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The polarization state of the white light produced by a femtosecond laser pulse through a water cell is investigated. The depolarization of the white light was found to be induced by magnification of the polarization perturbation in the incident light which is caused by the focus lens. Cross-phase modulation (XPM) of the third order nonlinear polarization is proposed as the depolarization mechanism.
©2010 Optical Society of America
1. Introduction
The interaction of an intense ultrashort optics pulse with transparent media is strongly nonlinear, and can cause intense white light generation. The white light is widely observed in a variety of materials including gases [1,2], liquids [3], and solids [4]. It is commonly assumed to be induced by the combined effects of several physical mechanisms including self-phase modulation, self-steepening, space-time focusing, plasma generated by ionization of the medium, four-wave mixing and phase matching “scattering” [5–13]. Different mechanisms generate different components of the white light spectrum at certain positions along the propagation pathway of the pulse [9,10]. Self-steepening and ionization can cause the sharp trailing edge of the pulse, and add new frequencies on the blue side of the spectrum. Phase matching “scattering” process contributes to angle-dependent spectrums [12,13]. An initial pulse centered at 800 nm can spread over the whole visible spectrum [11].
Because of its special properties, white light has many applications including femtosecond time-resolved spectroscopy [14], optical pulse compression for generation of ultrashort pulses [15], and as seed pulse of an optical parametric amplifier [16]. For many applications, the polarization of the white light is very important. Initially, it was commonly assumed that the polarization of the white light is the same as the incident laser when generated in isotropic amorphous media like air, water and BK-7 glass [17]. In crystals, the polarization of the white light becomes different from the incident laser due to the anisotropy of the nonlinear refraction (described by the third-order susceptibility χ(3)) [18]. Recently, there has been some debate about the polarization properties of the white light generated in isotropic amorphous media. Some experiments support the early assumption [19,20], while others disagreed with it [18,21]. They show that the polarization of the white light can be different from the incident laser even in isotropic amorphous media. This depolarization is attributed to scattering by electron density inhomogeneities, described by the dielectric tensor of the plasma [22].
In this paper, the polarization of the white light induced by the propagation of a femtosecond laser pulses through a water cell was investigated. It was found that the polarization depends greatly on the initial polarization perturbation induced by the focus lens. The depolarization of the white light is attributed to the cross-phase modulation (XPM) of the nonlinear third-order polarization.
2. Experimental results and discussion
Figure 1 shows our experimental setup. We perform experiments using laser pulses of 120 fs duration at 805 nm wavelength, with a 1 kHz repetition rate. The intensity of the laser is adjusted with a half wave plate and the Grin-Taylor Prism P1. The extinction ratio of the Grin-Taylor Prism can reach 10−5. An achromatic lens Li of 15 cm focal length focuses the laser into a water cell. In our experiment, lens L1 or L2 is used. The diameter of the lens is 2.5cm and the laser beam diameter on the lens is about 6mm. The second polarizer P2 chooses the polarization direction of the white light and an iris is placed before P2 to select the central part of the white light spot. Finally a fiber spectrometer is used to detect the results. The incident light pulse propagates along z direction, and the polarization is along x direction after polarizer P1
Fig. 1 Experimental setup. M, 800nm reflector; HWP1, half wave plates; P1,P2, Grin-Taylor Prisms; Li, lens with focal length of 15cm, diameter of 2.5cm (i = 1 or 2: two lenses named L1 and L2 are used in our experiment)
To quantify the polarization of the white light, a ratio T (λ) is defied as I⊥(λ)/I∥(λ), where I⊥(λ) is the detected intensity when the analyzer P2 is in the cross position with P1, and I∥(λ)is the detected intensity when the analyzer is in the parallel position. Hence, a bigger T represents a larger depolarization. The ratio T of the incident laser without the focus lens is less than 10−5, as measured by an energy meter instead of the fiber spectrometer. 10−5 is the measurement limit in our experiment.
At first, the polarizer P1 is placed before the lens L1, as shown in Fig.1. The parallel and perpendicular polarized white light spectrums are detected at different input powers as shown in Fig.2 . There is a dip at about 635nm in the white light spectrums that can also be seen in other papers [23,24]. It is caused by the Raman effect of water [25]. The ratio T (λ) is calculated for different input powers and shown in Fig.3 . At an input power of 290 mW, T (750 nm) reaches 1/5. T (λ) increases over the whole spectrum as the input power increases. Every curve exhibits a dip at the input wavelength of 805nm, and significant depolarization near 805 nm. T (λ) decreases toward the blue edge of the spectrum. These results corroborate references 18 and 21.
