Abstract

A description by the author of the early days of nonlinear optics (NLO), and the motivation for the formulation of the quantum theory of NLO, implications to a number of diverse areas, and the background for the prediction of spontaneous parametric fluorescence.

© 2011 Optical Society of America

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References

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  1. A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112, 1940–1949 (1958).
    [CrossRef]
  2. R. Serber and C. H. Townes, “Limits on electromagnetic amplification due to complementarity,” in Quantum Electronics, C. H. Townes, ed. (Columbia University Press, 1960), pp. 233–255.
  3. H. Heffner, “Parametric amplifiers and their comparison with masers,” in Quantum Electronics, C. H. Townes, ed (Columbia University Press, 1960), p. 269.
  4. See, for example, A. Yariv, Quantum Electronics (John Wiley and Sons, 1986), pp. 54–56.
  5. W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes,” Phys. Rev. 124, 1646–1654 (1961).
    [CrossRef]
  6. A. Yariv and P. Yeh, Photonics, 6th ed. (Oxford University Press, 2007), pp. 370–371.
  7. S. E. Harris, M. K. Oshman, and R. L. Byer, “Observation of tunable optical parametric fluorescence,” Phys. Rev. Lett. 18732–734 (1967).
    [CrossRef]
  8. R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12592–595 (1964).
    [CrossRef]
  9. A. Yariv, “Quantum theory for parametric interactions of light and hypersound,” IEEE J. Quantum Electron. 128–36 (1965).
    [CrossRef]
  10. C. Kittel, Quantum Theory of Solids (John Wiley and Sons, 1963).
  11. J. B. Khurgin, “Phonon lasers gain a sound foundation,” Physics 3, 1–3 (2010).
    [CrossRef]

2010

J. B. Khurgin, “Phonon lasers gain a sound foundation,” Physics 3, 1–3 (2010).
[CrossRef]

1967

S. E. Harris, M. K. Oshman, and R. L. Byer, “Observation of tunable optical parametric fluorescence,” Phys. Rev. Lett. 18732–734 (1967).
[CrossRef]

1965

A. Yariv, “Quantum theory for parametric interactions of light and hypersound,” IEEE J. Quantum Electron. 128–36 (1965).
[CrossRef]

1964

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12592–595 (1964).
[CrossRef]

1961

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes,” Phys. Rev. 124, 1646–1654 (1961).
[CrossRef]

1958

A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112, 1940–1949 (1958).
[CrossRef]

Byer, R. L.

S. E. Harris, M. K. Oshman, and R. L. Byer, “Observation of tunable optical parametric fluorescence,” Phys. Rev. Lett. 18732–734 (1967).
[CrossRef]

Chiao, R. Y.

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12592–595 (1964).
[CrossRef]

Harris, S. E.

S. E. Harris, M. K. Oshman, and R. L. Byer, “Observation of tunable optical parametric fluorescence,” Phys. Rev. Lett. 18732–734 (1967).
[CrossRef]

Heffner, H.

H. Heffner, “Parametric amplifiers and their comparison with masers,” in Quantum Electronics, C. H. Townes, ed (Columbia University Press, 1960), p. 269.

Khurgin, J. B.

J. B. Khurgin, “Phonon lasers gain a sound foundation,” Physics 3, 1–3 (2010).
[CrossRef]

Kittel, C.

C. Kittel, Quantum Theory of Solids (John Wiley and Sons, 1963).

Louisell, W. H.

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes,” Phys. Rev. 124, 1646–1654 (1961).
[CrossRef]

Oshman, M. K.

S. E. Harris, M. K. Oshman, and R. L. Byer, “Observation of tunable optical parametric fluorescence,” Phys. Rev. Lett. 18732–734 (1967).
[CrossRef]

Schawlow, A. L.

A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112, 1940–1949 (1958).
[CrossRef]

Serber, R.

R. Serber and C. H. Townes, “Limits on electromagnetic amplification due to complementarity,” in Quantum Electronics, C. H. Townes, ed. (Columbia University Press, 1960), pp. 233–255.

Siegman, A. E.

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes,” Phys. Rev. 124, 1646–1654 (1961).
[CrossRef]

Stoicheff, B. P.

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12592–595 (1964).
[CrossRef]

Townes, C. H.

