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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 5 — Mar. 1, 2010
  • pp: 4206–4211
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Energy transfer from wide-band supercontinuum to narrow-band second harmonic generation

Jing Wen, Hongbing Jiang, Li Chen, Xipeng Zhang, and Qihuang Gong  »View Author Affiliations


Optics Express, Vol. 18, Issue 5, pp. 4206-4211 (2010)
http://dx.doi.org/10.1364/OE.18.004206


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Abstract

We present an experimental and theoretical study of energy transfer from a wide-band supercontinuum to narrow-band second harmonic light during propagation of a femtosecond pulse in a MgO:LiNbO3 crystal. The energy removed from the supercontinuum at 1038 nm by phase-matched second harmonic generation is compensated by energy transfer from other wavelengths within the supercontinuum by self phase modulation via the Kerr effect.

© 2010 OSA

1. Introduction

During propagation of intense laser pulses in transparent materials, the spectral bandwidth may experience outstanding broadening and result in a supercontinuum generation (SCG). SCG has attracted significant research interest since it was discovered by Alfano and Shapiro in 1970 [1

1. R. R. Alfano and S. L. Shapiro, “Observation of self-phase modulation and small-scale filaments in crystals and glasses,” Phys. Rev. Lett. 24(11), 592–594 (1970). [CrossRef]

] and then explained by Bloembergen in 1973 [2

2. N. Bloembergen, “The influence of electron plasma formation on superbroadening in light filaments,” Opt. Commun. 8(4), 285–288 (1973). [CrossRef]

]. Now, femtosecond light induced SCG has been used widely in pulse compression [3

3. A. V. Husakou, V. P. Kalosha, and J. Herrmann, “Supercontinuum generation and pulse compression in hollow waveguides,” Opt. Lett. 26(13), 1022–1024 (2001). [CrossRef]

,4

4. M. Spanner, M. Pshenichnikov, V. Olvo, and M. Ivanov, “Controlled supercontinuum generation for optimal pulse compression: a time-warp analysis of nonlinear propagation of ultra-broad-band pulses,” Appl. Phys. B 77(2-3), 329–336 (2003). [CrossRef]

], optical parametric amplification [5

5. C. Homann, C. Schriever, P. Baum, and E. Riedle, “Octave wide tunable UV-pumped NOPA: pulses down to 20 fs at 0.5 MHz repetition rate,” Opt. Express 16(8), 5746–5756 (2008). [CrossRef] [PubMed]

], time-resolved broadband pump-probe spectroscopy [6

6. S. A. Kovalenko, A. L. Dobryakov, J. Ruthmann, and N. P. Ernsting, “Femtosecond spectroscopy of condensed phases with chirped supercontinuum probing,” Phys. Rev. A 59(3), 2369–2384 (1999). [CrossRef]

]. It’s generally accepted that supercontinuum generation is a result of the interplay of a number of dynamical processes, such as self phase modulation (SPM), self-steepening, and plasma generation by multiphoton ionization [7

7. S. Akturk, A. Couairon, M. Franco, and A. Mysyrowicz, “Spectrogram representation of pulse self compression by filamentation,” Opt. Express 16(22), 17626–17636 (2008). [CrossRef] [PubMed]

,8

8. L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007). [CrossRef]

].

During propagation of focused femtosecond laser pulses in a quadratic nonlinear medium, second order nonlinear polarization will also be involved, and then new phenomena could occur. SCG and second harmonic generation (SHG) from the input wavelength are generated simultaneously in KDP [9

9. R. Sai Santosh Kumar, S. Sree Harsha, and D. Narayana Rao, “Broadband supercontinuum generation in a single potassium di-hydrogen phosphate(KDP) crystal achieved in tandem with sum frequency generation,” Appl. Phys. B 86(4), 615–621 (2007). [CrossRef]

, 10

10. N. K. M. N. Srinivas, S. S. Harsha, and D. N. Rao, “Femtosecond supercontinuum generation in a quadratic nonlinear medium (KDP),” Opt. Express 13(9), 3224–3229 (2005). [CrossRef] [PubMed]

] and BBO crystals [11

11. H. Zeng, J. Wu, H. Xu, K. Wu, and E. Wu, “Colored conical emission by means of second harmonic generation in a quadratically nonlinear medium,” Phys. Rev. Lett. 92(14), 143903 (2004). [CrossRef] [PubMed]

