MICROSPHERES
Chapter 3 Chapter 3 High Q Measurements for Fused Silica Microspheres in the NIR
3.2 Measurements
3.2.2 What is Limiting the Q?
Surface Roughness
One possible reason for reduceii d) is surface contaruinatiorl, althoilgli tile cleaning procedure outli~li?cl in Sec. 3.1.1 was developed t o eliniinate virtiuxlly ,111 diffuse scat- t,cririg froirl particles ori the preform surface. Furthermore, as described in Sec. 2.2.2, t,tie limit set, by radiative losses is irrelevant for these "large" spheres with D =-> 20X.
In thc al~sence of a more rigorous test of the cleaning procedure, scattering from surface inhon~ogeneities is now investigated as another candidat,e loss mechanism.
Tlle forrnatioli of the sphere si~lrfacc is determined 137 the annealing history of t,he silica ball as it is wit,ildrawn from the flame and cooled. Although scanning electron microscopy (SEh'I) was initially atternptcd, high resolution atornic force microscopy ( A F M ) proved to be nluch rnorc fr~ritful in provitiing quant,it,at,ive data on the sur- face quality of the microsplieres. Surface morphology was measured in a 20 nm x 20 nrn square grid of 256 x 256 poiritys near the sphere equator; with a nominal ver- tical resolution of 0.01 nm. Features with curvatrlre on this scale could reliably be reco~lstruct,ed.
These data. were organized as 256 line scarls of 256 poi~lts each (i.e., heights hi (z)
,
wit'h z ( j ) = 2Oj/256 [run], i , j = (1..
,2561 and (hi ( x ) ) ~ = 0 ) , of wilich three typical line scaris are shown in Fig. 3.5(a). Calculating the standard deviationLT! = (hi (z) hi ( x ) ) ~ of surface roughness horn each line scan results in an average
3 = (2.5
-+
0.7) nrn. Sirnilasly, for each line sca,n Isi ( u ) = (hi (z) hi (x+
u )j,
is cal-culated and an average correlation function R ( u ) = jRi ( 7 ~ ) ) ~ c011structed, as in Fig.
3.5(b). A statistical correlat,ion lengtli of U = ( 5
-+
0.5) rtm can be identified from this plot. The Fourier trarisforrn P ( k ) of R ( u ) is shown in Fig. 3.5(c) and gives the"power spectruni" of surface fliictuatior~s in reciprocal space, wiiich is correspondingly flat ola to a spat,ial frequency ko
-
l / B . Though no analjlic model has heen con- structed, rtote that tile fur~ctiorial form of R ( u ) has cllaracteristics of both R, ( u )-
! u (Pi ( k )
-
1 - W (ikj - 8 ) with ti ( b ) tlic: step fnnction) as for bandpass, ad- ditive white Ganssiar~ noise arid IZ2 ( u )-
exp (- lu! / B ) (or I$ ( k )- &).
as forL I
a rantlorn telegraph signal. with the interpretation of
B
as ttlie correlation lerigth the sarrie in both cases. It was verified that an increase in the scan region to 100 nm x 100 nm while accordi~igly decreasing the resolution (as set by the 256 point, sample) tlitl not affect the surface height distribution data, but did inhibit t,he extraction ofB fro111 surface correlations due to spatial undersampling.
distance along surface [nrn] histogram bins for cr [nrn]
Figure 3.5: (a) Typical line scans of surface data showing feat,ures at, 11x11 rr:solution. In (b), the dist,ributiori of riverageti surface roughrless for 256 differexit lirir: sca~ls is sl.~own:
frorrr -rulich 0 = (1.7 i 0.5) nrri. (c) Correlation fi~rrctiori R (u) and (ii) estimate of it,s Fourier Transforru: the power spectral density P ( k ) , s f i o u ~ ~ ~ after averaging over 256 scans of the type in
(a)
on a 20 ri111 scliiare grid, ns explained in the text. Both support the idt:rtificrition of the correlntion length U -. 5 rlrllGiven (IT: B ) : tlie surface scattering lirnited Q , , nlust take into account precisely how the energy of the resonailt niodo fielcl distribution is scattered into the con~l>lete set of rnodes pcrt,inr:nt, to the splierical geometry. For example, surface scattering lirnits arc expected to depeuci upon radial mode riurnl)er q. but because tlie modes
exciteti here have q
<
3, a sinlple estimate may bc based upon scattering from particles of ciielectric constant E = n 2 and voluine 00'< xX".
