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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 1 — Jan. 14, 2013
  • pp: 454–462
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Dual colour cw mode-locking through soft aperture based on second order cascaded nonlinearity

Sourabh Mukhopadhyay, Shyamal Mondal, Satya Pratap Singh, Aditya Date, Kamal Hussain, and Prasanta Kumar Datta  »View Author Affiliations


Optics Express, Vol. 21, Issue 1, pp. 454-462 (2013)
http://dx.doi.org/10.1364/OE.21.000454


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Abstract

Large nonlinear phase shift achieved by exploiting intracavity second order cascaded nonlinear process in a non-phasematched second harmonic generating crystal is transformed into amplitude modulation through soft aperturing the nonlinear cavity mode variation within the laser gain medium to mode-lock a Nd:YVO4 laser. The laser delivers stable dual wavelength cw mode-locked pulse train with pulse duration 10.3 ps and average power of 1.84 W and 255 mW at 1064 nm and 532 nm respectively for a pump power of 12 W. A comprehensive theoretical analysis finds the regime of self starting and stable cascaded second order mode-locking, inconformity with the experimental result.

© 2013 OSA

1. Introduction

In the present report we demonstrate for the first time, to the best of our knowledge, soft aperture dual wavelength CSM delivering pulse train of width 10.3 ps in both 1064 nm and 532 nm simultaneously from a single laser oscillator. Without using any physical aperture, the nonlinear loss modulation is achieved through reducing mode size with intracavity power at the gain medium and thus increasing effective gain for a short duration through better overlapping between pump and the cavity mode size. Theoretical investigation on the nonlinear phase shift and it’s variation on intracavity intensity and the phase mismatch is carried out to understand the behaviour of intensity dependent refractive index of the nonlinear crystal, arises due to the cascaded second order nonlinear interaction. Finally a direct insight to the CSM mechanism is obtained by calculation of the nonlinear variation of the cavity mode size at the gain medium and comparing the theoretical results with the experiment. The theoretical and experimental work being reported here is carried out at the Dept. of Physics, IIT Kharagpur. The developed dual wavelength picosecond source can find application in soft tissue ablation, photo chemistry, nondegenerate pump probe experiment, biomedical application and micro-structuring. The developed laser can also be used for efficient generation of picosecond UV pulses, which has significant importance for generation of colour centre in dielectric, time resolved photoluminescence and Raman study.

2. Experiment

The schematic of the laser layout is shown in Fig. 1
Fig. 1 Schematic of the soft aperture CSM laser: LDA, laser diode array; L1 and L2 focusing lenses; RM, rear mirror; M1 and M2, folding mirrors; OC, output coupler.
. The pump is a 808 nm fiber coupled laser diode array of maximum output power 12 W and is focused to a spot size of 240 µm at the centre of the gain medium which is a 4x4x8 mm3, a-cut, Nd:YVO4 crystal having Nd3+ concentration of 0.5%. The rear face of the RM is anti-reflection coated at 808 nm and has high reflectivity (>99.5%) at 1064 nm on the other side. The Nd:YVO4 crystal is anti-reflection coated on both of its parallel faces for wavelengths 1064 nm and 808 nm and is tilted by an angle of 2° to reduce the effect of undesired satellite cavity. Two concave mirrors M1 and M2 of radius of curvature 500 mm and 250 mm respectively are used to focus the beam at the OC. The tilting angle of M1 and M2 is kept as low as possible to avoid cavity astigmatism and thus providing TEM00 mode throughout the cavity which has been found to be necessary for stable cw ML operation.

