In this letter we theoretically study the frequency mixing of two off-axis focused Gaussian beams. The optimal phase mismatch corresponding to maximized conversion efficiency depends on the separation of off-axis beams and can be expressed in terms of the phase velocities analytically, which provides an effective approach to measure the phase velocity distribution of a Gaussian beam.

1.
M. D.
Perry
,
D.
Pennington
,
B. C.
Stuart
,
G.
Tietbohl
,
J. A.
Britten
,
C.
Brown
,
S.
Herman
,
B.
Golick
,
M.
Kartz
,
J.
Miller
,
H. T.
Powell
,
M.
Vergino
, and
V.
Yanovsky
,
Opt. Lett.
24
,
160
(
1999
).
2.
R.
Kienberger
,
M.
Hentschel
,
M.
Uiberacker
,
Ch.
Spielmann
,
M.
Kitzler
,
A.
Scrinzi
,
M.
Wieland
,
Th.
Westerwalbesloh
,
U.
Kleineberg
,
U.
Heinzmann
,
M.
Drescher
, and
F.
Krausz
,
Science
297
,
1144
(
2002
).
3.
J. X.
Wang
,
Y. K.
Ho
,
Q.
Kong
,
L. J.
Zhu
,
L.
Feng
,
S.
Scheid
, and
H.
Hora
,
Phys. Rev. E
58
,
6575
(
1998
).
4.
P. X.
Wang
,
Y. K.
Ho
,
X. Q.
Yuan
,
Q.
Kong
,
N.
Cao
,
A. M.
Sessler
,
E.
Esarey
, and
Y.
Nishida
,
Appl. Phys. Lett.
78
,
2253
(
2001
).
5.
J.
Pang
,
Y. K.
Ho
,
X. Q.
Yuan
,
N.
Cao
,
Q.
Kong
,
P. X.
Wang
, and
L.
Shao
,
Phys. Rev. E
66
,
066501
(
2002
).
6.
P.
Sprangle
,
E.
Esarey
, and
J.
Krall
,
Phys. Plasmas
3
,
2183
(
1996
).
7.
P.
Sprangle
,
E.
Esarey
,
A.
Ting
, and
G.
Joyce
,
Appl. Phys. Lett.
53
,
2146
(
1988
).
8.
C. I.
Moore
,
A.
Ting
,
S. J.
Mcnaught
,
J.
Qiu
,
H. R.
Burris
, and
P.
Sprangle
,
Phys. Rev. Lett.
82
,
1688
(
1999
).
9.
D.
Umstadter
,
S. Y.
Chen
,
A.
Maksimchuk
,
G.
Mourou
, and
R.
Wagner
,
Science
273
,
472
(
1996
).
10.
K.
Nakajima
,
D.
Fisher
,
T.
Kawakuba
,
H.
Nakanishi
,
A.
Ogata
,
Y.
Kato
,
Y.
Kitagawa
,
R.
Kodama
,
K.
Mima
,
H.
Shiraga
,
K.
Suzuki
,
K.
Yamakawa
,
T.
Zhang
,
Y.
Sakawa
,
T.
Shoji
,
Y.
Nishida
,
N.
Yugami
,
M.
Downer
, and
T.
Tajima
,
Phys. Rev. Lett.
74
,
4428
(
1995
).
11.
C.
Gahn
,
G. D.
Tsakiris
,
A.
Pukhov
,
J.
Meyer-ter-Vehn
,
G.
Pretzler
,
P.
Thirolf
,
D.
Habs
, and
K. J.
Witte
,
Phys. Rev. Lett.
83
,
4772
(
1999
).
12.
G. D.
Boyd
and
D. A.
Kleinman
,
J. Appl. Phys.
39
,
3897
(
1968
).
13.
A. M.
Weiner
,
A. M.
Kan’an
, and
D. E.
Leaird
,
Opt. Lett.
23
,
1411
(
1998
).
14.
S.
Yu
and
A. M.
Weiner
,
J. Opt. Soc. Am. B
16
,
1300
(
1999
).
15.
R. W.
Boyd
,
Nonlinear Optics
(
Academic
,
New York
,
1992
).
17.
G. D.
Xu
,
T. W.
Ren
,
Y. H.
Wang
,
Y. Y.
Zhu
,
S. N.
Zhu
, and
N. B.
Ming
,
J. Opt. Soc. Am. B
20
,
360
(
2003
).
18.
S. M.
Saltiel
,
K.
Koynov
,
B.
Agate
, and
W.
Sibbett
,
J. Opt. Soc. Am. B
21
,
591
(
2004
).
19.
M.
Born
and
E.
Wolf
,
Principles of Optics
, 7th ed. (expanded) (
Cambridge University Press
,
Cambridge
,
1999
).
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