Fig. 2 The parallel (a) and perpendicular (b) polarized white light spectrums detected at different input powers
As we known that the critical power for self-focusing in water is Pcr=4.4MW [26], the input powers of 25mW, 100mW, and 290mW in our experiment correspond to 47Pcr, 189 Pcr and 549 Pcr respectively. Filament is formed at these powers. The length of the filament obtain is about 5mm at 290mW and 2mm at 100mW. At the power of 25mW, the length of the filament is shorter than 1 mm. During the process of filamentation, an energy reservoir is formed, and most of the energy is distributed in the reservoir [27]. The intensity of the laser field in the reservoir is lower than that in the filament, and then the nonlinear effect is lower, so the depolarization effect in the reservoir is lower, which causes the dip at the input wavelength of the depolarization curve [18]. The structure of the curve further from the central wavelength can be explained by the mechanism that different spectral components of the SC are generated at different positions along the propagation pathway of the pulse. The interaction length of the SC spectrum components with the most intense part of the pulse near 805nm decreases toward the blue part of spectrum [28], so the ratio T decreases toward the blue edge of the spectrum.
However, when we put polarizer P1 just after the lens L1, T (750 nm) is measured to be only 1/4400 at the input power of 290 mW, as shown in Fig.4 . We can see that T (λ) is about three orders of magnitude smaller than the values shown in Fig.3 over the whole spectrum.
Fig. 4 T (λ) of the white light when the polarizer P1 is put after the lens L1 at the input power of 290mW.
It is known that a lens can slightly change the polarization state of the incidence laser [29]. Considering this effect, we measure the energy of the pulse with two polarizations without the water cell. When the polarizer P1 is placed before the lens L1 as shown in Fig.1 and the pulse energy was measured after P2. The ratio T in this situation is measured to be 3×10−4. When the polarizer P1 is placed after the lens L1, this ratio becomes less than 10−5.
It is also found that the use of a different lens L2 results in a different amount of polarization perturbation, even though the focal length and diameter are unchanged. This is because the physical lens is neither ideally thin nor perfectly machined, and different lens can induce different amount of perturbation. We measured the polarization perturbation induced by lens L2 and the ratio T is less than 10−5. When L2 is used, the spectral structure and intensity of the parallel polarized white light are almost the same as those when L1 is used. The structure of the spectrum of the perpendicular white light is also very close to the L1 case, but with much lower intensity. The ratio T (750 nm) of the white light is measured to be 1/67 at the input power of 290 mW. For ease of comparison, we list the experimental results in Table 1 .
Table 1. T (λ) of the white light at different situations with the input power of 290 mW
When L2 is used, L2 is set after the polarizer P1, so the polarization perturbation is regarded larger than that when L1 is placed before P1, though these two values could not be measured precisely in our experiment. It is shown that the polarization perturbation of the white light increases as the polarization perturbation of the incident light increases. Therefore, we conclude that the white light depolarization is caused by magnification of the polarization perturbation of the incident light.
3. Reason for magnifying of small perturbation
The depolarization of generated white light increases with the incident polarization perturbation. This leads to our inference that the small perturbation has been magnified by nonlinear processes during propagation.
Cross-phase modulation (XPM) of the third order nonlinear polarization may be the reason why a slight perturbation in polarization is magnified during propagation. When the incident light is not purely linearly polarized, the two perpendicularly polarized components will couple. We know that in an isotropic media, the following relationship exists:
Here when, and when,and when the dominant contribution to the nonlinear process is of electronic origin [30].The third-order nonlinear polarization of the two perpendicular directions is [30]:
The third order nonlinear polarization is the main reason of the white light generation. It can be seen from Eq. (2) that the two polarizations are coupled. Because of this, the small perturbation can be magnified during propagation. It’s similar like the situation studied in ref.31. In this paper, the propagation of pulses with initial polarization state from linear, through elliptic to circular has been simulated, and the results reveal that the polarization state of an initial linear polarization with a small elliptic perturbation appears to be unstable during propagation [31].
