Table Of ContentTunable Resonant Optical MicroCavities by Self-Assembled Templating
G.V. Prakash,1 L. Besombes,1 T. Kelf,1 P.N. Bartlett,2 M.E. Abdelsalam,2 and J.J. Baumberg1
1School of Physics & Astronomy, University of Southampton, Southampton, SO17 1BJ, UK
1School of Chemistry, University of Southampton, Southampton, SO17 1BJ, UK
(February 2, 2008)
Micron-scale optical cavities are produced using a combination of template sphere self-assembly
and electrochemical growth. Transmission measurements of the tunable microcavities show sharp
4 resonantmodeswithaQ-factor>300,and25-foldlocalenhancementoflightintensity. Thepresence
0 of transverse optical modes confirms the lateral confinement of photons. Calculations show sub-
0 micron mode volumes are feasible. The small mode volume of these microcavities promises to lead
2 toawiderangeofapplicationsinmicrolasers, atomoptics, quantuminformation, biophotonicsand
single molecule detection.
n
a PACS numbers:42.15.-i,07.60.Ly,81.15.Pq,42.60.Da
J
3
2 The operation of every type of laser, as well as many
varieties of atomic traps and optical sensors, depend on
]
s the formation of an optical cavity. The resonant optical
c modesinsidethiscavitydeterminethespatialfielddistri-
i
t butionandspectralperformanceofthedevice. Themost
p
common optical designs use spherical mirrors to form a
o
. confocal cavity that is insensitive to misalignment and
s
confines the optical mode to the smallest lateral dimen-
c
i sions. [1] The length of this cavity is on the order of the
s
y radius of curvature of the mirrors. There has been much
h interestintheproblemofreducingthedimensionsofsuch
p cavities: planar microcavities have been widely used as
[
a way to control spontaneous emission and to enhance
2 the interactionof light with matter, as in quantum wells
v [2] or quantum dots [3] but these structures only confine
6
photons in one dimension. Confinement in lateral di-
1 FIG. 1. (a) SEM and (b) optical micrograph of spheri-
mensions such as in photonic crystals [4] or microcavity
1 cal micro-mirror of pore diameter 8µm, radius of curvature
1 mesas [5,6] can inhibit spontaneous emission altogether, R=5µm, in 2.5µm-thick Au on ITO. (c) Microcavity design.
0 butinvolvecomplexandexpensivefabricationstrategies.
(d) Microcavity transmission spectra collected through the
4 Herewepresentasimplerapproachutilisingconfocalmi- fibre for increasing separation, L, of cavity mirrors (spectra
0
crocavities. While traditional lasers built from discrete displacedverticallyupwards,foreachincreaseincavitylength
/
s componentsusemacroscopicsphericalmirrors,sofarmi- ∼200nm).
c
crocavity lasers do not. Preliminary theoretical work on
i
s the mode structure in parabolic dome [7] and spherical spheres or micro-disks have larger mode volumes and
y
cavities [8] highlight the promise of such 0D microcav- broadband tuning of the resonant cavity wavelengths is
h
p ities, but confirm that fabrication is nontrivial. Simi- a severe problem. By robustly embedding our spherical
: larly glass or polymer microspheres show high Q-factors micro-mirrorsin thin metal films, we obtain simple volt-
v
in whispering gallery modes but it is generally hard to age tuning by piezo-electric translation of a top planar
i
X control them and to couple light into and out of them. mirror. We thus show that at length-scales approaching
r [9] the wavelength of light, the electric field distribution in
a
To construct cavities with the smallest possible mode suchmicrocavitiescanbe controlledbynanoscaletuning
volumerequiressmallradius-of-curvaturemirrors. Using ofthemirror,andcanstillbeinterpretedusingGaussian
our recently devised route to simple fabrication of such beam optics.
