Far-field measurements of the in-plane polarization properties of spontaneous emission from optical nanocavities formed in two-dimensional photonic crystal slab waveguides are presented. A strong polarization signature, even subthreshold, is found for a pair of highly localized dipolelike resonant modes. This polarization signature is used to study the effects of symmetry lowering within the cavity

Painter, Oskar

Srinivasan, Kartik

English

Caltech Authors - Main

March 1, 2002 / Vol. 27, No. 5 / OPTICS LETTERS 339Polarization properties of dipolelike defect modes in
photonic crystal nanocavities
Oskar Painter and Kartik Srinivasan
Department of Applied Physics, California Institute of Technology, Pasadena, California 91125Received July 20, 2001
Far-field measurements of the in-plane polarization properties of spontaneous emission from optical nanocavi-
ties formed in two-dimensional photonic crystal slab waveguides are presented. A strong polarization signa-
ture, even subthreshold, is found for a pair of highly localized dipolelike resonant modes. This polarization
signature is used to study the effects of symmetry lowering within the cavity. © 2002 Optical Society of
America
OCIS codes: 140.5960, 230.5750.Optical nanocavities formed in two-dimensional (2D)
photonic crystal (PC) slab waveguides1,2 can be de-
signed to support resonant modes with modal volumes
close to the theoretical limit of a cubic half-wave-
length.3,4 The ability to define the cavity geometry
through the use of planar fabrication techniques pro-
vides a great deal of f lexibility in the design of cavity
modes, their wavelength, polarization, and emission
patterns. Such f lexibility, which is important for
nano-optic devices capable of high-density integration
within light-wave circuits, has already been used
to create a multiwavelength 2D laser array5 and
resonant cavities capable of supporting both highly lo-
calized donor- and acceptor-type modes.6 Significant
progress has also been made using similar planar PC
waveguide structures to form in-plane waveguides,7 – 9
coupled-resonator waveguide systems,10,11 and reso-
nant add–drop devices.12
In this Letter we study the polarization properties of
a pair of highly localized deep donor (DD) type modes,
termed x and y dipolelike modes, as they transform
as vector components within the plane of the slab
waveguide.3 The PC defect cavities studied here are
realized in an optically thin dielectric slab patterned
with a 2D hexagonal array of air holes13 [Fig. 1(a)].
As a result of the localized nature of the defect region
and the symmetry of the PC in which it is embedded,
the field patterns of the DD modes resemble that
of an oscillating electric dipole in the plane of the
waveguide [Figs. 2(a) and 2(b)]. For defect cavities
in which the PC lattice is relatively porous, as is
the case here, radiation from the dipolelike modes
is predominantly *90% emitted out of plane from
the patterned slab waveguide. A plot based upon
finite-difference time-domain (FDTD) simulations of
collection efficiency versus collection angle for the
vertically emitted power from the x dipole mode is
given in Fig. 2(c). FDTD calculations show that
*99% of this vertically emitted power is carried in
the dominant (Ex or Ey) polarization of the (x or y)
dipolelike modes.
In defect cavities that maintain the sixfold symme-
try [C6v (Ref. 3)] of the host hexagonal lattice, the DD0146-9592/02/050339-03$15.00/0 ©dipolelike modes are degenerate, and any mixture of
the x and y dipolelike modes shown in Fig. 2 may be ex-
cited. To break this degeneracy and to resolve the po-
larized x and y dipolelike modes, the cavity symmetry
must be reduced to C2v. To this end, three different
cavity geometries, shown in Figs. 1(b)–1(d), are cre-
ated. The symmetric (S) cavity, created by the com-
plete removal of a central hole, eliminates translational
symmetries while maintaining the point group symme-
try of the lattice, C6v. The X- and Y-split cavities rep-
resent slight modifications of the S cavity that reduce
the symmetry of the system from C6v to C2v.3 In the
X-split cavity, air holes on the top and at the bottom of
the central missing hole are moved inward a distance
Fig. 1. (a) Cross section of a defect cavity in a 2D PC
slab waveguide (WG). QWs, quantum wells. (b)–(d) PC
cavity geometries with different symmetries. For opera-
tion at l  1.5 mm, the slab thickness, hole radius, and
lattice spacing are roughly d  200 nm, r  175 nm, and
a  500 nm, respectively.2002 Optical Society of America
