Sorting Dielectric Microspheres by using Light

The Art of the Impossible: Sorting Dielectric Microspheres by using Light Luiz Poffo1,2*, Farzaneh Abolmaali1, Aaron Brettin1, Boya Jin1, James Page1, Nicholaos I. Limberopoulos,3 Igor Anisimov,3 Ilya Vitebskiy,3 Augustine M. Urbas,4 Alexey V. Maslov,5 and Vasily N. Astratov1,3,* 1

Department of Physics and Optical Science, Center for Optoelectronics and Optical Communications, University of North Carolina at Charlotte, Charlotte, NC 28223-0001, USA 2 Institut Foton, CNRS, Université de Rennes 1, IUT Lannion, F22305, Lannion, France 3 Air Force Research Laboratory, Sensors Directorate, Wright Patterson AFB, OH 45433, USA 4 Air Force Research Laboratory, Materials and Manufacturing Directorate, Wright Patterson AFB, OH 45433, USA 5 University of Nizhny Novgorod, Nizhny Novgorod 603950, Russia *E-mails: [email protected], [email protected]

Abstract— Use of resonant light forces opens up a unique approach to high-volume sorting of microspherical resonators with 1/Q accuracy, where Q is the resonance quality factor. Based on a two-dimensional model, it is shown that the sorting can be realized by allowing spherical particles to traverse a focused beam. Under resonance with the whispering gallery modes (WGM), the particles acquire significant velocity along the laser beam which should allow sorting dielectric microspheres with almost identical positions of their WGM resonances. This is an enabling technology for developing super-low-loss coupled-cavity structures and devices.

Optical coupling between WGMs can be described by a tight-binding approximation for photonic atoms [2]. Based on this concept, many structures and devices have been designed including coupled-resonator optical waveguides (CROWs) [2], delay lines [3], high-order spectral filters [4], sensors [5,6], laser-resonator arrays [7,8], and photonic molecules [9]. Coupling between WGMs have been extensively studied in microspheres and these studies revealed significant optical losses due to the variations of the WGM resonant frequencies in the neighboring spheres [10-13]. Although the individual photonic atoms can be tuned in resonance by using local micro-heaters or other techniques [3], these approaches are too complicated for developing practical devices. The size uniformity of commercial microspheres is limited at ~1% level which is insufficient for an efficient coupling between the WGMs in neighboring spheres. In the present work, we present a method to sorting microspheres based on the enhancement of the optical forces under the resonant excitation of WGMs [14-16], applicable to any microspheres in vacuum, air, or liquid environment. In 1977, the resonant force enhancement was observed in microdroplets by Ashkin and Dziedzic [17]. Recent work on the optical propulsion of microspheres in evanescent waterimmersed fiber-couplers showed that the force peaks can reach the total absorption limit for the momentum flow of light or even exceed it [18]. Although the strong peaks are helpful for sorting resonant microspheres, this method was applicable only to polystyrene microspheres with density sufficiently close to that for water and with the refractive index contrast significantly reduced in the water environment. As a result, the resonant enhancement of the optical force was observed for sufficiently large spheres with diameters D > 15 m were required for achieving WGM quality factors Q > 103.

Keywords— optical force; microsphere; whispering gallery mode; optical coupling, photonic molecule.

I.

INTRODUCTION

Microresonators are structures of upmost importance in optics due to their potential applications in nonlinear optics, optical signal processing and sensing. The interaction of matter and light can be dramatically increased by the presence of a microcavity. Dielectric microspheres represent a special class of microresonators since Mother Nature favors spherical shape of microresonators due to a great variety of different physics phenomena involved in formation of microspheres such as minimization of their surface energy. Another property of microspheres is a high quality of their surface which results in minimal scattering losses for internal optical resonances, so called whispering gallery modes (WGMs). They can be interpreted as electromagnetic waves that circulate and are strongly confined within the sphere due to total internal reflection. The quality (Q) factors of WGM resonances are usually determined by the surface imperfections and by the material absorption and they can reach exceptionally high values Q~ 108 - 109 [1].

