Giant second-harmonic generation in a one-dimensional GaN photonic crystal
J. Torres, D. Coquillat,* R. Legros, J. P. Lascaray, F. Teppe, D. Scalbert, D. Peyrade, Y. Chen, O. Briot,
M. Le Vassor d’Yerville, E. Centeno, D. Cassagne, and J. P. Albert
Groupe d’Etude des Semiconducteurs, UMR 5650, CNRS-Universite ´ Montpellier II, pl. E. Bataillon, 34095 Montpellier, France
and Laboratoire de Photonique et des Nanostructures, CNRS UPR 20, Route de Nozay, 91460 Marcoussis, France
Received 8 July 2003; revised manuscript received 8 October 2003; published 20 February 2004
In order to determine the angular geometry that satisfies quasi-phase matching conditions for enhanced
second-harmonic generation SHG, the equi-frequency surfaces of the resonant photonic modes that lie above
the light line of a one-dimensional GaN photonic crystal have been experimentally and theoretically studied as
a function of frequency, angle of incidence, and azimuthal direction. Enhancement of the SHG has been
observed when the angular configuration satisfies the quasi-phase matching conditions, i.e., when both the
fundamental and second-harmonic fields coincide with resonant modes of the photonic crystal. The SHG
enhancement achieved to the double resonance was 5000 times with respect to the unpatterned GaN layer. A
smaller, but still substantially enhanced SHG level was also observed when the fundamental field is coupled
into a resonant mode, while the second-harmonic field is not.
DOI: 10.1103/PhysRevB.69.085105 PACS numbers: 42.70.Qs, 42.65.Ky, 78.66.Fd
I. INTRODUCTION
Photonic crystals PhCs have attracted widespread inter-
est in recent years because of their ability to alter the disper-
sion relations of photons.
1–3
Among the many practical ap-
plications which are likely to be found for the unique optical
properties of PhCs, one of the most exciting issues resides in
the possibility of obtaining a large enhancement in the non-
linear optical response.
4
In the case of noncentrosymmetric crystals with signifi-
cant second-order nonlinear coefficients, the phase-matching
conditions for processes such as second-harmonic generation
SHG are not normally fulfilled because of material disper-
sion. This problem can be solved however by using periodi-
cally modulated materials.
5–10
In this case it is the periodicity
which provides the phase matching conditions for the inci-
dent and generated beam. This mechanism is called quasi-
phase matching QPM
11,12
and takes into account the recip-
rocal lattice vectors of the periodic structure to compensate
for the wave vector mismatch in situations where direct
phase matching is not possible. Furthermore, PhCs high re-
fractive index contrast contribute to the SHG enhancement in
two ways: not only do they make it possible to satisfy the
QPM conditions, but the strong spatial confinement of the
fundamental and second-harmonic SH fields can enhance
the nonlinear response considerably.
8
Previous reports have
demonstrated that efficient SHG can be achieved in one-
dimensional PhCs.
8,9,13,14
PhCs in planar geometry can support two kinds of modes
classified according to their position with respect to the light
line: i purely guided bound modes that are completely con-
fined inside the waveguide, without any coupling to external
radiation; these modes lie below the light line of the cladding
material; ii resonant modes also termed quasi-guided
modes,
15,16
located in the vicinity of the waveguide; the latter
modes lie above the light line and possess in-plane Fourier
components which can be phase-matched to external radia-
tion. Cowan and Young recently reported in Ref. 17 a calcu-
lation showing that the SH conversion efficiency can in prin-
ciple be enhanced by up to six orders of magnitude when
both the fundamental and the SH fields are coupled into such
resonant modes. In this case the QPM condition is written
as
17
k=k
2 -2 k
G=0, 1
where k
( ) and k
(2 ) refer to the in-plane wave vectors
of the resonant fundamental mode at and of the resonant
SH mode at 2, respectively, while G is a reciprocal lattice
vector. Because these QPM conditions might occur away
from the high-symmetry directions, it is then essentially im-
portant to consider the full photonic band structure of the
PhC.
Although the strong confinement of both the fundamental
and the SH fields has been shown to play a decisive role in
SHG enhancement,
8
experimental SHG enhancement has so
far been observed when only the fundamental field is
confined.
7,18
To obtain efficient SHG, a nonlinear material with high
nonlinear coefficients is required. Nitrides are attractive ma-
terials for optical wavelength conversion
19
with second-order
susceptibility
(2)
comparable to conventional nonlinear
crystals such as KDP or LiNbO
3
, a wide electronic bandgap
without absorption either of the fundamental wave in the
near infrared or of the second-harmonic in the near UV, and
a high optical damage threshold. Nevertheless, the efficiency
of the SHG in bulk GaN is too low for practical
applications
19,20
because GaN is a highly dispersive material.
Appropriate PhC structures patterned in GaN on sapphire
waveguides should provide the flexibility required to fulfill
QPM conditions and enable much higher conversion effi-
ciency. We have previously reported band-structure measure-
ments of two-dimensional PhC structures realized in GaN on
sapphire samples
21–23
as well as measurements of their pho-
toluminescence properties.
24,25
The full band diagram for all k wave vectors in the first
Brillouin zone not only along the high symmetry directions
has been also calculated or experimentally investigated in
PHYSICAL REVIEW B 69, 085105 2004
0163-1829/2004/698/0851058/$22.50 ©2004 The American Physical Society 69 085105-1