A KTP crystal of length 9 mm, cut for type-II SHG (θ = 90°, φ = 23.5°) of 1.064 µm, is placed near the OC. The OC is chosen to have reflectivity of 96% at 1064 nm and 20% at 532 nm such that maximizing intracavity power the cascaded effect can be enhanced as well as optimum SH power can be coupled out . The different arms of the Z-shaped passive cavity of length 81.7 cm are optimized to be 250 mm, 405 mm and 162 mm respectively which gives a cavity mode size of 442 µm at the gain medium and 213 µm at the centre of the KTP crystal, as determined by the ABCD matrix formalism. No mode-locking is observed when the KTP crystal is set at exact phase matched condition (φ = 23.5°) corresponding to ΔkL=(k2ωekωokωe)L=0, where ki are the wave numbers and L is the length of the KTP crystal. As the crystal is detuned from phase matching by an angle more than 1° in the direction of increasing φ, mode-locking is found to set in but initially with a smaller depth of modulation of the mode-locked pulses. Depth of modulation of the mode-locked pulses is found to increase as the phase mismatch angle (Δφ) is continued to increase in the same direction and full depth of modulation is achieved around Δφ ≈1.5°. As the crystal is further detuned, the depth of modulation decreases and when the phase mismatch angle increases over 2°, mode-locking finally disappears. However, no mode-locking is observed for any phase mismatch in the other side of the phase matching angle. Most stable operation with full depth of modulation of the mode-locked pulses is found to occur when the crystal is set approximately by an angle of 25°20. Finally the laser is optimized for stable mode-locked operation by varying the separation between KTP and the OC and the distance is finally kept 3mmfor optimum operation.

3. Results

The laser generates mode-locked pulse train simultaneously at both 1064 nm and 532 nm with pulse repetition rate 178 MHz. In Fig. 2(a)
Fig. 2 (a) Non collinear SHG intensity autocorrelation trace, Dots: experimental data. Continuous line: sech2 fit. (b) Optical spectrum of the pulse.
, we show a typical measured trace of non-collinear back ground free intensity autocorrelation, employing a 3 mm long BBO crystal, for 1064 nm pulse. The FWHM of the autocorrelation trace is measured to be 15.9 ps, corresponding to a pulse width of 10.3 ps for assumed sech2 pulse shape. The spectrum of the pulse is shown in Fig. 2(b) as measured by a grating based spectrometer having resolution of 0.08 nm. The spectral bandwidth is measured to be 0.18 nm which is greater than 0.11 nm, the transform limited bandwidth corresponding to 10 ps pulse. The ML sets in for input pump power of 9 W and maximum mode-locked output power achieved are 1.84 W and 255 mW at 1064 nm and 532 nm respectively corresponding to the input pump power of 12W (Fig. 3
Fig. 3 Laser output power versus pump power for mode-locked operation. The open (-□-) and filled squares (-■-) are the measured data for 1064 nm and 532 nm respectively.
).

Owing to the high effective nonlinear coefficient of KTP (3.5 pm/V) and the intra-cavity effect, power obtained at 532 nm and at 1064 nm, proves the laser to be an efficient dual wavelength ps source. More over the output power can be scaled up since the ML scheme is not restricted by the input pump power. The ML regime is found to be highly stable in both short and long time scale and is never affected by the Q-switching instability. The stability of the mode-locking is evident from oscilloscope trace of the mode-locked pulse train in different time scale (Fig. 4
Fig. 4 Oscilloscope trace of mode-locked pulse train in ns (a) and in µs (b) time scale.
). The output power fluctuation is less than 1% and does not drop even after running for hours. The pulse amplitude fluctuation as measured in oscilloscope is less than 5% rms.

