High quality factor nanophotonic resonators in
bulk rare-earth doped crystals
Tian Zhong,
1,2
Jake Rochman,
1
Jonathan M. Kindem,
1,2
Evan Miyazono,
1,2
and Andrei
Faraon
1,2,*
1
T. J. Watson Laboratory of Applied Physics and Kavli N
anoscience Institute, California
Institute of Technology,
1200 E California Blvd, Pasadena, CA, 91125, USA
2
Institute for Quantum Information and
Matter, California Institute of Technol
ogy, Pasadena, California 91125, USA
*
faraon@caltech.edu
Abstract:
Numerous bulk crystalline materials exhibit attractive nonlinear
and luminescent properties for classical and quantum optical applications.
A chip-scale platform for high quality factor optical nanocavities in these
materials will enable new optoelectro
nic devices and quantum light-matter
interfaces. In this article, photonic cr
ystal nanobeam resonators fabricated
using focused ion beam milling in bulk insulators, such as rare-earth doped
yttrium orthosilicate and yttrium vanadate, are demonstrated. Operation in
the visible, near infrared, and teleco
m wavelengths with quality factors up
to 27,000 and optical mode volumes close to one cubic wavelength is
measured. These devices enable new nanolasers, on-chip quantum optical
memories, single photon sources, and non-linear devices at low photon
numbers based on rare-earth ions. The techniques are also applicable to
other luminescent centers and crystal.
©20
1
6
Optical Society of America
OCIS codes:
(350.4238) Nanophotonics and photonic crystals; (140.4780) Optical resonators;
(220.4241) Nanostructure fabrication;
(160.4330) Nonlinear optical materials.
References and links
1. K. J. Vahala, “Optical microcavities,” Nature
424
(6950), 839–846 (2003).
2. M. Aspelmeyer, T. J. Kippenberg, and F. Mar
quardt, “Cavity optomechanics,” Rev. Mod. Phys.
86
(4), 1391–
1452 (2014).
3. J. L. O’Brien, A. Furusawa, and J. Vu
č
kovi
ć
, “Photonic quantum technol
ogies,” Nat. Photonics
3
(12), 687–69
5
(2009).
4. G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and
S. W. Koch, “Nonlinear optics of normal-mode-coupling
semiconductor microcavities,” Rev. Mod. Phys.
71
(5), 1591–1639 (1999).
5. O. Painter, R. K. Lee, A. Sche
rer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dim
ensional
photo
nic band-Gap defect mode laser,” Science
284
(5421), 1819–1821 (1999).
6. S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “U
ltralow-threshold Raman laser using a spherical dielectric
microcavity,” Nature
415
(6872), 621–623 (2002).
7. P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamo
ğ
lu, “A
quantum dot single-photon turnstile device,” Science
290
(5500), 2282–2285 (2000).
8. A. Faraon, C. Santori, Z. Huang, V. M. Acosta, and
R. G. Beausoleil, “Coupling of
nitrogen-vacancy centers to
photonic crystal cavities in monocrystalline diamond,” Phys. Rev. Lett.
109
(3), 033604 (2012).
9.
J. Vuckovi
ć
, M. Loncar, H. Mabuchi, and A. Scherer, “Des
ign of photonic crystal microcavities for cavity
QED,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.
65
(1 Pt 2), 015508 (2002).
10. H. Kim, R. Bose, T. C. Shen, G. S. Solomon, a
nd E. Waks, “A quantum logic
gate between a solid-state
quantum bit and a photon,” Nat. Photonics
7
(5), 373–377 (2013).
11. M. J. Burek, Y. Chu, M. S. Z. Liddy, P. Patel, J. Rochman, S. Meesala, W. Hong, Q. Quan, M. D. Lukin, and M.
Lon
č
ar, “High quality-factor optical nanocavities in
bulk single-crystal diamond,” Nat. Commun.
5
,
5718
(2014).