978-1-5386-6557-2/18/$31.00 ©2018 IEEE

499

On the other hand, sorting microspheress based on thee enhhancement of the optical forces under the resonantt exccitation of WG GMs can be reallized by allowiing particles to o travverse a focused d laser beam in n a free falling g motion in airr or vvacuum enviro onment [19] att a specific waavelength as iss illuustrated in Figu ure 1. We show thatt this is an enaabling technolo ogy for sorting g of rresonant micro ospheres with better b than 0.01% uniformity y of W WGM peaks. It I is particularlly important th hat this method d is aapplicable to high-index h sph heres, such ass n~1.9, which h cann possess Q  104 in sufficiently small paarticles, D ~ 3 m m, suitable for developing d pho otonic integrated circuits and d manny devices bassed on coupled microresonato ors. I.

only two forces determine thee motion of the particle: Under gravity accceleration in graviitational and opptical force. U vacuuum, the particlle velocity incrreases very fasst. Due to this factoor, the interacttion time withh the laser beeam becomes shortt if particle w was released att some distancce above the laser beam. For thiss reason, the m most favorable cconfiguration for oobservation laaser-induced sshifts of the particles in vacuuum is to releasse the microsphheres as close aas possible to the laaser beam edgee (a ~ 0 in Figgure 1). Takingg into account initiaal zero velocityy, the interactioon time with thhe laser beam is maaximal in this case. After crrossing the lasser beam, the particcle sustains iits horizontal velocity com mponent that signiificantly increaases its horizonntal displacem ment. Figure 2 show ws the total dispplacement exppected for diffeerent particles sizess that cross a laser beam w with a waist off 1 mm in a vacuuum chamber w with the 30 cm m free-falling distance in y direcction (b=30 cm m in Figure 1).

OPTICAL FO ORCE SIMULATIO ONS

In a previewss work, we used a two-dimeensional (2-D)) model to estimatee the optical force and the vellocity acquired d by spherical partiicles with the radius r R and reefractive index x nw when it traversees an optical laaser beam with h the frequency y  [[19]. It was shhown that the particles with more efficientt exccitation of thee WGM reson nances experieence increased d opttical force com mpared to the offf-resonant exccitation. As thee parrticle traversess the laser beaam, it acquirees a horizontall velocity componeent which depends on a detu uning between n the laser and WG GM resonance peak. The ratiio between on-andd off-resonant velocities can n reach a facttor of two forr som me cases. This difference of o on- and offf-resonant forr horrizontal velocitties should lead to a measuraable separation n of the particles; that will be equal e to the product p of thee velocity differencce and the tim me interval un nder which thee parrticle sustains such s velocity difference. d

Figuree 2. Total displaccement in x direcction by different size spheres in vacuum m.

Iff the particle fa falls in the air, we need to acccount for the drag force. The tiime of achievving the term minal velocity woulld depend on tthe sphere sizee and dynamic viscosity. In mostt of the pracctical situationns, the terminnal velocities shoulld be reacheed for both vertical andd horizontal compponents. The terminal veloocity in verticcal direction shoulld determine thhe time of interraction with thhe laser beam. How wever, the distaance (a) at whiich the sphere is dropped is not iimportant, if tthe terminal velocity is quicckly reached. The terminal veloocity in horizzontal directionn should be reachhed during the time when thee particle interssects the laser beam m. This horizonntal componennt of the velociity should be quickkly lost after crossing the laser beam. Thus, in air envirronment the horizontal displacementts can be signiificantly reducced compared to the vacuuum case. The opticcal forces can also create a rrotation of thee particle that may affect the draag force. The presence of thhe drag force does not change thhe sorting mechanism and caan be used as an addditional tuningg parameter byy changing the air pressure.

Figuure. 1. Schematic of sorting spherees by focused lasser beam. a is thee distaance between spheeres to fall and the edge of the focu used laser beam, w is thhe waist of the laseer beam and b is the t distance betweeen the edge of thee laseer beam and the flo oor.

The dynamicss of such motion is differentt in two cases,, freee falling in vaacuum and in air a environmen nt. In vacuum,,

500

Let us consid der the motion n of the partiicle in the airr assuuming that thee spheres fall a distance of 3 cm beforee reaching the edgee of the laser beam b (a = 3 cm m in Figure 1). If the viscosity is high, the particles reacch a terminall velocity () when n the optical or gravitational force is equall to the drag forcee, Fd = 6R, where  iss the dynamicc visccosity. The dyn namic viscositty of the air at 25 °C is 18.54 4 Paas. To simulate the changes of air pressuree, the dynamicc visccosity was diviided by 10 and d 100. After thee spheres crosss the laser, the free-fall distancee in y direction n is b=30 cm. Figgure 3(a) show ws the horizontal distance x traveled t by thee parrticle directly inside in the laser beam an nd Figure 3(b)) shoows the total diisplacement alo ong x direction n for a vacuum m chaamber of 30 cm m size in y direection calculateed for differentt visccosities.

