PHYSICAL REVIEW APPLIED 3, 014006 (2015)

Localized Guided-Mode and Cavity-Mode Double Resonance in Photonic
Crystal Nanocavities
X. Liu,1 T. Shimada,1 R. Miura,1 S. Iwamoto,2 Y. Arakawa,2 and Y. K. Kato1,*
1

Institute of Engineering Innovation, The University of Tokyo, Tokyo 113-8656, Japan
2
Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan(Received 5 October 2014; revised manuscript received 5 December 2014; published 21 January 2015)
We investigate the use of guided modes bound to defects in photonic crystals for achieving double
resonances. Photoluminescence enhancement by more than 3 orders of magnitude is observed when the
excitation and emission wavelengths are simultaneously in resonance with the localized guided mode andcavity mode, respectively. We find that the localized guided modes are relatively insensitive to the size ofthe defect for one of the polarizations, allowing for flexible control over the wavelength combinations. This
double-resonance technique is expected to enable the enhancement of photoluminescence and nonlinear
wavelength-conversion efficiencies in a wide variety of systems.
DOI: 10.1103/PhysRevApplied.3.014006

I. INTRODUCTION
Photonic crystals allow high degrees of control overlight through periodic modulation of the refractive index[1]. In particular, the photonic band gap, which inhibits
propagation of light with a frequency within the gap,
can be used to confine light and form optical nanocavities
with state-of-the-art quality factors exceeding one million[2,3]. Combined with their small mode volumes, thesenanocavities are ideal for coupling to a variety of nanoscale emitters [4–7]. By matching the luminescencewavelength to the cavity resonance, emission rates canbe enhanced and radiation patterns can be redirected toachieve higher efficiencies [8,9].
When the emitters are optically excited, further control
can be achieved by tuning another mode in a cavity to theexcitation wavelength to obtain a double resonance [10,11].
Such a double resonance is also desirable for nonlinear
wavelength-conversion processes such as sum and difference frequency generation, four-wave mixing, and Raman
scattering. It is, however, a challenge to match two cavity
modes to a specific pair of wavelengths, as they are usually
not independently tunable. A recent demonstration of asilicon Raman laser takes advantage of modes with different symmetry to fine-tune the double resonance [12],while polarization can also be used to control the mode
separation [13,14]. For independent tuning of resonancesat large wavelength differences, a cross-beam design has
also been used [15,16].
*

Corresponding author.
ykato@sogo.t.u‑tokyo.ac.jp
Published by the American Physical Society under the terms of
the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) andthe published article’s title, journal citation, and DOI.

2331-7019=15=3(1)=014006(6)Here we characterize guided-mode resonances localized
at defects in photonic crystals using photoluminescence(PL) microscopy for their use in achieving double resonances. Unlike the cavity-mode resonances, these localized
guided modes are at frequencies outside the photonic bandgap, and large wavelength separation from the cavity
modes is possible. When both the excitation and theemission wavelengths coincide with the localized guided
mode and the cavity mode, respectively, we observe a PL
enhancement factor as high as 2400. Changing the defectstructure does not cause significant shifts in the localized
resonances for one of the polarizations, allowing for a
simple design procedure to achieve double resonances forvarious wavelength combinations. We demonstrate suchflexibility by tuning the double resonance in a wide rangeof excitation and emission wavelengths.
II. EXCITATION RESONANCES IN A PHOTONICCRYSTAL NANOCAVITY
Our devices are linear defect L-type cavities in hexagonal lattice photonic crystal slabs made from siliconon-insulator wafers [7,17]. Electron-beam lithography
followed by a dry-etching process defines the air holes
in the 200-nm-thick top Si layer. We design the air holeradius to be r ¼ 0.29a where a is the lattice constant.
Linear defects are introduced to form Ln cavities, where ndenotes the number of missing holes. Subsequent selective
wet etching removes the 1000-nm-thick buried oxide layer,
thereby forming a free-standing photonic crystal membrane. Scanning electron micrographs of a typical device
are shown in Fig. 1(a).
The cavities are characterized with a laser-scanningconfocal microscope [7,18]. A wavelength-tunable
continuous-wave Ti:sapphire laser allows for PL excitation(PLE) spectroscopy, and PL images are acquired by

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PHYS. REV. APPLIED 3, 014006 (2015)

