Table Of ContentBarium Fluoride Whispering-Gallery Mode Disk-Resonator
with one Billion Quality-Factor
Guoping Lin∗, Souleymane Diallo, R´emi Henriet, Maxime Jacquot,
and Yanne K. Chembo
FEMTO-ST Institute [CNRS UMR6174], Optics Department,
15B Avenue des Montboucons, 25030 Besan¸con cedex, France.
∗Corresponding author: [email protected]
CompiledJanuary13,2015
5 We demonstrate a monolithic optical whispering gallery mode resonator fabricated with barium fluoride
1 (BaF2) with an ultra-high quality (Q) factor above 109 at 1550 nm, and measured with both the linewidth
0 and cavity-ring-down methods. Vertical scanning optical profilometry shows that the root mean square
2 surface roughness of 2 nm is achieved for our mm-size disk. To the best of our knowledge, we show for
the first time that one billion Q-factor is achievable by precision polishing in relatively soft crystals with
n mohs hardness of 3. We show that complex thermo-optical dynamics can take place in these resonators.
a Beside usual applications in nonlinear optics and microwave photonics, high energy particle scintillation de-
J tectionutilizingmonolithicBaF2resonatorspotentiallybecomesfeasible. (cid:13)c 2015 OpticalSocietyofAmerica
0 OCIS codes: 140.4780;350.3950;140.6810;260.1180;290.5930
1
s] Monolithic whispering gallery mode (WGM) res- Tunablezcwzlaser PC L1 Prism L2 Att
c onators are idoneous platforms to study various prop-
i
t erties of optical materials. These resonators have at-
p
tracted large interest, as they can feature ultra-high Q
o Piezozcontroller
. factors and small mode volumes [1]. Light in such res- WGMR PD
s
onators is trapped by a process of successive total inter-
c
i nalreflectionsattheinnersideofthediskcircumference. Oscilloscope
s
y Therefore, they do not require additional precision opti- Functionzgenerator
h cal coating and are able to reach Q factors close to the
p material absorption limit.
[
Beside the surface tension [1] and chemical etching [2]
Fig.1.(Coloronline)Schematicillustrationoftheexper-
1 techniques that have been reported to fabricate ultra-
imental setup for the WGM resonator characterization.
v high Q resonators (above 100 million at 1550 nm), me-
PC: fiber polarization controller; L1, L2: GRIN lenses;
4 chanical polishing methods can be used for various host
2 Att: attenuator; PD: photodetector.
materials, especially optical crystals [3]. Owing to the
3
low absorption of crystalline materials, extremely high
2
0 Q(intheorderof1011)havealreadybeendemonstrated
this crystal using optical resonator structures. So far, Q
. withcalciumfluoride[4].Manycrystallinematerialssuch
1 factors above 109 at 1550 nm have only been demon-
0 as quartz [5], sapphire [6], calcium fluoride [7–11], mag- strated on resonators made from four optical crystals,
5 nesium fluoride [12–14], lithium niobate [15,16], beta
namely quartz, calcium fluoride (CaF ), magnesium flu-
1 barium borate [17,18] and more recently diamond [19] 2
oride(MgF )andsapphire.Itshouldbenotedthatthese
v: have also been used to manufacture ultra-high Q WGM 2
crystals have mohs scale material hardness between 4
i resonators. These resonators can be used for various
X and 9. It still remains unknown whether the same order
applications such as Raman lasing [9], Brillouin las-
r ing[10],second-harmonicgenerations[15,16,18],electro- ofQfactorscanbeobtainedonsoftercrystalslikeBaF2
a whose mohs hardness is only 3, a feature that is of ut-
opticmodulatorsandmicrowavereceivers[20],frequency
termost importance at the time to consider large-scale
comb generation [8,11,13,14], optoelectronic microwave
automated fabrication.
oscillators [21,22], laser locking and stabilization [23],
In this letter, we show for the first time that one bil-
amongst others.
lion Q factor is achievable in optical resonators made
Barium fluoride is a particularly interesting optical
fromrelativelysoftcrystalwithmohshardnessof3using
material which is transparent from ultraviolet to mid-
precisionpolishing.Theexperimentalsetuppresentedin
infrared. It is the most resistant to high energy radia-
Fig. 1 has been used to determine accurately the value
tion among all fluoride crystals. It is also known as one
of this quality factor. We have also performed a ver-
of the fastest scintillators for the detection of high en-
tical scanning profilometry on the rim of the polished
ergyparticlessuchasX-raysandgammarays[24].How-
disk,thatenabledustodemonstratearootmeansquare
ever, to this date, few efforts have been made to study
surface roughness of 2 nm. We also report the obser-
1
vation of different thermal distortions in such crystal, fiber. As a result, fiber tapers can not be used to ef-
which originate from the interplay between the negative ficiently excite high Q WGMs due to phase mismatch,
thermo-optic coefficient and other positive effects such althoughitisaconvenientwaytoquicklyprobetheres-
as thermal expansion and Kerr nonlinearity. onator without the risk of scratching its surface. Never-
Wehavefabricatedtheultra-highQWGMresonators theless,onecanchooseanotherevanescentwavecoupling
from commercially available BaF disks with diameters method by using an optical prism that has a higher re-
2
of 12 mm and thicknesses of 1 mm. To monitor the fractive index. In this experiment, a SF11 prism is used.
