Efficient second harmonic generation between photonic
and plasmonic modes in a tunable transparent
conducting oxide waveguide
Fu Xu (许 福)
†
and Yu Sun (孙 钰)*
,†
School of Information Science and Technology, Beijing Forestry University, Beijing 100083, China
*Corresponding author: sunyv@bjfu.edu.cn
Received October 30, 2015; accepted December 24, 2015; posted online February 22, 2016
Efficient second harmonic generation (SHG) in a nonlinear transparent conducting oxide (TCO) stripe wave-
guide that incorporates an organic polymer is theoretically investigated. The phase match condition between the
fundamental photonic mode at the second harmonic and the fundamental long-range plasmonic mode at the
fundamental frequency can be satisfied by dynamically or statically tuning the free carrier concentration of
the TCO. The theoretically generated signal reaches its maximum up to 56.4 mW at a propagation distance
of 34.8 μm for a pumping power of 1 W. The corresponding normalized conversion efficiency of the
phase-matched SHG is up to 4.65 × 10
3
W
−1
cm
−2
.
OCIS codes: 190.2620, 190.4390.
doi: 10.3788/COL201614.031901.
Among nonlinear processes, second harmonic generation
(SHG) is frequently studied for its concise principles,
simple implementation, and extensive applications
[1–3]
.
Due to the dramatic locally enhanced confinement of light
beyond the diffraction limit, plasmonic-based structures
are among the most promising candidates for nonlinear
devices
[4]
. Enhanced SHGs have been presented in a variety
of metallic nanostructures, including plasmonic slot wave-
guides
[5]
, long-range plasmonic waveguides
[6]
, and hybrid
plasmonic waveguides
[7–9]
. Although the aforementioned
approaches reveal the potential of efficient frequency dou-
bling, all of these structures incorporate noble metals as
plasmonic materials and are electrically passive. In plas-
monic waveguides, the phase-matching condition is usually
fulfilled via the modal phase-matching technique by stati-
cally engineering the geometric parameters, which require
the fab rication of an array of nonlinear waveguides with
gradual changes. The intrinsic Ohm loss of the metal
reduces the distance of interaction between different
frequencies and in turn limits the efficiency of the SHG.
Pioneering works in the search for new plasmonic
materials have reported that transparent conducting
oxides (TCOs) are promising CMOS-compatible, low-loss
materials with tunable optical properties
[10,11]
. The applica-
tion of the electric field by external gates results a charge
depletion or accumulation in TCOs, which tunes its per-
mittivity by shifting the plasma frequency
[12,13]
. Based on
the extraordinary tuning capabilities of TCOs, active
components in the linear regime have been intensively
studied
[12–14]
. Conversely, nonlinear optical processes asso-
ciated with TCOs remain relatively unexplored compared
with their linear counterparts.
In this Letter, we propose a nonlinear TCO stripe wave-
guide that incorporates an organic polymer for an SHG
and incorporates a tunable TCO material. As schemati-
cally illustrated in Fig.
1, a thin layer of TCO is sandwiched
between a doped, cross-linked organic polymer with a non-
linear susceptibility of χ
ð2Þ
111
¼ 619 pm∕V
[5,15]
and a refrac-
tive index of n ¼ 1.643
[16]
. The cladding material is silica.
To focus on the tunability of TCO, the width of the wave-
guide, the thickness of the polymer, and the TCO are fixed
at w ¼ 2.5 μm, t
p
¼ 1.5 μm, and t
t
¼ 25 nm, respectively.
The TCO selected for SHG in this Letter is Ga-doped zinc
oxide (GZO), which is described by the Drude–Lorentz
oscillator model as follows
[17]
:
εðωÞ¼ε
∞
−
ω
2
p
ωðω þ iΓ
p
Þ
þ
f
1
ω
2
1
ðω
2
1
− ω
2
− iωΓ
1
Þ
; (1)
where the experimentally obtained background permittiv-
ity ε
∞
¼ 2.475, the unscreened plasma frequency ω
p
¼
1.927 eV, and the collision frequency γ ¼5.07×10
16
rad∕s.
The carrier relaxation rate Γ
p
¼ 0.117 eV. The strength,
center frequency, and damping of the Lorentz oscillator
Fig. 1. Schematic of the nonlinear TCO stripe waveguide.
COL 14(3), 031901(2016) CHINESE OPTICS LETTERS March 10, 2016
1671-7694/2016/031901(4) 031901-1 © 2016 Chinese Optics Letters