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OPTICS LETTERS / Vol. 36, No. 15 / August 1, 2011
Fiber coupling to BaTiO3 glass microspheres in an aqueous environment Oleksiy Svitelskiy,1 Yangcheng Li,1 Arash Darafsheh,1 Misha Sumetsky,2 David Carnegie,3 Edik Rafailov,3 and Vasily N. Astratov1,* 1
Department of Physics and Optical Science, Center for Optoelectronics and Optical Communications, University of North Carolina at Charlotte, Charlotte, North Carolina 28223, USA 2 3
OFS Laboratories, 19 Schoolhouse Road, Somerset, New Jersey 08873, USA
Photonics and Nanoscience Group, School of Electronic Engineering and Physics, University of Dundee, Nethergate, Dundee DD1 4HN, UK *Corresponding author:
[email protected] Received June 1, 2011; revised July 2, 2011; accepted July 2, 2011; posted July 5, 2011 (Doc. ID 148477); published July 25, 2011
Compact microspheres with high-quality (Q) whispering gallery modes are required for many applications involving liquid immersion, such as sensing nanoparticles and studying resonant radiative pressure effects. We show that high-index (1.9 and 2.1) barium titanate glass (BTG) microspheres are perfect candidates for these applications due to their high-Q (∼104 in the 1100–1600 nm range) resonances evanescently excited in spheres with diameters of 4–15 μm. By reattaching the spheres at different positions along a tapered optical fiber, we show that the coupling constant exponentially increases with thinner fiber diameters. We demonstrate the close to critical coupling regime with intrinsic Q ¼ 3 × 104 for water immersed 14 μm BTG spheres. © 2011 Optical Society of America OCIS codes: 140.4780, 230.5750, 120.3150.
In recent years there has been a great deal of attention focused on the coupling between whispering gallery modes (WGMs) in microspheres [1,2] and on developing evanescent couplers to spheres based on tapered fibers [3–8], surface waveguides [9,10], and prisms [11]. This interest arises from a number of optical properties determined by the high-quality (Q) WGM resonances: (i) nonlinear effects in spheres made from special materials with high nonlinearity [6,7], (ii) nanoparticle sensor effects [3,8], and (iii) resonant radiative pressure effects [12,13]. Because of a strong size dependence of the WGM frequencies, the resonant optical forces can be used for size sorting the microspheres with an unprecedented small standard deviation of the spheres’ diameters on the level of ∼1=Q [12,13]. Such size-matched microspheres can be used as building blocks for coupled resonator optical waveguides based on the tight binding of WGMs [1,2]. Realization of this concept requires a liquid environment where the spheres can be optically propelled [9]. The problem, however, is a significant reduction of WGM Q factors in a liquid due to the reduced index contrasts. For example, in order to possess Q ≳ 104 in water in the near-IR range, conventional microspheres made from silica glass with index N s ≈ 1:45 or polystyrene (1.59) should have diameters above 30 μm. Such spheres are too massive and bulky for efficient optical propulsion. The general solution to this problem is offered by higher index materials, such as chalcogenide glass [6], lead silicate glass [7], and silicon [7] microspheres. However, their manufacturing process is less well established and they are not available commercially. In this work, we developed a tapered fiber-tomicrosphere platform for coupling light to a variety of spheres with indices of 1:47 ≲ N s ≲ 2:1 and diameters of 3 ≲ D ≲ 22 μm in a liquid environment. We observed Q factors approaching 104 in compact (D ≈ 5 μm) barium titanate glass (BTG) microspheres [14] with N s ≈ 1:9 and 0146-9592/11/152862-03$15.00/0
