Dynamics and characteristics of self-trapping of intense light beam

Chiao, R. Y.

Garmire, E.

Townes, C. H.

English

NASA Technical Reports Server

Dynamics and Characterist ics 
.b 
of the Self-trapping of Intense Light Beams". 
E. Garmire,  R .  Y.  Chiao, and C. H. Townes 
Physic s Department , M a s  sac hus et t s Ins t i  tute of T ec hnolo gy 
In an optical medium with non-linear refractive index, an intense light beam 
may form i t s  own optical waveguide and propagate without diffracting. (1)(2) There 
has  already been some experimental evidence for this phenomenon, especially in 
glasses(3) and Raman active liquids. (4)(5) This paper reports direct  observation of 
the evolution of beam trapping in CS2 in the simplest cylindrical mode. The threshold, 
trapping length, change in index of refraction, and steady-state beam profile have 
been found to be consistent with theoretical predictions (1)(6)(7)calculated from the 
non-linear refractive index due to the Kerr  effect. (8) It has been demonstrated that 
a steady-state condition is asymptotically approached in which the beam collapses to 
a bright filament a s  small  as 50p. 
l 
A Q-switched (rotating pr ism) ruby laser beam impinging on a 0. 5 mm pinhole 
produced a diffraction-limited plane wave 10 to 100 kilowatts in power. Changes in 
beam diameter were obtained by placing various lenses their focal distance ai ter  the 
pinhole. 
microscope slides every two centimeters along the beam in order  to reflect a small  
fraction of i t  out of the cell. Figure 1 shows the experimental setup and magnified 
images (8X) of the beam profile a s  i t  reflects off the glass plates. 
The development of trapping in a cell of CS2 was studied by immersing 
Each plate causes 
two reflections, only one of which is shown here.  
trapping have been observed to be introduced by the plates, which a r e  very thin 
No changes in properties of self- 
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- 2 -  
compared with d is tmcss  in  which the beam is characteristically trapped. 
Figure l b  shows the results obtainable with such configuration. It is clear  
that after a certain distance a steady-state condition is approached consisting of a 
bright filament, here 100p in diameter. 
such a beam in the distance to the next glass plate, proving that w e  do indeed have 
beam trapping, i. e.  propagation of a beam without spreading by ordinary diffraction. 
Eventually losses  such as two-photon a b ~ o r p t i o n ' ~ )  deplete the beam intensity 
allowing some spreading. 
the entrance to the cell and compared w i t h  t h ~  theoretical intensity profile. '') The 
observed profile (cf. Fig. 2a) w 3 s  found t o  consist of a strongly peaked distribution 
in reasonable agreement wfEh the theoretical curve, super-imposed on a broad 
background of untrapped radiation. 
brighter than the background, with roughly half the total radiation in the trapped 'peak. 
This peak appeared to be 10 per  cent depolarized due to wave guide effects. 
radiation was found to be emitted from the 100p trapped negion, in several  smal l  
filaments the order  of lop En diameter, with intensity 1% that of the trapped beam. 
A threshold was observed in total power, a s  expected, which remained the 
The measured threshold was about 
Simple diffraction would double the s ize  of 
Intensity profiles of the beam were measured 50cm. f rom 
The central peak power was  twenty-five t imes 
Stokes 
same even when the beam diameter was halved. 
25+5 kilowatts, somewhat higher than the theoretical threshold of 10 kw" "calculated 
f rom the optical K e r r  constant n 
the incident beam profile is not ideal and only par t  of the beam traps.  
From examination of photographs such a s  those in Fig, lb ,  a characterist ic 
= 1. 8 x 10- l '  e ~ u ' ~ ) .  This is not unexpectedsince 2 
distance for  the collapse of the beam into a bright filament can be determined. 
xheoretical trapping distance has been calculated for Gaussian beams by Kelley, 
A 
- 3 -  
a /? with n2Eo 2 /2 the nonlinear contribution to the refractive ITJ giving - 2 
index, and a the beamkadius.  ( 6 )  For a 90 kilowatt beam 0. 5 mm in diameter, the 
0 
theoretical trapping length of 11 cm,  calculated with the optical Kerr  coefficient 
n2 = 1 .8  x 10 
the same power levels halving the beam area roughly halved the trapping length, as 
expected. 
intensity w e r e  hampered by a degree of variability in trapping lengths, expecially a t  
smal le r  beam diameters. 
field gradients such as those introduced by dust particles,  o r  multimoding of the ruby 
