1.

A. H. Aitken, J. H. Hayes, P. B. Ulrich: “*Propagation of High Energy 10.6 Micron Laser Beams Through The Atmosphere*”; U. S. Naval Research Laboratory, Washington, D. C., Rept. 7293 (1971); P. B. Ulrich, J. H. Hayes, J. H. Hancock, J. T. Ulrich: “*Documentation of* PROPE,*A Computer Program for Propagation of High Power Laser Beams Through Absorbing Media*”; U. S. Naval Research Laboratory, Washington, D. C., Rept. 7681 (1974)

2.

J. Hermann, L. C. Bradley: “*Numerical Calculation of Light Propagation*”; MIT Lincoln Laboratory, Cambridge, Mass., Rept. LTP-10 (1971)

3.

P. B. Ulrich: “*A Numerical Calculation of Thermal Blooming of Pulsed Focused Laser Beams*”; U. S. Naval Research Laboratory, Washington, D. C., Rept. 7382 (1971)

4.

P. B. Ulrich, J. Wallace, J. Opt. Soc. Am.**63**, 8 (1973)

5.

H. Kleiman, K. W. O'Neil, Appl. Phys. Letters

**23**, 43 (1973)

CrossRef6.

L. C. Bradley: “*Simulation of Atmospheric Index Fluctuations*”; Lincoln Laboratory, Cambridge, Mass. (preprint)

7.

W. P. Brown, Jr.: “*High Energy Laser Propagation*”; Hughes Research Laboratory, Rept. on contract N00014-B-C-0460 (1973)

8.

A. Edwards: Lawrence Livermore Laboratory, Rept. UCIR-902 (1975)

9.

L. C. Bradley: “*Thermal Blooming in the Transonic Regime*”; MIT Lincoln Laboratory, Cambridge, Mass., Rept. LTP-24 (1974)

10.

J. A. Fleck, Jr.: J. Comp. Phys.

**16**, 324 (1974)

CrossRefADSMathSciNet11.

M. D. Feit, J. A. Fleck, Jr.: Bull. Am. Phys. Soc. (Series II)**19**, 962 (1974)

12.

An unsymmetrized exponential transformation was used by, J. Hermann and L. C. Bradley: “*Numerical Calculation of Light Propagation*”; MIT Lincoln Laboratory, Cambridge, Mass., 1971)

13.

V. I. Talanov: JETP Letters**11**, 799 (1970) [ZhETP Pis. Red.**11**, 303 20 (March 1969)]

14.

The DFT method of solving the propagation equation is also employed by other workers, e. g. H. J. Breaux: “*An Analysis of Mathematical Transformations and a Comparison of Numerical Techniques for Computation of High Energy* CW*Laser Propagation in an Inhomogeneous Medium*”; Ballistic Research Laboratories, Rept. No. 1723 (1974); P. B. Ulrich: In*NRL Optical Radiation Program Progress Report*”; U.S. Naval Research Laboratory, Washington, D. C., Memorandum Report 2874 (1974)

15.

W. T. Cochran, J. W. Cooley, D. L. Favin, H. D. Helms, R. A. Kaenel, W. W. Lang, G. C. Moling, Jr., D. E. Nelson, C. M. Rader, P. D. Welch: Proc. IEEE**55**, 1664 (1967)

16.

A. J. Campillo, J. E. Pearson, S. L. Shapiro, N. J. Terrell, Jr.: Appl. Phys. Letters

**23**, 85 (1973)

CrossRef17.

N.J. Terrell, Jr.: Los Alamos Scientific Laboratory, Los Alamos, N. M., private communication (1975)

18.

R. D. Richtmyer, K. W. Morton:

*Difference Methods for Initial Value Problems*, (Interscience, New York 1967)

MATH19.

M. G. Rusbridge: J. Comp. Phys.

**2**, 288 (1968)

CrossRef20.

We are indebted to E. H. Canfield, Jr., Lawrence Livermore Laboratory, for these more accurate expressions

21.

F. H. Harlow, A. A. Amsden: J. Comp. Phys.

**8**, 197 (1971)

CrossRef22.

Results for the thermal blooming of a single collimated pulse are presented in [4] P. B. Ulrich, J. Wallace, J. Opt. Soc. Am.**63**, 8 (1973)

23.

A nonlinear solution for the flow near “March=1” as a function of Mach number has been derived by J. H. Hayes: Appl. Opt.

**13**, 2072 (1972)

ADSMathSciNet24.

J. N. Hayes: unpublished report, U. S. Naval Research Laboratory, Washington, D. C.

25.

C. B. Hogge, R. R. Butts: “*Propagation Effects of a Slewed Beam with Transverse Wind Null Spots*”; Air Force Weapons Laboratory, Kirkland AFB, N. M., Rept. AFWL-TR-73-76 (1973)

26.

R. T. Brown, P. J. Berger, F. G. Gebhardt, H. C. Smith: “*Influence of Dead Zones and Transonic Slewing on Thermal Blooming*”; United Aircraft Research Laboratory, East Hartford, Conn., Rept. N921724-7 (1974)

27.

P. J. Berger, F. G. Gebhardt, D. C. Smith: “*Thermal Blooming Due to a Stagnation Zone in a Slewed Beam*”; United Aircraft Research Laboratory, East Hartford, Conn., Rept. N921724-12 (1974)