12. J. Lin, Y. Xu, Z. Fang, M. Wang, J. Song, N. Wang,
L. Qiao, W. Fang, and Y. Cheng, “Fabrication of high-
Q
lithiu
m niobate microresonators using femt
osecond laser micromachining,” Sci. Rep.
5
, 8072 (2015).
13. I. Bayn, B. Meyler, J. Salzman, and R. Kalish,
“Triangular nanobeam photonic cavities in single-crystal
diamond,” New J. Phys.
13
(2), 025018 (2011).
14. J. Riedrich-Möller, L. Kipfstuhl, C. Hepp, E. Neu, C.
Pauly, F. Mücklich, A. Baur, M. Wandt, S. Wolff, M.
Fischer, S. Gsell, M. Schreck, and C. Becher, “One
- and two-dimensional photonic crystal microcavities in
single crystal diamond,” Nat. Nanotechnol.
7
(1), 69–74 (2011).
#256023
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(C)
2016
OSA
11
Jan
2016
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15. Y. Tanaka, M. Tymczenko, T. Asano,
and S. Noda, “Fabrication of two-di
mensional photonic crystal slab point-
defect cavity employing local three-dimens
ional structures,” Jpn. J. Appl. Phys.
45
(8A), 6096–6102 (2006).
16. J. S. Foresi, P. R. Villeneuve, J.
Ferrera, E. R. Thoen, G. Steinmey
er, S. Fan, J. D. Joannopoulos, L. C.
Kimerling, H. I. Smith, and E. P. Ippen, “Photoni
c-bandgap microcavities in optical waveguides,” Nature
390
(6656), 143–145 (1997).
17. J. Chan, M. Eichenfield, R. Camacho, and O. Painte
r, “Optical and mechanical
design of a “zipper” photonic
crystal optomechanical cavity,” Opt. Express
17
(5), 3802–3817 (2009).
18. Q. Quan and M. Loncar, “Deterministic design of
wavelength scale, ultra-high Q photonic crystal nanobeam
cavities,” Opt. Express
19
(19), 18529–18542 (2011).
19. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible
free-software package for electromagnetic simulati
ons by the FDTD method,” Comput. Phys. Commun.
181
(3),
687–702 (2010).
20. D. L. McAuslan, J. J. Longdell, and M. J. Sellars
, “Strong-coupling cavity QED using rare-earth-metal-ion
dopants in monolithic resonators: What you can
do with a weak oscillator,” Phys. Rev. A
80
(6), 062307 (2009).
21. W. Tittel, M. Afzelius, T. Chaneliére, R. L. Cone
, S. Kröll, S. A. Moiseev, and M. Sellars, “Photon-echo
quantum memory in solid state systems,” Laser Photonics Rev.
4
(2), 244–267 (2010).
22. T. Zhong, J. M. Kindem, E. Miya
zono, and A. Faraon, “Nanophotonic cohe
rent light-matter interfaces based on
rare-earth-doped crystals,” Nat. Commun.
6
, 8206 (2015).
23. F. S. Jamaludin, M. F.
Mohd Sabri, and S. M. Said
, “Controlling parameters of focused ion beam (FIB) on high
aspect ratio micro holes milling,” Microsyst. Technol.
19
(12), 1873–1888 (2013).
24. W. C. L. Hopman, F. Ay, W. Hu, V. J. Gadgil, L. Kuipers, M. Pollnau, and R. M. de Ridder, “Focused ion beam
scan routine, dwell time and dose optimizations for
submicrometre period planar photonic crystal components
and stamps in silicon,” Nanotechnology
18
(19), 195305 (2007).
25. J. Tian, W. Yan, Y. Liu, J. L
uo, D. Zhang, Z. Li, and M. Qiu, “O
ptical quality improvement of Si photonic
devices fabricated by focused-ion-
beam milling,” J. Lightwave Technol.
27
(19), 4306–4310 (2009).
1. Introduction
Optical nanocavities with high quality factors and small mode volumes are an enabling
technology for on-chip photonic devices such as low-power opto-electronic switches, low
threshold lasers, cavity-optomechanics, and on-chip quantum information processing [1–3].