FIG. 1. (a) A scanning electron micrograph of a device with an
L3 cavity and a ¼ 370 nm. The scale bar is 2 μm. Red, green,
and blue dots indicate the positions at which the curves with thecorresponding colors in (b) and (c) are taken. Inset shows amagnified view of the cavity. (b) Red, green, and blue thick solidlines show the PL spectra taken at the cavity, patterned area, andunetched slab area, respectively, with λex ¼ 832 nm. The thin redline shows a PL spectra taken at the cavity with λex ¼ 900 nm.
Green, blue, and thin red curves have been multiplied by 30 forclarity. (c) PLE spectra taken at the cavity (red), patterned area
(green), and unetched slab area (blue). PL intensities in (d) areintegrated between λem ¼ 1090 and 1130 nm to obtain these PLE
spectra. (d) A PLE map taken at the cavity. All data in (b)–(d) aretaken with x-polarized excitation with P ¼ 1 mW.

scanning the laser beam with a fast steering mirror. An
objective lens with a numerical aperture (NA) of 0.8
focuses the excitation laser beam on the sample to a spot
size of approximately 1 μm, and the same lens collects the
PL from silicon. Linear polarization of the excitation laser
can be rotated using a half-wave plate placed just before
the objective lens. A single-grating spectrometer disperses
PL onto a liquid-nitrogen-cooled InGaAs photodiode arrayfor detection. All measurements are done in air at room
temperature.
Typical PL spectra are shown in Fig. 1(b) for excitation
with its electric field E polarized along the x axis and an
incident power P ¼ 1 mW. The thin red line is the
spectrum taken with the laser spot on the cavity at an
excitation wavelength λex ¼ 900 nm, clearly showing acavity mode at an emission wavelength λem ¼ 1148 nmwith a quality factor Q ¼ 360, which is assigned to the fifthmode of the L3 defect [9]. Interestingly, when λex is tuned
to 832 nm, we observe an approximate fiftyfold increase in
the PL intensity throughout the spectrum (thick red line).
In order to study this effect in detail, PLE spectroscopy
is performed [Figs. 1(c) and 1(d)]. We see a clear “cross”
pattern in the PLE map taken at the cavity [Fig. 1(d)],where the vertical line corresponds to the cavity mode inresonance with emission, while the horizontal line represents a resonance in the excitation wavelength. At theintersection, we have a double resonance, where both

excitation and emission are resonant. In Fig. 1(b), thedouble-resonance condition is met at the strongest peak in
the thick red curve, and we find that the detected PL peakintensity is enhanced by a factor of approximately 2400
compared to an unetched part of the Si slab (blue curve) at
the same wavelength.
We characterize the excitation resonance using PLE
spectra obtained by plotting the integrated PL intensity
I PL as a function of λex [Fig. 1(c), red curve]. The spectral
integration is performed over a 40-nm window centeredat λem ¼ 1110 nm to eliminate the effects of the cavity
modes. There are several sharp peaks on top of a broad
spectral feature, and the strongest excitation resonance at
λex ¼ 832 nm has Q ¼ 290.
Such high-Q resonances cannot be attributed to cavity
modes that are confined by the photonic band gap, as thehigh-energy band edge is located at around 1100 nm forthis lattice constant [9]. At shorter wavelengths, guided
modes exist which allow photons to freely propagate in theplane of the photonic crystal slab. These guided modes cancouple to free-space modes if they exist above the light line
[19] and can enhance light emission over a large area
because they are delocalized [9,20].
We evaluate the effects of the guided modes by performing measurements within the photonic crystal pattern but
away from the cavity. The green curve in Fig. 1(b) showsa PL spectrum with some enhancement compared to theemission from the unetched slab area, although theenhancement is significantly smaller than that observedat the cavity. A PLE spectrum on the pattern [Fig. 1(c),green curve] shows a broad spectral feature which is
expected for guided modes because they have angledependent frequency [19] and excitation with a high-NA
lens will couple to a wide range of frequencies. We notethat the high-Q resonances are absent in this spectrum,suggesting that they are observed only near the defect.
The spatial extent of the high-Q excitation resonances
are investigated by performing imaging measurements.
In Fig. 2, we present PL images taken at 16 different
excitation wavelengths. As the emission spectral integration window is chosen not to include the cavity modes,
these images mostly reflect the excitation efficiency profiles. The images change drastically for the different
wavelengths, and an image taken at λex ¼ 800 nm showsthat the PL enhancement occurs throughout the photonic
crystal pattern, consistent with the delocalized nature of theguided modes. In comparison, it is clear that the high-Q
excitation resonances at λex ¼ 832 and 846 nm are highly
localized at the defect. Similar localized resonances canbe seen at other wavelengths as well, although the PL
enhancements are smaller.
III. LOCALIZED GUIDED MODES
In order to identify the physical origin of the high-Q
excitation resonances, three-dimensional finite-difference

