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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 9 — May. 2, 2005
  • pp: 3224–3229
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Femtosecond supercontinuum generation in a quadratic nonlinear medium (KDP)

N. K. M. Naga Srinivas, S. Sree Harsha, and D. Narayana Rao  »View Author Affiliations


Optics Express, Vol. 13, Issue 9, pp. 3224-3229 (2005)
http://dx.doi.org/10.1364/OPEX.13.003224


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Abstract

We report the first ever femtosecond supercontinuum generation in a KDP crystal using ~100 fs pulses at 790 nm irradiation. Due to the quadratic nonlinearities of the KDP crystal an enhanced bandwidth of 385–960 nm is generated. The spatial and temporal coherence of the generated white light is demonstrated using Young’s double slit interference configuration and a Michelson interferometer.

© 2005 Optical Society of America

1. Introduction

The interaction of intense ultrashort optical pulses with transparent materials can become strongly nonlinear. The temporal, spatial, and spectral properties of an ultrashort pulse undergo modification when it propagates through such a medium [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, 592–594 (1970). [CrossRef]

]. The appearance of a large frequency sweep, which can extend from the ultraviolet to the infrared, is the spectral representation of the spatio-temporal modification of the pulse in the medium [2

2. R. R. Alfano, The Supercontinuum laser source, Springer-Verlag, Berlin (1989).

, 3

3. V. P. Kandidov, O. G. Kosareva, I. S. Golubtsov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, “Self-transformation of a powerful femtosecond laser pulse into a white-light pulse in bulk optical media (or super continuum generation),” Appl. Phys. B 77, 149–165 (2003). [CrossRef]

]. This physical phenomenon is popularly termed as supercontinuum generation (SCG) [4

4. R. L. Fork, C. V. Shank, C. Hirlimann, R. Yen, and W. J. Tomlinson, “Femtosecond white-light continuum pulses,” Opt. Lett. 8, 1–3 (1983). [CrossRef] [PubMed]

]. The primary process responsible for these changes is self-focusing, which causes the pulse to compress in space, resulting in a corresponding increase in the peak intensities [5

5. P. B. Corkum, C. Rolland, and T. Srinivasan Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett. 57, 2268–2271 (1986). [CrossRef] [PubMed]

]. The other dominant processes and starting mechanisms leading to spectral broadening are self phase modulation, self-steepening, parametric four-photon mixing, Raman scattering, and others. These processes are particularly efficient if the phase matching condition for the k vectors for the participating waves is satisfied [2

2. R. R. Alfano, The Supercontinuum laser source, Springer-Verlag, Berlin (1989).

6

6. A. Brodeur, F. A. Ilkov, and S. L. Chin, “Beam filamentation and the white light continuum divergence,” Opt. Commun. 129, 193–198 (1996). [CrossRef]

].

Since its first observation, SCG has been demonstrated in a variety of materials, including solids, liquids, and gases [2

2. R. R. Alfano, The Supercontinuum laser source, Springer-Verlag, Berlin (1989).

, 7

7. G. Yang and Y. R. Shen, “Spectral broadening of ultrashort pulses in a nonlinear medium,” Opt. Lett. 9, 510–512 (1984). [CrossRef] [PubMed]

11

11. A. K. Dharmadhikari, F. A. Rajgara, N. C. S. Reddy, A. S. Sandhu, and D. Mathur, “Highly efficient white light generation from barium fluoride,” Opt. Express 12, 695–700 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-695 [CrossRef] [PubMed]

]. Its unique characteristics make the supercontinuum an ideal broadband ultrafast light source for applications such as femtosecond time-resolved spectroscopy, optical pulse compression for the generation of ultrashort pulses, or as a seed pulse for optical parametric amplifiers, and biomedical applications [12

12. J. H. Glownia, J. Misewich, and P. P. Sorokin, “Ultrafast ultraviolet pump-probe apparatus,” J. Opt. Soc. Am. B 3, 1573–1579 (1986). [CrossRef]

19

19. E. Hugonnot, M. Somekh, D. Villate, F. Salin, and E. Freysz, “Optical parametric chirped pulse amplification and spectral shaping of a continuum generated in a photonic band gap fiber,” Opt. Express 12, 2397–2403 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-11-2397 [CrossRef] [PubMed]

]. For spectroscopic studies, SCG has proven to be a useful source of broadly tunable ultrafast pulses from the near ultraviolet to the far infrared.

