One obstacle for ultrafast laser materials processing is the nonlinear beam distortion due to changes in refractive index of the beam delivery gas medium, which are induced by the extremely high optical intensity of the focused femtosecond laser beam. The Kerr effect increases the refractive index and causes self-focusing, while plasma generated by multiphoton and tunneling ionization decreases the refractive index and defocuses the beam. The overall effects from these nonlinear mechanisms both spatially and temporally distort the original homogeneous beam profile, resulting in reduced feature quality for ultrafast laser materials processing. In this work, a theoretical model based on the nonlinear Schrödinger equation describing laser pulse propagation coupled with a rate equation for plasma evolution in a gas is used to simulate the beam distortion due to self-focusing and plasma defocusing. The resulted beam profile at the focal point in air exhibits ring-like structures, and the intensity distribution can significantly deviate from the original Gaussian profile. The model also shows that the nonlinear beam distortion can be dramatically reduced by delivering the beam using an inert gas, e.g., helium, rather than air, due to its unique physical properties, which suggests a novel beam delivery technique for high quality ultrafast laser-material processing.

1.
Liu
,
X.
,
Du
,
D.
and
Mourou
,
G.
Laser Ablation and Micromachining With Ultrashort Laser Pulses
.
IEEE Journal of Quantum Electronics.
Vol.
33
:
1997
; pp.
1706
1716
.
2.
Varel
,
H.
,
Ashkenasi
,
D.
,
Rosenfeld
,
A.
,
Wahmer
,
M.
and
Campbell
,
E. E. B.
Micromachining of Quartz With Ultrashort Laser Pulses
.
Applied Physics A.
Vol.
65
:
1997
; pp.
367
373
.
3.
Nolte
,
S.
,
Momma
,
C.
,
Jacobs
,
H.
,
Tunnermann
,
A.
,
Chichkov
,
B. N.
,
Wellegehausen
,
B.
and
Welling
,
H.
Ablation of Metals by Ultrashort Laser Pulses
.
Journal of the Optical Society of America B.
Vol.
14
:
1997
; pp.
2716
2722
.
4.
Szörényi
,
T.
,
Fogarassy
,
E.
,
Fuchs
,
C.
,
Hommet
,
J.
and
Le Normand
,
F.
Chemical Analysis of a-Cnx Thin Films Synthesized by Nanosecond and Femtosecond Pulsed Laser Deposition
.
Applied Physics A.
Vol.
69
:
1999
; pp.
S941
S944
.
5.
Hammer
,
D. X.
,
Noojin
,
G. D.
,
Thomas
,
R. J.
,
Clary
,
C. E.
,
Rockwell
,
B. A.
,
Toth
,
C. A.
and
Roach
,
W. P.
Intraocular Laser Surgical Probe for Membrane Disruption by Laser-Induced Breakdown
.
Applied Optics.
Vol.
36
:
1997
; pp.
1684
1693
.
6.
Shah
,
L.
,
Tawney
,
J.
,
Richardson
,
M.
and
Richardson
,
K.
Femtosecond Laser Deep Hole Drilling of Silicate Glasses in Air
.
Applied Surface Science.
Vol.
183
:
2001
; pp.
151
164
.
7.
Braun
,
A.
,
Korn
,
G.
,
Liu
,
X.
,
Du
,
D.
,
Squier
,
J.
and
Mourou
,
G.
Self-Channeling of High-Peak-Power Femtosecond Laser-Pulses in Air
.
Optics Letters.
Vol.
20
:
1995
; pp.
73
75
.
8.
Siders
,
C. W.
,
Rodriguez
,
G.
,
Siders
,
J. L. W.
,
Omenetto
,
F. G.
and
Taylor
,
A. J.
Measurement of Ultrafast Ionization Dynamics of Gases by Multipulse Interferometric Frequency-Resolved Optical Gating
.
Physical Review Letters.
Vol.
87
:
2001
; pp.
263002
.
9.
Brodeur
,
A.
,
Chien
,
C. Y.
,
Ilkov
,
F. A.
,
Chin
,
S. L.
,
Kosareva
,
O. G.
and
Kandidov
,
V. P.
Moving Focus in the Propagation of Ultrashort Laser Pulses in Air
.
Optics Letters.
Vol.
22
:
1997
; pp.
304
306
.
10.
Sun
,
J.
and
Longtin
,
J. P.
Inert Gas Beam Delivery for Ultrafast Laser Micromachining at Ambient Pressure
.
Journal of Applied Physics.
Vol.
89
:
2001
; pp.
8219
8224
.
11.
Siegman
,
A. E.
Lasers,
Sausalito, CA, USA
:
University Science Books
,
1986
.