, 12

12. H. Zeng, J. Wu, H. Xu, and K. Wu, “Generation and weak beam control of two-dimensional multicolored arrays in a quadratic nonlinear medium,” Phys. Rev. Lett. 96(8), 083902 (2006). [CrossRef] [PubMed]

]. Parametric amplification seeded by supercontinuum could generate new wavelength signal in a KTP crystal [13

13. X. Zhang, H. Jiang, L. Chen, Y. Jiang, H. Yang, and Q. Gong, “Wavelength femtosecond light pulse generated from filamentation-assisted fourth-order nonlinear process in potassium titanyl phosphate crystal,” Opt. Lett. 33(12), 1374–1376 (2008). [CrossRef] [PubMed]

].

In this paper, we investigate propagation of femtosecond laser pulses in a MgO:LiNbO3 crystal. When the wavelength of the pulse is broadened to overlap 1038nm, signal at 519nm could be emerged by phase matched second harmonic generation. The energy transfer process in this phenomenon is also studied.

Our experimental setup and results are presented in Section 2, and the simulation results and discussion are presented in Section 3.

2. Experimental setup and results

The experiment was performed using a chirped-pulse-amplified Ti-sapphire laser system. The central wavelength of the amplified laser pulse is 830 nm, the duration is 120 fs and the repetition rate is 10 Hz. As illustrated in Fig. 1
Fig. 1 Experimental setup. The Glan prism is indicated by G, the lens by L1 and L2.
, the pulses were focused inside the crystal with lens L1 (f = 200 mm) and the position of the focus was about 2 mm inside the front surface of the crystal, which is cut normal to its x-axis. After passing through the crystal with thickness of 5 mm, the pulse was collimated with lens L2. A visible and near-infrared grating was used to separate the light, and the energy per pulse at 519 and 1038 nm was monitored using a single pulse energy detector located at the focus of L2. The spectrum was recorded using an optical fiber spectrometer set at the focus of L2 without the grating (not shown in Fig. 1). The pump power was controlled using a λ/2 plate and a Glan prism, and the crystal position was controlled using the three-dimensional translation stage T.

In our experiment, the pump pulses propagate in the crystal along the x-axis. When the pump pulses are polarized along the z-axis of the crystal (i.e., extraordinary light), only the pump at 830 nm and the phase mismatched SHG at 415 nm are detected. When the pump pulses are polarized along the y-axis (i.e., ordinary light), a supercontinuum is generated. Figure 2
Fig. 2 Panel (a) shows the pulse spectrum after passing through the crystal; Panel (b) shows spectrum of the output near-infrared light when the pump pulse energy is 0.23 mJ.
shows typical spectra in the visible and near infrared, respectively, with a pump pulse energy of 0.23 mJ per pulse. To obtain Fig. 2(a), color filters which can absorb the energy within wavelength range from 690nm to 1100nm were used to decrease the pump power. The phase mismatched SH signal at 415 nm, phase-matched SH signal at 519 nm, and supercontinuum broadened to 670 nm are all shown in Fig. 2(a). To the best of our knowledge, it’s the first report to generate a supercontinuum in a crystal, and simultaneously get phase matched SHG from part of the continuum.

The spectral width of the phase-matched SH signal at full width half maximum (FWHM) is from 518 to 520 nm and its center is at 519 nm. The SH pulse duration is measured to be 480fs. When the pump pulse energy is 0.23 mJ, the SH pulse energy is 216 nJ, and from 518 to 520 nm the pulse energy is 166 nJ. The corresponding energy of the fundamental light from 1036 to 1040 nm is measured to be 26 nJ per pulse. Thus, the SH (518–520 nm) pulse energy is 6.4 times larger than the fundamental (1036–1040 nm) pulse energy. Even so, there is no obvious dip at 1038 nm in the supercontinuum spectrum (see Fig. 2(b)). To get Fig. 2(b), a color filter is used to block light with wavelength shorter than 950nm.

To compare this process with SHG without the Kerr effect (i.e. no supercontinuum), we performed the following experiment. We focused the femtosecond laser pulse into a water cell to generate a supercontinuum, then filtered the supercontinuum with the same color filter to get Fig. 2(b) to block light with wavelengths shorter than 950 nm before focusing the pulse into the same crystal. After the color filter the pulse energy is very low since the major part of the power around 830nm is blocked, then supercontinuum generation would not take place in the MgO:LiNbO3 crystal. The incident and output spectra are shown in Fig. 3(a)
Fig. 3 Panel (a) shows the spectra around 1038nm for both the IR continuum incident light (dashed black line) and the exit light (solid red line); Panel (b) shows the corresponding SH spectrum.
. To compare the intensity of the incident and output spectra, the amplitude of the incident spectrum is calibrated by considering the transmission of the front and rear surface of the crystal in Fig. 3(a).