In particular, nanoresonators with a large quality
factor-to-mode volume ratio are desirable
for strong Purcell enhancement of light-matter interactions that leads to high optical
nonlinearity [4], efficient lasing [5,6], bright quantum light emissions [7, 8], and opto-
electronic devices operating at the single photon level [9,10]. Most nanophotonic platforms
are based on commonly used semiconductor materials such as silicon, gallium arsenide and
indium phosphide. However, there are numerous other materials, including complex oxide
crystals (e. g. yttrium orthosilicate (YSO),
yttrium vanadate (YVO), lithium niobate
(LiNbO
3
), and potassium titanyl phosphate (KTiOPO
4
)), with interesting nonlinear and
luminescent properties that can be exploited for applications in classical and quantum nano-
optics. Nano-fabrication techniques for these materials are very limited due to the
unavailability of either selective etching chem
istries or high-quality thin films on which
photonic devices can be made. Several attempts to fabricate nanocavities on unconventional
materials, such as single-cryst
al diamond [8, 11] or lithium niobate crystals [12], have been
successful, but their methods cannot be easily tr
ansferred to other substrates. On the other
hand, focused ion beam (FIB) milling provides a universal tool for micromachining virtually
any bulk materials without requiring thin films.
While several studies on fabricating photonic
cavities using FIB have been carried out, the results have mostly been of low quality factors
[13–15], which have been attributed to optical property degradation, unrepeatable patterning
or significant material stress. Specifically,
Ref [13]. demonstrated a nanobeam photonic
crystal cavity in diamond with a maximum Q of 221. Ref [14]. employed a diamond thin film
on which both 1-D and 2-D photonic crystal cavities were milled. The achieved Q ranged
from 180 to 700. Lastly, Ref [15]. obtained a Q of 900 by milling a point defect in a silicon-
on-insulator slab cavity.
In this work we demonstrate a new design and a robust fabrication platform for
nanophotonic resonators based on triangular nanobeams with longitudinal grooves milled in
bulk complex oxide crystals (YSO and YVO), which are common hosts for rare-earth
emitters. Unlike a common photonic crystal design based on air holes in a thin slab of
substrate, the triangular nanobeam geometry
combined with a rect
angular subwavelength
groove optical lattice results in better toleran
ces to drifts perpendi
cular to the nano-beam
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direction that occur during the fabrication process. The fabricated devices exhibit high quality
factors up to 27,000 and small mode volumes of ~1 (
λ
/n)
3
over a wide spectrum range, from
visible to near infrared, to telecom, with resonance wavelengths closely matched to atomic
transitions of multiple rare-earth ion dopants
including Europium (Eu), Praseodymium (Pr),
Neodymium (Nd) and Erbium (Er). The quality
factors of these devices are several times
better than the highest Qs reported to date in FIB-machined cavities [14].
2. Design
Many photonic crystal cavity designs use circul
ar perforations in the center of a 1-D
nanobeam to create a photonic bandgap and use modulations of the perforation’s geometry to
obtain a local cavity mode within the structure [16–18]. When using focused ion beam
milling, this method presents difficulty for making high-Q cavities largely due to
misalignment of the perforations with respect to the nanobeam axis. To minimize this issue, a
photonic crystal cavity design consisting of a triangular nanobeam [13] with a lattice of sub-
wavelength grooves, shown in Fig. 1, is proposed. The pattern of grooves on the triangular
beam is milled across the entire beam width, wh
ich eases the alignment of the grooves to the
nanobeam and permits significant design robustness against fabrication errors due to ion
beam drift during milling. Another benefit of the triangular nanobeam design is that all its
dimensions can be globally scaled to attain re
sonances in a wide spectral range on the same
chip. This flexibility is generally less available for photonic devices fabricated on thin films,
for which a different thin film thickness is re
quired to match specific resonance wavelengths.
Fig. 1. Schematic of the triangular nanobeam re
sonator. The zoom-in view shows the photonic
crystal structure of the optical lattices
labeled with relevant
design parameters.