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LOCALIZED GUIDED-MODE AND CAVITY-MODE DOUBLE …

FIG. 2. PL images of the device shown in Fig. 1 at various λextaken using x-polarized excitation with P ¼ 1 mW. The images
are constructed by integrating the PL intensity within a 40-nm
window centered at 1110 nm and normalizing by the maximum
value. The scale bar is 2 μm. All panels share the scale bar andthe color scale.

time-domain (FDTD) calculations are performed.
Figure 3(a) shows the photonic band diagram fortransverse-electric modes in a defect-free hexagonal-latticephotonic crystal slab. The band gap is formed at normalized
frequencies a=λ ¼ 0.25 to 0.33, where λ is the freespace wavelength. The strongest excitation resonance at
λex ¼ 832 nm observed in the experiments corresponds to anormalized frequency of 0.445, far above the band gap.
Looking at the band diagram near this frequency, several
modes exist above the light line around the Γ point.
Calculations show that these modes can be weakly
bound to a defect to form a localized state with a reasonably
high Q [21].
Using FDTD simulations, we search for such localizedstates bound to an L3 defect. Indeed, several modes are
identified, and Fig. 3(b) shows the field distribution for
an x-polarized resonance with a mode volume V ¼
4.92ðλ=nÞ3 and Q ¼ 300. The mode profile shows thatthe field is localized at the defect, consistent with the resultsof imaging measurements. In addition, the mode has anormalized frequency a=λ ¼ 0.454 which is in the vicinityof the strongest resonance observed in the experiments.
Although precise mode assignment is difficult at thesefrequencies because of dispersion and absorption effects,
the characteristics of the excitation resonances can be
explained by the simulated mode. With a reasonable agreement between calculations and experiments, we attribute

PHYS. REV. APPLIED 3, 014006 (2015)

FIG. 3. (a) Photonic band diagram of transverse-electric modes
computed for a defect-free structure with r=a ¼ 0.305 and aslab thickness of 0.54a. Temporal Fourier transforms of impulse
response are plotted, where wave vectors are specified byappropriate boundary conditions. Refractive index n ¼ 3.6 isused for Si, and a slightly larger value of r=a as determined fromelectron micrographs is used. The orange line indicates the light
line. (b),(c) Simulated electric-field amplitude patterns of localized guided modes with x and y polarization, respectively. Scalebars are 1 μm, and both panels share the color scale at the top. Ex
and Ey are plotted for the x- and y-polarized modes, respectively.
The x-polarized mode is at a=λ ¼ 0.454 with V ¼ 4.92ðλ=nÞ3
and Q ¼ 300, while the y-polarized mode is at a=λ ¼ 0.449 withV ¼ 2.05ðλ=nÞ3 and Q ¼ 100. (d),(e) Reciprocal-space Fourier
amplitude maps of the fields shown in (b) and (c), respectively.
The orange circle represents the light line, and the hexagon is thefirst Brillouin zone.

the high-Q excitation resonances to localized guided
modes (LGMs). We also perform calculations for y polarization [Fig. 3(c)] and find LGMs at similar frequencies.
The spatial Fourier transform of the mode profile gives
additional insight into the origin of the LGMs. As shown in
Fig. 3(d), the x-polarized mode has most of its amplitude
within the light line, which implies good coupling tofree-space modes. It can also be seen that there are twopoints with intense amplitudes above and below the zone
center. Such a reciprocal-space distribution suggests a
simple interpretation that this LGM consists of linear
combinations of unbound guided modes. It is reasonable
that reciprocal-space amplitude shows high intensities atpoints along the y axis, because these guided modes are x
polarized. As expected from this picture, the spatial Fouriertransform of the y-polarized mode [Fig. 3(e)] shows strong
amplitudes for wave vectors along the x axis.
Now we consider how the LGMs can be controlled.
We expect the resonances to shift linearly with the lattice
constant, as they should depend on the photonic band
structure. In Fig. 4(a), we present the a dependence of PLE
spectra from L3 defects taken with x-polarized excitation.
Indeed, the LGMs can be tuned over more than 100 nm
by changing the lattice constant. In addition to the two
prominent resonances observed for the device with