4. Theoretical analysis of CSM

To gain a deep insight to the CSM mechanism and optimize it appropriately, it is absolutely necessary to calculate the nonlinear phase shift suffered by the FW beam after round trip through the KTP crystal. The FW beam, in it’s forward pass through KTP generate SH under type-II interaction. If the phase differenceΔϑ=ϑ2ω2ϑω, accumulated between the SH and FW beam due to propagation between the KTP and the OC is properly adjusted the SH, in its return pass through KTP will be completely down converted to FW. These two cascaded processes can theoretically be modeled using the coupled amplitude equation given by
dASHdz=iωn2ωcdeffAFW2exp(iΔkz)
(1a)
dAFWdz=iω2nωcdeffASHAFWexp(iΔkz)
(1b)
where AFW and ASH are the field amplitudes of fundamental and second harmonic respectively, nω and n are the refractive indices of FW and SH and deff is the effective nonlinear coefficient for the interaction. Since the sample length (L = 9 mm) is much smaller than the Rayleigh length (~130 mm), we can neglect diffraction effects and treat every point on the beam cross section as independent of others. So the plane wave approximation is valid enough for the beam propagation through the KTP crystal only. Normalizing the field amplitudes to the initial fundamental amplitude AFW(0) and setting ξ=z/L, we get the following dimensionless equations:
dASHdξ=iγSAF2exp(iΔkLξ)
(2a)
dAFWdξ=iγFASHAFWexp(iΔkLξ)
(2b)
whereγS=ωnSHcdeffLAFW(0)andγF=ω2nFWcdeffLAFW(0)
The above equations are readily solved for two passes to give the total non-linear phase shift at the end of the double pass. We need to factor in the different reflectivity of the fundamental and second harmonic at the output coupler as well as the phase shiftΔϑ. Complete back conversion of the SH beam into the FW takes place forΔϑ=π, independently of the crystal phase mismatch. Figure 5
Fig. 5 Nonlinear phase shift (ΔΦNL), in color code (in units of π) as a function of crystal phase mismatch, ΔkL (in units of π) and intracavity FW intensity at KTP crystal.
shows a plot of the nonlinear phase shift ΔΦNL, represented by the color code (in units of π), as a function of intensity and phase mismatch, ΔkL (in units of π).

We see that the phase shift changes sign at the phase-matching angle. Thus the cascaded interaction gives rise to a self-focussing or defocussing nature similar to that of a Kerr medium, with an intensity dependent refractive index given by:
n=nFW+n2effI
(3)
where, I is the intracavity fundamental intensity at KTP crystal. For large nonlinear phase shift, when ΔΦNL varies linearly with the intensity [4

4. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17(1), 28–30 (1992). [CrossRef] [PubMed]

], n2eff can be calculated from (assuming nonlinear phase shift of ΔΦNL /2 per pass):
ΔΦNL2=ωcn2effLI
(4)
It is clear that for ΔkL<0, the nonlinear phase shift is positive and the KTP crystal behaves as a self-focussing medium with positive n2eff and on the other side, for ΔkL>0, we have a negative phase shift giving rise to a self-defocussing behaviour with negative n2eff.

Finally we apply the formalism for closed form Gaussian beam analysis of a resonator with an intracavity Kerr medium [18

18. V. Magni, G. Cerullo, and S. De Silvestri, “ABCD matrix analysis of propagation of gaussian beams through Kerr media,” Opt. Commun. 96(4-6), 348–355 (1993). [CrossRef]

,19

19. V. Magni, G. Cerullo, and S. De Silvestri, “Closed form Gaussian beam analysis of resonators containing a Kerr medium for femtosecond laser,” Opt. Commun. 101(5-6), 365–370 (1993). [CrossRef]

] to calculate the nonlinear mode size variation at the laser gain medium with the intracavity peak power. Our analysis shows that mode size at the laser gain medium decreases with an increase in the peak power when the cascaded nonlinear process makes to behave the KTP crystal as a self-focussing medium corresponding to a positive nonlinear phase shift. Figure 6
Fig. 6 Variation of mode size at the laser gain medium as a function of intracavity peak power for (i) ΔkL = -π/2 ; blue dashed, (ii) ΔkL = -π ; black solid, and (iii) ΔkL = −2π ; red doted. Low power variation of the same mode size, when the pulse formation starts is shown in the inset.
shows the mode size variation at the laser gain medium as a function of intracavity peak power for different values of ΔkL. Comparing Fig. 5 and 6, it is evident that for ΔkL = -π, the nonlinear phase shift and also the self-focussing power of the KTP reaches maximum, resulting in a maximum mode size variation at the laser gain medium. Thus at ΔkL = -π, corresponding to the KTP crystal angle φ = 25°5′38, the driving force for the CSM, analogous to the KLM [20

20. G. Cerullo, S. D. Silvestri, and V. Magni, “Self-starting Kerr-lens mode locking of a Ti:Sapphire laser,” Opt. Lett. 19(14), 1040–1042 (1994). [CrossRef] [PubMed]

,21

21. K. H. Lin and W. F. Hsieh, “Analytical design of symmetrical Kerr-lens mode-locking laser cavities,” Opt. Lett. 11, 737–739 (1994).