As seen in Fig. 1, the proposed photonic cr
ystal structure can be characterized by the
following parameters: beam width
w
B
, lattice constant
a
, groove width
w
G
, groove depth
h
,
and nanobeam interior angle
θ
. The cavity defect was implem
ented by perturbing the lattice
spacing to reach a value of 0.95
a
in the center of the cavity. To minimize scattering and
maintain a small mode volume, the lattice spacing was quadratically modulated over 7 lattice
spacings from the nominal value a to 0.95
a
at the center of the cavity. A total of 40 grooves
are milled into the beam (14 of which have a
perturbed lattice spacing), which permits a high-
Q design while maintaining reasonable collection and excitation of light through the cavity
mirrors. A beam interior angle of 60° is implemented to maximize the symmetry of the mode
profile for ease of coupling to the cavity mode through the cavity mirrors. The groove depth h
was 70% of the total beam depth to obtain a photonic band gap while maintaining the
mechanical integrity of the beam.
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3. Methods
A. Device fabrication
YSO (Scientific Materials Corp.) and YVO (Unite
d Crystals) crystals were coated with a 50
nm chrome film using an electron beam evaporator to provide a charge-dissipation and hard
mask layer for subsequent milling. The nanobeam cavities were milled in their respective
crystals with a focused Ga
+
ion beam (FEI NOVA 600). First,
a long beam with a triangular
cross-section was released from the substrate by
milling two rectangular features using a high
current at an incidence angle of 30°. The triangular nanobeam was thinned down to the target
beam width by gradually milling material (with a low current) on both sides of the beam to
minimize the sidewall roughness and remove re-deposited material on the sidewalls. Once the
target beam width was obtained, the sample was
rotated such that the ion beam was normal to
the crystal for patterning of the photonic crysta
l grooves, with a low current. Rectangular
grooves were milled across the entire nanobeam
, where the groove width, depth, and lattice
spacing contributed the photonic crystal character. All nanobeam milling was monitored in
situ via SEM imaging. Two coupling ports were milled at both ends of the beam at 45° with
respect to the sample surface to permit broadb
and excitation and collec
tion through the cavity
mirrors. All milling was performed with an ion beam voltage of 20 keV and at the lowest
possible current while maintaining a reasonable
milling time (typically 23-760 pA for milling
times under 10 minutes per elementary pattern). For instance, to fabricate a 883 nm YSO
resonator, 760 pA milling current was first used for quick release of the triangular beam,
followed by a 37 pA to trim the beam width down to its design values. The last step used a 23
pA current to pattern the grooves. The total time for making one such device was ~30
minutes. Finally, the chrome layer was removed
with chrome etchant (CR-7S) before optical
characterization of the devices.
Fig. 2. Scanning electron microscope images
of the fabricated na
nobeam resonators. (a)
Devices for different spectrum range with identi
cal structure features but different global
scaling factors. (b) The fabricated device in YVO crystal, which has the same geometric
structures as devices in YSO. The side-view in (c) shows the non-vertical sidewalls due to FIB
beam divergence, which can be improved by va
rying the ion beam voltage and current. The
top-view in (d) reveals the grooves on a thin s
upport beam. The triangular cross-section of the
beam is seen in (e).
Figure 2(a) shows a SEM image of three fabri
cated nanobeam resonators for operation at
visible, near infrared and telecom wavelength
s. All three devices share the identical design
and differ only by a global scaling factor. A typical nanobeam resonator with two coupling
ports can be seen in Fig. 2(b). Here, the target resonance wavelength is 1064 nm, but the
structure is representative of all fabricated cavities. The high-aspect ratio grooves with an
estimated sidewall angle of 6° are shown in Fig.
2(c). This angle is largely characteristic of
the focused ion beam parameters implemented, e.g. current, voltage, and beam alignment.
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Grooves that extend across the entire beam width, and a thin support beam with a width of
0.3
w
B
underneath the grooves can be observed from the top view of the cavity in Fig. 2(d).
