Abstract

The theory of ultrabroadband multifrequency Raman generation is extended, for the first time, to allow for beam-propagation effects in one and two transverse dimensions. We show that a complex transverse structure develops even when diffraction is neglected. In the general case, we examine how the ultrabroadband multifrequency Raman generation process is affected by the intensity, phase quality, and width of the input beams, and by the length of the Raman medium. The evolution of power spectra, intensity profiles, and global characteristics of the multifrequency beams are investigated and explained. In the two-dimensional transverse case, bandwidths comparable to the optical carrier frequency, spanning the whole visible spectrum and beyond, are still achievable.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. L. Losev and A. P. Lutsenko, “Parametric Raman laser with a discrete output spectrum equal in width to the pump frequency,” Quantum Electron. 23, 919–926 (1993).
    [CrossRef]
  2. G. S. McDonald, G. H. C. New, L. L. Losev, A. P. Lutsenko, and M. J. Shaw, “Ultrabroad bandwidth multi-frequency Raman generation,” Opt. Lett. 19, 1400–1402 (1994).
    [CrossRef] [PubMed]
  3. G. S. McDonald, G. H. C. New, L. L. Losev, A. P. Lutsenko, and M. J. Shaw, “On the generation of ultrabroad bandwidth light for inertial confinement fusion,” Inst. Phys. Conf. Ser. 140, 85–88 (1995).
  4. G. S. McDonald, “Ultrabroad bandwidth multi-frequency Raman soliton pulse trains,” Opt. Lett. 20, 822–824 (1995).
    [CrossRef] [PubMed]
  5. G. S. McDonald, G. H. C. New, L. L. Losev, and A. P. Lutsenko, “On the generation of ultra-broad bandwidth light in air at atmospheric pressure,” J. Phys. B 30, L719–L725 (1997).
    [CrossRef]
  6. G. S. McDonald, Yuk-Ming Chan, G. H. C. New, L. L. Losev, and A. P. Lutsenko, “Competing nonlinear effects in multi-frequency Raman generation,” J. Mod. Opt. 45, 1099–1110 (1998).
    [CrossRef]
  7. T. Imasaka, S. Yamanishi, S. Kawasaki, and N. Ishibashi, “Multi-frequency laser emission generated by two-color stimulated Raman effect using a single-frequency laser beam and a dye–Raman composite resonator,” Appl. Opt. 32, 6633–6637 (1993).
    [CrossRef] [PubMed]
  8. Y. Irie and T. Imasaka, “Generation of vibrational and rotational emissions by four-wave Raman mixing using an ultraviolet femtosecond pump beam,” Opt. Lett. 20, 2072–2074 (1995).
    [CrossRef] [PubMed]
  9. H. Kawano, C. H. Lin, and T. Imasaka, “Generation of high-order rotational lines by four-wave Raman mixing using a high-power picosecond Ti:sapphire laser,” Appl. Phys. B 63, 121–124 (1996).
    [CrossRef]
  10. C. H. Lin, T. Ohnishi, and T. Imasaka, “Vibrational stimulated Raman emission from dibromomethane as seed beam for four-wave rotational Raman mixing in hydrogen,” Jpn. J. Appl. Phys. 36, L412–L414 (1997).
    [CrossRef]
  11. H. Kawano, Y. Ishidzu, and T. Imasaka, “Generation of more than 40 rotational lines by picosecond and femtosecond Ti:sapphire laser for Fourier synthesis,” Appl. Phys. B 65, 1–4 (1997).
    [CrossRef]
  12. H. Kawano, Y. Hirakawa, and T. Imasaka, “Generation of high-order rotational lines in hydrogen by four-wave Raman mixing in the femtosecond regime,” IEEE J. Quantum Electron. 34, 260–268 (1998).
    [CrossRef]
  13. T. Mori, Y. Hirakawa, and T. Imasaka, “Role of supercontinuum in the generation of rotational Raman emission based on stimulated Raman gain and four-wave Raman mixing,” Opt. Commun. 148, 110–112 (1998).
    [CrossRef]
  14. A. P. Hickman, J. A. Paisner, and W. K. Bischel, “Theory of multiwave propagation and frequency conversion in a Raman medium,” Phys. Rev. A 33, 1788–1797 (1986).
    [CrossRef] [PubMed]
  15. A. P. Hickman and W. K. Bischel, “Theory of Stokes and anti-Stokes generation by Raman frequency conversion in the transient limit,” Phys. Rev. A 37, 2516–2523 (1988).
    [CrossRef] [PubMed]
  16. A. Flusberg, S. Fulghum, H. Lotem, M. Rokni, and M. Tekula, “Multiseed stimulated rotational Raman scattering for wave-front control,” J. Opt. Soc. Am. B 8, 1851–1875 (1991).
    [CrossRef]
  17. G. P. Agrawal, Nonlinear Fiber Optics (Academic, London, 1989).
  18. Y. R. Shen and N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. 137, A1787–A1805 (1965).
    [CrossRef]
  19. C. Reiser, T. D. Raymond, R. B. Michie, and A. P. Hickman, “Efficient anti-Stokes Raman conversion in collimated beams,” J. Opt. Soc. Am. B 6, 1859–1869 (1989).
    [CrossRef]

