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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 12 — Jun. 17, 2013
  • pp: 13969–13974
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Quasi-phase-matched second-harmonic Talbot self-imaging in a 2D periodically-poled LiTaO3 crystal

Dongmei Liu, Dunzhao Wei, Yong Zhang, Jiong Zou, X. P. Hu, S. N. Zhu, and Min Xiao  »View Author Affiliations


Optics Express, Vol. 21, Issue 12, pp. 13969-13974 (2013)
http://dx.doi.org/10.1364/OE.21.013969


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Abstract

We demonstrate the improved second-harmonic Talbot self-imaging through the quasi-phase-matching technique in a 2D periodically-poled LiTaO3 crystal. The domain structure not only composes a nonlinear optical grating which is necessary to realize nonlinear Talbot self-imaging, but also provides reciprocal vectors to satisfy the phase-matching condition for second-harmonic generation. Our experimental results show that quasi-phase-matching can improve the intensity of the second-harmonic Talbot self-imaging by a factor of 21.

© 2013 OSA

1. Introduction

The QPM technique in periodically-poled nonlinear optical crystals has been widely studied because it can efficiently realize laser frequency conversion by introducing a reciprocal vector to compensate the mismatch between the wave vectors [9

9. Z. D. Gao, S. N. Zhu, S. Tu, and A. H. Kuang, “Monolithic red-green-blue laser light source based on cascaded wavelength conversion in periodically poled stoichiometric lithium tantalate,” Appl. Phys. Lett. 89(18), 181101 (2006). [CrossRef]

, 10

10. A. Jechow, M. Schedel, S. Stry, J. Sacher, and R. Menzel, “Highly efficient single-pass frequency doubling of a continuous-wave distributed feedback laser diode using a PPLN waveguide crystal at 488 nm,” Opt. Lett. 32(20), 3035–3037 (2007). [CrossRef] [PubMed]

]. Now, all-solid-state lasers based on the QPM method have been developed to generate high-power red, green, and blue lights, which have been applied in laser projector and display [9

9. Z. D. Gao, S. N. Zhu, S. Tu, and A. H. Kuang, “Monolithic red-green-blue laser light source based on cascaded wavelength conversion in periodically poled stoichiometric lithium tantalate,” Appl. Phys. Lett. 89(18), 181101 (2006). [CrossRef]

, 10

10. A. Jechow, M. Schedel, S. Stry, J. Sacher, and R. Menzel, “Highly efficient single-pass frequency doubling of a continuous-wave distributed feedback laser diode using a PPLN waveguide crystal at 488 nm,” Opt. Lett. 32(20), 3035–3037 (2007). [CrossRef] [PubMed]

]. Moreover, the concept of nonlinear photonic crystals [11

11. V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81(19), 4136–4139 (1998). [CrossRef]

] (i.e. 2D periodically-poled crystals) inspires the discoveries of many interesting nonlinear optical effects, such as broadband second-harmonic generation (SHG) [12

12. R. Fischer, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, “Broadband femtosecond frequency doubling in random media,” Appl. Phys. Lett. 89(19), 191105 (2006). [CrossRef]

], nonlinear Cerenkov radiations [13

13. Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008). [CrossRef] [PubMed]

], and nonlinear Airy beams [14

14. T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009). [CrossRef]

]. QPM not only enhances these nonlinear effects, but also provides an efficient way to modulate them.

In this article, we demonstrate, both in theory and experiment, the improved second-harmonic (SH) Talbot self-imaging through the QPM technique in a squarely-poled LiTaO3 crystal. The periodic SH pattern generated at the output face of the crystal composes a nonlinear optical “grating”, which is necessary to realize the Talbot self-imaging [6

6. Y. Zhang, J. M. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104(18), 183901 (2010). [CrossRef] [PubMed]

]. Meanwhile, the domain structure provides reciprocal vectors to satisfy the phase-matching condition for SHG [9

9. Z. D. Gao, S. N. Zhu, S. Tu, and A. H. Kuang, “Monolithic red-green-blue laser light source based on cascaded wavelength conversion in periodically poled stoichiometric lithium tantalate,” Appl. Phys. Lett. 89(18), 181101 (2006). [CrossRef]

], which can greatly enhance the intensity and quality of the SH self-images.