The triangular shape of the beam, with an interior angle of 60°, can be seen in Fig. 2(e).
B. Optical measurement
Cavity transmission spectra were measured with a custom-built microscope, where the input
from a supercontinuum source was focused with a 50x microscope objective (NA = 0.65)
onto the 45°-angled coupler at the end of the beam. The coupler reflects the input light
propagating normal to the crystal surface into the waveguide. The couplers rely on total
internal reflection and have minimal dependence on wavelength, which allows broadband
coupling to the nanobeams. Th
e coupler efficiency was measured to be ~20% from
transmission measurement in a bare nanobeam without grooves. Transmitted light was
collected from the other coupler at the opposite end of the nanobeam and passed through a
pinhole at the output path to spatially filter
the transmitted light for measurement with a
spectrometer. We also measured a 25% coupling ef
ficiency of the output light from the cavity
into a single-mode fiber.
4. Results
A. YSO photonic crystal nanobeam cavities
YSO triangular photonic crystal nanobeams were simulated with MEEP [19], a finite-
difference time-domain (FDTD) solver, to op
timize the quality factor (Q) by sweeping the
values for
w
B
, a, w
G
, and
h
. The simulations used actual geom
etries of the milled structure
from SEM measurements, which included the 6°-sloped sidewalls of the grooves. A refractive
index of n
YSO
= 1.8 was used for the YSO TE-polarized resonance mode. The optimal design
parameters were a beam width of
w
B
= 0.93
λ
, a groove width of
w
G
= 0.227
λ
, and a lattice
spacing of
a
= 0.386
λ
. The resultant theoretical Q-factor is ~7 × 10
4
with a mode volume V
~1.6 (
λ
/n
YSO
)
3
for the fundamental resonance mode as shown in Fig. 3. The mode is largely
confined within the defect re
gion, where the top-view, side-view, and cross-section field
profiles are shown in Figs. 3(a)-3(c), respectively. Since the structure’s dimensions scale
globally, the same design was used for cavities matching the visible
3
H
4
-
1
D
2
transition in
Pr
3+
:YSO (605 nm), the near-infrared
4
I
9/2
-
4
F
3/2
transition in Nd
3+
:YSO (883 nm), and the
telecom
4
I
15/2
-
4
I
13/2
transition in Er
3+
:YSO (1536 nm) [20]. Transmission spectra of three
independent YSO nanocavities for Pr, Nd, and Er transitions are shown in Figs. 3(e) and 3(f).
A Q~3000 was measured at
λ
= 596 nm in the device designed for Pr dopant. On a second
resonator for operation in near infrared, a higher Q of ~12,000 was measured at
λ
= 877.8 nm.
On a third nanobeam scaled up for operation at telecom wavelengths, the highest Q of
~27,000 was measured at
λ
= 1526.6 nm. The increasing Q factors with resonance
wavelengths are expected, as scattering loss due
to surface roughness in those larger devices
is less significant.
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Fig. 3. Nanobeam resonators in the YSO crystal.
(a-c) Top, side and cross-section views of the
simulated mode profiles of the TE-mode res
onance. (d) Typical TE broadband transmission
spectrum of a YSO nanobeam resonators showing
a resonance in the photonic bandgap. Inset
shows the transmission measurement scheme
in which broadband super-continuum light
vertically couples into the nanobeam from one
end and is collected from the other end. (e)
Resonance close to the target 605 nm atomic transition of Pr
3+
ions. (f) Resonance close to the
883 nm transition of Nd
3+
ions. (g) Resonance close to the 1536 nm transition of Er
3+
ions.