sphericalmicro-mirrors,we demonstrate here the forma- Untilrecently,makingcurvedmirrorsinthesizerange
tion of stable microcavities on size-scales below 10 mi- requiredhas been difficult, but advances in electrochem-
crons. Comparablevertical-cavitysurface-emittingsemi- istry and directed self-assembly of colloidal templates
conductor lasersuse planar mirrorstacksintegratedinto now offer a cheap and simple way to produce an ar-
the layeredsemiconductor growth,and then require sen- ray of well-ordered spherical reflecting surfaces. [12] For
sitivelateralfabricationtoproducesmallvolumedevices. the purposes of constructing microcavities, we combine
[5,10,11]Comparablewhisperinggallerymodesinmicro- spherical micro-mirrors of Au with radii R < 10µm em-
1
beddedinathinfilm,withaplanartopAumirrorcoated
on a cleavedsingle-mode optical fibre. The guidedmode
of the fibre is then also used to efficiently couple light
out of the cavity. Briefly, we use a template prepared
through sedimentation of a confined colloidal solution of
latex spheres on an indium-tin-oxide (ITO) coated sub-
strate electrode to leave a self-assembled arrangement.
Either close-packed arrays or isolated sphere templates
can be obtained by adjusting the sphere concentration
or by pre-patterning. The substrate is then placed in
an electrochemical cell with a solution of aqueous metal
complex ions which are deposited through reduction in
theinterstitialspacesofthetemplate. The resultingfilm
thickness can be controlled precisely through measure-
ment of the total charge, yielding cavity shapes that
range from shallow dishes to nearly-complete spherical
voids. The latex spheres are removed by dissolving in
tetrahydrofuran,leavingaporousmetallic‘cast’withthe
orderingand size of the originaltemplate. Both electron
and optical microscopy (Figs.1a,b) give an indication of
the mirror quality, discussed elsewhere. [13] FIG.2. Transmissionspectraforcavitylengths,L∼7.9µm,
Bygrowingthemicro-mirrorsonsemi-transparentsub- R=10µm, for (a) plane (dashed) and confocal (solid) mi-
crocavities, and for (d) confocal microcavity with the fi-
strates,wetakeadvantageofthenegligiblythinAucoat-
bre increasingly laterally shifted from the central axis
ing at the base of the mirror in order to couple light
(Y=0,1,2µm). (b) Longitudinal cavity mode separation for
into the cavity. The results shown here use radius-of-
planar and confocal cavities, together with the prediction
curvature mirrors, R=5 and 10µm grown up to a Au
from Gaussian optics (line). (c) Peak cavity transmission as
thickness of around 2µm to form dish-like spherical re-
thecavity length increases.
flectors between 5µm and 15µm across. However we
have also successfully grown spherical reflectors down to in most well-formed spherical micro-reflectors. As ex-
R=100nmradius-of-curvature. Theuppercavitymirrors pected,thespacingoflongitudinalmodesbecomescloser
are formed by evaporating a 28nm thick Au film (80% together as the cavity length increases. The absolute
reflectivity at λ=750nm) on a perpendicularly-cleaved transmissionis only low here because the input coupling
stripped single-mode optical fibre (SM660) of 100µm throughthe sub-micronapertureisverysmallforthein-
outer diameter, which is mounted in an XYZ piezoelec- cident incoherent white light source. Equivalent scans
tric (PZT)translationstageand alignednormallyto the on a plane mirror reveal similar longitudinal modes but
micro-mirror film (Fig.1c). A white-light source is fo- with a much lower finesse. A direct comparisonbetween
cussedtoa10µmspotontherearsideofthemicro-mirror the plane-plane mirrors (a ‘planar’ cavity) and plane-
film, and co-linear imaging allows us to back-illuminate spherical mirrors (termed ‘confocal’) is shown in Fig.2a
individualsphericalmirrors. As the fibre approachesthe for a cavity length, L 7.9µm, with R=10µm. The gen-
∼
film, optimising the collected transmission signal brings eral formula for the resonant frequency, ωnpl, that pro-
it into correct alignment with the micro-mirror, forming duceszeronetopticalphase afteroneroundtripis given
the microcavity. The detected light emerging from the by [1]
fibre is the product of the cavity transmission and the
c L
coupling strength to the fundamental fibre mode. Us- ω = πn θ +(2p+l+1)tan−1 (1)
npl L{ − Au rR L}
ing the fibre as the top mirror thus allows a self-aligned
−
detection geometry. We record the spectra by directly where n,p,l are positive integers describing the longi-
couplingtheoutputendofthefibretoa0.5mmonochro- tudinal, transverse radial and azimuthal mode numbers
mator and CCD of combined 0.05nm resolution. of the resonance, the second term represents the phase
◦ ◦
Spectral characterisation of the optical transmission shift onreflection from the metal film (θ 180 24
Au
≃ −
through the device allows us to compare the microcavi- is the non-ideal phase shift on reflection for Au at these
ties with simple models based on Gaussian beam optics. wavelengths),andthe thirdtermisthe Gouy phaseshift
We also produce similar 28nm-thick plane Au reflectors arisingfromtherangeofpropagationanglescontainedin
to directlycompareourresultsto the plane-planemicro- the Gaussian mode. From this paraxial approximation,
cavitygeometryusingthesametopfibremirror. Typical theseparationofthelongitudinalmodesyieldsthecavity
experimental results for the transmitted modes are seen length directly. Plotting the experimental and theoreti-
in Fig.1d, and are stable and reproducible, and similar callongitudinalmodesplitting,∆ω ,asafunctionofthe
L
2
cavity length derived from the calibration of the PZT Z
translation gives an excellent fit for both types of cavity
(Fig.2c).