It is evident from Fig. 3 that a dip forms in the fundamental spectrum when SHG occurs without being accompanied by SCG. In fact, at 1038 nm, the pulse energy is reduced by 35%. The wavelengths of SH signal at half maximum are 518 and 520 nm as shown in Fig. 3(b), and the corresponding wavelengths of the depleted fundamental (FD) are 1026 and 1055 nm. The pulse energy within the FWHM of the SH is 71% that of the corresponding fundamental light (1036–1040 nm). Notice that the depleted fundamental has a wider bandwidth than the corresponding SH signal, and that the fundamental pulse is slightly broadened because of the Kerr-like cascading processes [14

14. G. Xu, H. Zhu, T. Wang, and L. Qian, “Large high-order nonlinear phase shifts produced by χ(2) cascaded processes,” Opt. Commun. 207(1-6), 347–351 (2002). [CrossRef]

16

16. G. Xu, L. Qian, T. Wang, H. Zhu, C. Zhu, and D. Fan, “Spectral Narrowing and Temporal Expanding of Femtosecond Pulses by Use of Quadratic Nonlinear Processes,” IEEE J. Sel. Top. Quantum Electron. 10(1), 174–180 (2004). [CrossRef]

].

The pulse energy ratio SH/FD in Fig. 2 is 6.4, which is much larger than the 0.71 found in Fig. 3. Whereas a dip in the spectrum is present in Fig. 3(a), no obvious dip is present in Fig. 2(b). This result indicates that a significant energy transfer process occurs from the wide-band supercontinuum to the narrow-band second harmonic signal. To understand this energy transfer process we simulated the propagation of intense light pulses in the crystal.

3. Numerical simulation

To simplify the simulation of the propagation of a femtosecond pulse in the crystal, we use the plane-wave approximation. The electric fields of the pulses can be written as:
E1(z,t)=12A1(z,t)eiω1t+ik1z+c.cE2(z,t)=12A2(z,t)eiω2t+ik2z+c.c
(1)
where ω2=2ω1, k1=(ω1×no1))/c, and k2=(ω2×ne2))/c are the central frequencies and corresponding wave vectors of the SH (index 2) and fundamental (index 1) pulses. Using Eq. (1) and the slowly varying amplitude approximation to solve Maxwell’s equations [17

17. C. Y. Chien, G. Korn, J. S. Coe, J. Squier, G. Mourou, and R. S. Craxton, “Highly efficient second-harmonic generation of ultraintense Nd:glass laser pulses,” Opt. Lett. 20(4), 353–355 (1995). [CrossRef] [PubMed]

,18

18. V. Krylov, A. Rebane, A. G. Kalintsev, H. Schwoerer, and U. P. Wild, “Second-harmonic generation of amplified femtosecond Ti:sapphire laser pulses,” Opt. Lett. 20(2), 198–200 (1995). [CrossRef] [PubMed]

], we can simulate both SHG and SCG. The equations for the coupled fundamental and second harmonic pulses propagating in the moving frame τ=t-k'(ω0)z are given by:
A1z+(k1'k2')A1t+0.5ik12A1t2=iω1χ(2)2n1cA2A1*eiΔkz+i3ω1χ(3)4n1c(|A1|2+2|A2|2)A1A2z+0.5ik22A2t2=iω2χ(2)2n2cA12eiΔkz+i3ω2χ(3)4n2c(2|A1|2+|A2|2)A2.
(2)
where Δk=k2-k1 represents the wave vector phase mismatch, and the index 1 (2) indicates the fundamental (second harmonic). For the crystal MgO:LiNbO3, the central frequency ω1 of the fundamental pulse corresponds to 1038 nm and the central frequency ω2 of the SH pulse corresponds to 519 nm.