surface profile of BaF resonators, we carried out sur- Figure 1 shows the schematic illustration of our ex-
2
faceprofilemeasurementsusingwhitelightverticalscan- perimental setup. The excitation source is a tunable
ning interferometry with conventional phase shifting al- continuous-wave (cw) fiber laser at 1550 nm with sub-
gorithm. Figure 2(a) presents a white light interference kHz instantaneous linewidth. The laser frequency is
patternontheedgeofthediskat40×magnificationwith scanned using a piezo driver controlled by the function
a Mirau objective. It should be mentioned that a spher- generator.Afiberpolarizationcontrollerisaddedbefore
ical surface produces circular symmetric fringes. The el- launching the light into the prism. The gradient-index
lipticfringescomesfromatoroidaloroblatesurface.An (GRIN) lens (L1) focuses the laser beam on the prism,
exampleofthecomputerreconstructed3Dsurfaceprofile whiletheotheronecollectstheoutputbeambackintoa
on the resonator with 11.6 mm diameter is presented in single mode fiber for detection. A piezoelectric actuator
Fig.2(b).Itcoversasurfaceareaof100µm×60µm.We is inserted into a translation stage to finely control the
can thereby determine the rms surface roughness profile coupling gap between the resonator and the prism.
as shown in Fig. 2(c). The measured rms surface rough- There are two methods to evaluate the Q factors of
ness is about 2 nm (∼λ/800 at the telecom wavelength a resonator, which are namely linewidth and ring-down
window). Straight nano-sctrach lines created during the measurements.Inthisletter,wecarryoutbothmeasure-
polishing process are also observed (depth ∼10 nm). It ments on our BaF resonators.
2
should be noted that the fundamental (torus-like) mode Figure3(a)showsatypicaltransmissionspectrumfea-
in a mm-size disk resonator usually features a spot size tured with the observed ultra-high Q WGMs from the
less than 20 µm in its cross section, and as a result, oscilloscope. The laser frequency is scanned across the
these lines could cause additional scattering losses. On optical resonances at the speed of 1.1 GHz/s and with
theotherhand,iftheyarecreatedinthedirectionparal- an incident power of 9.5 mW. The coupling gap is set
leltothesymmetryaxisofthedisk,gratingeffectscould to be large enough so that the resonances are strongly
also be observed [25]. under-coupled.Inthiscase,thecouplinglossesarenegli-
Afterconfirmingthatwehaveachievedagoodsurface gible and the measured resonance linewidth approaches
roughness, we move forward to WGM excitation experi- the intrinsic one. We also make sure that we do not see
ments. Therefractiveindexof BaF at1550nm is1.466 visible thermal distortions at both up and down detun-
2
which is slightly larger than that of a regular optical ing directions. The Lorentzian fit on the data is shown
in Fig. 3(a). A linewidth ∆f as narrow as 0.17 MHz is
obtained. The corresponding Q factor is 1.1×109 us-
(a) (b) ing the formula Q = f /∆f. It should be mentioned
0
Z (μm)
that the double resonances with splitting of 1.1 MHz
)m could result from stimulated Rayleigh scattering in the
μ resonator which is often observed in ultra-high Q res-
( Z
onators [26,27].
10 μm The ring-down spectroscopy can be performed by
Y(μm) X (μm) switching off the probe laser using a fast shutter. It is
also known that ring-down can be observed when the
(c)
laser frequency is swept across the resonance at a fast
speed [4,28]. The light accumulated in the mode is re-
emitted and interferes with the laser through-put in the
Y exit port. In order to observe this phenomenology, we
(μm increase the modulation rate and frequency range of the
) laser.Withthedetuningspeedsetat65GHz/s,aWGM
X (μm) ringdown spectrum is obtained as shown in Fig. 3(b).
ThetheoreticalfitgivesanintrinsicQvalueof1.3×109.
Fig.2.(Coloronline)(a)Anexampleofinterferencepat- We have also excited WGM families with an orthogonal
ternfromtheedgesurfaceonanultra-highQBaF disk, polarizationandobservedasmallerQfactorof1.1×109.
2
takenwithaverticalscanningmicroscopeat40×magni- The Q factors differ by a factor of 1.2, which is smaller
fication.(b)Reconstructed3Dsurfaceprofile.(c)Recon- than n4. Therefore, we believe that the cleaning of the
0
structed surface roughness profile, showing rms surface resonator is sufficient for the Q factors observed [19].
roughness of 2 nm. The Q factor measurement is also an interesting
2
(a) On the other hand, the material absorption limited Q
1
is expressed as:
n
missio 0.98 datfait Δf1 ΔQf11==00..9211xM1H09z Qα =2πn0/(λa) (2)
s Δf
Tran 0.96 2 ΔQf22==10..11x71M0H9z where n0 = 1.466 is the refractive index of BaF2 at
1550 nm. Therefore, we can derive the material absorp-
0.94 tion coefficient of 4.6×10−5 cm−1 at this wavelength.