We know that the second harmonic and third harmonic generation takes the fundamental easily into UV and far UV regions through the usage of proper phase matching crystals. Therefore, there is a need to find materials suitable for frequency conversion as well as continuum generation at high intensities. Hence, we have chosen potassium dihydrogen phosphate (KDP), which is a well-known efficient harmonic generator possessing high damage threshold [20

20. M. Aoyama, T. Harimoto, J. Ma, Y. Akahane, and K. Yamakawa, “Second - harmonic generation of ultra-high intensity femtosecond pulses with a KDP crystal,” Opt. Express9, 579–585 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-11-2397 [CrossRef] [PubMed]

].

In this paper we report the first ever demonstration of supercontinuum generation in a nonlinear crystal KDP, pumped with ~100 fs pulses at 790nm. The coherence properties of the SCG are demonstrated using Young’s double slit interference and a Michelson interferometer.

2. Experimental details

Ultrashort laser pulses used in the present study are generated using a conventional chirped pulse amplification (CPA) system. The laser system comprises of an oscillator (MaiTai, Spectra Physics Inc.) that delivers a ~80 fs, 82MHz pulse train with pulse energy of 1nJ at 790 nm. The full width half maximum bandwidth of the oscillator pulses, as measured with a spectrometer, is ~11 nm. The pulse train from the oscillator is directed into a regenerative amplifier (Spitfire, Spectra Physics Inc.) pumped by a 150 ns, 1 kHz, Q-switched Nd: YLF laser (Evolution-X, Spectra Physics Inc.). After compression we obtained pulses of ~100 fs duration (measured with a home built autocorrelator) with output energy of upto 1mJ, at 1 kHz repetition rate with the corresponding bandwidth measured to be ~9 nm. The output beam diameter is 8 mm.

In a typical experiment, the beam is focused into the sample (1 cm×1 cm×1 cm KDP cube) and the generated continuum is detected using a fiber coupled CCD spectrometer (Ocean Optics - SD2000). The KDP that is used in the present experiment has been supplied to us by Mr. Bob Zewada of USA, cut for SHG of 1064 nm. Through the X-Ray studies, we found that the face that is kept normal to the laser beam has (h k l) values (-20 3 14). It may be noted here that since the crystal face is manually oriented in the X-ray setup, there could be an error of 10% in the orientation of the crystal face. The laser energy that was incident on the material under study was measured using an energy meter with a nearly flat and wide spectral response. The same energy meter was also used to measure the energy of the entire white light continuum after attenuation of the fundamental through an IR filter.

3. Results and discussion

The very first material to be used and exploited for their nonlinear optical (NLO) and electro-optic properties was KDP [21

21. A. Yariv, Quantum Electronics, John Wiley & Sons, New York, USA, 1988.

]. Several groups have reported SHG from KDP crystal using ultrashort sources. Aoyama et al. [20

20. M. Aoyama, T. Harimoto, J. Ma, Y. Akahane, and K. Yamakawa, “Second - harmonic generation of ultra-high intensity femtosecond pulses with a KDP crystal,” Opt. Express9, 579–585 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-11-2397 [CrossRef] [PubMed]

] have demonstrated SHG of ultra-high intensity femto second pulses with KDP crystal. They achieved efficiency as high as 80% with 130 fs pulses at an intensity of 192 GWcm-2 with a crystal of thickness 1 mm. This clearly demonstrates the high conversion efficiency and damage threshold of the material.