In our experiment, however, the central wavelength of the pump pulse is at 830 nm instead of 1038 nm. We thus have to add a frequency-shifted component to the initial pump pulse to make its central wavelength 1038 nm. The initial pump pulse is taken to be a Gaussian pulse:
A1(z=0,t)=A0exp[i(ω0ω1)tt2tp2].
(3)
with tp = 101.9 fs (which gives a pulse duration of 120 fs), ω0 corresponding to wavelength of 830 nm, ω1 corresponding to wavelength of 1038 nm. The maximum electric field intensity A0 is 0.95 × 109 V/m, which corresponds to an intensity of 1.2 × 1013 W/cm2, and the propagation distance is 3 mm. The second order nonlinear optical coefficient is taken as χ(2) = 0.37 × 10−11 m/V, and the third order nonlinear coefficient is set to χ(3) = 0.65 × 10−20 m2/V2.

To determine how SCG affects the fundamental pulse, we simulated the following three conditions: I) χ(2) and χ(3) are considered simultaneously in the crystal with thickness of 3mm. The result of this case is shown in Fig. 4
Fig. 4 Comparison of output spectra with wavelengths above 960nm. red line (dashed): SHG and SCG taking place at the same time; black line (solid): only SCG is considered; blue line (dotted): after SHG using SCG as the pump pulse.
by the dashed red line. II) χ(2) is set to 0 and only χ(3) is considered with the crystal thickness of 3mm. The resulting supercontinuum spectrum is shown in Fig. 4 by the solid black line. III) The supercontinuum result from case II is used as the incident light, and only SHG is considered in the crystal with thickness of 2.2mm. The resulting spectrum for this final case is shown in Fig. 4 by the dotted blue line. The SHG under I and III has equal intensity, but only in case III is a dip present in the spectrum. The three curves coincide for wavelengths shorter than 960 nm, so only wavelengths above this limit are shown in the figure:

When SHG and SCG occur independently, as shown by the dotted blue line, the energy lost between 1024 and 1063 nm (creating the dip in the spectrum) is transferred due to the cascade processes of χ(2)(2ω, ω, ω) and χ(2)(ω, 2ω, −ω) to the SH and also to the wavelength bands centered around 1075 and 1005 nm. As a result, the fundamental spectrum is broadened and the dip around 1038 nm is deepened. This simulated phenomenon is the same as the experimental result shown in Fig. 3(a). When SHG and SCG occur simultaneously, energy transfer from the wide-band spectrum (from 970 to 1090 nm) to the narrow-band SH, makes the dip around 1038 nm less apparent. Thus, when SCG is involved with SHG, energy transfer from the fundamental wavelength to the SH can be increased.

As discussed above, the energy transfer process resulting from the Kerr effect can transfer energy from wavelengths both above and below the fundamental wavelength to compensate for the energy consumed by phase-matched SHG. Under the appropriate conditions, this process constitutes a promising method to increase SHG conversion efficiency. It also provides a new way to achieve phase-matched SHG with a pump laser whose wavelength is far from the SH phase-matching condition.

4. Conclusion

We investigated the propagation of femtosecond pulses in MgO:LiNbO3. A supercontinuum is generated and when the spectrum is broadened to reach 1038 nm, narrow-band phase matched SHG occurs. The SH energy originates from not only the fundamental wavelength, but also from the supercontinuum due to the Kerr effect. Thus, it is possible for the SH pulse energy to be much larger than the pulse energy in the corresponding fundamental wavelength region.

Acknowledgments

We gratefully acknowledge the support of the National Basic Research Program (2006CB806007, 2006CB921601), the National Science Foundation of China (10574006, 10634020 and 10521002).

References and links

1.

R. R. Alfano and S. L. Shapiro, “Observation of self-phase modulation and small-scale filaments in crystals and glasses,” Phys. Rev. Lett. 24(11), 592–594 (1970). [CrossRef]

2.

N. Bloembergen, “The influence of electron plasma formation on superbroadening in light filaments,” Opt. Commun. 8(4), 285–288 (1973). [CrossRef]

3.

A. V. Husakou, V. P. Kalosha, and J. Herrmann, “Supercontinuum generation and pulse compression in hollow waveguides,” Opt. Lett. 26(13), 1022–1024 (2001). [CrossRef]

4.

M. Spanner, M. Pshenichnikov, V. Olvo, and M. Ivanov, “Controlled supercontinuum generation for optimal pulse compression: a time-warp analysis of nonlinear propagation of ultra-broad-band pulses,” Appl. Phys. B 77(2-3), 329–336 (2003). [CrossRef]

5.