], would reach a maximum value. At this optimum value of ΔkL, one should expect a self starting and self sustained mode-locking and it agrees remarkably well with our experimental findings. In fact the driving force corresponding to the optimum value of ΔkL is so strong that one does not even need to control the cavity elements to work at the limit of geometrical cavity instability, rather can safely work in the stable cavity regime.

5. Discussion

6. Conclusion

Second order cascaded nonlinear interaction in an intracavity nonphasematchesd type-II SHG KTP crystal produces large nonlinear phase shift on the FW wave and induces large Re(χeff(3))to make the KTP crystal to behave as a Kerr media. For a positive ΔΦNL, KTP exhibits self-focussing behaviour, which under closed form Gaussian beam analysis shows the cavity mode at the gain medium to decrease with the power and gives direct nonlinear loss modulation through better overlapping between pump and the cavity mode resulting in an efficient, stable CSM. The developed soft aperture CSM laser generates dual colour picosecond pulses of width 10.3 ps at 1064 nm and 532 nm simultaneously from a single resonator. The laser delivers average power of 1.84 W and 255 mW at 1064 nm and 532 nm respectively corresponding to a pulse repetition rate of 178 MHz. The theoretical analysis shows the ΔΦNL and n2effto reach a maximum for ΔkL = -π, which in turn provides strong CSM driving force through maximum mode size variation with power. The theoretical analysis agrees well with the experimental observations and finds the regime of stable, self starting and self sustained CSM.

Acknowledgments

S. Mukhopadhyay gratefully acknowledges Department of Higher Education, Govt. of West Bengal and Indian Institute of Technology Kharagpur for necessary support. S. Mondal acknowledges CSIR, Govt. of India for maintenance fellowship and P. K. Datta acknowledges DRDO (ERIP), Govt. of India, and DST, Govt. of India, for financial support. Prof. S. K. Bhakta is acknowledged for useful discussion.

References and links

1.

D. E. Spence, P. N. Kean, and W. Sibbett, “60-fsec pulse generation from a self-mode-locked Ti:Sapphire laser,” Opt. Lett. 16(1), 42–44 (1991). [CrossRef] [PubMed]

2.

M. Piche and F. Salin, “Self-mode locking of solid-state lasers without apertures,” Opt. Lett. 18(13), 1041–1043 (1993). [CrossRef] [PubMed]

3.

M. A. Larotonda, A. A. Hnilo, and F. P. Diodati, “Diode-pumped self-starting Kerr-lens mode locking Nd:YAG laser,” Opt. Commun. 183(5-6), 485–491 (2000). [CrossRef]

4.

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17(1), 28–30 (1992). [CrossRef] [PubMed]

5.

G. I. Stegeman, M. Sheik-Bahae, E. Van Stryland, and G. Assanto, “Large nonlinear phase shifts in second-order nonlinear-optical processes,” Opt. Lett. 18(1), 13–15 (1993). [CrossRef] [PubMed]

6.

K. A. Stankov and J. Jethwa, “A new mode-locking technique using a nonlinear mirror,” Opt. Commun. 66(1), 41–46 (1988). [CrossRef]

7.

K. A. Stankov, “25ps pulses from a Nd:YAG laser mode-locked by a frequency doubling β-BaB2O4 crystal,” Appl. Phys. Lett. 58(20), 2203–2204 (1991). [CrossRef]

8.

P. K. Datta, S. Mukhopadhyay, S. K. Das, L. Tartara, A. Agnesi, and V. Degiorgio, “Enhancement of stability and efficiency of a nonlinear mirror mode-locked Nd:YVO4 oscillator by an active Q-switch,” Opt. Express 12(17), 4041–4046 (2004). [CrossRef]

9.