Earlier work [8

8. P. B. Corkum, P. P. Ho, R. R. Alfano, and J. T. Manassah, “Generation of infrared supercontinuum covering 3–14 µm in dielectrics and semiconductors,” Opt. Lett. 10, 624–626 (1985). [CrossRef] [PubMed]

, 9

9. A. Brodeur and S. L. Chin, “Band-gap dependence of the ultrafast white light continuum,” Phys. Rev. Lett. 80, 4406–4409 (1998). [CrossRef]

] in solids has shown that the cutoff wavelength on the blue side scales roughly with the bandgap of the material and that, as long as the bandgap energy is equal to or greater than 4.7 eV, SCG can occur. Various high band gap materials have been investigated for continuum generation. The direct band gap of KDP is found to be 7.12 eV (174 nm), which is quite high [22

22. V. G. Dimitriev, G. G. Gurzaddyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 2nd revised ed. (Springer, Berlin, 1977).

]. This combination of high band gap and presence of high nonlinearity propelled us to investigate the SCG in KDP.

The laser beam is focused with a lens of focal length 200 mm. The calculated beam waist at the focal point in vacuum is ~70 µm. Beam waist could however be different in the crystal from vacuum due to different nonlinear processes. The crystal, however, was always placed at a point 1.5 cm before the focal point in order to avoid any damage to the surface. The diameter of the beam on the front face of the crystal is ~1 mm. The phase matching angle of the KDP crystal for SHG of 790 nm is 44.9° and Type I critical phase matching has been used. The SCG is investigated at phase matching angle (indicated by 0°) and also away from the phase matching angle. The visual appearance of the generated supercontinuum, at and away from the phase matching angle is shown in Fig. 1. The picture in the left panel clearly shows the tandem generation of SHG as well as SCG at phase matching angle. It may be noted that blue color seen in the left panel is the emission from the screen due to SHG. The right panel shows the SCG generated away from the phase matching angle. The faint blue ring seen on the right panel has its origin in the conical emission, which generally accompanies SCG. The spectral content of the continuum generated away from the phase matching angle (θ=+25°, where θ is taken as +ve for clock wise rotation and –ve for anti clock wise rotation) is depicted in Fig. 2. The observed bandwidth is from 420–960 nm. As we rotate the crystal towards the phase matching angle, SHG starts showing up. The evolution of the spectral content of SCG as well as the SHG, as we rotate the crystal away from the phase matching angle is depicted in Fig. 3.

Fig. 1. The left panel shows the supercontinuum generated at the phase matching angle of KDP crystal and the right panel at an angle far away from phase matching angle. The figures are as seen on a white screen. The blue color in the left panel is due to the emission from the screen due to SHG.
Fig. 2. Dispersion and Spectrum measured away from phase matching angle of the generated supercontinuum (after attenuating the pump beam with an IR filter).
Fig. 3. Evolution of the SHG and SCG as we rotate the crystal towards the phase matching angle (Here 0° refers to phasematching angle and the angular variation is measured with respect to it).
Fig. 4. Dispersion and Spectrum measured θ=-55° away from phase matching angle of the generated supercontinuum (after attenuating the pump beam with an IR filter).

For angles away from the phase matching direction for SHG, we observe an increase in the intensity of the continuum while the SHG intensity reduces. At the phase matching angle the intensity of the second harmonic is dominant compared to the intensity of the SCG. This could be because of the depletion of the input field by the SHG conversion before the onset of self-focusing initiating continuum generation. A crystal that was cut at an angle of nearly θ=-55° with respect to the phase matching angle shows a blue enhanced spectral region as shown in Fig. 4. This enhancement in the spectral region around blue could be due to parametric wave mixing of the IR with the continuum, as the position of this peak is found to depend on the angle of the crystal and varies from 350 nm to 575 nm. Detailed studies of the enhancement in the blue region observed in the KDP crystal are under investigation and the results would be reported later. Earlier reports [9