This explanation agrees with the experimental result that the depolarized ratio increases as either the input pulse energy or incident polarization perturbation increase.
Cross-phase modulation is also related to the recent observation of filamentation induced birefringence [32–34] where the difference of the nonlinear refractive index in x and y directions plays an important role. In our situation, the ratio of the nonlinear polarization in y and x directions plays an important role to decide the depolarization degree of the white light.
4. Conclusion
We find that the polarization of the white light is nearly identical to that of the linearly polarized input laser during propagation of a femtosecond laser pulse through the water cell. The polarization perturbation induced by the focus lens is greatly magnified in the nonlinear propagation process. This may be due to the Cross-phase modulation (XPM) of two perpendicular components of the third-order nonlinear polarization. This result is very helpful for studies employing the white light as a coherent light source with well-defined polarization properties.
Acknowledgment
We acknowledge the support of the National Basic Research Program under Grant No. 2006CB806007, the National Science Foundation of China under Grants No. 10634020 and 10521002.
References and links
1. A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett. 20(1), 73–75 (1995). [CrossRef] [PubMed]
2. P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett. 57(18), 2268–2271 (1986). [CrossRef] [PubMed]
3. W. Liu, O. Kosareva, I. S. Golubtsov, A. Iwasaki, A. Becker, V. P. Kandidov, S. L. Chin, I. S. Golubtsov, S A Iwasaki, A Becker, V. P Kandidov, and S. L Chin, “Random deflection of the white light beam during self-focusing and filamentation of a femtosecond laser pulse in water,” Appl. Phys. B 75(4-5), 595–599 (2002). [CrossRef]
4. S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Berge, “Self-Guided Propagation of Ultrashort IR Laser Pulses in Fused Silica,” Phys. Rev. Lett . 87, 213902–1-213902–4 (2001).
5. A. Brodeur and S. L. Chin, “Ultrafast white-light continuum generation and self-focusing in transparent condensed media,” J. Opt. Soc. Am. B 16(4), 637–650 (1999). [CrossRef]
6. G. Yang and Y. R. Shen, “Spectral broadening of ultrashort pulses in a nonlinear medium,” Opt. Lett. 9(11), 510–512 (1984). [CrossRef] [PubMed]
7. A. Penzkofer, A. Laubereau, and W. Kaiser, “Stimulated Short-Wave Radiation due to Single-Frequency Resonances of χ (3),” Phys. Rev. Lett. 31(14), 863–866 (1973). [CrossRef]
8. M. Wittmann and A. Penzkofer, “Spectral superbroadening of femtosecond laser pulses,” Opt. Commun. 126(4-6), 308–317 (1996). [CrossRef]
9. A. K. Dharmadhikari, F. A. Rajgara, and D. Mathur, “Plasma effects and the modulation of white light spectra in the propagation of ultrashort, high-power laser pulses in barium fluoride,” Appl. Phys. B 82(4), 575–583 (2006). [CrossRef]
10. A. K. Dharmadhikari, F. A. Rajgara, and D. Mathur, “Systematic study of highly efficient white light generation in transparent materials using intense femtosecond laser pulses,” Appl. Phys. B 80(1), 61–66 (2005). [CrossRef]
11. J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J. P. Wolf, Y.-B. André, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, M. Rodriguez, H. Wille, and L. Wöste, “Infrared extension of the super continuum generated by femtosecond terawatt laser pulses propagating in the atmosphere,” Opt. Lett. 25(18), 1397–1399 (2000). [CrossRef]
12. M. Kolesik, E. M. Wright, and J. V. Moloney, “Dynamic Nonlinear X Waves for emtosecond Pulse Propagation in Water,” Phys. Rev. Lett. 92(25), 253901–253904 (2004). [CrossRef] [PubMed]
13. M. Kolesik, E. M. Wright, and J. V. Moloney, “Interpretation of the spectrally resolved far field of femtosecond pulses propagating in bulk nonlinear dispersive media,” Opt. Express 13(26), 10729–10741 (2005). [CrossRef] [PubMed]
14. V. I. Klimov and D. W. McBranch, “Femtosecond high-sensitivity, chirp-free transient absorption spectroscopy using kilohertz lasers,” Opt. Lett. 23(4), 277–279 (1998). [CrossRef]
15. E. T. J. Nibbering, O. Dühr, and G. Korn, “Generation of intense tunable 20-fs pulses near 400nm by use of a gas-filled hollow waveguide,” Opt. Lett. 22(17), 1335–1337 (1997). [CrossRef]
16. V. V. Yakovlev, B. Kohler, and K. R. Wilson, “Broadly tunable 30-fs pulses produced by optical parametric amplification,” Opt. Lett. 19(23), 2000–2002 (1994). [CrossRef] [PubMed]
17. I. Golub, “Optical characteristics of supercontinuum generation,” Opt. Lett. 15(6), 305–307 (1990). [CrossRef] [PubMed]
18. R. Sai Santosh Kumar, K. L. N. Deepak, and D. Narayana Rao, “Depolarization properties of the femtosecond supercontinuum generated in condensed media,” Phys. Rev. A 78, 043818–1-04381–10 (2008).