1998

G. S. McDonald, Yuk-Ming Chan, G. H. C. New, L. L. Losev, and A. P. Lutsenko, “Competing nonlinear effects in multi-frequency Raman generation,” J. Mod. Opt. 45, 1099–1110 (1998).
[CrossRef]

H. Kawano, Y. Hirakawa, and T. Imasaka, “Generation of high-order rotational lines in hydrogen by four-wave Raman mixing in the femtosecond regime,” IEEE J. Quantum Electron. 34, 260–268 (1998).
[CrossRef]

T. Mori, Y. Hirakawa, and T. Imasaka, “Role of supercontinuum in the generation of rotational Raman emission based on stimulated Raman gain and four-wave Raman mixing,” Opt. Commun. 148, 110–112 (1998).
[CrossRef]

1997

C. H. Lin, T. Ohnishi, and T. Imasaka, “Vibrational stimulated Raman emission from dibromomethane as seed beam for four-wave rotational Raman mixing in hydrogen,” Jpn. J. Appl. Phys. 36, L412–L414 (1997).
[CrossRef]

H. Kawano, Y. Ishidzu, and T. Imasaka, “Generation of more than 40 rotational lines by picosecond and femtosecond Ti:sapphire laser for Fourier synthesis,” Appl. Phys. B 65, 1–4 (1997).
[CrossRef]

G. S. McDonald, G. H. C. New, L. L. Losev, and A. P. Lutsenko, “On the generation of ultra-broad bandwidth light in air at atmospheric pressure,” J. Phys. B 30, L719–L725 (1997).
[CrossRef]

1996

H. Kawano, C. H. Lin, and T. Imasaka, “Generation of high-order rotational lines by four-wave Raman mixing using a high-power picosecond Ti:sapphire laser,” Appl. Phys. B 63, 121–124 (1996).
[CrossRef]

1995

1994

1993

1991

1989

1988

A. P. Hickman and W. K. Bischel, “Theory of Stokes and anti-Stokes generation by Raman frequency conversion in the transient limit,” Phys. Rev. A 37, 2516–2523 (1988).
[CrossRef] [PubMed]

1986

A. P. Hickman, J. A. Paisner, and W. K. Bischel, “Theory of multiwave propagation and frequency conversion in a Raman medium,” Phys. Rev. A 33, 1788–1797 (1986).
[CrossRef] [PubMed]

1965

Y. R. Shen and N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. 137, A1787–A1805 (1965).
[CrossRef]

Bischel, W. K.