l a se r .  Nevertheless i t  was  observed that the trapping length decreased with 
increasing power. 
-11 esu, agrees well with the measured trapping length of 12  cm. At 
Accurate meaeurements of the trapping length a s  a function of peak 
Such variability may be caused by unreproducible . 
A monotonic collapse of the beam into a steady-state condition did not always 
occur, especially a t  shorter  trapping lengths. 
r ings often w e r e  present (Fig. IC) .  
between a spherical  wave diffracting from a point in the liquid and the untrapped 
beam. 
Transient phenomena in the form of 
Some of these rings appear to be interference 
These phenomena died out in sufficiently long cells leaving only the steady- 
state profile discussed above. However at higher powers, a persistent ring (Fig. Id) 
appeared which may be related to the higher order  steady-state modes. (1 1 )  
An essential  feature of self-trapped optical beams is the increase in 
refract ive index in the trapped region. 
beam causes an accumulation of the phase of a trapped r a y  relative to those which 
are untrapped. 
the cell  over the trapped beam profile in the manner shown in Figure 2a. 
The resulting slower velocity of the trapped 
To detect this phase change, two s l i ts  were placed immediately after 
These 
s l i t s  w e r e  magnified ten times along their length by a cylindrical lens without 
- 4- 
' altering the two-slit interference pattern. When one of the slits was centered on the 
intense trapped filament, the resulting interference pattern from a 50 c m  cell 
revealed a phase change greater than 27. However, when the sl i t  was moved off 
center,  the pattern shown in Figure 2b was obtained, implying a gradual rather than 
discontinuous phase change across  the beam profile. This confirms that not all the 
beam reached the steady-state waveguide condition in which the entire beam travels 
with fixed phase. A 10 cm cell yielded 0 . 6  of a fringe shift (Fig. 2c) , which implies 
-5  A n = 1. 4 x 10 
optical Ker r  effect calculated in the filament which was ten times brighter than the 
untrapped radiation of 16 Mwatts/cm . 
.since the filament w a s  3 cm long. This is consistent with the 
2 
Most ruby laser  beams have intensities far above threshold for trapping in 
CS2 and a r e  sufficiently inhomogeneous to give the complex patterns which have been 
previously p h ~ t o g r a p h e d . ' ~ )  Figure 1 e shows the developments of many filaments 
from an apparently homogeneous beam about 1 mm i n  diameter and considerably 
above threshold power, 
ca l  and w a s  surrounded by a bright ring in this stage of development. 
Each trapped filament was in itself approximately cylindri- 
We would like to acknowledge valuable laboratory help from Howard Smith, 
Michael Johnson, and Samuel Krinsky, and very useful discussions with D r .  Paul 
Kelley. 
I 
8 
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References 
1. 
2. 
3. 
4. 
5. 
6.  
7. 
8.  
9. 
10. 
R. Y .  Chiao, E. Garmire ,  and C. H. Townes, Phys. Rev. Let ters ,  13, A79 
( 1 964). 
V. I. Talanov, Izv. Vysshikh Uchebn. Zavedenii, Kadisfizika, - 7,  564 (1 964). 
M. Hercher,  3. Opt. So@. Am., 54, 5 6 3  (1964). G. N.  Steinberg, J. G. Atwood, 
P. H. Lee,  to be published. 
G. Maycr and G o  Hauchecorne, Compt. Rend. 261, 4014 (1965). P. Lallemand 
and N. Bloembergen, Phys. Rev. Letters,  - 14, 1010 (1965). 
N.  F. Pilipetskii and A. R .  Rustamov, Sov. Phys.  JETP Let ters ,  - 2,  55 (1965). 
P. L. Kelley, Phys.  Rev. Letters,  - 15, 1005 (1965). 
V. I. Talanov, Sov. Phys.  JETP Letters,  - 2,  138 (1965). 
G. Mayer and F. Gires,  Compt. Rend., - 258, 2039 (1964). 
J. A.  Giordmaine and J. A. Howe, Phys. Rev. Letters,  - 11, 207 (1963). 
-
T 
-
1 5. 7t  
The computed power in  reference 1 should be Pc = (z) -
n = n  + 
87-r-n n 
n2E02 2 0  
2 "  0 
where 
11. H. Haus, to be published. Z. Jankauskas, to  be published. 
- 6 -  
Figure Captions 
Figure 1: Evolution of beam-trapping in CS2. Left: without dashed cell; right: 
dashed cell adds 25  cm path length. 
trapping at  increasing power (e) 1 mm pinhole. 
(a) gas laser  control (b, c,  d) beam- 
Figure 2: Two-slit interference experiment. (a) Trapped beam profile showing 
location of s l i ts  (b , c )  interference patterns f rom 50 and 10 cm cells,  
r e  speciively . 
r------ 
L- - - - - - - 
+ I  - 
-I- 
V V V V V V 
a 
b 
C 
d -  (r 
e 
FIG. I 
.. - . ’  
I 
Q b C 


Dynamics and Characteristics of the Self-trapping of Intense Light Beams

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