2. Experimental setup and theory

The sample is a squarely-poled LiTaO3 crystal with a size of 10 mm (x) × 5 mm (y) × 0.5 mm (z), which was fabricated through an electric-field poling process. The period of the domain structure is Λ = 5.5 µm and the duty cycle is ~35%. The experimental setup is shown in Fig. 1(a)
Fig. 1 (a) Experimental setup. The fundamental beam propagates along the y-axis of the crystal. The near-field images are collected by a CCD camera and the far-field images are projected on a screen. (b) The schematic diagram of QPM SH Talbot self-images. At the end face of the LiTaO3 crystal, the fundamental lights that travel through the negative domains (dashed arrows in red) produce bright SH stripes while the fundamental waves that do not pass the inverted domains (dashed arrow in black) generate dark stripes. In the far-field, five SH spots (A, B1, B1', B2, and B2') are generated due to QPM. The collinear (c) and noncollinear (d) phase-matching schemes in the 2D PPLT crystal are also shown.
. A tunable Ti:Sapphire femtosecond laser serves as the input fundamental field. The pulse width is about 140 fs and the repetition rate is 80 MHz. The wavelength can be continuously tuned from 690 nm to 1050 nm. The polarization of the laser is parallel to the z-axis of the crystal. The fundamental wave was first reshaped to produce a near-parallel beam with a spot size of ~100 μm in diameter and was then directed into the PPLT slice along the y-axis of the crystal. Before collecting the SH patterns, a filter was used to filter out the fundamental beam. Under this experimental configuration, the involved nonlinear optical coefficient is d33 [15

15. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).

], which is periodically modulated in the PPLT crystal.

The phase-matching condition in a 2D PPLT crystal can be written as [11

11. V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81(19), 4136–4139 (1998). [CrossRef]

]
2kω+Gm,n=k2ω
(1)
where kω and k are the wave vectors of the fundamental and second-harmonic waves, respectively. Gm,n=2πm2+n2Λ is the reciprocal vector of the 2D domain structure with the subscripts m and n representing the orders of the reciprocal vectors [16

16. P. Ni, B. Ma, X. Wang, B. Cheng, and D. Zhang, “Second-harmonic generation in two-dimensional periodically poled lithium niobate using second-order quasiphase matching,” Appl. Phys. Lett. 82(24), 4230–4232 (2003). [CrossRef]

]. Both collinear and noncollinear QPM SHG can be realized in such a 2D PPLT crystal. Figure 1(b) presents the far-field SH pattern projected on a screen 26 cm away from the end face of the sample. The SH pattern was excited by a fundamental input with λ = 958 nm. Five SH spots can be clearly observed. The spot A at the center results from the collinear SHG with the participation of the reciprocal vector G01 [Fig. 1(c)]. It is brightest because the collinear SHG process is phase-matched. The other four SH spots are generated by the noncollinear SHG processes [Fig. 1(d)]. B1 and B1' involve noncollinear reciprocal vectors G11 and G-11, respectively. The corresponding emit angle is 0.092 radian, which agrees well with the calculated 0.086 radian from Eq. (1). B2 and B2' correspond to G21 and G-21, respectively. Their emit angle is measured to be 0.18 radian while the calculated value is 0.17 radian. The intensities of the four noncollinear SH spots are much weaker than spot A (i.e. IA:IB1:IB2 = 1:0.18:0.85) because their corresponding effective nonlinear coefficients are smaller and their phase-matching conditions are not totally fulfilled at this wavelength [11

11. V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81(19), 4136–4139 (1998). [CrossRef]

].