A. P. Hickman and W. K. Bischel, “Theory of Stokes and anti-Stokes generation by Raman frequency conversion in the transient limit,” Phys. Rev. A 37, 2516–2523 (1988).
[CrossRef] [PubMed]

A. P. Hickman, J. A. Paisner, and W. K. Bischel, “Theory of multiwave propagation and frequency conversion in a Raman medium,” Phys. Rev. A 33, 1788–1797 (1986).
[CrossRef] [PubMed]

Bloembergen, N.

Y. R. Shen and N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. 137, A1787–A1805 (1965).
[CrossRef]

Chan, Yuk-Ming

G. S. McDonald, Yuk-Ming Chan, G. H. C. New, L. L. Losev, and A. P. Lutsenko, “Competing nonlinear effects in multi-frequency Raman generation,” J. Mod. Opt. 45, 1099–1110 (1998).
[CrossRef]

Flusberg, A.

Fulghum, S.

Hickman, A. P.

C. Reiser, T. D. Raymond, R. B. Michie, and A. P. Hickman, “Efficient anti-Stokes Raman conversion in collimated beams,” J. Opt. Soc. Am. B 6, 1859–1869 (1989).
[CrossRef]

A. P. Hickman and W. K. Bischel, “Theory of Stokes and anti-Stokes generation by Raman frequency conversion in the transient limit,” Phys. Rev. A 37, 2516–2523 (1988).
[CrossRef] [PubMed]

A. P. Hickman, J. A. Paisner, and W. K. Bischel, “Theory of multiwave propagation and frequency conversion in a Raman medium,” Phys. Rev. A 33, 1788–1797 (1986).
[CrossRef] [PubMed]

Hirakawa, Y.

H. Kawano, Y. Hirakawa, and T. Imasaka, “Generation of high-order rotational lines in hydrogen by four-wave Raman mixing in the femtosecond regime,” IEEE J. Quantum Electron. 34, 260–268 (1998).
[CrossRef]

T. Mori, Y. Hirakawa, and T. Imasaka, “Role of supercontinuum in the generation of rotational Raman emission based on stimulated Raman gain and four-wave Raman mixing,” Opt. Commun. 148, 110–112 (1998).
[CrossRef]

Imasaka, T.

T. Mori, Y. Hirakawa, and T. Imasaka, “Role of supercontinuum in the generation of rotational Raman emission based on stimulated Raman gain and four-wave Raman mixing,” Opt. Commun. 148, 110–112 (1998).
[CrossRef]

H. Kawano, Y. Hirakawa, and T. Imasaka, “Generation of high-order rotational lines in hydrogen by four-wave Raman mixing in the femtosecond regime,” IEEE J. Quantum Electron. 34, 260–268 (1998).
[CrossRef]

C. H. Lin, T. Ohnishi, and T. Imasaka, “Vibrational stimulated Raman emission from dibromomethane as seed beam for four-wave rotational Raman mixing in hydrogen,” Jpn. J. Appl. Phys. 36, L412–L414 (1997).
[CrossRef]

H. Kawano, Y. Ishidzu, and T. Imasaka, “Generation of more than 40 rotational lines by picosecond and femtosecond Ti:sapphire laser for Fourier synthesis,” Appl. Phys. B 65, 1–4 (1997).
[CrossRef]

H. Kawano, C. H. Lin, and T. Imasaka, “Generation of high-order rotational lines by four-wave Raman mixing using a high-power picosecond Ti:sapphire laser,” Appl. Phys. B 63, 121–124 (1996).
[CrossRef]

Y. Irie and T. Imasaka, “Generation of vibrational and rotational emissions by four-wave Raman mixing using an ultraviolet femtosecond pump beam,” Opt. Lett. 20, 2072–2074 (1995).
[CrossRef] [PubMed]

T. Imasaka, S. Yamanishi, S. Kawasaki, and N. Ishibashi, “Multi-frequency laser emission generated by two-color stimulated Raman effect using a single-frequency laser beam and a dye–Raman composite resonator,” Appl. Opt. 32, 6633–6637 (1993).
[CrossRef] [PubMed]

Irie, Y.