We also report interesting thermal dynamic processes
0 2 4 6 8 10
Offsetqfrequencyq(MHz) observed in BaF2 resonators. In WGM resonators, the
resonance frequency shift ∆f(t) obeys the following for-
(b)
1.1
mulation:
data ∆f(t) (cid:20) 1 dn 1 dR n P (t)(cid:21)
mission 1 fit f0 =− n0dT∆T1+ RdT∆T2(t)+ n02 Aceff (3)
s
Tran wthheerKeefrr0 ciosetffihceiecnotl,d∆caTvitiys trheseotneamncpeerfarteuqrueencchya,ngne2 iins
1
0.9 Q0=1.3x109 the mode area, ∆T2 is the temperature change in the
whole resonator, dn/dT and (dR/R)/dT represent the
thermo-optic (−16 × 10−6/K) and thermal expansion
0 5 10 15 20
Timeq(μs) (18.4×10−6/K) coefficients of BaF [29], P (t) desig-
2 c
nates the intracavity optical power, A is the cross sec-
eff
Fig. 3. (Color online) (a) Transmission spectrum of
tionmodearea.Itshouldbenotedthatthesecondterm
WGM resonances. The Lorentzian fit yields a linewidth
on the right side is a very slow time-scale phenomenon,
∆f as narrow as 0.17 MHz, corresponding to a Q factor
as the optical heating requires time to diffuse heat into
of1.1×109.(b)Transmissionspectrumwitharing-down
the full volume in the case of a mm-size resonator. Nev-
structure.AtheoreticalfitprovidesanintrinsicQfactor
ertheless, it is interesting to note that the interplay of
of 1.3×109.
positiveandnegativecoefficientstogetherwithslowand
fast phenomena could lead to complex thermo-optical
method to evaluate the material absorption coefficient dynamics [30,31].
in highly transparent crystals. Theoretically, the intrin- Figure 4(a) shows a typical thermal distortion in a
sic factor Q of a resonator is mainly determined by crystalline resonator dominated by its negative thermo-
0
three different loss mechanisms. The corresponding lim- optic coefficient. The increasing of the laser frequency
ited Q factors are surface scattering loss related Q , (decreasing the wavelength) is followed by the simulta-
ss
material absorption loss related Q and radiation loss neous blue shift of the resonance, which is interpreted
α
related Q . The final Q is then determined by 1/Q = by the first term on the right side of Eq. (3). As a re-
r 0 0
1/Q +1/Q +1/Q .Inthecaseofamm-sizeresonator sult, the resonance is broadened on the short frequency
ss α r
with a good circular symmetry, the last term 1/Q is side of the center resonance when the laser frequency
r
usually negligible. Concerning surface scattering limited detuning is increasing. This effect has been used for fast
Q , under the condition that the surface roughness is microlasercharacterizations[32].Wealsoobservedanin-
ss
muchsmallerthantheopticalwavelength,thisvaluecan teresting thermal distortion in a different optical mode
be estimated using [27]: as shown in Fig. 4(b), where the larger frequency side is
broadened. The laser was swept at 2.7 GHz/s, that is,
3λ3R
Q ≈ (1) 10 times faster. Hence, we believe that Kerr nonlinear-
ss 8π2n B2σ2
0 ityisdominantinthiscase.Wealsoobservedoscillatory
where λ is the wavelength, R is the radius of the res- behaviors on the same mode when we further reduced
onator, n is the refractive index of the material, σ and the ramp speed to 27 MHz/s. In this case, the interplay
0
B are the surface roughness and the correlation length ofpositiveandnegativecoefficientscausesanoscillatory
of the roughness. Assuming that B is equal to σ = 2 behavior, as shown in Fig. 4(c). Similar oscillation phe-
nm, we obtain an estimated Q value of 3.7×1013 at nomenon was reported in hybrid resonators aiming for
ss
the wavelength of 1550 nm for a radius of 6 mm. This self-thermo compensations [31].
valueisfarlargerthantheexperimentaloneof1.3×109 In conclusion, we have reported for the first time a
as shown in Fig. 3. Even we use B = σ = 10 nm, the monolithic BaF WGM resonator with one billion Q
2
estimatedQ of5.8×1010 isstillmuchlarger.Although factor. It is the softest material ever reported featuring
ss
we didn’t check the whole periphery of the mm size res- with such Q factors. We also derive a new upper bound
onator which is a lengthy task, we expect that no deep of material absorption coefficient at 1550 nm. Interest-
scratchesappearonthesurfaceandthematerialabsorp- ing thermal effects are also observed. These observation
tion is the dominant factor that limits Q . willbenefitfutureapplicationsonstablefrequencycomb
0
3
Offset frequency
8. A.A.Savchenkov,A.B.Matsko,V.S.Ilchenko,I.Solo-
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matine,D.Seidel,andL.Maleki,Phys.Rev.Lett.101,
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(2010).
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