M. Li, S. Z. Zhao, K. J. Yang, G. Li, D. Li, J. Wang, J. An, and W. Qiao, “Actively Q-switched and mode-locked diode-pumped Nd:GdVO4-KTP laser,” IEEE J. Q. Electron. 44(3), 288–293 (2008). [CrossRef]

10.

A. Ray, S. K. Das, S. Mukhopadhyay, and P. K. Datta, “Acousto-optic-modulator stabilized low-threshold mode-locked Nd:YVO4 laser,” Appl. Phys. Lett. 89(22), 221119 (2006). [CrossRef]

11.

P. K. Datta, S. Mukhopadhyay, G. K. Samanta, S. K. Das, and A. Agnesi, “Realization of inverse saturable absorption by intra-cavity third harmonic generation for efficient nonlinear mirror mode-locking,” Appl. Phys. Lett. 86(15), 151105 (2005). [CrossRef]

12.

G. Cerullo, S. De Silvestri, A. Monguzzi, D. Segala, and V. Magni, “Self-starting mode locking of a cw Nd:YAG laser using cascaded second-order nonlinearities,” Opt. Lett. 20(7), 746–748 (1995). [CrossRef] [PubMed]

13.

M. Zavelani-Rossi, G. Cerullo, and V. Magni, “Mode locking by cascading of second-order nonlinearities,” IEEE J. Quantum Electron. 34(1), 61–70 (1998). [CrossRef]

14.

S. J. Holmgren, V. Pasiskevicius, and F. Laurell, “Generation of 2.8 ps pulses by mode-locking a Nd:GdVO4 laser with defocusing cascaded Kerr lensing in periodically poled KTP,” Opt. Express 13(14), 5270–5278 (2005). [CrossRef] [PubMed]

15.

H. Iliev, D. Chuchumishev, I. Buchvarov, and V. Petrov, “Passive mode-locking of a diode-pumped Nd:YVO4 laser by intracavity SHG in PPKTP,” Opt. Express 18(6), 5754–5762 (2010). [CrossRef] [PubMed]

16.

H. Iliev, I. Buchvarov, S. Kurimura, and V. Petrov, “High-power picosecond Nd:GdVO4 laser mode locked by SHG in periodically poled stoichiometric lithium tantalate,” Opt. Lett. 35(7), 1016–1018 (2010). [CrossRef] [PubMed]

17.

C. Schäfer, C. Fries, C. Theobald, and J. A. L’huillier, “Parametric Kerr lens mode-locked, 888 nm pumped Nd:YVO4 laser,” Opt. Lett. 36(14), 2674–2676 (2011). [CrossRef] [PubMed]

18.

V. Magni, G. Cerullo, and S. De Silvestri, “ABCD matrix analysis of propagation of gaussian beams through Kerr media,” Opt. Commun. 96(4-6), 348–355 (1993). [CrossRef]

19.

V. Magni, G. Cerullo, and S. De Silvestri, “Closed form Gaussian beam analysis of resonators containing a Kerr medium for femtosecond laser,” Opt. Commun. 101(5-6), 365–370 (1993). [CrossRef]

20.

G. Cerullo, S. D. Silvestri, and V. Magni, “Self-starting Kerr-lens mode locking of a Ti:Sapphire laser,” Opt. Lett. 19(14), 1040–1042 (1994). [CrossRef] [PubMed]

21.

K. H. Lin and W. F. Hsieh, “Analytical design of symmetrical Kerr-lens mode-locking laser cavities,” Opt. Lett. 11, 737–739 (1994).

22.

T. R. Schibli, E. R. Thoen, F. X. Kärtner, and E. P. Ippen, “Suppression of Q-switched mode locking and break-up into multiple pulses by inverse saturable absorption,” Appl. Phys. B 70(S1), S41–S49 (2000). [CrossRef]

23.