Ishibashi, N.

Ishidzu, Y.

H. Kawano, Y. Ishidzu, and T. Imasaka, “Generation of more than 40 rotational lines by picosecond and femtosecond Ti:sapphire laser for Fourier synthesis,” Appl. Phys. B 65, 1–4 (1997).
[CrossRef]

Kawano, H.

H. Kawano, Y. Hirakawa, and T. Imasaka, “Generation of high-order rotational lines in hydrogen by four-wave Raman mixing in the femtosecond regime,” IEEE J. Quantum Electron. 34, 260–268 (1998).
[CrossRef]

H. Kawano, Y. Ishidzu, and T. Imasaka, “Generation of more than 40 rotational lines by picosecond and femtosecond Ti:sapphire laser for Fourier synthesis,” Appl. Phys. B 65, 1–4 (1997).
[CrossRef]

H. Kawano, C. H. Lin, and T. Imasaka, “Generation of high-order rotational lines by four-wave Raman mixing using a high-power picosecond Ti:sapphire laser,” Appl. Phys. B 63, 121–124 (1996).
[CrossRef]

Kawasaki, S.

Lin, C. H.

C. H. Lin, T. Ohnishi, and T. Imasaka, “Vibrational stimulated Raman emission from dibromomethane as seed beam for four-wave rotational Raman mixing in hydrogen,” Jpn. J. Appl. Phys. 36, L412–L414 (1997).
[CrossRef]

H. Kawano, C. H. Lin, and T. Imasaka, “Generation of high-order rotational lines by four-wave Raman mixing using a high-power picosecond Ti:sapphire laser,” Appl. Phys. B 63, 121–124 (1996).
[CrossRef]

Losev, L. L.

G. S. McDonald, Yuk-Ming Chan, G. H. C. New, L. L. Losev, and A. P. Lutsenko, “Competing nonlinear effects in multi-frequency Raman generation,” J. Mod. Opt. 45, 1099–1110 (1998).
[CrossRef]

G. S. McDonald, G. H. C. New, L. L. Losev, and A. P. Lutsenko, “On the generation of ultra-broad bandwidth light in air at atmospheric pressure,” J. Phys. B 30, L719–L725 (1997).
[CrossRef]

G. S. McDonald, G. H. C. New, L. L. Losev, A. P. Lutsenko, and M. J. Shaw, “On the generation of ultrabroad bandwidth light for inertial confinement fusion,” Inst. Phys. Conf. Ser. 140, 85–88 (1995).

G. S. McDonald, G. H. C. New, L. L. Losev, A. P. Lutsenko, and M. J. Shaw, “Ultrabroad bandwidth multi-frequency Raman generation,” Opt. Lett. 19, 1400–1402 (1994).
[CrossRef] [PubMed]

L. L. Losev and A. P. Lutsenko, “Parametric Raman laser with a discrete output spectrum equal in width to the pump frequency,” Quantum Electron. 23, 919–926 (1993).
[CrossRef]

Lotem, H.

Lutsenko, A. P.

G. S. McDonald, Yuk-Ming Chan, G. H. C. New, L. L. Losev, and A. P. Lutsenko, “Competing nonlinear effects in multi-frequency Raman generation,” J. Mod. Opt. 45, 1099–1110 (1998).
[CrossRef]

G. S. McDonald, G. H. C. New, L. L. Losev, and A. P. Lutsenko, “On the generation of ultra-broad bandwidth light in air at atmospheric pressure,” J. Phys. B 30, L719–L725 (1997).
[CrossRef]

G. S. McDonald, G. H. C. New, L. L. Losev, A. P. Lutsenko, and M. J. Shaw, “On the generation of ultrabroad bandwidth light for inertial confinement fusion,” Inst. Phys. Conf. Ser. 140, 85–88 (1995).