B. YVO photonic crystal nanobeam cavities
Nonlinear optical processes often have strong polarization selectivity. Quantum emitters
embedded in crystals also have preferred dipole orientations that should match with the cavity
polarization. It is thus desirable for the nanocavity to support both TE and TM-polarized
modes. Here we investigated YVO triangular nanobeam resonators using a different set of
design parameters than the YSO cavities,
because of a larger refractive index n
YVO
= 2.2
along the c-crystallographic axis of YVO. A TM resonance mode is designed to align to the
c-axis, which also coincides with the strongest dipole axis of neodymium ions in the YVO
crystal. The optimal design parameters were a beam width of
w
B
= 0.852
λ
, a groove width of
w
G
= 0.210
λ
, and a lattice spacing of
a
= 0.352
λ
, which resulted in a theoretical Q-factor of
~3 × 10
5
and mode volume V~1(
λ
/n
YVO
)
3
. A significantly higher quality factor is predicted
here due to the larger refractive index. A +/
−
5% change in any geometric parameter of the
nanocavity had minimal effect on the simulated quality factors, which remained above 105.
This optimized set of parameters was used to fabricate cavities with target wavelengths of 880
nm for the
4
F
3/2
-
4
I
9/2
quantum memory transition [21], and 1064 nm for the
4
F
3/2
-
4
I
11/2
lasing
transitions in Nd
3+
:YVO by globally scaling all the dimensions. The measured transmission
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spectra of two YVO cavities are shown in Fig. 4. A Q of ~20,000 at
λ
= 869.7 nm was
measured as shown in Fig. 4(e). In a second YVO cavity scaled for the 1064 nm lasing
transition, a spectrometer-limited Q of ~20,700 at
λ
= 1058.5 nm was measured.
Fig. 4. Nanobeam resonators in the YVO crystal.
(a-c) Top, side and cross-section views of the
simulated mode profiles of the TM-mode resona
nce. (d) Typical TM broadband transmission
spectrum of YVO nanobeam resonators showing
a resonance in the photonic bandgap. (e)
Resonance close to the target 880 nm atomic transition of Nd
3+
ions. (f) Resonance close to the
target 1064 nm lasing transition of Nd
3+
ions.
5. Discussion
The design and characterization pa
rameters for all the devices investigated are summarized in
Table 1. As important figures of merit, the Q/V (V is in units of (
λ
/n)
3
) ratios are shown in the
last column, of which a peak value of 16,870 is
obtained for the TE mode in YSO and 20,700
for TM mode in YVO. Following an analysis si
milar to the one in [20], where materials like
Pr
3+
:YSO, Nd
3+
:YSO, Er
3+
:YSO and Nd
3+
:YVO have been theoretically analyzed in detail,
the single ion cooperativity is greater than one when Q/V has a value of a few thousands, as
already achieved in this work. Using the devi
ces presented in this paper, the singe ion
coupling rate g would range from ~1 MHz for Er
3+
in YSO to ~25 MHz for Nd
3+
in YVO.
The high Q/V values in these resonators fulfill one of the essential requirements for achieving
coherent light-matter interactions in the cavity. The other important factor is that the
fabricated nano-structures surrounding the ions should preserve the same properties as high
quality bulk materials. In that regard, the high Qs of the fabricated devices already suggest
that no significant optical property degradation was present. Additionally, we have recently
shown in [22] an excellent preservation of the narrow inhomogeneous linewidths and the long
optical coherence times (up to 100
μ
s) of Nd
3+
ions in one of these YSO nanocavities (similar
to no. 2 cavity in Table 1), confirming minimal
crystal damage due to ion beam milling. The
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high quality optical nanocavities demonstrated here combined with the ability to preserve
emitters’ coherent properties [22]
indicate a strong prospect of
this platform for scalable
quantum information applications, including ensemble-based quantum memories [21] and
single rare-earth-ion qubits [20].
Table 1. Summary of parameters for nanobe
am resonators fabricated in YSO and YVO
crystals.