9. A. Brodeur and S. L. Chin, “Band-gap dependence of the ultrafast white light continuum,” Phys. Rev. Lett. 80, 4406–4409 (1998). [CrossRef]

, 10

10. A. Brodeur and S. L. Chin, “Ultrafast white light continuum generation and self-focusing in transparent condensed media,” J. Opt. Soc. Am. B 16, 637–650 (1999). [CrossRef]

] established that, at sufficiently high input power, self-focusing overcomes dispersive effects, leading to an increase in the peak intensity and to the occurrence of other higher-order nonlinear optical processes. Experimentally it is found that, as the input power is increased above a certain threshold power Pth > Pcr, an extremely broad pedestal appears on the blue side of the transmitted pulse spectrum [4

4. R. L. Fork, C. V. Shank, C. Hirlimann, R. Yen, and W. J. Tomlinson, “Femtosecond white-light continuum pulses,” Opt. Lett. 8, 1–3 (1983). [CrossRef] [PubMed]

]. We observed continuum generation at a threshold power of ~16 mW (~16 µJ/pulse) by keeping the crystal at the focus of the lens. The data presented in the present study is recorded with 800 mW average power (~800 µJ/pulse), and keeping the front surface of the crystal a 1.5 cm before the focal point. This has been done in order to avoid any damage to the crystal during the data collection. An efficiency of ~12 % (after the attenuation of the pump beam with an IR filter) is observed in the continuum generation. However, when an input energy of ~100 µJ is focused at the center of the crystal, a conversion efficiency of ~23% was observed.

Fig. 5. Young’s double slit fringes with a slit separation of ~0.25 mm and ~80 µm slit width.

Filamentation is found to occur above a certain threshold input power. Each of the individual filaments can then generate white light continuum [23

23. R. G. Brewer, J. R. Lifsitz, E. Garmire, R. Y. Chiao, and C. H. Townes, “Small-scale trapped filaments in intense laser beams,” Phys. Rev. 166, 326–331 (1968). [CrossRef]

]. The supercontinuum that is generated from each of these filaments possesses a high degree of spatial coherence, which has been demonstrated using a simple Young’s double slit configuration [24

24. K. Cook, A. K. Kar, and R. A. Lamb, “White-light supercontinuum interference of self – focused filaments in water,” Appl. Phys. Lett. 83, 3861–3863 (2003). [CrossRef]

]. High degree of spatial coherence from the white light generated from multiple filaments is reported recently [25

25. W. Watanabe and K. Itoh, “Spatial coherence of supercontinuum emitters from multiple filaments,” Jpn. J. Appl. Phys. 40, 592–595 (2001). [CrossRef]

]. In these experiments, a stable interference is obtained in the far field that indicates that for the white light generated in these filaments, each spectral component has the same coherence as the initial pump pulse. We demonstrated the coherence properties of SCG by using Young’s double slit experiment and a Michelson interferometer. A Young’s double slit geometry is used to determine the spatial coherence. We have done this by placing two slits of width ~80 µm and separated by ~0.25 mm normal to the direction of propagation of white light, and by measuring the fringe visibility of the interference pattern that is obtained in the far field. The fringe pattern is depicted in Fig. 5. Fringes are observed until the separation between the slits is increased to 4 mm, for an input beam diameter of 12 mm. Part of the laser beam was directed to Michelson interferometer to confirm the temporal coherence of the supercontinuum generated by observing the fringes on a screen.

4. Conclusions

We have demonstrated supercontinuum generation in a 1 cm long nonlinear crystal KDP, which is known for its high damage threshold, in the presence of the second harmonic and far away from SHG phase matching angle. Depending on the angle of incidence the crystal shows blue enhanced continuum. The large bandwidth from 385–960 nm has been achieved in the visible region. An efficiency of ~23 % over the entire spectral range is achieved. The coherent nature of the white light is confirmed using Young’s double slit experiment and Michelson interferometer.