G. S. McDonald, G. H. C. New, L. L. Losev, A. P. Lutsenko, and M. J. Shaw, “Ultrabroad bandwidth multi-frequency Raman generation,” Opt. Lett. 19, 1400–1402 (1994).
[CrossRef] [PubMed]

L. L. Losev and A. P. Lutsenko, “Parametric Raman laser with a discrete output spectrum equal in width to the pump frequency,” Quantum Electron. 23, 919–926 (1993).
[CrossRef]

McDonald, G. S.

G. S. McDonald, Yuk-Ming Chan, G. H. C. New, L. L. Losev, and A. P. Lutsenko, “Competing nonlinear effects in multi-frequency Raman generation,” J. Mod. Opt. 45, 1099–1110 (1998).
[CrossRef]

G. S. McDonald, G. H. C. New, L. L. Losev, and A. P. Lutsenko, “On the generation of ultra-broad bandwidth light in air at atmospheric pressure,” J. Phys. B 30, L719–L725 (1997).
[CrossRef]

G. S. McDonald, G. H. C. New, L. L. Losev, A. P. Lutsenko, and M. J. Shaw, “On the generation of ultrabroad bandwidth light for inertial confinement fusion,” Inst. Phys. Conf. Ser. 140, 85–88 (1995).

G. S. McDonald, “Ultrabroad bandwidth multi-frequency Raman soliton pulse trains,” Opt. Lett. 20, 822–824 (1995).
[CrossRef] [PubMed]

G. S. McDonald, G. H. C. New, L. L. Losev, A. P. Lutsenko, and M. J. Shaw, “Ultrabroad bandwidth multi-frequency Raman generation,” Opt. Lett. 19, 1400–1402 (1994).
[CrossRef] [PubMed]

Michie, R. B.

Mori, T.

T. Mori, Y. Hirakawa, and T. Imasaka, “Role of supercontinuum in the generation of rotational Raman emission based on stimulated Raman gain and four-wave Raman mixing,” Opt. Commun. 148, 110–112 (1998).
[CrossRef]

New, G. H. C.

G. S. McDonald, Yuk-Ming Chan, G. H. C. New, L. L. Losev, and A. P. Lutsenko, “Competing nonlinear effects in multi-frequency Raman generation,” J. Mod. Opt. 45, 1099–1110 (1998).
[CrossRef]

G. S. McDonald, G. H. C. New, L. L. Losev, and A. P. Lutsenko, “On the generation of ultra-broad bandwidth light in air at atmospheric pressure,” J. Phys. B 30, L719–L725 (1997).
[CrossRef]

G. S. McDonald, G. H. C. New, L. L. Losev, A. P. Lutsenko, and M. J. Shaw, “On the generation of ultrabroad bandwidth light for inertial confinement fusion,” Inst. Phys. Conf. Ser. 140, 85–88 (1995).

G. S. McDonald, G. H. C. New, L. L. Losev, A. P. Lutsenko, and M. J. Shaw, “Ultrabroad bandwidth multi-frequency Raman generation,” Opt. Lett. 19, 1400–1402 (1994).
[CrossRef] [PubMed]

Ohnishi, T.

C. H. Lin, T. Ohnishi, and T. Imasaka, “Vibrational stimulated Raman emission from dibromomethane as seed beam for four-wave rotational Raman mixing in hydrogen,” Jpn. J. Appl. Phys. 36, L412–L414 (1997).
[CrossRef]

Paisner, J. A.

A. P. Hickman, J. A. Paisner, and W. K. Bischel, “Theory of multiwave propagation and frequency conversion in a Raman medium,” Phys. Rev. A 33, 1788–1797 (1986).
[CrossRef] [PubMed]

Raymond, T. D.

Reiser, C.

Rokni, M.

Shaw, M. J.

G. S. McDonald, G. H. C. New, L. L. Losev, A. P. Lutsenko, and M. J. Shaw, “On the generation of ultrabroad bandwidth light for inertial confinement fusion,” Inst. Phys. Conf. Ser. 140, 85–88 (1995).