The near-field SH imaging was magnified by a 100x objective lens with N.A. = 0.7 and was then recorded through a CCD camera. Different imaging planes were selected by moving the objective lens along the propagation direction of the SH waves. The SH Talbot length can be calculated by ZT = 4Λ2/λ, where λ is the wavelength of the fundamental beam [6

6. Y. Zhang, J. M. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104(18), 183901 (2010). [CrossRef] [PubMed]

]. To realize nonlinear Talbot effect, it is necessary to achieve a periodic SH pattern, which can be easily satisfied under our experimental configuration. As the fundamental beam propagates along the y-axis of the crystal, it can be split into two groups. One group travels through the periodically inverted domains [see the dashed arrows in red in Fig. 1(b)] and the generated nonlinear polarization waves are modulated, i.e. QPM works. In this case, the phase mismatch in SHG is totally or partially compensated, depending on the incident wavelength, and the bright SH stripes are produced. The other group of the fundamental beam experiences no inverted domains [see the dashed arrow in black in Fig. 1(b)], which results in the dark stripes because no reciprocal vectors get involved. Hence, a SH amplitude “grating”, having a structure determined by the domain structure along the x-axis of the crystal, exhibits at the end face of the crystal and produces the SH Talbot self-images at the Talbot planes [6

6. Y. Zhang, J. M. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104(18), 183901 (2010). [CrossRef] [PubMed]

].

3. Experimental results and discussions

As expected, we observed SH Talbot self-images at the first Talbot plane in our experiments (Fig. 2
Fig. 2 The SH self-images at the first Talbot plane with different input wavelengths. The phase-matching condition is satisfied at 958 nm with the involvement of G01.
), which result from the periodic SH patterns at the output face of the crystal. The structure period of 5.5 µm in the SH self-image is the same as the period of the domains in the PPLT sample. To achieve the maximum intensity of the SH self-images, we tuned the input wavelength to fit the QPM condition. The fundamental power was kept at 60 mW for all the wavelengths. As shown in Figs. 2(a)-2(e), the intensity of the SH pattern at the first Talbot plane dramatically changes when modulating the incident wavelengths. The brightest SH self-image appears with an incident fundamental beam of λ = 958 nm [Fig. 2(c)] because SHG is totally phase-matched and the conversion efficiency reaches maximum at this wavelength. The wavelength of the generated SH waves is 479 nm. Considering that the reciprocal vector G01 participates, the theoretical QPM wavelength can be easily calculated from Eq. (1) to be 963 nm. The small deviation may result from that the dispersion relation of the PPLT crystal used in the calculations [17

17. K. S. Abedin and H. Ito, “Temperature-dependent dispersion relation of ferroelectric lithium tantalite,” J. Appl. Phys. 80(11), 6561–6563 (1996). [CrossRef]

] does not perfectly fit our sample. The corresponding SH Talbot length is calculated to be 124 µm which is well consistent with the measured Talbot length of 126 µm. In the experiments, the intensity of the SH stripes became weaker as the incident wavelength was tuned away from 958 nm. For example, the SH intensities of the self-images at excitation wavelengths of 958 nm, 952 nm, and 946 nm are 170 a.u., 119 a.u., and 8 a.u., respectively. This is because the QPM condition is partially satisfied at λ = 952 nm and QPM is negligible at λ = 946 nm. The SH self-images at λ = 946 nm is not shown here because it is too weak to be clearly observed. By comparing the SH intensity at λ = 958 nm and λ = 946 nm, an improvement by a factor of 21 can be achieved through the introduction of QPM to nonlinear Talbot effect.

We also recorded the far-field images of the collinear SHG [Fig. 3(a)
Fig. 3 (a) The far-field SH spot of the collinear SHG with different input wavelengths. (b) The dependence of the SH intensity on the incident wavelength. The SH intensity is normalized to the peak intensity.
]. The results show that the collinear SHG is phase-matched at an input fundamental wavelength of λ = 958 nm, which shares the same QPM condition as the near-field SH imaging in the PPLT crystal. Figure 3(b) shows the dependence of the SH intensity on the fundamental wavelength. The bandwidth of the phase-matching is measured to be 12 nm, which can be attributed to the wide linewidth of the femtosecond laser.