Acknowledgments

Financial support from Department of Science and Technology-FIST and ITPAR is acknowledged. We acknowledge the timely help of Dr. Reji Phillip of RRI, Bangalore, India for extending his lab facilities.

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, 592–594 (1970). [CrossRef]

2.

R. R. Alfano, The Supercontinuum laser source, Springer-Verlag, Berlin (1989).

3.

V. P. Kandidov, O. G. Kosareva, I. S. Golubtsov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, “Self-transformation of a powerful femtosecond laser pulse into a white-light pulse in bulk optical media (or super continuum generation),” Appl. Phys. B 77, 149–165 (2003). [CrossRef]

4.

R. L. Fork, C. V. Shank, C. Hirlimann, R. Yen, and W. J. Tomlinson, “Femtosecond white-light continuum pulses,” Opt. Lett. 8, 1–3 (1983). [CrossRef] [PubMed]

5.

P. B. Corkum, C. Rolland, and T. Srinivasan Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett. 57, 2268–2271 (1986). [CrossRef] [PubMed]

6.

A. Brodeur, F. A. Ilkov, and S. L. Chin, “Beam filamentation and the white light continuum divergence,” Opt. Commun. 129, 193–198 (1996). [CrossRef]

7.

G. Yang and Y. R. Shen, “Spectral broadening of ultrashort pulses in a nonlinear medium,” Opt. Lett. 9, 510–512 (1984). [CrossRef] [PubMed]

8.

P. B. Corkum, P. P. Ho, R. R. Alfano, and J. T. Manassah, “Generation of infrared supercontinuum covering 3–14 µm in dielectrics and semiconductors,” Opt. Lett. 10, 624–626 (1985). [CrossRef] [PubMed]

9.

A. Brodeur and S. L. Chin, “Band-gap dependence of the ultrafast white light continuum,” Phys. Rev. Lett. 80, 4406–4409 (1998). [CrossRef]

10.

A. Brodeur and S. L. Chin, “Ultrafast white light continuum generation and self-focusing in transparent condensed media,” J. Opt. Soc. Am. B 16, 637–650 (1999). [CrossRef]

11.

A. K. Dharmadhikari, F. A. Rajgara, N. C. S. Reddy, A. S. Sandhu, and D. Mathur, “Highly efficient white light generation from barium fluoride,” Opt. Express 12, 695–700 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-695 [CrossRef] [PubMed]

12.

J. H. Glownia, J. Misewich, and P. P. Sorokin, “Ultrafast ultraviolet pump-probe apparatus,” J. Opt. Soc. Am. B 3, 1573–1579 (1986). [CrossRef]

13.

T. Kobayashi, T. Saito, and H. Ohtani, “Real-time spectroscopy of transition states in bacteriorhodopsin during retinal isomerization,” Nature 414, 531–534 (2001). [CrossRef] [PubMed]

14.

S. Cussat-Blanc, A. Ivanov, D. Lupinski, and E. Freysz, “KTiOPO4, KTiOAsO4, and KNbO3 crystals for mid-infrared femtosecond optical parametric amplifiers: analysis and comparison,” Appl. Phys. B 70, S247–S252 (2000). [CrossRef]

15.

T. Kobayashi and A. Shirakawa, “Tunable visible and near-infrared pulse generator in a 5 fs regime”, App. Phys. B 70, S239–S246 (2000). [CrossRef]

16.

K. R. Wilson and V. V. Yakovlev, “Ultrafast rainbow: tunable ultrashort pulses from a solid-state kilohertz system,” J. Opt. Soc. Am. B 14, 444–448(1997). [CrossRef]

17.

A. Baltuska and T. Kobayashi, “Adaptive shaping of two-cycle visible pulses using a flexible mirror,” App. Phys. B 75, 427–443 (2002). [CrossRef]

18.