A. Agnesi, A. Guandalini, A. Tomaselli, E. Sani, A. Toncelli, and M. Tonelli, “Diode-pumped passively mode-locked and passively stabilized Nd3+:BaY2F8 laser,” Opt. Lett. 29(14), 1638–1640 (2004). [CrossRef] [PubMed]

24.

V. Couderc, F. Louradour, and A. Barthelemy, “2.8 ps pulses from a mode-locked diode pumped Nd:YVO4 laser using quadratic polarization switching,” Opt. Commun. 166(1-6), 103–111 (1999). [CrossRef]

25.

I. Buchvarov, S. Saltiel, C. Iglev, and K. Koynov, “Intensity dependent change of polarization state as a result of nonlinear phase shift in type II frequency doubling crystals,” Opt. Commun. 141(3-4), 173–179 (1997). [CrossRef]

OCIS Codes
(140.0140) Lasers and laser optics : Lasers and laser optics
(140.4050) Lasers and laser optics : Mode-locked lasers
(190.0190) Nonlinear optics : Nonlinear optics
(190.3270) Nonlinear optics : Kerr effect
(190.7110) Nonlinear optics : Ultrafast nonlinear optics

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: October 19, 2012
Revised Manuscript: December 7, 2012
Manuscript Accepted: December 10, 2012
Published: January 4, 2013

Citation
Sourabh Mukhopadhyay, Shyamal Mondal, Satya Pratap Singh, Aditya Date, Kamal Hussain, and Prasanta Kumar Datta, "Dual colour cw mode-locking through soft aperture based on second order cascaded nonlinearity," Opt. Express 21, 454-462 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-1-454