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FIG. 4. (a),(b) PLE spectra for various lattice constants taken
under x- and y-polarized excitation, respectively. (c) Evolution of
PL spectra with a taken with λex tuned to the maximum PL
intensity and x-polarized excitation. The spectra from bottom to
top correspond to a ¼ 270 to 500 nm in 10-nm steps. The devices
have L3 defects, and all spectra are taken with the laser spot on
the cavity with P ¼ 1 mW.

a ¼ 370 nm, we observe a few other series of weaker
resonances. For larger lattice constants, we observe an
emergence of a broader spectral structure at shorter wavelengths, likely composed of many peaks. Such a broadfeature is reasonable, as the band structure becomes more
complicated for higher normalized frequencies [9].
We also investigate PLE spectra under y-polarized
excitation [Fig. 4(b)]. Here we find excitation resonancesthat scale with a as well but at slightly different wavelengths compared to those observed for x polarization.
For guided modes in a perfect photonic crystal, bothpolarizations should be degenerate at the Γ point where
coupling to free-space modes are allowed [19]. As the defectreduces the symmetry of the system, such an energy splitting
for different polarization is expected for the LGMs.

FIG. 5. (a),(b) PLE spectra of linear defect cavities ofvarious sizes under x- and y-polarized excitation, respectively.
(c) PL spectra of L-type cavities taken with λex ¼ 710 nm andy-polarized excitation. The spectra from bottom to top correspondto L1 to L8 defects. The devices have a ¼ 310 nm, and all
spectra are taken at the center of the cavity with P ¼ 1 mW.

The number of the modes increases, and the resonances
appear at different positions within the photonic band gap.
The lattice constant dependence and the defect length
dependence of the LGMs and the cavity modes are
summarized in Fig. 6. We locate the peak positions for
x-polarized and y-polarized LGMs (λxLGM and λyLGM ,respectively), as well as the cavity resonance wavelength
λcav . Relatively weak intensity peaks that are hard to
identify in Fig. 4 are also plotted in Figs. 6(a)–(c). The
defect length dependence of the cavity modes is shown in
Fig. 6(d), where the mode polarization is identified byplacing a linear polarizer in the collection path. Cavity size
dependence of the strongest LGMs is shown in Figs. 6(e)IV. FLEXIBLE TUNING OF DOUBLERESONANCES
If tuning of a double resonance to a specific combinationof two wavelengths is desired, the LGMs and cavity modes
need to be controlled independently. When we change thelattice constant, however, the cavity modes also shift
linearly [Fig. 4(c)]. The simultaneous shifts show that theresonances cannot be tuned independently and implies thatthe double resonance can be moved only along a line in a
λex -λem plane.
In order to find a way to design doubly resonant cavities,
we investigate PLE spectra from linear defects of various
lengths. Interestingly, for x-polarized excitation, the LGM
resonances appear at similar wavelengths despite thedifferent cavity structures [Fig. 5(a)]. In contrast, they-polarized resonances can differ in wavelength by almost
40 nm [Fig. 5(b)]. The cavity-mode spectra [Fig. 5(c)] show
a complex evolution as the defect length is increased.

FIG. 6. Lattice constant dependence of (a) cavity modes,(b) y-polarized LGMs, and (c) x-polarized LGMs for L3 cavities.
(d) Defect length dependence of both x- (solid symbols) andy-polarized (open symbols) cavity modes. (e),(f) The strongest
y- and x-polarized LGMs, respectively, as a function of the defectlength.