Such scatterers will have an absorption cross-section scaling as (volilnlc)" (jwavele~~gtlr)" and scat,tering density proportional to (l/volume); so the effective absorption coefficient for these scatterers is-
k 4 r B 2 . Tising the volumetric ratio .Yr/m
of a surface layer of such particles to that of the mode, one fincis at1 effective absorptiori coeificierit which scales as k4 (02B')/ (m)
so that,An equivalerrt expression can be derived using a different approach based on sur- face scattering from planar waveguides j56, 57, 58: by substituting t,he ratio of ex- ternal t,o internal rrtode volumes of the sphere for the ratio of external to internal guided power in the waveguide. Using (IT, R ) from above and (D, A) =
(800 pm, 800 nm) , we estiniate Q ,.,
-
(7.5 i 5) x 10"which cornpares to the measurernent,s wit11 (2-
8 x log.Size Dependence of Q
In Fig. 3.6, the highest
Q
achieved as a function of D is plotted for my work with splreres at fixed X = 670 rlrn with the cavetit that the repeatability in obtaining the "highest" Q for ix givcn D accounts for the consitlerable scatter in the data.Nevertheless; a fit .x D1I2 as sllggested by Eq. (3.1) yields nB
-
5 nm" whicli coincides we11 wit11 our aiialysis of the experimental AFM data. Though the trend in Fig. 3.6 argues for ~neasrire~rle~ints with &ill larger spheress; our fixbricat,ion technology is riot suited for D rriuc:h in excess of 1 rnrn.Water Absorption on the Surface
As in [45], il tirtre dependent rcciuction in Q is seen, with tlie ilighest C) data rneasirred within At = 1.5 rrlirlutcs of fabrication. A simple lnechanisrri for this process is based on the 2iyclration of a "fresh" silica surface in air j59> 60j. When a sphere is first
Figure 3.6: The higliest Q values measured in spheres of diameter D at 670 nrn. Tlre dependence C),, cx 0'12 is suggested by Eq. 3.1.
formed from a rod of Si02; tliere are dangling surface silicon bonds, which then undergo changes to t,heir chemistry deperiding upon the surrounding erivironment. In air, O2 ~ilolecxiles see a potential nlinirrrum xiear the silica surface and are absorbed by a physical borid with a typical time scaIe of l o 7 s. Dissociation of Oz c a i further reduce the surface energy in a process known as chemisorption, d i d 1 has a time scale of 10 s (t,he competirig clesorption process has a 350 s time scale). Hydrogen, in the forrrr of kiydroxyl radicals, then forms a cl~ernical bond wiih the oxygen wit,h a characteristic ti~rre scale of T , N 50 s, depending upon the presence of water in the air as a hydroxyl source. This snrface water layer is ;~ssurxied t o cause the t,inle dependent light absorption (and srrbsequerit Q tlegraclat,ion) due to 0-15 bond resonances. 111 fact, for a water layer of width 6
<
X i 2 ~ occul~yir~g a frat:tion of the rota1 rnode volurne x 6jm; and absorption coefficientP,,
(A), we estirnatewhich shows the same degenderlce as I),,.. Though the exact clrernjstry of t,he surface adsorption process w u l d seem to be very importarit in cleterrnining both
3,
(A) a r ~ d 6 at ttlie time At of our measrrre~iients, arr estirnate using ,?, of bulk water24
in the 500 ilm to 900 nrn range frorn R.ef. [ G l j and 6
-
0.2 nm as appropriate for 1 to 2 monolayers givesQQ,. -
7 x 10'' for our data point at; 670 nm with D = 750(likewise, the data of Fig. 3.6 at 670 nrn would predict
S
about an order of magnitude too largc). This estinlat,c? favors material absorptiori and silrface scattering losses a t long visible n~ar~elengtlis allti snlall At. Wo~ve~ier, there is a r a i d decrease to Q,-
8 x lo9 at 850 nm (with D = 680 pm)> strongly suggestirig that water absorption plays a fundanientd role furt,her into the NIR. The depexlclence suggest,ed by Eq. 3.2 is also shown in Fig. 3.4.There is a real possibility t,kiat even higher Q could he recorded in a dry environ- merit as At
-.
0, as cliemical changes in t,he surface diie to oxygen alone should not causc the absorption. This immediately suggests drying of the air its a n approacll t,o nmintaining high Q . At STP and a. relative humidity of 5070, there is a water vapor partial pressure of 11,500 ppm in air. Hence, I next attempted to inlple-7 1 0 , ~
ment a dry glove box irrto tlie fabrication and memureitlent scheme, but dry nitrogen purging made it very difficillt to light tlie torch. I then iilvestigated an industrial lab- oratory gas dryer based on dehurrlidificatiorl of the Caltecl-1 compressed air line using a molecular sieve desiccant that can produce