Pei-Lin Hsiung, Yu Chen, Tony H. Ko, James G. Fujimoto, C. J. S. de Matos, S. V. Popov, J. R. Taylor, and V. P. Gapontsev, “Optical coherence tomography using a continuous-wave, high-power, Raman continuum light source, “Opt. Express 12, 5287–5295(2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5287 [CrossRef] [PubMed]

19.

E. Hugonnot, M. Somekh, D. Villate, F. Salin, and E. Freysz, “Optical parametric chirped pulse amplification and spectral shaping of a continuum generated in a photonic band gap fiber,” Opt. Express 12, 2397–2403 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-11-2397 [CrossRef] [PubMed]

20.

M. Aoyama, T. Harimoto, J. Ma, Y. Akahane, and K. Yamakawa, “Second - harmonic generation of ultra-high intensity femtosecond pulses with a KDP crystal,” Opt. Express9, 579–585 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-11-2397 [CrossRef] [PubMed]

21.

A. Yariv, Quantum Electronics, John Wiley & Sons, New York, USA, 1988.

22.

V. G. Dimitriev, G. G. Gurzaddyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 2nd revised ed. (Springer, Berlin, 1977).

23.

R. G. Brewer, J. R. Lifsitz, E. Garmire, R. Y. Chiao, and C. H. Townes, “Small-scale trapped filaments in intense laser beams,” Phys. Rev. 166, 326–331 (1968). [CrossRef]

24.

K. Cook, A. K. Kar, and R. A. Lamb, “White-light supercontinuum interference of self – focused filaments in water,” Appl. Phys. Lett. 83, 3861–3863 (2003). [CrossRef]

25.

W. Watanabe and K. Itoh, “Spatial coherence of supercontinuum emitters from multiple filaments,” Jpn. J. Appl. Phys. 40, 592–595 (2001). [CrossRef]

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
(320.2250) Ultrafast optics : Femtosecond phenomena

ToC Category:
Research Papers

History
Original Manuscript: March 2, 2005
Revised Manuscript: April 13, 2005
Published: May 2, 2005

Citation
N.K. M. Naga Srinivas, S. Sree Harsha, and D. Narayana Rao, "Femtosecond supercontinuum generation in a quadratic nonlinear medium (KDP)," Opt. Express 13, 3224-3229 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-9-3224