G. S. McDonald, G. H. C. New, L. L. Losev, A. P. Lutsenko, and M. J. Shaw, “Ultrabroad bandwidth multi-frequency Raman generation,” Opt. Lett. 19, 1400–1402 (1994).
[CrossRef] [PubMed]

Shen, Y. R.

Y. R. Shen and N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. 137, A1787–A1805 (1965).
[CrossRef]

Tekula, M.

Yamanishi, S.

Appl. Opt.

Appl. Phys. B

H. Kawano, Y. Ishidzu, and T. Imasaka, “Generation of more than 40 rotational lines by picosecond and femtosecond Ti:sapphire laser for Fourier synthesis,” Appl. Phys. B 65, 1–4 (1997).
[CrossRef]

H. Kawano, C. H. Lin, and T. Imasaka, “Generation of high-order rotational lines by four-wave Raman mixing using a high-power picosecond Ti:sapphire laser,” Appl. Phys. B 63, 121–124 (1996).
[CrossRef]

IEEE J. Quantum Electron.

H. Kawano, Y. Hirakawa, and T. Imasaka, “Generation of high-order rotational lines in hydrogen by four-wave Raman mixing in the femtosecond regime,” IEEE J. Quantum Electron. 34, 260–268 (1998).
[CrossRef]

Inst. Phys. Conf. Ser.

G. S. McDonald, G. H. C. New, L. L. Losev, A. P. Lutsenko, and M. J. Shaw, “On the generation of ultrabroad bandwidth light for inertial confinement fusion,” Inst. Phys. Conf. Ser. 140, 85–88 (1995).

J. Mod. Opt.

G. S. McDonald, Yuk-Ming Chan, G. H. C. New, L. L. Losev, and A. P. Lutsenko, “Competing nonlinear effects in multi-frequency Raman generation,” J. Mod. Opt. 45, 1099–1110 (1998).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. B

G. S. McDonald, G. H. C. New, L. L. Losev, and A. P. Lutsenko, “On the generation of ultra-broad bandwidth light in air at atmospheric pressure,” J. Phys. B 30, L719–L725 (1997).
[CrossRef]

Jpn. J. Appl. Phys.

C. H. Lin, T. Ohnishi, and T. Imasaka, “Vibrational stimulated Raman emission from dibromomethane as seed beam for four-wave rotational Raman mixing in hydrogen,” Jpn. J. Appl. Phys. 36, L412–L414 (1997).
[CrossRef]

Opt. Commun.

T. Mori, Y. Hirakawa, and T. Imasaka, “Role of supercontinuum in the generation of rotational Raman emission based on stimulated Raman gain and four-wave Raman mixing,” Opt. Commun. 148, 110–112 (1998).
[CrossRef]

Opt. Lett.

Phys. Rev.

Y. R. Shen and N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. 137, A1787–A1805 (1965).
[CrossRef]

Phys. Rev. A

A. P. Hickman, J. A. Paisner, and W. K. Bischel, “Theory of multiwave propagation and frequency conversion in a Raman medium,” Phys. Rev. A 33, 1788–1797 (1986).
[CrossRef] [PubMed]

A. P. Hickman and W. K. Bischel, “Theory of Stokes and anti-Stokes generation by Raman frequency conversion in the transient limit,” Phys. Rev. A 37, 2516–2523 (1988).
[CrossRef] [PubMed]

Quantum Electron.

L. L. Losev and A. P. Lutsenko, “Parametric Raman laser with a discrete output spectrum equal in width to the pump frequency,” Quantum Electron. 23, 919–926 (1993).
[CrossRef]

Other

G. P. Agrawal, Nonlinear Fiber Optics (Academic, London, 1989).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Evolution of plane-wave intensities at distinct frequencies as a function of normalized propagation distance; individual curves are labeled with the appropriate channel number n: (a) conventional (single pump beam) stimulated Raman scattering (SRS); (b)–(d) the effect of symmetric two-color pumping. (b) High dispersion ultimately results in a single (nonparametric) downconversion ladder that is similar to conventional SRS. (c),(d) A low level of dispersion; significant parametric conversion over a relatively short propagation distance is demonstrated.