12.
Mourou
,
G.
The Ultrahigh-Peak-Power Laser: Present and Future
.
Applied Physics B.
Vol.
65
:
1997
; pp.
205
211
.
13.
Chin
,
S. L.
,
Brodeur
,
A.
,
Petit
,
S.
,
Kosareva
,
O. G.
and
Kandidov
,
V. P.
Filamentation and Supercontinuum Generation During the Propagation of Powerful Ultrashort Laser Pulses in Optical Media (White Light Laser
).
Journal of Nonlinear Optical Physics & Materials.
Vol.
8
:
1999
; pp.
121
146
.
14.
Sprangle
,
P.
,
Esarey
,
E.
and
Krall
,
J.
Self-Guiding and Stability of Intense Optical Beams in Gases Undergoing Ionization
.
Physical Review E.
Vol.
54
:
1996
; pp.
4211
4232
.
15.
Rae
,
S. C.
Spectral Blueshifting and Spatial Defocusing of Intense Laser-Pulses in Dense Gases
.
Optics Communications.
Vol.
104
:
1994
; pp.
330
335
.
16.
Chiron
,
A.
,
Lamouroux
,
B.
,
Lange
,
R.
,
Ripoche
,
J. F.
,
Franco
,
M.
,
Prade
,
B.
,
Bonnaud
,
G.
,
Riazuelo
,
G.
and
Mysyrowicz
,
A.
Numerical Simulations of the Nonlinear Propagation of Femtosecond Optical Pulses in Gases
.
European Physical Journal D.
Vol.
6
:
1999
; pp.
383
396
.
17.
Saleh
,
Bahaa
E. A.
and
Teich
,
Malvin
C.
Fundamentals of Photonics,
New York
:
John Wiley & Sons, Inc
.,
1991
.
18.
Poon
,
Ting-Chung
and
Banerjee
,
Partha
P.
Contemporary Optical Image Processing with MATLAB,
New York
:
Elsevier Science Ltd.
,
2001
.
19.
Newell
,
Alan
C.
and
Moloney
,
Jerome
V.
Nonlinear Optics, Redwood City,
California, USA
:
Addison-Wesley Publishing Company
,
1992
.
20.
Agrawal
,
Govind
P.
Nonlinear Fiber Optics,
San Diego, California, USA
:
Academic Press, INC.
,
1989
.
21.
Taha
,
T. R.
and
Ablowitz
,
M. J.
Analytical and Numerical Aspects of Certain Nonlinear Evolution-Equations.2. Numerical, Nonlinear Schrodinger-Equation
.
Journal of Computational Physics.
Vol.
55
:
1984
; pp.
203
230
.
22.
Chin
,
S. L.
,
Akozbek
,
N.
,
Proulx
,
A.
,
Petit
,
S.
and
Bowden
,
C. M.
Transverse Ring Formation of a Focused Femtosecond Laser Pulse Propagating in Air
.
Optics Communications.
Vol.
188
:
2001
; pp.
181
186
.
23.
Keldysh
,
L. V.
Ionization in the Field of a Strong Electromagnetic Wave
.
Soviet Physics JETP.
Vol.
20
:
1965
; pp.
1307
1314
.
24.
Rae
,
S. C.
and
Burnett
,
K.
Detailed Simulations of Plasma-Induced Spectral Blueshifting
.
Physical Review A.
Vol.
46
:
1992
; pp.
1084
1090
.
25.
Larochelle
,
S. F. J.
,
Talebpour
,
A.
and
Chin
,
S. L.
Coulomb Effect in Multiphoton Ionization of Rare-Gas Atoms
.
Journal of Physics B.
Vol.
31
:
1998
; pp.
1215
1224
.
26.
Perelemov
.
A.M
,
Popov
,
V. S.
and
Terentev
,
M. V.
Ionization of Atoms in an Alternating Electric Field
.
Soviet Physics JETP-USSR.
Vol.
23
:
1966
; pp.
924
934
.
27.
Mlejnek
,
M.
,
Wright
,
E. M.
and
Moloney
,
J. V.
Femtosecond Pulse Propagation in Argon: a Pressure Dependence Study
.
Physical Review E.
Vol.
58
:
1998
; pp.
4903
4910
.
28.
Subbarao
,
D.
,
Singh
,
P.
,
Uma
,
R.
and
Bhaskar
,
S.
Computer Simulation of Laser-Beam Self-Focusing in a Plasma
.
Journal of Plasma Physics.
Vol.
61
:
1999
; pp.
449
467
.
29.
Bracewell
,
Ronald
N.
The Fourier Transform and its Applications, 3rd.
New York
:
McGraw-Hill College Div.
,
1999
.
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