Abstract

A method has been developed for experimentally measuring the irradiance (energy per unit area) of optical radiation required to stimulate nonlinear processes. The method involves examining the spatial dependence of the process in the vicinity of a laser beam focus. A laser operating in the lowest order transverse mode is required. The treatment is exact for multiphoton processes in the absence of relaxation of recombination and is approximate for other nonlinear processes.

© 1978 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. L. Peticolas, Ann. Rev. Phys. Chem. 18, 233 (1967).
    [CrossRef]
  2. N. B. Delone, Sov. Phys. Usp. 18, 169 (1975).
    [CrossRef]
  3. J. P. Aldridge, J. H. Birely, C. D. Cantrell, D. C. Cartwright, in Laser Photochemistry, Tunable Lasers, and Other Topics, S. F. Jacobs, M. Sargent, M. O. Scully, C. T. Walker, Eds. (Addison-Wesley, Reading, Mass., 1976), p. 57.
  4. M. Born, E. Wolf, Principles of Optics (MacMillan, New York, 1964).
  5. H. Kogelnik, T. Li, Appl. Opt. 5, 1550 (1966).
    [CrossRef] [PubMed]
  6. V. E. Merchant, N. R. Isenor, IEEE J. Quantum Electron. QE-12, 603 (1976).
    [CrossRef]
  7. M. R. Cervenan, N. R. Isenor, Opt. Commun. 13, 175 (1975).
    [CrossRef]
  8. M. Abramowitz, I. Stegun, Eds., Handbook of Mathematical Functions (Dover, New York, 1965).
  9. N. R. Isenor, V. E. Merchant, R. S. Hallsworth, M. C. Richardson, Can. J. Phys. 51, 1281 (1973).
    [CrossRef]
  10. J. L. Lyman, S. D. Rockwood, J. Appl. Phys. 28, 595 (1976).
    [CrossRef]

1976

V. E. Merchant, N. R. Isenor, IEEE J. Quantum Electron. QE-12, 603 (1976).
[CrossRef]

J. L. Lyman, S. D. Rockwood, J. Appl. Phys. 28, 595 (1976).
[CrossRef]

1975

M. R. Cervenan, N. R. Isenor, Opt. Commun. 13, 175 (1975).
[CrossRef]

N. B. Delone, Sov. Phys. Usp. 18, 169 (1975).
[CrossRef]

1973

N. R. Isenor, V. E. Merchant, R. S. Hallsworth, M. C. Richardson, Can. J. Phys. 51, 1281 (1973).
[CrossRef]

1967

W. L. Peticolas, Ann. Rev. Phys. Chem. 18, 233 (1967).
[CrossRef]

1966

Aldridge, J. P.

J. P. Aldridge, J. H. Birely, C. D. Cantrell, D. C. Cartwright, in Laser Photochemistry, Tunable Lasers, and Other Topics, S. F. Jacobs, M. Sargent, M. O. Scully, C. T. Walker, Eds. (Addison-Wesley, Reading, Mass., 1976), p. 57.

Birely, J. H.

J. P. Aldridge, J. H. Birely, C. D. Cantrell, D. C. Cartwright, in Laser Photochemistry, Tunable Lasers, and Other Topics, S. F. Jacobs, M. Sargent, M. O. Scully, C. T. Walker, Eds. (Addison-Wesley, Reading, Mass., 1976), p. 57.

Born, M.

M. Born, E. Wolf, Principles of Optics (MacMillan, New York, 1964).

Cantrell, C. D.

J. P. Aldridge, J. H. Birely, C. D. Cantrell, D. C. Cartwright, in Laser Photochemistry, Tunable Lasers, and Other Topics, S. F. Jacobs, M. Sargent, M. O. Scully, C. T. Walker, Eds. (Addison-Wesley, Reading, Mass., 1976), p. 57.

Cartwright, D. C.

J. P. Aldridge, J. H. Birely, C. D. Cantrell, D. C. Cartwright, in Laser Photochemistry, Tunable Lasers, and Other Topics, S. F. Jacobs, M. Sargent, M. O. Scully, C. T. Walker, Eds. (Addison-Wesley, Reading, Mass., 1976), p. 57.

Cervenan, M. R.

M. R. Cervenan, N. R. Isenor, Opt. Commun. 13, 175 (1975).
[CrossRef]

Delone, N. B.

N. B. Delone, Sov. Phys. Usp. 18, 169 (1975).
[CrossRef]

Hallsworth, R. S.

N. R. Isenor, V. E. Merchant, R. S. Hallsworth, M. C. Richardson, Can. J. Phys. 51, 1281 (1973).
[CrossRef]

Isenor, N. R.