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12592–595 (1964).
[CrossRef]

A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112, 1940–1949 (1958).
[CrossRef]

R. Serber and C. H. Townes, “Limits on electromagnetic amplification due to complementarity,” in Quantum Electronics, C. H. Townes, ed. (Columbia University Press, 1960), pp. 233–255.

Yariv, A.

A. Yariv, “Quantum theory for parametric interactions of light and hypersound,” IEEE J. Quantum Electron. 128–36 (1965).
[CrossRef]

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes,” Phys. Rev. 124, 1646–1654 (1961).
[CrossRef]

See, for example, A. Yariv, Quantum Electronics (John Wiley and Sons, 1986), pp. 54–56.

A. Yariv and P. Yeh, Photonics, 6th ed. (Oxford University Press, 2007), pp. 370–371.

Yeh, P.

A. Yariv and P. Yeh, Photonics, 6th ed. (Oxford University Press, 2007), pp. 370–371.

IEEE J. Quantum Electron.

A. Yariv, “Quantum theory for parametric interactions of light and hypersound,” IEEE J. Quantum Electron. 128–36 (1965).
[CrossRef]

Phys. Rev.

A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112, 1940–1949 (1958).
[CrossRef]

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes,” Phys. Rev. 124, 1646–1654 (1961).
[CrossRef]

Phys. Rev. Lett.

S. E. Harris, M. K. Oshman, and R. L. Byer, “Observation of tunable optical parametric fluorescence,” Phys. Rev. Lett. 18732–734 (1967).
[CrossRef]

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12592–595 (1964).
[CrossRef]

Physics

J. B. Khurgin, “Phonon lasers gain a sound foundation,” Physics 3, 1–3 (2010).
[CrossRef]

Other

C. Kittel, Quantum Theory of Solids (John Wiley and Sons, 1963).

A. Yariv and P. Yeh, Photonics, 6th ed. (Oxford University Press, 2007), pp. 370–371.

R. Serber and C. H. Townes, “Limits on electromagnetic amplification due to complementarity,” in Quantum Electronics, C. H. Townes, ed. (Columbia University Press, 1960), pp. 233–255.

H. Heffner, “Parametric amplifiers and their comparison with masers,” in Quantum Electronics, C. H. Townes, ed (Columbia University Press, 1960), p. 269.

See, for example, A. Yariv, Quantum Electronics (John Wiley and Sons, 1986), pp. 54–56.

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Figures (3)

Fig. 1.
Fig. 1.

The basic transition involved in the laser amplifier. The atom undergoes a transition from an excited state to a lower one while an EM mode interacting with it gains the released energy ωa.

Fig. 2.
Fig. 2.

The basic arrangement for an optical parametric amplifier.

Fig. 3.
Fig. 3.

The quantum states of the system of three modes: pump, signal, and idler. The basic PA process is shown as a quantum transition between pure “harmonic oscillator” states. Transitions originate at the base of the arrows and terminate at the tips.

Equations (20)

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

Haua(ex)=Eaua(ex),
Hmun=(n+1/2)ωmun,
Houtotal=(Ha+Hm)utotal=[Ea+(n+12)ωm]utotal,
Hsystem=Ha+Hm+HI.
uoun+1|HI|uaund3rmd3rau0*un+1*rauaun,
Piω=χijEjω,
Piω3=dijkEjω1Ek±ω2,ω3=ω1±ω2.
ΔEinteraction(joules)=VdijkEiω3Ejω1Ekω2d3r,
Epconst(apap),
ap|np=np+1|np+1,ap|np=np|np1.
ΔHI=A(apap)(asas)(aiai).
H=ωp(apap+1/2)+ωs(asas+1/2)+ωi(aiai+1/2)+A(apap)(asas)(aiai).
Winitialfinal|nso+1,nio+1,np1|asaiap|nso,nio,np|2δ(ωpωsωi)
=(nso+1)(nio+1)np,
dasdt=iωsas+iκei(ωpt+ϕ)ai,daidt=iωiaiiκei(ωpt+ϕ)as,
as(t)=exp(iωst){as(0)cosh(κt)+ieiϕai(0)sinh(κt)},ai(t)=exp(iωit){ai(0)cosh(κt)ieiϕas(0)sinh(κt)},
ns(t)=nsocosh2(κt)+(1+nio)sinh2(κt)
ni(t)=niocosh2(κt)+(1+nso)sinh2(κt)
ns(t)=ni(t)=sinh2(κt)
HI=κ(asas)(apap)(aiai)+hermitian adjoint

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