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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, 592-594 (1970). [CrossRef]
  2. R. R. Alfano, The Supercontinuum laser source, Springer�??Verlag, Berlin (1989).
  3. V. P. Kandidov, O. G. Kosareva, I. S. Golubtsov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, S. L. Chin, �??Self-transformation of a powerful femtosecond laser pulse into a white-light pulse in bulk optical media (or super continuum generation),�?? Appl. Phys. B 77, 149-165 (2003). [CrossRef]
  4. R. L. Fork, C. V. Shank, C. Hirlimann, R. Yen, and W. J. Tomlinson, �??Femtosecond white-light continuum pulses,�?? Opt. Lett. 8, 1-3 (1983). [CrossRef] [PubMed]
  5. P. B. Corkum, C. Rolland, and T. Srinivasan Rao, �??Supercontinuum generation in gases,�?? Phys. Rev. Lett. 57, 2268�??2271 (1986). [CrossRef] [PubMed]
  6. A. Brodeur, F. A. Ilkov, and S. L. Chin, �??Beam filamentation and the white light continuum divergence,�?? Opt. Commun. 129, 193-198 (1996). [CrossRef]
  7. G. Yang and Y. R. Shen, �??Spectral broadening of ultrashort pulses in a nonlinear medium,�?? Opt. Lett. 9, 510-512 (1984). [CrossRef] [PubMed]
  8. P. B. Corkum, P. P. Ho, R. R. Alfano, and J. T. Manassah, �??Generation of infrared supercontinuum covering 3 - 14 µm in dielectrics and semiconductors,�?? Opt. Lett. 10, 624-626 (1985). [CrossRef] [PubMed]
  9. A. Brodeur and S. L. Chin, �??Band-gap dependence of the ultrafast white light continuum,�?? Phys. Rev. Lett. 80, 4406�??4409 (1998). [CrossRef]
  10. A. Brodeur and S. L. Chin, �??Ultrafast white light continuum generation and self-focusing in transparent condensed media,�?? J. Opt. Soc. Am. B 16, 637-650 (1999). [CrossRef]
  11. A. K. Dharmadhikari, F. A. Rajgara, N. C. S. Reddy, A. S. Sandhu, and D. Mathur, �??Highly efficient white light generation from barium fluoride,�?? Opt. Express 12, 695-700 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-695">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-695</a> [CrossRef] [PubMed]
  12. J. H. Glownia, J. Misewich, and P. P. Sorokin, �??Ultrafast ultraviolet pump-probe apparatus,�?? J. Opt. Soc. Am. B 3, 1573-1579 (1986). [CrossRef]
  13. T. Kobayashi, T. Saito, and H. Ohtani, �??Real-time spectroscopy of transition states in bacteriorhodopsin during retinal isomerization,�?? Nature 414, 531 - 534 (2001). [CrossRef] [PubMed]
  14. S. Cussat-Blanc, A. Ivanov, D. Lupinski, and E. Freysz, �??KTiOPO4, KTiOAsO4, and KNbO3 crystals for mid-infrared femtosecond optical parametric amplifiers: analysis and comparison,�?? Appl. Phys. B 70, S247- S252 (2000). [CrossRef]
  15. T. Kobayashi and A. Shirakawa, �??Tunable visible and near-infrared pulse generator in a 5 fs regime�??, App. Phys. B 70, S239-S246 (2000). [CrossRef]
  16. K. R. Wilson and V. V. Yakovlev, �??Ultrafast rainbow: tunable ultrashort pulses from a solid-state kilohertz system,�?? J. Opt. Soc. Am. B 14, 444-448(1997). [CrossRef]
  17. A. Baltuska and T. Kobayashi, �??Adaptive shaping of two-cycle visible pulses using a flexible mirror,�?? App. Phys. B 75, 427-443 (2002). [CrossRef]
  18. Pei-Lin Hsiung, Yu Chen, Tony H. Ko, James G. Fujimoto, C. J. S. de Matos, S. V. Popov, J. R. Taylor, and V. P. Gapontsev, �??Optical coherence tomography using a continuous-wave, high-power, Raman continuum light source, �??Opt. Express 12, 5287 - 5295(2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5287">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5287</a> [CrossRef] [PubMed]
  19. E. Hugonnot, M. Somekh, D. Villate, F. Salin, and E. Freysz, �??Optical parametric chirped pulse amplification and spectral shaping of a continuum generated in a photonic band gap fiber,�?? Opt. Express 12, 2397 �?? 2403 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-11-2397">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-11-2397</a> [CrossRef] [PubMed]
  20. M. Aoyama, T. Harimoto, J. Ma, Y. Akahane, and K. Yamakawa, �??Second - harmonic generation of ultrahigh intensity femtosecond pulses with a KDP crystal,�?? Opt. Express 9, 579 �?? 585 (2001), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-11-2397">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-11-2397</a> [CrossRef] [PubMed]
  21. A. Yariv, Quantum Electronics, John Wiley & Sons, New York, USA, 1988.
  22. V. G. Dimitriev, G. G. Gurzaddyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 2nd revised ed. (Springer, Berlin, 1977).
  23. R. G. Brewer, J. R. Lifsitz, E. Garmire, R. Y. Chiao, and C. H. Townes, �??Small-scale trapped filaments in intense laser beams,�?? Phys. Rev. 166, 326�??331 (1968). [CrossRef]
  24. W. Watanabe and K. Itoh, �??Spatial coherence of supercontinuum emitters from multiple filaments,�?? Jpn. J. Appl. Phys. 40, 592-595 (2001). [CrossRef]
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