The difference between the planar and confocal mi-
crocavities becomes clearer when the transmission peak
heights and linewidths are compared. At cavity lengths
L<R=10µm,the finesse of the confocal microcavity ap-
proaches 10, while the quality-factor, Q>300. On the
other hand, the finesse of the planar microcavity does
not exceed 4 due to the diffraction losses of the optical
modes. This improvement can be directly seen from the
peak transmission intensity vs. cavity length (Fig.2d),
which is strongly enhanced for mirror separations<R.
FIG. 3. Transmission spectra vs. lateral fibre X position
To prove that the spherical mirror is acting to localise
(log scale over 1.5 decades) for (a) Y=0 and (b) Y=2µm,
the optical modes in the transverse direction, the core
around the spectral position of a single longitudinal mode
of the optical fibre is laterally scanned in the XY-plane
for the confocal cavity (with R=10µm) at a cavity length of
acrossthe topopening ofthe sphericalmicro-mirrorata
7.6µm. Thewhitecrossesin(a)arepredictedpositionsofthe
fixedcavitylength. Typicalspectra areshownin Fig.2b, transverse modes collected by the fibre core. (c) Transverse
andresolveanumberofnewopticalmodes. Thesemodes mode separation vs. cavity length for Y=1µm. (d) Cavity
alwaysappearontheshortwavelengthsideoftheoriginal finesse vs. cavity length for planar (×) and confocal micro-
longitudinal mode and thus can be identified as trans- cavities with one (•) and two (◦,△) transverse modes.
verse modes formed by the lateral optical confinement
drednanometres,providingapotentiallyeffectivewayto
of the spherical micro-mirror. They are never seen in
couple into specific cavity modes.
plane-plane microcavities. To further study the spatial
The finesse of the different spectral modes is shown in
dependence of the spectral transmission, we systemati-
Fig.3d as a function of the cavity length. Whereas the
callycollectspectraatdifferentX positionsandplotthe
finesse of the planar structure is 4, independent of the
resultingimages. Scanningacrossthecentreofthemicro- ∼
spacing between the mirrors, the confocal microcavity
cavity (Fig.3a, Y=0) clearly shows the emergence of the
performsbestatsmallcavityseparations. Themaximum
transverse modes away from the cavity axis. The higher
finesse of 15 is achieved for the lowest of the transverse
transverse modes dominate the spectra for scans across
modes. This agrees well with the theoretical finesse of
a chord of the circular opening (Fig.3b, Y=2µm). Up
π√r/(1 r) 14,where r=0.8 is the productof the am-
to 6 transverse modes with similar linewidths make up − ∼
plitude reflectivity coefficients of the two mirrors. The
each longitudinal mode. Scanning in the orthogonal di-
correspondingintensityconcentratedwithinthecavityis
rectiongivessimilarresults,indicating anear-cylindrical
−2
(1 r) 25 times greater than that of the incident
symmetry of the micro-resonator. − ∼
light at the resonant wavelength. However, as the cav-
These results thus allow one to directly image the dif-
ity length increases beyond the mirror curvature R, the
ferent spatial mode distributions inside the microcavity,
finesse drops. This is due to the increasing diameter of
and show that the mode spectrum consists of discrete
the transversefieldprofile onthe sphericalmicro-mirror,
frequencies. An emitter inside a planar microcavity can
eventually leading to it being clipped when L>R.