II.

RATUS, PROCED DURE, AND EXPERIIMENTAL APPAR RES SULTS

med using a O Our preliminarry experimentts are perform Coherent with the maximal Ti:Saapphire tunable laser from C m. A homem made vacuum 2W CW powers at ~800 nm mensions alonng x, y and z cham mber with 303010 cm dim direcctions was usedd to provide suupport to the syystem to drop the spheres at ccontrollable ppressure. Thiss setup was mpt to control the dynamic vviscosity and develloped in attem curreently the experiiments are in thhe beginning pphase. W We had to deveelop an apparaatus which alloows a release of m microspheres oon demand. Ideally, the microspheres shoulld intersect and interactt with the laser beam microspheres indivvidually, but inn practice the silica (SiO2) m tend to stick to a suubstrate and too each other byy the van der minimum forcee required to Waalls’ (attractive)) force. The m m a surface is called the “puull-off force”. separrate them from microspheres The ppull-off force bbetween two iddentical glass m is preedicted by the model of Derjaaguin, Muller, and Toporov to bee: Fsphere  sphere  D ,

(a) 

wherre  is the effeective solid suurface energy. The pull-off forcee between a glaass microspherre and a flat glass surface is two ttimes more thaan the pull-off fforce between two identical glasss microspheres. Inn our experimeent, the microsspheres were rreleased from The required the ssubstrate usingg an ultrasoniic vibration. T accelleration to breeak the van deer Waals’ bonnd between a flat surface is: microosphere and a fl

(aa) 

a

Fsphhere flat M



4R 1  2 4 3 R  sphere R 3

wherre M is the maass of the micrrosphere, R is the radius of the m microsphere annd  the densitty of the micrrosphere. The smalller the microssphere, the largger acceleratioon is required to breeak the van der Waals bond. microspheres W We achieved a controllable sseparation of m m the substrrate by usinng ultrasonicc transducer from mechhanically couppled to the substrate, as illusttrated in Fig. 4. Fiirst the mechhanical resonannces of the ssystems were studiied by observiing the motionn of microspheeres over the substtrate in responnse to a frequenncy sweep prooduced by the ultrassonic transduccer. After that the frequency was selected match one of thhe resonances of the system m in order to to m faciliitate the contrrollable separaation of microospheres. The releaase of microsppheres was prrovided by usiing a pulsed excittation via ultraasonic transduucer. After sepparation from the substrate, the microspheress were fallingg through a metaallic pinhole inn order to bettter define the trajectory of microospheres fallinng without laaser. The resuults obtained curreently allow achieving thhe distributioons of the microospheres on tthe substrate with the milllimeter-scale charaacteristic dimeensions after ffalling approxiimately b~30 cm ddistances in a loow-pressure chhamber.

(b) 

Figuure 3. a) Horizonttal distance x travveled by different size s spheres insidee the llaser beam for 3 different d dynamic viscosities. b) Tota al displacement in n x dirrection by differen nt size spheres for 3 different dynamiic viscosities.