Cavit
y
Host
(Polarizatio
n
)
Resonant
λ
(nm)
(atomic
transition)
Beam
width w
B
(nm)
Lattice
a (nm)
Groove
width w
G
(nm)
Q-factor (Q
th
)V
(
μ
m
3
)
Q/V
(
λ
/n)
3
(Q
th
/
V)
1
YSO (TE)
595.8 (605)
600
250
145
3,000 (70,000)
0.058
1875
(43,7
50)
2
YSO (TE)
877.9 (883)
820
340
200
12,200 (70,000)
0.186
7,625
(43,7
50)
3
YSO (TE)
1526.6 (1536)
1530
580
360
27,000 (70,000)
0.977
16,87
5
(43,7
50)
4
YVO
(TM)
869.7 (880)
740
310
185
20,000
(300,000)
0.062
20,00
0
(300,
000)
5
YVO
(TM)
1058.5 (1064)
880
370
215
20,700
(300,000)
0.112
20,70
0
(300,
000)
Fabricated devices currently have average qua
lity factors ~10 times lower than theoretical
predictions (Q
th
). The deviation can be attributed to imprecision in the geometry, materials
absorption or surface roughness. Possible methods
to increase the quality factors include
decreasing the sidewall angle [23, 24] and post-fabrication annealing [25]. For example, a
slight change in the sidewall angle from 6° to 4° can increase the theoretical quality factor of
the YSO design by a factor of ~2 from 70,000 to 150,000 in YSO. Further optimization of the
ion beam parameters could make such an angle possible. Previous reports with other materials
suggest that post-fabrication annealing can decrease material absorption [25], which may lead
to increased quality factors. Effects of annea
ling on FIB nanocavities have yet to be studied
with current samples, but could be implemented for improved material quality. It should also
be noted that here devices were fabricated in
materials with a relatively low refractive index.
Materials with a higher refractive index are li
kely to produce nanocavities with higher quality
factors using the proposed design.
Lastly, it is noted that the cavity resonance is generally +/
−
10 nm of the target
wavelength. This demonstrates repeatable fabr
ication of nanocavities at specified target
resonant wavelengths, a requirement for quantum optical applications. Within +/
−
10 nm,
several techniques can be used to tune the resonance, such as gas tuning for red-shifting or
isotropic etching for blue-shifting. We tested the N2 gas tuning technique on the resonators at
cryogenic temperatures (4 K)
[22], and found that the resonances at ~880 nm can be
continuously red-shifted up to 15 nm in YSO devices without noticeable degradation of Q.
The N
2
gas tuning range for YVO devices operating at 880 nm is ~10 nm.
6. C
onclusion
In summary, we have demonstrated a new photonic crystal nanocavity design and fabrication
scheme to produce devices with high Q factors and small mode volumes. Quality factors
approaching 30,000 at telecom and 12,000 at near infrared wavelengths in low-index YSO
with a TE-polarized mode were demonstrated.
Cavities with a quality factor exceeding 20,000
at infrared wavelengths were measured in YVO w
ith a TM-polarized mode. To the best of our
knowledge, these devices provide the highest Q/V ratios using FIB fabrication scheme. The
#256023
Received 28 Sep 2015; accepted 5 Jan 2016; published 7 Jan 2016
(C) 2016 OSA
11 Jan 2016 | Vol. 24, No. 1 | DOI:10.1364/OE.24.000536 | OPTICS EXPRESS 543
technique demonstrates versatility in terms of material, wavelength and cavity mode
polarization, opening the doors for various optical materials to be studied and utilized in a
nanophotonic platform.
Acknowledgments
T. Zhong and J. Rochman contributed equally
to this work. J. Rochman is currently at
University of Waterloo, Canada. This work is funded by NSF CAREER 1454607, NSF
Institute for Quantum Information and Matter
PHY-1125565 with support from Gordon and
Betty Moore Foundation GBMF-12500028, AFOSR Young Investigator Award FA9550-15-
1-0252, AFOSR Quantum Transduction MURI #FA9550-15-1-002. Device fabrication was
performed in the Kavli Nanoscience Institut
e with support from Gordon and Betty Moore
Foundation.
#256023
Received 28 Sep 2015; accepted 5 Jan 2016; published 7 Jan 2016
(C) 2016 OSA
11 Jan 2016 | Vol. 24, No. 1 | DOI:10.1364/OE.24.000536 | OPTICS EXPRESS 544