always emit in some particular direction - equation (1)
In this cylindrically symmetric micro-resonator, the
isvalidonlyfornormalincidence,andatdifferentangles
field modes in the paraxial approximation are given by
of incidence the resonance frequency gradually shifts to
Laguerre-Gauss functions, [1] plotted in Fig.(4a) at the
shorterwavelengths. In fundamentalcontrastto this be-
position of the top fibre mirror. This demonstrates how
haviour,an emitter in the confocal microcavity does not
the microcavity dimensions here are nearly optimal to
havethis flexibility andcanonly emitin the appropriate
couple cavitymodes into the lowestguided modes in the
field mode, ω . The transversemode separation,∆ω ,
npl T
fibre. Higher ordertransversemodes havea largerdiam-
also decreases as the cavity length increases (Fig.3c), as
eteronthecavitymirrorshencetheysufferextralossand
expectedfromdifferentvalues of(2p+l)inequation(1).
exhibitlowerfinesse,asseeninFig.(3d). Howeverasym-
Howeverthepredictedseparations(Fig.3c,lines)onlyac-
metric modes possess a field null on axis that is useful
count reasonably for the data if the radius-of-curvature,
for the optical trapping of dark field species. [14]
R , of the spherical micro-mirror is 45µm (as dis-
fit
∼ To understand the expected spatial patterns collected
cussed below). Less pronounced transverse modes are
by the fibre core (with its field distribution also illus-
also seen in R=5µm microcavities, with similar trans-
tratedinFig.4a),weconvolvethecavityandfibremodes
verse splittings, ∆ω =12meV at L=8µm. The trans-
T
to calculate the mode overlap as a function of lateral
verse spectral separation produces a corresponding lat-
fibre position. The higher transverse modes are gener-
eral mode spatial separation on the order of a few hun-
3
(1µm)3. This shows that our templating scheme is suit-
able for sub-micron optical devices. For example, sub-
picosecond optical modulators using resonant cavity en-
hancementofnonlinearitiesrequireshortcavitylifetimes
and hence short cavity lengths.
Tosummariseourkeyresults,wehavebeenabletofab-
ricate near-spherical micro-mirror optical cavities with
FIG.4. (a) Optical field profiles for the fibre and the first mode volumes below (5µm)3, a Q>300and finesse >10,
four Laguerre-Gauss modes of the R=10µm confocal cavity
and an intensity enhancement >25. Both longitudinal
withp=0. (b)Calculatedfielddistributioninasphericalcon-
and transverse optical modes are observed, and can be
focal microcavity on resonance, R=880nm, L= 704nm.
simply wavelength-tuned by PZT translation of the pla-
ally not seen for on-axial alignment due to the averag- nar top mirror which also extracts light from the cav-
ity. In addition, this top fibre mirror can be replaced
ing of the oscillating electric field by the larger extent
by high-reflectivity multilayers supporting luminescent
of the fibre mode. This is even more pronounced in the
nano-particles,such as semiconductor quantum dots, for
smaller(R<5µm)sphericalmicrocavitieswhichgivecor-
enhanced emission and microlasing. The new route this
respondingly smaller mode diameters. The calculated
opens for cavity enhancement of light-matter coupling
lateral offsets which optimise collection of the different
canbefurtherdevelopedbyreducingstillfurtherthecav-
transverse modes are plotted as white crosses in Fig.3a
ity volume (we routinely produce sub-micron reflectors)
for R=45µm,giving excellent agreementwith the exper-
andimprovingthe finesse (using Ag or multilayerdielec-
imental data. This concurs with the need for a larger
tric coatings),both nowinprogress. We note thatmetal
R that is required to account for the transverse mode
fit
mirror cavities with similar finesse have already been
spectral separation, and suggests that the spherical ge-
shown to be sufficient for attaining strong light-matter
ometry of our micro-mirrors is imperfect. In fact, as is
coupling in organic chromaphores. [15] Our preliminary
visible on both the micrographs of Fig.1a,b and in scan-
measurements already suggest that these micro-mirror
ning force microscopy images (not shown), the central
cavities are useful for optical-dipole force trapping, for
portion of the micro-mirrors is completely flat (R = )
∞ enhancedcollectionofmicro-photoluminescencefromthe
wheretheelectrochemicalgrowthappearstobescreened
focal region, or for incorporation in experiments involv-
under the template spheres. The area of the flat region
ing cold atom interactions on integrated chips.