19. V. Kartazaev and R. R. Alfano, “Polarization properties of SC generated in CaF2,” Opt. Commun. 281, 463–468 (2008).
20. K. Midorikawa, H. Kawano, A. Suda, C. Nagura, and M. Obara, “Polarization properties of ultrafast white-light continuum generated in condensed media,” Appl. Phys. Lett. 80(6), 923–925 (2002). [CrossRef]
21. A. K. Dharmadhikari, F. A. Rajgara, and D. Mathur, “Depolarization of white light generated by ultrashort laser pulses in optical media,” Opt. Lett. 31(14), 2184–2186 (2006). [CrossRef] [PubMed]
22. F. Orsitto and N. Tartoni, “Proposal for a new electron temperature diagnostic for fusion reactors,” Rev. Sci. Instrum. 70(1), 798–801 (1999). [CrossRef]
23. W. Liu, S. Petit, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, “Intensity clamping of a femtosecond laser pulse in condensed matter,” Opt. Commun. 202(1-3), 189–197 (2002). [CrossRef]
24. W. Liu, O. Kosareva, I. S. Golubtsov, A. Iwasaki, A. Becker, V. P. Kandidov, and S. L. Chin, “Femtosecond laser pulse filamentation versus optical breakdown in H2O,” Appl. Phys. B 76(3), 215–229 (2003). [CrossRef]
25. D. Cavaille, D. Combes, and A. Zwick, “Effect of High Hydrostatic Pressure and Additives on the Dynamics of Water: a Raman Spectroscopy Study,” J. Raman Spectrosc. 27(11), 853–857 (1996). [CrossRef]
26. A. Brodeur and S. L. Chin, “Band-Gap Dependence of the Ultrafast White-Light Continuum,” Phys. Rev. Lett. 80(20), 4406–4409 (1998). [CrossRef]
27. G. Méchain, C. D. Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, “Range of plasma filaments created in air by a multi-terawatt femtosecond laser,” Opt. Commun. 247(1-3), 171–180 (2005). [CrossRef]
28. I. Buchvarov, A. Trifonov, and T. Fiebig, “Toward an understanding of white-light generation in cubic media - polarization properties across the entire spectral range,” Opt. Lett. 32(11), 1539–1541 (2007). [CrossRef] [PubMed]
29. A. Yoshida and T. Asakura, “Electromagnetic Field near the focus of Gaussian Beams,” Optik (Stuttg.) 41, 281–292 (1974).
30. G. P. Agrawal, Nonlinear Fiber Optics (3rd ed., Elsevier, Pte Ltd, Singapore, 2004), Chap. 6.
31. M. Kolesik, J. V. Moloney, and E. M. Wright, “Polarization dynamics of femtosecond pulses propagating in air,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(4), 046607–046608 (2001). [CrossRef] [PubMed]
32. P. Béjot, Y. Petit, L. Bonacina, J. Kasparian, M. Moret, and J.-P. Wolf, “Ultrafast gaseous half-wave plate,” Opt. Express 16(10), 7564–7570 (2008). [CrossRef] [PubMed]
33. Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Polarization separator created by a filament in air,” Opt. Lett. 33(23), 2731–2733 (2008). [CrossRef] [PubMed]
34. C. Marceau, Y. Chen, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Ultrafast birefringence induced by a femtosecond laser filament in gases,” Opt. Lett. 34(9), 1417–1419 (2009). [CrossRef] [PubMed]
