. Shen et al. [12–14] have derived an expression for the TL signal using diffraction approximation for Gaussian beams in steady state case as:   2 h 2mV 1 SðzÞ ¼ 1  tan  1; ð1Þ 2 1 þ 2m þ V 2

where

D. Goswami / Optics Communications 261 (2006) 158–162 2

m ¼ ðxp =xo Þ ; 2

V ¼ ðz  ap Þ=zp þ ½ðz  ap Þ þ

z2p =½zp ðL

xp;o ¼ bp;o ½1 þ ðz  ap;o Þ2 =z2p;o 1=2 ;

 zÞ;

ð2Þ

h ¼ P o a0 lðds=dT Þ=jkp ; z is sample position with respect to the focal point, ap, ao, zp, zo and bp, bo, are position of the waists, the confocal parameters and the beam radius for the probe- and pump-beams, respectively. kp is the wavelength of the probe-beam, j is thermal conductivity coefficient of the sample. L is the detector position, Po is the total power of the pump-beam and l is the sample thickness. The value of a0 is obtained from the closed aperture data. The solid line in the Fig. 5 is the result of a theoretical fit to Eq. (1). This fit gives the value of phase shift, h = 9.957 ± 0.001, which when substituted in Eq. (2) with the parameters [18] ds/dT = 9.1 · 105 K1 and j = 0.598 · 102 WK/cm for pure water, we get the calculated value for a0 as 10.6327 ± 0.01 cm1 for the 1560 nm beam. Our experimental results discussed above also enables us to determine the nonlinear absorption coefficients of water. We did the scan in fully open aperture case with 1560 nm wavelength. The result is shown in Fig. 2. The solid line is the theoretical fit, which is derived by solving the differential equation [19] for the transmitted light through a thin sample of thickness l T ðzÞ ¼ g þ

bI 0 l ; ð1 þ z2 =z20 Þ

ð3Þ

where z0 ¼ kw20 =2, k and w0 are the wave vector and the minimum spot size in the focal point, respectively, while g and b are the fitting parameters. The best fit gives the value of b = 2.58 ± 0.01 cm/GW. Thus, a0 and b value of the sample at 1560 nm wavelength are known. Next, we collected z-scan data by closing 40% of the aperture. The result is shown in Fig. 3. The valley-peak structure suggests a self-focusing effect inside the sample. The Ryleigh range (Z(r)) for 1560 mm is 1.15 mm. From Fig. 3, valley to peak separation at 1560 nm is 4 mm, which is 3.4 · Z(r) indicating that all the effects at 1560 nm are thermal in nature [20]. So we use the Gaussian decomposition method to fit this closed aperture z-scan data quite convincingly (Fig. 3, solid line fit to the raw data), and we obtain c = (1.57 ± 0.01) · 103 cm2/GW, which is proportional to n2 = (4.9 ± 0.1) · 1012 esu. Thus, a0, b and n2 values of the water sample at 1560 nm wavelength are determined. As mentioned earlier, when only the 780 nm beam passes through the sample, there is a constant signal and we do not see any peak or valley. The absorption coefficient of water at 780 nm is so small that at our intensities, there is no saturation effect. However, when 1560 nm beam is simultaneously present, it affects the propagation of the 780 nm beam. As the 1560 nm beam starts to saturate the sample at its focal point, the 780 nm beam also experiences a saturated environment, whereby its transmittance increases at

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its focal point (Fig. 6). This statement is further reinforced by the fact that the open-aperture plot of 1560 nm beam alone from Fig. 2 essentially has the same behavior as is evident when plotted along with the results from 780 nm results in Fig. 6. Essentially, as the 1560 nm beam starts to saturate the sample at its focal point, the 780 nm beam also experiences a saturated environment, whereby its transmittance increases at its focal point and shows an identical transmission behavior although the signal level is two orders of magnitude lower. Such a result indicates the thermal capacity of water that can affect the spectroscopic behavior of water. Thus, this technique can be used to measure the nonlinear absorption coefficient of materials, whose linear absorption coefficients are extremely small. We can use the same fitting of the experimental data using a theoretical expression given by Eq. (3) to result in the expected value of b = 2.58 ± 0.05 cm/GW as was found for the 1560 nm data. The higher value of error-bar is a manifestation of the extremely small signal value. We have been able to estimate both the linear absorption coefficient as well as the real and imaginary parts of thirdorder optical susceptibility of water with the pump–probe technique and the z-scan technique in a single experimental setup. This indicates the very small induced effect in the probe-beam of 780 nm by the presence of the pump-beam of 1560 nm causing thermal lens. However, the sensitivity of the technique is good enough to reproduce the expected b value as determined from the independent 1560 nm experiments. Thus, this technique can measure the nonlinear absorption coefficient of materials at wavelengths with negligible linear absorption. Such a technique is not limited to the choice of either of the wavelengths or on the material concerned and as such can be treated as a completely generic technique of pump–probe femtosecond z-scan technique. Acknowledgements The author thanks the Ministry of Information Technology and the Department of Science and Technology, Govt. of India and the International SRF Program of the Wellcome Trust (UK) for funding the research results presented here. References [1] M.J. Weber, D. Milam, W.L. Smith, Opt. Eng. 17 (1978) 463. [2] M.J. Moran, C.Y. She, R.L. Carman, IEEE J. Quantum Electron. QE-11 (1975) 259. [3] S.R. Fribrg, P.W. Smith, IEEE J. Quantum Electron. QE-23 (1987) 2089. [4] R. Adair, L.L. Chase, S.A. Payne, J. Opt. Soc. Am. B 4 (1987) 875. [5] W.E. Williams, M.J. Soileau, E.W. Van Stryland, Opt. Commun. 50 (1984) 256. [6] M. Sheik-Bahaei, A.A. Said, T. Wei, D.J. Hagan, E.W. Van Stryland, IEEE J. Quantum Electron. 26 (1990) 760. [7] G.T. Fraser, A.S. Pine, W.J. Lafferty, R.E. Miller, J. Chem. Phys. 87 (1987) 1502. [8] H. Petek, D.J. Nesbitt, D.C. Darwin, C.B. Moore, J. Chem. Phys. 86 (1987) 1172.

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