C. Homann, C. Schriever, P. Baum, and E. Riedle, “Octave wide tunable UV-pumped NOPA: pulses down to 20 fs at 0.5 MHz repetition rate,” Opt. Express 16(8), 5746–5756 (2008). [CrossRef] [PubMed]

6.

S. A. Kovalenko, A. L. Dobryakov, J. Ruthmann, and N. P. Ernsting, “Femtosecond spectroscopy of condensed phases with chirped supercontinuum probing,” Phys. Rev. A 59(3), 2369–2384 (1999). [CrossRef]

7.

S. Akturk, A. Couairon, M. Franco, and A. Mysyrowicz, “Spectrogram representation of pulse self compression by filamentation,” Opt. Express 16(22), 17626–17636 (2008). [CrossRef] [PubMed]

8.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007). [CrossRef]

9.

R. Sai Santosh Kumar, S. Sree Harsha, and D. Narayana Rao, “Broadband supercontinuum generation in a single potassium di-hydrogen phosphate(KDP) crystal achieved in tandem with sum frequency generation,” Appl. Phys. B 86(4), 615–621 (2007). [CrossRef]

10.

N. K. M. N. Srinivas, S. S. Harsha, and D. N. Rao, “Femtosecond supercontinuum generation in a quadratic nonlinear medium (KDP),” Opt. Express 13(9), 3224–3229 (2005). [CrossRef] [PubMed]

11.

H. Zeng, J. Wu, H. Xu, K. Wu, and E. Wu, “Colored conical emission by means of second harmonic generation in a quadratically nonlinear medium,” Phys. Rev. Lett. 92(14), 143903 (2004). [CrossRef] [PubMed]

12.

H. Zeng, J. Wu, H. Xu, and K. Wu, “Generation and weak beam control of two-dimensional multicolored arrays in a quadratic nonlinear medium,” Phys. Rev. Lett. 96(8), 083902 (2006). [CrossRef] [PubMed]

13.

X. Zhang, H. Jiang, L. Chen, Y. Jiang, H. Yang, and Q. Gong, “Wavelength femtosecond light pulse generated from filamentation-assisted fourth-order nonlinear process in potassium titanyl phosphate crystal,” Opt. Lett. 33(12), 1374–1376 (2008). [CrossRef] [PubMed]

14.

G. Xu, H. Zhu, T. Wang, and L. Qian, “Large high-order nonlinear phase shifts produced by χ(2) cascaded processes,” Opt. Commun. 207(1-6), 347–351 (2002). [CrossRef]

15.

X. Liu, L. Qian, and F. Wise, “High-energy pulse compression by use of negative phase shifts produced by the cascade χ((2))((2)) nonlinearity,” Opt. Lett. 24(23), 1777–1779 (1999). [CrossRef]

16.

G. Xu, L. Qian, T. Wang, H. Zhu, C. Zhu, and D. Fan, “Spectral Narrowing and Temporal Expanding of Femtosecond Pulses by Use of Quadratic Nonlinear Processes,” IEEE J. Sel. Top. Quantum Electron. 10(1), 174–180 (2004). [CrossRef]

17.

C. Y. Chien, G. Korn, J. S. Coe, J. Squier, G. Mourou, and R. S. Craxton, “Highly efficient second-harmonic generation of ultraintense Nd:glass laser pulses,” Opt. Lett. 20(4), 353–355 (1995). [CrossRef] [PubMed]

18.

V. Krylov, A. Rebane, A. G. Kalintsev, H. Schwoerer, and U. P. Wild, “Second-harmonic generation of amplified femtosecond Ti:sapphire laser pulses,” Opt. Lett. 20(2), 198–200 (1995). [CrossRef] [PubMed]

OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(320.7110) Ultrafast optics : Ultrafast nonlinear optics
(320.6629) Ultrafast optics : Supercontinuum generation

ToC Category:
Ultrafast Optics

History
Original Manuscript: November 12, 2009
Revised Manuscript: December 22, 2009
Manuscript Accepted: February 5, 2010
Published: February 17, 2010

Citation
Jing Wen, Hongbing Jiang, Li Chen, Xipeng Zhang, and Qihuang Gong, "Energy transfer from wide-band supercontinuum to narrow-band second harmonic generation," Opt. Express 18, 4206-4211 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-5-4206