is about 10% of the total mirror area, a ratio which re-
We gratefully thank Ed Hinds and Tim Freegarde for
mains approximately the same for spherical mirrors of
helpfuldiscussionsofresonatordesign,andOliverWright
radius down to 100nm. Thus an effective cavity radius-
and Dave Hanna for critical comments. We acknowl-
of-curvaturedeterminedby boththe curvedandflatsec-
edge financial support from JSPS, EPSRC GR/N37261,
tions is appropriate for the theory, in accord with the
GR/R54194,GR/S02662 and GR/N18598.
experimental results. More detailed calculations based
on realistic micro-mirror shapes cannot rely on the for-
[1] A.E. Seigman, Lasers (University Science Books, Mill
malism for Gaussian mode propagation. However, the
Valley, Calif., 1986).
closematchbetweenexperimentalandtheoreticalfinesse [2] G. Khitrovaet al.,Rev.Mod. Phys.71, 1591 (1999).
proves that this non-spherical mirror does not degrade [3] H. Saito, K. Nishi, I. Ogura, S. Sugou, Y. Sugimoto,
the phase front of the lowest cavity mode, and that the Appl. Phys.Lett. 69, 3140 (1996).
mirror flatness is not a serious problem. [4] E. Yablonovitch,Phys.Rev. Lett. 58, 2059 (1987).
In 5µm radius-of-curvature cavities, the tight trans- [5] J.M. Gerard et al.,Appl.Phys. Lett. 69, 449 (1996).
verse field profiles (radius w) imply diffraction angles [6] J.M. Gerard, B. Gayral, J. Lightwave Technol. 17, 2089
(1999).
θ λ/πw > 0.50 radians in the cavity, leading to signif-
≃ [7] J. Nockelet al.,Phys.Rev. E62, 8677 (2000).
icant errors of order 5% in the paraxial approximation,
[8] R.A.Abram,S.Brand,M.A.Kaliteevski,V.V.Nikolaev,
sinθ =θ. As the size of such cavities is further reduced,
Phys. Stat. Sol. 183, 183 (2001).
theseerrorsrapidlymakeconventionalopticalmodelsin-
[9] R.Jia,D-S.Jiang,P-H.Tan,B-QSun,Appl.Phys.Lett.
appropriate. Theoretical modelling to demonstrate the 79, 153 (2001).
sizescalingofthesemicrocavitiesshouldthereforebecar- [10] J.L. Jewell et al.,Electron. Lett. 25, 1123 (1989).
ried out using a full solution of Maxwells’ equations in [11] K.L. Lear, E.D. Jones, MRS Bull. 27, 497 (2002).
these wavelength-scale geometries. The ultimate aim is [12] P.N. Bartlett, P.R. Birkin, M.A. Ghanem, Chem. Com-
to create the smallest optical cavities (L λ/2) with mun., 1671 (2000).
∼
the highestfinesse. A typicalelectric field distribution is [13] S.Coyle, G.V.Prakash,J.J. Baumberg, M.Abdelsalam,
showninFig.4bforR=880nm,L=704nm,andλ=750nm P.N. Bartlett, Appl.Phys. Lett. 83, 767 (2003).
[14] M. P. MacDonald et al., Science296, 1101 (2002).
with metallic reflectors (of conductivity 200/Ωm hence
[15] P.A. Hobson et al.,Appl.Phys. Lett. 81, 3519 (2002).
80%reflectivity),correspondingtoamodevolumebelow
4