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References

  1. D. E. Spence, P. N. Kean, and W. Sibbett, “60-fsec pulse generation from a self-mode-locked Ti:Sapphire laser,” Opt. Lett.16(1), 42–44 (1991). [CrossRef] [PubMed]
  2. M. Piche and F. Salin, “Self-mode locking of solid-state lasers without apertures,” Opt. Lett.18(13), 1041–1043 (1993). [CrossRef] [PubMed]
  3. M. A. Larotonda, A. A. Hnilo, and F. P. Diodati, “Diode-pumped self-starting Kerr-lens mode locking Nd:YAG laser,” Opt. Commun.183(5-6), 485–491 (2000). [CrossRef]
  4. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett.17(1), 28–30 (1992). [CrossRef] [PubMed]
  5. G. I. Stegeman, M. Sheik-Bahae, E. Van Stryland, and G. Assanto, “Large nonlinear phase shifts in second-order nonlinear-optical processes,” Opt. Lett.18(1), 13–15 (1993). [CrossRef] [PubMed]
  6. K. A. Stankov and J. Jethwa, “A new mode-locking technique using a nonlinear mirror,” Opt. Commun.66(1), 41–46 (1988). [CrossRef]
  7. K. A. Stankov, “25ps pulses from a Nd:YAG laser mode-locked by a frequency doubling β-BaB2O4 crystal,” Appl. Phys. Lett.58(20), 2203–2204 (1991). [CrossRef]
  8. P. K. Datta, S. Mukhopadhyay, S. K. Das, L. Tartara, A. Agnesi, and V. Degiorgio, “Enhancement of stability and efficiency of a nonlinear mirror mode-locked Nd:YVO4 oscillator by an active Q-switch,” Opt. Express12(17), 4041–4046 (2004). [CrossRef]
  9. M. Li, S. Z. Zhao, K. J. Yang, G. Li, D. Li, J. Wang, J. An, and W. Qiao, “Actively Q-switched and mode-locked diode-pumped Nd:GdVO4-KTP laser,” IEEE J. Q. Electron.44(3), 288–293 (2008). [CrossRef]
  10. A. Ray, S. K. Das, S. Mukhopadhyay, and P. K. Datta, “Acousto-optic-modulator stabilized low-threshold mode-locked Nd:YVO4 laser,” Appl. Phys. Lett.89(22), 221119 (2006). [CrossRef]
  11. P. K. Datta, S. Mukhopadhyay, G. K. Samanta, S. K. Das, and A. Agnesi, “Realization of inverse saturable absorption by intra-cavity third harmonic generation for efficient nonlinear mirror mode-locking,” Appl. Phys. Lett.86(15), 151105 (2005). [CrossRef]
  12. G. Cerullo, S. De Silvestri, A. Monguzzi, D. Segala, and V. Magni, “Self-starting mode locking of a cw Nd:YAG laser using cascaded second-order nonlinearities,” Opt. Lett.20(7), 746–748 (1995). [CrossRef] [PubMed]
  13. M. Zavelani-Rossi, G. Cerullo, and V. Magni, “Mode locking by cascading of second-order nonlinearities,” IEEE J. Quantum Electron.34(1), 61–70 (1998). [CrossRef]
  14. S. J. Holmgren, V. Pasiskevicius, and F. Laurell, “Generation of 2.8 ps pulses by mode-locking a Nd:GdVO4 laser with defocusing cascaded Kerr lensing in periodically poled KTP,” Opt. Express13(14), 5270–5278 (2005). [CrossRef] [PubMed]
  15. H. Iliev, D. Chuchumishev, I. Buchvarov, and V. Petrov, “Passive mode-locking of a diode-pumped Nd:YVO4 laser by intracavity SHG in PPKTP,” Opt. Express18(6), 5754–5762 (2010). [CrossRef] [PubMed]
  16. H. Iliev, I. Buchvarov, S. Kurimura, and V. Petrov, “High-power picosecond Nd:GdVO4 laser mode locked by SHG in periodically poled stoichiometric lithium tantalate,” Opt. Lett.35(7), 1016–1018 (2010). [CrossRef] [PubMed]
  17. C. Schäfer, C. Fries, C. Theobald, and J. A. L’huillier, “Parametric Kerr lens mode-locked, 888 nm pumped Nd:YVO4 laser,” Opt. Lett.36(14), 2674–2676 (2011). [CrossRef] [PubMed]
  18. V. Magni, G. Cerullo, and S. De Silvestri, “ABCD matrix analysis of propagation of gaussian beams through Kerr media,” Opt. Commun.96(4-6), 348–355 (1993). [CrossRef]
  19. V. Magni, G. Cerullo, and S. De Silvestri, “Closed form Gaussian beam analysis of resonators containing a Kerr medium for femtosecond laser,” Opt. Commun.101(5-6), 365–370 (1993). [CrossRef]
  20. G. Cerullo, S. D. Silvestri, and V. Magni, “Self-starting Kerr-lens mode locking of a Ti:Sapphire laser,” Opt. Lett.19(14), 1040–1042 (1994). [CrossRef] [PubMed]
  21. K. H. Lin and W. F. Hsieh, “Analytical design of symmetrical Kerr-lens mode-locking laser cavities,” Opt. Lett.11, 737–739 (1994).
  22. T. R. Schibli, E. R. Thoen, F. X. Kärtner, and E. P. Ippen, “Suppression of Q-switched mode locking and break-up into multiple pulses by inverse saturable absorption,” Appl. Phys. B70(S1), S41–S49 (2000). [CrossRef]
  23. A. Agnesi, A. Guandalini, A. Tomaselli, E. Sani, A. Toncelli, and M. Tonelli, “Diode-pumped passively mode-locked and passively stabilized Nd3+:BaY2F8 laser,” Opt. Lett.29(14), 1638–1640 (2004). [CrossRef] [PubMed]
  24. V. Couderc, F. Louradour, and A. Barthelemy, “2.8 ps pulses from a mode-locked diode pumped Nd:YVO4 laser using quadratic polarization switching,” Opt. Commun.166(1-6), 103–111 (1999). [CrossRef]
  25. I. Buchvarov, S. Saltiel, C. Iglev, and K. Koynov, “Intensity dependent change of polarization state as a result of nonlinear phase shift in type II frequency doubling crystals,” Opt. Commun.141(3-4), 173–179 (1997). [CrossRef]

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