Fourth-harmonic generation via nonlinear diffraction in a
2D LiNbO
3
nonlinear photonic crystal from mid-IR
ultrashort pulses
Boqin Ma (马博琴)
1,2,
*, Kyle Kafka
2
, and Enam Chowdhury
2
1
Faculty of Science and Technology, Communication University of China, Beijing 100024, China
2
Department of Physics, Ohio State University, Columbus, Ohio 43210, USA
*Corresponding author: maboqin@cuc.edu.cn
Received October 16, 2016; accepted February 10, 2017; posted online March 13, 2017
Five conical harmonic beams are generated from the interaction of femtosecond mid-infrared (mid-IR) pulses at
a nominal input wavelength of 1997 nm with a 2D LiNbO
3
nonlinear photonic crystal with Sierpinski fractal
superlattices. The main diffraction orders and the corresponding reciprocal vectors involved in the interaction
are ascertained. Second and third harmonics emerging at external angles of 23.82° and 36.75° result from non-
linear
ˇ
Cerenkov and Bragg diffractions, respectively. Three pathways of fourth-harmonic generation are
observed at external angles of 14.21°, 36.5°, and 53.48°, with the first one resulting from nonlinear
ˇ
Cerenkov
diffraction, and the other two harmonics are generated via different cascaded processes.
OCIS codes: 190.4420, 190.2620, 050.1940.
doi: 10.3788/COL201715.051901.
When a monochromatic wave passes through a homo-
geneous medium with its second-order nonlinear suscep-
tibility varying in some regions, e.g., χ
ð2Þ
in a nonlinear
photonic crystal (NPC), nonlinear diffraction can be
detected for the harmonic rings or spots of the input fun-
damental wave
[1–6]
. Nonlinear diffraction, which is based on
phase matching, includes nonlinear
ˇ
Cerenkov diffraction
(NCD), nonlinear Raman–Nath diffraction (NRND), and
nonlinear Bragg diffraction (NBD). For NCD, the longi-
tudinal phase matching (LPM) is satisfied when the longi-
tudinal direction is parallel to the incident fundamental
laser beam. This phase matching can be achieved by the
addition of integer multiples of the incident wave vector
or the combination of the incident wave vector and recip-
rocal vectors. In the case of NRND, the transverse
(perpendicular to the incident fundamental laser beam)
phase matching (TPM) has to be satisfied. This can be
achieved by the combination of the reciprocal vectors. How-
ever, for the NBD process to occur, both LPM and TPM
need to be satisfied. In the past twenty years, second-
harmonic generation (SHG) via various nonlinear diffrac-
tions in 1D and 2D NPCs had been the major focus
[7–13]
.
Although high-order harmonics (HH) are very important
to the field of nonlinear optics, until recently, publications
on HH generation using NPCs have been almost nonexist-
ent. Recently, there have been several significant efforts to
generate third harmonics in periodic, short-range ordered
or radially poled NPCs, NPC waveguide and random quad-
ratic media by NCD and NRND
[14–18]
. Also, high efficiency
quasi-phase-matched harmonic generation from the 2nd to
8th order have been observed within a single LiNbO
3
(LN)
NPC
[19]
. However, fourth-harmonic generation (FHG) via
nonlinear diffraction is rarely reported. The advantage of
using a 2D fractal superlattice is that it may allow the
freedom of optimization of many parameters such as input
wavelength, harmonic order, angle, and efficiency. In this
Letter, second, third, and especially multiple fourth har-
monics are achieved by nonlinear diffractions in an LN
NPC with Sierpinski fractal superlattices under femtosec-
ond pulses.
In our experiment, a fourth-order Sierpinski fractal super-
lattice as a unit is adopted in z-cut LN NPC
[20]
, where the
second order is square and the other three orders are circles.
On the basis of the fractal structure, the ratio of the distan-
ces between the two neighboring maximum circles and the
two neighboring minimum circles is 27. This unit is then
repeated in the xoy plane. The interval between the
repeated units is exactly the distance between the two
neighboring minimum circles, i.e., 13.64 μm. The second-
order susceptibilities χ
ð2Þ
in the circular and square regions
are reversed by an external high-voltage electric field. The
length, width, and thickness of the sample are 8, 8, and
0.4 mm, respectively. The diameters of the first-, third-,
and fourth-order circles are 110, 12, and 5 μm, respectively,
and the side length of the second-order square is 37 μm.
Based on the formation of the Sierpinski superlattices,
the magnitude of the basic reciprocal vector G
⇀
0
is set to
be G
0
¼ 2π∕13.64, as seen in Fig. 1. Multiple reciprocal vec-
tors distribute in the xoy plane.
The input fundamental 100 fs laser pulses with 2 μm
central wavelength are generated from an optical para-
metric amplifier (OPA, Spectra-Physics) pumped by a
home built 0.5 kHz Ti:sapphire laser operating at
780 nm wavelength with an 80 fs pulse width. The input
fundamental wavelength is linearly (vertically) polarized
with a pulse energy of approximately 30 μJ. The laser
pulses are incident along the z axis of the crystal so that
they are perpendicular to the reciprocal vectors of
COL 15(5), 051901(2017) CHINESE OPTICS LETTERS May 10, 2017
1671-7694/2017/051901(5) 051901-1 © 2017 Chinese Optics Letters
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