V. E. Merchant, N. R. Isenor, IEEE J. Quantum Electron. QE-12, 603 (1976).
[CrossRef]

M. R. Cervenan, N. R. Isenor, Opt. Commun. 13, 175 (1975).
[CrossRef]

N. R. Isenor, V. E. Merchant, R. S. Hallsworth, M. C. Richardson, Can. J. Phys. 51, 1281 (1973).
[CrossRef]

Kogelnik, H.

Li, T.

Lyman, J. L.

J. L. Lyman, S. D. Rockwood, J. Appl. Phys. 28, 595 (1976).
[CrossRef]

Merchant, V. E.

V. E. Merchant, N. R. Isenor, IEEE J. Quantum Electron. QE-12, 603 (1976).
[CrossRef]

N. R. Isenor, V. E. Merchant, R. S. Hallsworth, M. C. Richardson, Can. J. Phys. 51, 1281 (1973).
[CrossRef]

Peticolas, W. L.

W. L. Peticolas, Ann. Rev. Phys. Chem. 18, 233 (1967).
[CrossRef]

Richardson, M. C.

N. R. Isenor, V. E. Merchant, R. S. Hallsworth, M. C. Richardson, Can. J. Phys. 51, 1281 (1973).
[CrossRef]

Rockwood, S. D.

J. L. Lyman, S. D. Rockwood, J. Appl. Phys. 28, 595 (1976).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (MacMillan, New York, 1964).

Ann. Rev. Phys. Chem.

W. L. Peticolas, Ann. Rev. Phys. Chem. 18, 233 (1967).
[CrossRef]

Appl. Opt.

Can. J. Phys.

N. R. Isenor, V. E. Merchant, R. S. Hallsworth, M. C. Richardson, Can. J. Phys. 51, 1281 (1973).
[CrossRef]

IEEE J. Quantum Electron.

V. E. Merchant, N. R. Isenor, IEEE J. Quantum Electron. QE-12, 603 (1976).
[CrossRef]

J. Appl. Phys.

J. L. Lyman, S. D. Rockwood, J. Appl. Phys. 28, 595 (1976).
[CrossRef]

Opt. Commun.

M. R. Cervenan, N. R. Isenor, Opt. Commun. 13, 175 (1975).
[CrossRef]

Sov. Phys. Usp.

N. B. Delone, Sov. Phys. Usp. 18, 169 (1975).
[CrossRef]

Other

J. P. Aldridge, J. H. Birely, C. D. Cantrell, D. C. Cartwright, in Laser Photochemistry, Tunable Lasers, and Other Topics, S. F. Jacobs, M. Sargent, M. O. Scully, C. T. Walker, Eds. (Addison-Wesley, Reading, Mass., 1976), p. 57.

M. Born, E. Wolf, Principles of Optics (MacMillan, New York, 1964).

M. Abramowitz, I. Stegun, Eds., Handbook of Mathematical Functions (Dover, New York, 1965).

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 (2)

Fig. 1
Fig. 1

Experimental arrangement indicating the region in which excited species are detected. Note that the scale of distances perpendicular to the optic axis has been expanded with respect to distances along the optic axis.

Fig. 2
Fig. 2

Dependence of nonlinear effects on the position along the optic axis. Dashed curve is a plot of Eq. (9) fitted to the experimental data shown. The solid curve is the best fit of Eq. (7) to the data, obtained with n = 2.

Equations (11)

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

I ( z , ρ ) = 2 P π ω 2 exp ( 2 ρ 2 ω 2 ) ,
ω = ω 0 ( 1 + z 2 / z 0 2 ) 1 / 2 , and z 0 = π ω 0 2 / λ .
d N f d t = σ I n N i = d N i d t .
I = E a g ( t ) ,
E c = { σ 0 [ g ( t ) ] n d t } 1 / n ,
N f = N o [ 1 exp ( 0 σ I n d t ) ] = N o [ 1 exp ( E a E c ) n ] .
S ( z ) = S n β / n 0 1 / β n d x x [ 1 exp ( x ) ] = S n β ln 1 β + 1 n S n β [ E 1 ( 1 β n ) + Γ ] ,
x = E a / E c ,
β = C n [ 1 + z 2 z 0 2 ] E c E a o [ 1 + z 2 z 0 2 ] .
S ( z ) = { S C ( 1 + z 2 z 0 2 ) ln 1 C ( 1 + z 2 / z 0 2 ) , z L 0 for z L ,
f ( I ) = σ [ I ( t ) ] n 1 [ 0 t I ( t ) d t ] n 2

Metrics