501

SUMMARY

[6] K. R. Hiremath and V. N. Astratov, "Perturbations of whispering gallery modes by nanoparticles embedded in microcavities," Opt. Express 16(8), pp. 5421-5426 (2008). [7] B. E. Little, Member, IEEE, S. T. Chu,W. Pan, and Y. Kokubun, "Microring Resonator Arrays for VLSI Photonics," IEEE Photonics Technology Lett. 12(3), 323-325 (2000). [8] V. N. Astratov and S. P. Ashili, "Percolation of light through whispering gallery modes in 3D lattices of coupled microspheres," Opt. Express 15(25), 17351-17361 (2007). [9] Y. Li, F. Abolmaali, K. W. Allen, N. I. Limberopoulos, A. Urbas, Y. Rakovich, A. V. Maslov, and V. N. Astratov, "Whispering gallery mode hybridization in photonic molecules," Laser & Photonics Reviews 11(2), 1600278 (2017). [10] V. N. Astratov, J. Franchak, and S. Ashili, "Optical coupling and transport phenomena uin chains of spherical microresonators with size disorder," Appl. Phys. Lett. 85(23), 5508–5510 (2004). [11] A. V. Kanaev, V. N. Astratov, and W. Cai, "Optical coupling at a distance between detuned spherical cavities," Appl. Phys. Lett. 88(11), 111111 (2006). [12] S. Yang and V. N. Astratov, "Spectroscopy of coherently coupled whispering-gallery modes in size-matched bispheres assembled on a substrate," Opt. Lett. 34(13), 2057-2059 (2009) [13] V. N. Astratov, "Fundamentals and applications of microsphere resonator circuits", in: Photonic Microresonator Research and Applications, Springer Series in Optical Sciences, Vol. 156, edited by I. Chremmos, O. Schwelb, and N. Uzunoglu (Springer, New York, 2010), Chap. 17, pp. 423– 457, https://link.springer.com/chapter/10.1007/978-1-44191744-7_17 [14] V. N. Astratov, “Methods and devices for optical sorting of microspheres based on their resonant optical properties,” U.S. patent publication US20140069850 A1 (16 September 2011), http://www.google.com/patents/US20140069850. [15] Y. Li, O. V. Svitelskiy, A. V. Maslov, D. Carnegie, E. Rafailov, and V. N. Astratov, "Giant resonant light forces in microspherical photonics," Light: Sci. Appl. 2(4), e64 (2013). [16] A. Maslov, V. N. Astratov, and M. Bakunov, "Resonant propulsion of a microparticle by a surface wave," Phys. Rev. A 87(5), 053848 (2013). [17] A. Ashkin and J. M. Dziedzic, "Observation of resonances in the

Significant steps towards demonstration a novel technology of sorting microspheres by their resonant properties are made. These steps include a simplified modeling showing the magnitudes of horizontal shifts of microparticles intersecting the laser beam and free-falling in a chamber with the controllable pressure. The feasibility of the building such sorting apparatus is demonstrated using Ti:Sapphire tunable laser coupled into a vacuum chamber. The problem of controllable releasing microspheres is solved using an ultrasonic transducer. The current bottlenecks of this project include a large (millimeter-scale) spread of particles on a substrate observed without laser. This is explained by interactions of the particles and, potentially, by charging effects inside the chamber. In principle, this problem can be solved by using surface chemistry approaches for removing the surface charge of microspheres and careful electrostatic screening along the trajectory of the descending microspheres. Another problem is connected with a need to increase the power density along the trajectory of the descending microspheres in order to increase the horizontal shifts of the microparticles. This problem will be solved in our future work using an additional focusing of the laser beam by the cylindrical lens. We anticipate that this work will result in demonstration of new technology of the sorting of microspheres by using light. It will allow sorting microspheres with uniquely identical resonant properties which can be used for building lossless delay lines, CROW devices, and sensors. ACKNOWLEDGMENT This work was supported by the Center for Metamaterials, an NSF I/U CRC, award No. 1068050. REFERENCES

radiation pressure on dielectric spheres," Phys. Rev. Lett. 38, 1351–1354 (1977).

[1] M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, "Ultimate Q of optical microsphere resonators," Opt. Lett. 21(7), 453-455 (1996). [2] A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupledresonator optical waveguide: a proposal and analysis," Opt. Lett. 24(11), 711-713 (1999). [3] F. Morichetti, C. Ferrari, A. Canciamilla, and A. Melloni, "The first decade of coupled resonator optical waveguides: bringing slow light to applications," Laser & Photonics Reviews 6 (1), 74-96 (2012). [4] B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz,F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16(10), 2263–2265 (2004). [5] M. R. Foreman, J. D. Swaim, and F. Vollmer, "Whispering gallery mode sensors," Adv. Opt. Photonics 7(2), 168–240 (2015).

[18] Y. Li, A. V. Maslov, N. I. Limberopoulos, A. M. Urbas, and V. N. Astratov, "Spectrally resolved resonant propulsion of dielectric microspheres," Laser & Photonics Rev. 9(2), 263– 273 (2015). [19] A. V. Maslov and V. N. Astratov, "Microspherical photonics: Sorting resonant photonic atoms by using light," Appl. Phys. Lett. 105(12), 121113 (2014).

502