Fig. 2
Fig. 2

Evolution of the first Stokes beam over a normalized distance of Z=Zmax=200. Pump energy is rapidly converted into new frequencies during propagation, and the interplay of Raman and finite-beam effects alone is shown to lead to a significant transverse structure (αn=γn=0).

Fig. 3
Fig. 3

Bandwidth BN (in units of the Stokes shift) of 1D transverse multifrequency beams as a function of normalized distance Z. A 2-m chamber of H2 gas at 1-atm pressure is modeled. Dispersion and diffraction are accounted for (αn0, γn0, and ZD is the normalized diffraction length of the ω0 pump). The dispersion-optimized plane-wave curve is also shown (dotted).

Fig. 4
Fig. 4

One-dimensional transverse profiles, at normalized distances Z=100 and Z=200, of the total (incoherent) intensity (IΣ) of the multifrequency beam. Parameters are for H2 gas at 1-atm pressure and relatively strong diffraction (ZD=200).

Fig. 5
Fig. 5

Dependence of bandwidth BN of 2D transverse multifrequency beams on the intensity and the diffraction length of the pump beams (Z=60).

Fig. 6
Fig. 6

Evolution of the bandwidth of 2D transverse beams along a 10-cm Raman cell. Three normalized pump-beam diffraction lengths are considered (I0=30GW cm-2).

Fig. 7
Fig. 7

Evolution of the power spectrum of a multifrequency beam. The limits of the visible spectrum are indicated by two vertical lines. The pump parameters are I0=30GW cm-2 and ZD=600.

Fig. 8
Fig. 8

Transverse intensity profiles of beams within distinct frequency channels (Z=60, ZD=180, and I0=30GW cm-2). Moving downward through each column, the carrier frequency of the light increases, whereas adjacent columns (moving from left to right) give a continuation of the sequence. In column 1, the beams are in the infrared regime and then progress through the red section of the visible spectrum. Column 2 contains red, orange, yellow, and green beams, whereas column 3 has green, blue, and indigo components. Column 4 spans the spectral region from indigo, through violet, and into the ultraviolet.

Fig. 9
Fig. 9

Variation of beam radii with respect to frequency at two normalized propagation distances (Z=30 and 60) and for three levels of diffraction (ZD=180, 300, and 600). (a) Mean ring radii Rn, as defined in the text; (b) rms beam widths wrms are plotted.

Fig. 10
Fig. 10

Evolution of the rms beam radius of the whole multifrequency beam with respect to normalized propagation distance for three levels of diffraction (ZD=180, 300, and 600). The corresponding evolution for free-space propagation of a Gaussian beam at the pump frequency and with ZD=180 is also shown (dotted curve).

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

Fnz-i2kn0t2Fn=πρα12ωnc
×[q*Fn+1 exp(-iΔn+1z)-qFn-1 exp(iΔnz)].
qt=-qT2+a122 jFjFj-1* exp(-iΔj),
AnZ=iαnt2An+ωn2ω0[P*An+1×exp(-iγn+1Z)-PAn-1 exp(iγnZ)],
T2tp Pτ=-P+jAjAj-1* exp(-iγjZ),
P=jAjAj-1* exp(-iγjZ).
dA-1dZ=ω-12ω0|A0|2A-1=ω-12ω0A-112A-1,
dA-1dZ=ω-12ω0[|A0|2A-1+A1*A02 exp(iγ1Z)],
dA0dZ=12(|A1|2-|A-1|2)A0,
dA1dZ=ω12ω0[-|A0|2A1-A-1*A02 exp(iγ1Z)].
dA-1/dZA1A02/21/2.
Rn=0r2|An(r)|2dr0r|An(r)|2dr,

Metrics