It is obvious that the duty cycle of the SH pattern in the fractional image changes. For instance, the duty cycle in Fig. 4(d) is ~80% while it is ~50% in Fig. 4(a). Interestingly, in comparison with the traditional Talbot effect [1

1. K. Patorski, “The self-imaging phenomenon and its applications,” Prog. Opt. 27, 1–108 (1989). [CrossRef]

,2

2. J. M. Wen, Y. Zhang, and M. Xiao, “The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics,” Adv. Opt. Photon. 5(1), 83–130 (2013). [CrossRef]

], there is no obvious period change and lateral shift in the SH pattern as we move the imaging plane in our experiment. A possible explanation is that the wave-front of the SH wave is engineered by the domain structure in the PPLT crystal. We are performing further experiments and simulations to understand this interesting phenomenon.

4. Conclusion

In conclusion, we have experimentally demonstrated the QPM SH Talbot effect in a squarely-poled LiTaO3 crystal. The collinear SHG is phase-matched with the use of a reciprocal vector in the domain structure. Also, the SHG process produces a periodic SH pattern at the end face of the crystal, which originates from the periodic domain structure along the lateral direction in the crystal. The QPM SH Talbot effect can be then observed in the Fresnel near-field. The introduction of QPM can efficiently convert the fundamental wave into the SH wave. As a result, the intensity of the SH Talbot self-imaging are enhanced by a factor of 21 through the QPM technique. These improvements make it more practical to apply nonlinear Talbot self-imaging in lithography, array illuminator and imaging process.

Acknowledgments

This work was supported by the National Basic Research Program of China (Nos. 2012CB921804 and 2011CBA00205), the National Science Foundation of China (Nos. 11274162, 61222503, 11274165 and 11004097), the New Century Excellent Talents in University and the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20100091120010). The authors thank Jianming Wen for useful discussions.

References and links

1.

K. Patorski, “The self-imaging phenomenon and its applications,” Prog. Opt. 27, 1–108 (1989). [CrossRef]

2.

J. M. Wen, Y. Zhang, and M. Xiao, “The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics,” Adv. Opt. Photon. 5(1), 83–130 (2013). [CrossRef]

3.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95(5), 053902 (2005). [CrossRef] [PubMed]

4.

X. B. Song, H. B. Wang, J. Xiong, K. Wang, X. D. Zhang, K. H. Luo, and L. A. Wu, “Experimental observation of quantum Talbot effects,” Phys. Rev. Lett. 107(3), 033902 (2011). [CrossRef] [PubMed]

5.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008). [CrossRef] [PubMed]

6.

Y. Zhang, J. M. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104(18), 183901 (2010). [CrossRef] [PubMed]

7.

Z. H. Chen, D. M. Liu, Y. Zhang, J. M. Wen, S. N. Zhu, and M. Xiao, “Fractional second-harmonic Talbot effect,” Opt. Lett. 37(4), 689–691 (2012). [CrossRef] [PubMed]

8.

D. M. Liu, Y. Zhang, Z. H. Chen, J. M. Wen, and M. Xiao, “Acoustic-optic tunable second-harmonic Talbot effect based on peripdocally poled LiNbO3 crystals,” J. Opt. Soc. Am. B 29(12), 3325–3329 (2012). [CrossRef]

9.

Z. D. Gao, S. N. Zhu, S. Tu, and A. H. Kuang, “Monolithic red-green-blue laser light source based on cascaded wavelength conversion in periodically poled stoichiometric lithium tantalate,” Appl. Phys. Lett. 89(18), 181101 (2006). [CrossRef]

10.

A. Jechow, M. Schedel, S. Stry, J. Sacher, and R. Menzel, “Highly efficient single-pass frequency doubling of a continuous-wave distributed feedback laser diode using a PPLN waveguide crystal at 488 nm,” Opt. Lett. 32(20), 3035–3037 (2007). [CrossRef] [PubMed]

11.

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81(19), 4136–4139 (1998). [CrossRef]

12.

R. Fischer, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, “Broadband femtosecond frequency doubling in random media,” Appl. Phys. Lett. 89(19), 191105 (2006). [CrossRef]

13.

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008). [CrossRef] [PubMed]

14.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009). [CrossRef]

15.

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).

16.

