Electro-optically tunable self-focusing and self-defocusing
in KTP crystals by a cascaded second-order process
Ruma Debnath, Digvijay Singh Hada, Susheel Kumar Beda, and Ardhendu Saha*
Department of Electrical Engineering, National Institu te of Technology, Agartala 799046, India
*Corresponding author: arsagtwave@gmail.com
Received June 3, 2016; accepted October 14, 2016; posted online November 21, 2016
We report the transformation of a linear electro-optically tunable non-phase-matched second-order nonlinear
process into a cascaded second-order nonlinear process in a bulk KTP crystal to generate the effect of electro-
optically tunable Kerr-type nonlinearity. By applying an electric field on the x–y plane, parallel to the z-axis of
the crystal, phase mismatch is created, which introduces a nonlinear phase shift between the launched and
reconverted fundamental waves from the generated second harmonic wave. Due to the nonuniform radial
intensity distribution of a Gaussian beam, a curvature will be introduced into the fundamental wavefront, which
focuses or defocuses the incident beam while propagating through the crystal.
OCIS codes: 190.2620, 190.4360, 260.5950, 260.1180.
doi: 10.3788/COL201614.121902.
Cascaded second-order nonlinearity has been investigated
in various crystals so far by applying different methods; it
has vital applications in self-focusing and self-defocusing
[1]
,
spatial solitons
[2]
, all-optical switching, mode locking, tran-
sistor action
[3]
, high-speed optical shutters
[4]
, electro-optical
detection
[5]
, electro-optic switching
[6]
, etc. In cascaded
second-order nonlinearity (χ
ð2Þ
:χ
ð2Þ
), as the name suggests,
one second-order nonlinear process is followed by another
second-order nonlinear process in a phase-mismatch condi-
tion, which introduces a phase shift between the launched
fundamental wave (FW) and reconverted FW from the
generated second harmonic wave (SHW). Depending on
the phase mismatch, the FW focuses or defocuses within
the crystal with cascaded nonlinearity, similar to Kerr
media having χ
ð3Þ
nonlinearity. A large equivalent effective
third-order nonlinearity (χ
ð3Þ
nonlinearity) larger than the
natural third-order nonlinearity
[1,7]
can be obtained by cas-
caded second-order nonlinearities
[8]
and is applicable for
mode locking of solid-state lasers for CW operations,
known as cascaded second-order mode locking (CSM)
[9]
.
KTP is an excellent nonlinear optical crystal which is
widely used in cascaded secon d-order nonlinear applica-
tions
[10]
. Due to its high nonlinear coefficient and higher
optical damage threshold
[11]
, KTP is effectively used in
second harmonic generation (SHG)
[12]
for intracavity
high-power laser generation compared to other crystals
[13]
.
Besides its higher second-order nonlinearity, it also has
high indirect third-order nonlinearity
[1]
which can be
developed by the cascaded nonlinearity. Earlier, indirect
third-order nonlinearity was studied by different meth-
ods
[1,14]
, where reflection losses take place in the cavity.
But electro-optically tunable indirect third-order nonlin-
earity has not been reported until now, where less voltage
is required to create the required phase mismatch (Δk), as
compared to other crystals, as the electro-optic coefficients
of bulk KTP are high
[15]
. Iliev et al.
[16]
reported a temper-
ature-tuned cascaded χ
ð2Þ
lens mode-locking technique at
the non-phase-matched condition for SHG, where Kerr
lens mode-locking was investigated by putting a lens near
the PPKTP crystal within the cavity. In this technique,
the focusing and defocusing of the Kerr lens are controlled
by controlling the focal length of the lens, which is very
crucial to adjust.
In this work, a phase-mismatch (Δk) condition is intro-
duced into a bulk KTP crystal by applying a DC electric
field on the x–y plane of the crystal to analyze the cas-
caded χ
ð2Þ
nonlinearity. The application of a direct electric
field on a bulk KTP crystal has not yet been reported until
now. The Δk introduces a nonlinear phase shift (Δϕ
NL
)
within the launched FW and regenerated FW from the
generated SHW while propagating through the crystal.
Thus, this Δk can be controlled by the applied electric
field, and the sign of the nonlinear phase shift can easily
be changed by changing the polarity of the applied electric
field. Hence, focusing or defocusing of the FWs depends on
the sign of Δk, where the FWs focus for the positive values
of Δk and defocus for the negative values of Δk. The most
significant advantage of this method is that the value of
the effective nonlinear refractive index (n
eff
2
) can be rap-
idly changed compared with other methods, such that
the value of Δk is tuned by changing the incident angle
in an angle tuning method.
When an external DC electric field is applied in the
z (axis) direction of a bulk KTP crystal, the refractive
indices (RIs) of the crystal change, and due to Pockels
effect, the index ellipsoid of the crystal can also be modi-
fied as
[17]
½ð1∕n
02
x
Þþr
13
E
z
x
2
þ½ð1∕n
02
y
Þþr
23
E
z
y
2
þ½ð1∕n
02
z
Þþr
33
E
z
z
2
¼ 1; (1)
where n
0
x
, n
0
x
, and n
0
z
are the modified RIs of the bulk KTP
along the principal axes after applying the DC electric
field (E
z
), and
COL 14(12), 121902(2016) CHINESE OPTICS LETTERS December 10, 2016
1671-7694/2016/121902(5) 121902-1 © 2016 Chinese Optics Letters