340 OPTICS LETTERS / Vol. 27, No. 5 / March 1, 2002Fig. 2. (a), (b) FDTD-generated vector field patterns of
the electric f ield within the symmetry plane of the slab
waveguide for the x and y dipolelike modes. (c) Collec-
tion efficiency of the vertically emitted power versus collec-
tion half-angle (plot of the Ex intensity in the far f ield for
the x dipolelike mode shown in the inset). FDTD simu-
lations were performed with nslab  3.4, ra  0.30, and
da  0.55.
Dy, and in the Y-split cavity, the missing central hole
is accompanied on either side by an enlarged hole of
radius r0 . r.
Spectroscopy of the resonant mode structure of
the defect cavities was performed by analysis of the
light emission in the 1500-nm band from an integral
InGaAsPInP multiple-quantum-well active region
grown within the dielectric slab waveguide.13 A large
array of defect cavities was fabricated with varying
lattice spacings and hole sizes so that a wide range of
resonant mode wavelengths would be covered. The
defect cavities were fabricated in sets of three (S,
X, Y), with each of the different cavities within the
triplet designed to have the same lattice spacing and
nominal hole radius. A lattice spacing of approxi-
mately 550 nm ra  0.35,da  0.41 was found to
provide the best overlap of the DD modes of all three
cavities and the quantum-well emission band. The
defect cavities were fabricated with eight periods of
the PC surrounding the central defect region, limiting
the leakage of light in plane and allowing for efficient
light collection from the top of the sample.3
The sample was mounted on an x y z stage, and
the defect cavities were optically pumped by an 830-nmsemiconductor laser diode at an angle normal to the
sample surface (Fig. 3). A high-numerical-aperture
(N.A., 0.5), long-working-distance, 1003 objective lens
was used to image the defect cavities, collect the photo-
luminescence (PL), and focus the optical pump beam.
A GaAs filter was used to separate the pump beam
from the PL before detection. The spot size of the
pump beam on the sample surface was approximately
4 mm, covering half the diameter of a PC cavity.
Pulsed pumping conditions (10-ns pulses with 1% duty
cycle) were used to reduce heating of the membrane
structure. Pump power was maintained below the
lasing threshold of any of the cavity modes for all
measurements. The fraction of the total vertically
emitted power from the dipolelike modes collected
within the 30± half-angle of the objective lens is esti-
mated to be 30% from FDTD calculations [Fig. 2(c)].
The polarization of the collected PL was measured
with a polarizer placed in the beam path after the
collection lens. In this position, the polarizer f ilters
the different in-plane polarization components of
the emitted light from the PC slab waveguide. For
each of the cavities studied, three PL spectra were
taken: one with the polarizer removed (NP), one
with the polarizer oriented along PX, and one with
the polarizer oriented along PY. The orthogonal PX
and PY angles of the polarizer, shown projected onto
the surface of a defect cavity in the inset of Fig. 3,
were chosen to correspond to the orientation of the x
and y dipolelike modes, respectively. For reference,
a PL spectrum from an unprocessed region on the
sample is shown in Fig. 4(a). The two peaks in the
spectra correspond to the heavy-hole-to-conduction
band (hh-c) and light-hole-to-conduction band (lh-c)
transitions in the quantum well.13
The PL from a S cavity is shown in Fig. 4(b).
With the polarizer removed from beam path (NP), a
single resonance peak near 1550 nm is present. The
normalized frequency al0 of this peak is 0.355,
which lies near the middle of the TE-like guided-mode
λpump Power 
Meter
polarizer
NPB
Optical Spectrum 
Analyzer
Objective Lens
(100X, N.A.=0.5)
PY
PX
λPL
Fig. 3. Schematic of the polarization-selective PL mea-
surement setup. The inset shows a projection of the PX
and PY polarizer orientations onto a scanning electron mi-
croscope image of a fabricated defect cavity as it would
be mounted in the PL setup. NBP, nonpolarizing beam
splitter.
March 1, 2002 / Vol. 27, No. 5 / OPTICS LETTERS 341Fig. 4. Polarization-f iltered PL from the (a) unprocessed
area of the sample (no cavity), (b) S cavity, (c) X-split cavity,
and (d) Y-split cavity.
bandgap and corresponds well to the predicted
frequency of the dipolelike modes from FDTD simula-
tions. This resonance peak contains energy in both
the PX and the PY polarizations. The two polariza-
tion peaks are nearly degenerate, consistent with the