P. Ni, B. Ma, X. Wang, B. Cheng, and D. Zhang, “Second-harmonic generation in two-dimensional periodically poled lithium niobate using second-order quasiphase matching,” Appl. Phys. Lett. 82(24), 4230–4232 (2003). [CrossRef]

17.

K. S. Abedin and H. Ito, “Temperature-dependent dispersion relation of ferroelectric lithium tantalite,” J. Appl. Phys. 80(11), 6561–6563 (1996). [CrossRef]

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(070.6760) Fourier optics and signal processing : Talbot and self-imaging effects
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

ToC Category:
Nonlinear Optics

History
Original Manuscript: April 24, 2013
Revised Manuscript: May 27, 2013
Manuscript Accepted: May 28, 2013
Published: June 3, 2013

Citation
Dongmei Liu, Dunzhao Wei, Yong Zhang, Jiong Zou, X. P. Hu, S. N. Zhu, and Min Xiao, "Quasi-phase-matched second-harmonic Talbot self-imaging in a 2D periodically-poled LiTaO3 crystal," Opt. Express 21, 13969-13974 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-12-13969


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References

  1. K. Patorski, “The self-imaging phenomenon and its applications,” Prog. Opt.27, 1–108 (1989). [CrossRef]
  2. J. M. Wen, Y. Zhang, and M. Xiao, “The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics,” Adv. Opt. Photon.5(1), 83–130 (2013). [CrossRef]
  3. R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett.95(5), 053902 (2005). [CrossRef] [PubMed]
  4. X. B. Song, H. B. Wang, J. Xiong, K. Wang, X. D. Zhang, K. H. Luo, and L. A. Wu, “Experimental observation of quantum Talbot effects,” Phys. Rev. Lett.107(3), 033902 (2011). [CrossRef] [PubMed]
  5. F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nat. Mater.7(2), 134–137 (2008). [CrossRef] [PubMed]
  6. Y. Zhang, J. M. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett.104(18), 183901 (2010). [CrossRef] [PubMed]
  7. Z. H. Chen, D. M. Liu, Y. Zhang, J. M. Wen, S. N. Zhu, and M. Xiao, “Fractional second-harmonic Talbot effect,” Opt. Lett.37(4), 689–691 (2012). [CrossRef] [PubMed]
  8. D. M. Liu, Y. Zhang, Z. H. Chen, J. M. Wen, and M. Xiao, “Acoustic-optic tunable second-harmonic Talbot effect based on peripdocally poled LiNbO3 crystals,” J. Opt. Soc. Am. B29(12), 3325–3329 (2012). [CrossRef]
  9. Z. D. Gao, S. N. Zhu, S. Tu, and A. H. Kuang, “Monolithic red-green-blue laser light source based on cascaded wavelength conversion in periodically poled stoichiometric lithium tantalate,” Appl. Phys. Lett.89(18), 181101 (2006). [CrossRef]
  10. A. Jechow, M. Schedel, S. Stry, J. Sacher, and R. Menzel, “Highly efficient single-pass frequency doubling of a continuous-wave distributed feedback laser diode using a PPLN waveguide crystal at 488 nm,” Opt. Lett.32(20), 3035–3037 (2007). [CrossRef] [PubMed]
  11. V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett.81(19), 4136–4139 (1998). [CrossRef]
  12. R. Fischer, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, “Broadband femtosecond frequency doubling in random media,” Appl. Phys. Lett.89(19), 191105 (2006). [CrossRef]
  13. Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett.100(16), 163904 (2008). [CrossRef] [PubMed]
  14. T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics3(7), 395–398 (2009). [CrossRef]
  15. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).
  16. P. Ni, B. Ma, X. Wang, B. Cheng, and D. Zhang, “Second-harmonic generation in two-dimensional periodically poled lithium niobate using second-order quasiphase matching,” Appl. Phys. Lett.82(24), 4230–4232 (2003). [CrossRef]
  17. K. S. Abedin and H. Ito, “Temperature-dependent dispersion relation of ferroelectric lithium tantalite,” J. Appl. Phys.80(11), 6561–6563 (1996). [CrossRef]

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