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the top-left corner of our PLE maps. Next, we can use an
L3 cavity with a ¼ 380 nm to utilize the strong LGM at
844 nm and the fifth cavity mode at 1173 nm, obtaining
a double resonance at the top-right corner. Reducing thelattice constant down to 290 nm, this LGM is now at
758 nm, and by using an L1 cavity, the double resonance istuned to the bottom-left corner. Finally, keeping the same
LGM for excitation resonance, an L5 defect offers a cavity
mode at 1162 nm, completing the last corner. The ratioof the two wavelengths for the double resonance shownin Fig. 7(d) is 1.53, comparable to those achieved in
nanobeam cavities [15,16,22,23].
FIG. 7. Double resonance for (a) an L2 cavity witha ¼ 270 nm, (b) an L3 cavity with a ¼ 380 nm, (c) an L1
cavity with a ¼ 290 nm, and (d) an L5 cavity with a ¼ 300 nm.
All data are taken at the center of the cavities using x-polarized
excitation with P ¼ 1 mW.

and 6(f). It is noted that both x-polarized LGMs and thecavity modes are relatively insensitive to the defect length,
while the y-polarized modes show large changes.
Such a different behavior depending on the polarization
can be intuitively understood if we consider the LGMs
as linear combinations of unbound guided modes.
The x-polarized modes will consist of guided modes withwave vectors along the y axis, and, therefore, they should
be sensitive to the index of refraction profile along the y
direction. Since we are comparing linear defects, the index
profiles along the y axis are similar for all cavities, and it isreasonable that the LGMs appear at similar wavelengths.
In comparison, for the y-polarized modes, the wave vectors
will be in the x direction. Changing the length of the defectdirectly affects the index profile that those guided waves
see, and this should result in different resonant wavelengths
for the y-polarized modes.
The insensitivity of the x-polarized LGMs to the lengthof the defect provides a simple procedure for tuning the
double resonance to a specific combination of wavelengths.
First, we can choose a to tune a LGM to one wavelength,
then we can look for a cavity size which has a mode at
the other wavelength. Since the y-polarized cavity modes
are sensitive to the length of the defect, it should be possible
to find a cavity mode near the desired wavelength as longas it is within the photonic band gap. Even though
we are changing the defect structure in the latter step,
the LGMs will have more or less the same resonancewavelength, allowing for independent tuning of the cavity modes.
We demonstrate such flexibility in Fig. 7 by tuning the
double resonance to four different combinations of
excitation and emission wavelengths. First, we use thelowest normalized-frequency LGM that we observe, whichis resonant at 850 nm for a ¼ 270 nm. An L2 defect has acavity mode at 1040 nm, producing a double resonance in

V. CONCLUSION
The flexible tuning offered by the LGM and cavity-mode
double resonance should allow enhancement of emission
from a wide variety of luminescent materials, such as
quantum dots, molecules, fluorophores, and proteins.
For emitters that show sharp resonances in absorption suchas carbon nanotubes [24], tuning the double resonancewill be particularly effective. It should also be possible
to enhance Raman scattering from nanoscale materials
such as graphene [25]. Increased efficiency in wavelength
conversion such as sum and difference frequency generation is expected as well, if materials with large nonlinearity are used [16,22]. Although the quality factors of
LGMs are smaller compared to typical cavity modes, they
may be limited by the strong absorption of silicon. By usinga larger electronic band gap material and an enhancementof the Q factors in the L-type cavities [26], further increasein the efficiencies are anticipated.
In summary, we investigate the use of LGMs forachieving doubly resonant cavities in photonic crystals,
and an enhancement of silicon PL by a factor of 2400 isdemonstrated. We characterize guided modes bound to
linear defects in hexagonal lattice photonic crystal slabs
using PL spectroscopy and imaging techniques and findthat LGMs have weak dependence on the defect lengthfor one of the polarizations. Taking advantage of such aproperty, we show that the double resonance can be tuned
in a flexible manner by choosing a combination of lattice
constant and defect length. Our technique offers a simple
method for achieving double resonance in a nanocavity andis expected to be useful for enhancing PL and wavelength
conversion at the nanoscale.
ACKNOWLEDGMENTS
This work is supported by Japan Society for the
Promotion of Science KAKENHI (Grants No. 24340066,
No. 24654084, No. 26610080, and No. 26870167),
Strategic Information and Communications Research andDevelopment Promotion Programme of the Ministry ofInternal Affairs and Communications, Canon Foundation,
Asahi Glass Foundation, and KDDI Foundation, as

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well as the Project for Developing Innovation Systems,
Nanotechnology Platform, and Photon Frontier Network
Program of the Ministry of Education, Culture, Sports,
Science, and Technology, Japan.

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