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References

  1. R. R. Alfano and S. L. Shapiro, “Observation of self-phase modulation and small-scale filaments in crystals and glasses,” Phys. Rev. Lett. 24(11), 592–594 (1970). [CrossRef]
  2. N. Bloembergen, “The influence of electron plasma formation on superbroadening in light filaments,” Opt. Commun. 8(4), 285–288 (1973). [CrossRef]
  3. A. V. Husakou, V. P. Kalosha, and J. Herrmann, “Supercontinuum generation and pulse compression in hollow waveguides,” Opt. Lett. 26(13), 1022–1024 (2001). [CrossRef]
  4. M. Spanner, M. Pshenichnikov, V. Olvo, and M. Ivanov, “Controlled supercontinuum generation for optimal pulse compression: a time-warp analysis of nonlinear propagation of ultra-broad-band pulses,” Appl. Phys. B 77(2-3), 329–336 (2003). [CrossRef]
  5. C. Homann, C. Schriever, P. Baum, and E. Riedle, “Octave wide tunable UV-pumped NOPA: pulses down to 20 fs at 0.5 MHz repetition rate,” Opt. Express 16(8), 5746–5756 (2008). [CrossRef] [PubMed]
  6. S. A. Kovalenko, A. L. Dobryakov, J. Ruthmann, and N. P. Ernsting, “Femtosecond spectroscopy of condensed phases with chirped supercontinuum probing,” Phys. Rev. A 59(3), 2369–2384 (1999). [CrossRef]
  7. S. Akturk, A. Couairon, M. Franco, and A. Mysyrowicz, “Spectrogram representation of pulse self compression by filamentation,” Opt. Express 16(22), 17626–17636 (2008). [CrossRef] [PubMed]
  8. L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007). [CrossRef]
  9. R. Sai Santosh Kumar, S. Sree Harsha, and D. Narayana Rao, “Broadband supercontinuum generation in a single potassium di-hydrogen phosphate(KDP) crystal achieved in tandem with sum frequency generation,” Appl. Phys. B 86(4), 615–621 (2007). [CrossRef]
  10. N. K. M. N. Srinivas, S. S. Harsha, and D. N. Rao, “Femtosecond supercontinuum generation in a quadratic nonlinear medium (KDP),” Opt. Express 13(9), 3224–3229 (2005). [CrossRef] [PubMed]
  11. H. Zeng, J. Wu, H. Xu, K. Wu, and E. Wu, “Colored conical emission by means of second harmonic generation in a quadratically nonlinear medium,” Phys. Rev. Lett. 92(14), 143903 (2004). [CrossRef] [PubMed]
  12. H. Zeng, J. Wu, H. Xu, and K. Wu, “Generation and weak beam control of two-dimensional multicolored arrays in a quadratic nonlinear medium,” Phys. Rev. Lett. 96(8), 083902 (2006). [CrossRef] [PubMed]
  13. X. Zhang, H. Jiang, L. Chen, Y. Jiang, H. Yang, and Q. Gong, “Wavelength femtosecond light pulse generated from filamentation-assisted fourth-order nonlinear process in potassium titanyl phosphate crystal,” Opt. Lett. 33(12), 1374–1376 (2008). [CrossRef] [PubMed]
  14. G. Xu, H. Zhu, T. Wang, and L. Qian, “Large high-order nonlinear phase shifts produced by χ(2) cascaded processes,” Opt. Commun. 207(1-6), 347–351 (2002). [CrossRef]
  15. X. Liu, L. Qian, and F. Wise, “High-energy pulse compression by use of negative phase shifts produced by the cascade χ((2)):χ((2)) nonlinearity,” Opt. Lett. 24(23), 1777–1779 (1999). [CrossRef]
  16. G. Xu, L. Qian, T. Wang, H. Zhu, C. Zhu, and D. Fan, “Spectral Narrowing and Temporal Expanding of Femtosecond Pulses by Use of Quadratic Nonlinear Processes,” IEEE J. Sel. Top. Quantum Electron. 10(1), 174–180 (2004). [CrossRef]
  17. C. Y. Chien, G. Korn, J. S. Coe, J. Squier, G. Mourou, and R. S. Craxton, “Highly efficient second-harmonic generation of ultraintense Nd:glass laser pulses,” Opt. Lett. 20(4), 353–355 (1995). [CrossRef] [PubMed]
  18. V. Krylov, A. Rebane, A. G. Kalintsev, H. Schwoerer, and U. P. Wild, “Second-harmonic generation of amplified femtosecond Ti:sapphire laser pulses,” Opt. Lett. 20(2), 198–200 (1995). [CrossRef] [PubMed]

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