2.1 immersed in water. By reattaching the spheres at different positions along the taper, we demonstrated a critical coupling regime with intrinsic Q ¼ 3 × 104 for water immersed 14 μm BTG spheres. Based on the high Q factors of WGMs in compact commercially available BTG microspheres, we propose their use for studying resonant radiative pressure effects in microfluidic platforms. A sample cell was formed by a Plexiglas 10 mm × 20 mm frame with a 2 mm height [Fig. 1(a)]. A singlemode SMF-28 fiber was fixed in the frame with epoxy. The tapering was done by chemical etching in a meniscus over an overfilled vessel with 25% hydrofluoric acid solution [15]. The length of the etched part was ∼3–5 mm, with a diameter at the waist d ∼ 1 μm. The frame with the fiber was bottom sealed with a glass slide, forming a bath, which was filled with water. The microparticle was attached to the taper by Van der Vaals forces. The low-index spheres were either borosilicate (N s ≈ 1:47) or soda lime (1.50) glasses, whereas the BTG spheres were made [14] with a larger content either of barium (N s ≈ 1:9) or of titanium (2.1). The sphere positioning was done using a sharpened piece of optical fiber attached to a three-dimensional (3D) hydraulic micromanipulator. In the tapered region, light gets adiabatically converted into the water-guided modes, allowing their evanescent tails to interact with the spheres. The broad spectral range (1300–1700 nm) transmission spectra were measured with ∼0:1 nm resolution using an unpolarized fiber-integrated white-light source and an optical spectrum analyzer. For high-resolution measurements, we used mode-hop-free intervals of a semiconductor laser tunable in the 1140–1250 nm range (Toptica Photonics). Figure 1(b) shows the resonant spectrum of a 14 μm BTG sphere with N s ≈ 1:9 in contact with a d ≈ 2:5 μm fiber in water. The dips in transmission are due to coupling to WGMs with orthogonal polarizations, labeled TE and TM, respectively [11]. The radial (n ¼ 1; 2) numbers © 2011 Optical Society of America
August 1, 2011 / Vol. 36, No. 15 / OPTICS LETTERS
(a)
liquid port
plexiglas frame
fiber input
fiber output
liquid port
glass bottom
are shifted with respect to each other by 1 dB). The transmitted power near the resonance was approximated using a single-mode model [17]:
TM1 TM2
45
TE2
41
41
1600
1610
1620
Amplitude (dB)
Amplitude a.u.
0
-15
1630
1146.6
1146.8
Wavelength (nm)
45 47 44 TE1 53 52 51 50 49 48 46 48 44 52 47 46 51 50 49 43 45 TM1 40 46 44 48 43 42 39 47 45 41 TE2 41 40 43 42 39 TM2 48 47 46 45 44
(b)
1400
1440
1480
1520
ðβ − β0 Þ2 þ ðβ − β0 Þ2 þ
1560
1600
1640
1680
2
γ 2S
þα−κ
γ 2S
þαþκ
-5
Wavelength (nm)
Amplitude (a.u.)
P ¼ e−γ ×
-10
2 :
ð1Þ
Here, κ is the coupling constant, β ¼ 2πN s =λ is the propagation constant (β0 ¼ 2πN s =λ0 ), α is the field attenuation coefficient in the sphere, γ is the coupling loss, and S is the circumference of the sphere. It should be noted that the parameters in this model represent effective average values characterizing coupling among several modes in the tapered fiber and a few azimuthal WGMs. As an example, Fig. 2(b) shows fitted spectra near the λ0 ¼ 1614:4 nm WGM resonance. The facts that Q and λ0 are independent of d, and that the depth of the dip is limited to the level of a few decibels, indicate an undercoupled regime. In this regime, Δλ is determined by α ≈ 22 cm−1 , and the depth is determined by κ. Parameter γ, determining the level of the transmission away from the resonances, was found to be rather small and almost independent of the taper thickness, except for the thinnest fibers with d ≈ 2:2 μm and 1:3 μm. The reduced transmission in the latter case can be attributed to
Wavelength (nm) -66
11.0
-68
6.0 5.5
-70
4.7
-72
3.5 3.0
-74
2.2 1.25
-76 -78 1560
(a)
1600
1640
1680
1720
Wavelength, nm 0.0 101
-0.5
3.0 m 0
, cm-1
indicate the number of WGM intensity maxima along the radial direction. The angular number l represents the number of modal wavelengths that fit into the circumference of the equatorial plane of the sphere. In order to assign mode numbers and confirm the sphere diameter, the positions of the resonances were fitted using the Mie scattering formalism [16], as illustrated in the diagram at the bottom in Fig. 1(b). The observed dips are inhomogeneously broadened by the partial overlap of modes with different azimuthal numbers m, which are degenerate in a perfect sphere but split in the real physical beads due to their slight (