degeneracy of the x, y dipolelike modes in a cavity
with C6v symmetry. An observed 5-nm splitting of
the polarized PL peaks arises from asymmetries in
the defect cavity that are unintentionally introduced
during fabrication.
In Fig. 4(c), the PL spectrum from an X-split cavity
with Dy  25 nm is shown. The single resonant peak
of the S cavity has now split into two distinct peaks
separated in wavelength by 30 nm. The two peaks
are to be orthogonally polarized, the long-wavelength
peak along PY and the short-wavelength peak along
PX. Referring to the vector plots of Fig. 2, the
long-wavelength peak is the y dipole mode and the
short-wavelength peak is the x dipole mode. This
classification is further supported by FDTD simula-
tions, which predict that the x dipole mode will have
a shorter wavelength than the y dipole mode in an
X-split cavity.6
PL from a Y-split cavity with r 0a  0.5 is shown in
Fig. 4(d). A single resonance peak, polarized along
PX, remains. Energy in the orthogonal PY polar-
ization, which was present in both the S and X-split
cavities, is now absent. This result is consistent with
FDTD simulations, which show that the y dipole mode
is strongly perturbed for r0a . 0.45, leaving only the
x dipole mode in the guided-mode bandgap.3 The
measured peak power of the x dipole peak varies si-
nusoidally with polarizer angle, with a peak-to-valley
ratio of approximately 25:1. This value is lower thanthe theoretically estimated polarization extinction
ratio of the x dipole, most likely as a result of the
collection of nonresonant emission along with the x
dipole mode radiation.
In summary, the simple picture of the DD modes
as a pair of oscillating dipole sources, evoked by the
vector plots of Fig. 2, carries over quite well to the
far-field polarization measurements. Adjustments in
the defect-cavity symmetry result in splitting of the
dipole-mode degeneracy, as predicted by group theory.
Once they are split in frequency, the x and y dipolelike
modes are strongly polarized along two different
orthogonal directions, consistent with their near-f ield
dipole character. A polarization extinction ratio of
at least 25:1 is found for the x dipole mode of the
Y-split cavity. Apart from technological applications,
the polarization signature of the dipolelike modes
is extremely valuable in understanding the spectra
of more-complex defect cavities and in estimating
the accuracy of numerical models such as the FDTD
model.
The authors thank A. Scherer, P. D. Dapkus, and
J. D. O’Brien for their help with the growth and fab-
rication of samples. K. Srinivasan thanks the Hertz
Foundation for its f inancial support. O. Painter’s
e-mail address is opainter@its.caltech.edu.
References
1. P. St. J. Russell, D. M. Atkin, and T. A. Birks, Bound
Modes of Two-Dimensional Photonic Crystal Wave-
guides (Kluwer Academic, Dordrecht, The Nether-
lands, 1996), pp. 203–218.
2. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D.
Joannopoulos, and L. A. Kolodziejaki, Phys. Rev. B
60, 5751 (1999).
3. O. Painter, J. Vucˇkovic´, and A. Scherer, J. Opt. Soc.
Am. B 16, 275 (1999).
4. R. Coccioli, M. Boroditsky, K. W. Kim, Y. Rahmat-
Samii, and E. Yablonovitch, IEE Proc. Optoelectron.
145, 391 (1996).
5. O. Painter, A. Husain, A. Scherer, P. T. Lee, I. Kim,
J. D. O’Brien, and P. D. Dapkus, IEEE Photon. Tech-
nol. Lett. 12, 1126 (2000).
6. O. Painter, K. Srinivasan, J. D. O’Brien, A. Scherer,
and P. D. Dapkus, J. Opt. A 3, S161 (2001).
7. E. Chow, S. Y. Lin, J. R. Wendt, S. G. Johnson, and
J. D. Joannopoulos, Opt. Lett. 26, 286 (2001).
8. T. Baba, N. Fukaya, and J. Yonekura, Electron. Lett.
35, 654 (1999).
9. M. Loncˇar, D. Nedeljkovic´, T. Doll, J. Vucˇkovic´, A.
Scherer, and T. P. Pearsall, Appl. Phys. Lett. 77, 1937
(2000).
10. C. Smith, R. De la Rue, M. Rattier, S. Olivier, H.
Benisty, C. Weisbuch, T. Krauss, U. Oesterlé, and R.
Houdré, Appl. Phys. Lett. 78, 1487 (2001).
11. S. Olivier, C. Smith, M. Rattier, H. Benisty, C. Weis-
buch, T. Krauss, R. Houdré, and U. Oesterlé, Opt. Lett.
26, 1019 (2001).
12. S. Noda, A. Chutinan, and M. Imada, Nature 407, 608
(2000).
13. O. J. Painter, A. Husain, A. Scherer, J. D. O’Brien, I.
Kim, and P. D. Dapkus, J. Lightwave Technol. 17, 2082
(1999).


Polarization properties of dipolelike defect modes in photonic crystal nanocavities

A 3,

https://authors.library.caltech.edu/5947/1/PAIol02.pdf

Polarization properties of dipolelike defect modes in photonic crystal nanocavities

Abstract

Similar works

Full text

Available Versions

Caltech Authors - Main