Tellurite microspheres for nanoparticle sensing and novel light sources Yinlan Ruan,* Keiron Boyd, Hong Ji, Alexandre Francois, Heike EbendorffHeidepriem, Jesper Munch, and Tanya M. Monro Institute of Photonics and Advanced Sensing, University of Adelaide, Adelaide, 5005, Australia * [email protected]
Abstract: High index Er-Yb codoped tellurite spheres with diameter of 9 μm and good sphericity were fabricated using a CO2 laser. Upconversion modulated whispering gallery modes with a quality factor of 45,000 were observed in the sphere dipped in methanol. Refractometric sensing with detection sensitivity of 7.7 nm/RIU was demonstrated using a 9 μm diameter sphere. Such high index spheres have the potential to be used for nanoparticle sensing and mid-IR frequency conversion. ©2014 Optical Society of America OCIS codes: (140.4780) Optical resonators; (280.4788) Optical sensing and sensors.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
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20. T. Kishi, T. Kumagai, T. Yano, and S. Shibata, “On-chip fabrication of air-bubble-containing Nd3 + -dopedd tellurite glass microsphere for laser emission,” AIP Adv. 2(4), 042169 (2012). 21. K. Boyd, H. Ebendorff-Heidepriem, T. M. Monro, and J. Munch, “Surface tension and viscosity measurement of optical glasses using a scanning CO2 laser,” Opt. Mater. Express 2(8), 1101–1110 (2012). 22. M. Oxborrow, “Traceable 2D finite element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microw. Theory Tech. 55(6), 1209–1218 (2007). 23. I. Teraoka, S. Arnold, and F. Vollmer, “Perturbation approach to resonance shifts of whispering-gallery modes in a dielectric microsphere as a probe of a surrounding medium,” J. Opt. Soc. Am. B 20(9), 1937–1946 (2003). 24. A. François, K. J. Rowland, and T. Monro, “Highly efficient excitation and detection of whispering gallery modes in a dye-doped microsphere using a microstructured optical fiber,” Appl. Phys. Lett. 99(14), 141111 (2011). 25. N. M. Hanumegowda, C. J. Stica, B. C. Patel, I. White, and X. Fan, “Refractometric sensors based on microsphere resonators,” Appl. Phys. Lett. 87(20), 201107 (2005). 26. A. Weller, F. C. Liu, R. Dahint, and M. Himmelhaus, “Whispering gallery mode biosensors in the low-Q limit,” Appl. Phys. B 90(3–4), 561–567 (2008). 27. T. Ioppolo, N. Das, and M. V. Ötügen, “Whispering gallery modes of microspheres in the presence of a changing surrounding medium: A new ray-tracing analysis and sensor experiment,” J. Appl. Phys. 107(10), 103105 (2010). 28. F. Vollmer and L. Yang, “Label-free detection with high-Q microcavities: a review of biosensing mechanisms for integrated devices,” Nanophotonics 1(3–4), 267–291 (2012). 29. V. R. Dantham, S. Holler, V. Kolchenko, Z. Wan, and S. Arnold, “Taking whispering gallery-mode single virus detection and sizing to the limit,” Appl. Phys. Lett. 101(4), 043704 (2012). 30. M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, “Ultimate Q of optical microsphere resonators,” Opt. Lett. 21(7), 453–455 (1996). 31. A. Mori, “Tellurite-based fibers and their applications to optical communication networks,” J. Ceram. Soc. Jpn. 116(1358), 1040–1051 (2008). 32. N. Uchida and N. Uesugi, “Infrared optical loss increase in silica fibers due to hydrogen,” J. Lightwave Technol. 4(8), 1132–1138 (1986). 33. J. S. Wang, E. M. Vogel, and E. Snitzer, “Tellurite glass: a new candidate for fiber devices,” Opt. Mater. 3(3), 187–203 (1994).
1. Introduction The quality factor Q and mode volume Vmode are useful parameters in characterizing the performance of resonators. A high Q/Vmode ratio is desirable in many resonator applications such as lasers, biochemical sensing, frequency combs, and cavity quantum electrodynamics (cavity QED) [1], and the Purcell enhancement factor for the spontaneous emission rate of atoms in a single photon source scales as (Q/Vmode) [2]. Whispering gallery modes (WGMs) supported within silica microspheres have been widely investigated for applications ranging from sensing [3] to frequency conversion [4]. They are relatively easy to fabricate by thermal flow from standard optical fibers [1]. By heating the distal tip of a silica fiber, the glass reflows to form a spherical shape under the influence of surface tension. Q factors of up to 109 have been achieved for a 750 μm diameter silica sphere enabled by the smooth surface of the sphere produced under reflow conditions, low material absorption and low ellipticity [1]. The ellipticity e is defined as e = ( a 2 − c 2 ) c 2 , where a is the equatorial radius of the sphere and c is polar radius, and cω2), was then used to further taper the region to a diameter dt2. (c) The CO2 laser cut the region of diameter dt2, and the beam was then aligned at a length x2 from the cut section using the alignment HeNe Laser. The section was then irradiated with a spot size of 2ω3 giving (d) a microsphere of diameter ds.
Figures 1(c) and 1(d) show the Er-Yb doped tellurite spheres fabricated by this setup with diameters of 36 μm and 7.5 μm, respectively. The latter is the minimum size of the tellurite spheres achieved to date using this setup (but not characterised so far). Compared to Figs. 1(a) and 1(b), it can be clearly seen that the CO2 laser setup, which relied on the fiber weight to pull the fiber taper, significantly improved the sphere sphericity and centrality of the sphere positioned on the top of the fiber stem without any bending. The ellipticity in one plane of the spheres was measured as less than 1% using direct dimension measurement. The requirement for low ellipticity is particularly important for the spheres with diameter less than 10 μm. It allows them to maintain simply degenerate modes with their total quality factor Q that is not significantly affected by the resonator shape [8], as required for sensing applications discussed below. To decrease the sphere size further, the diameter of the fiber taper needs to be decreased significantly to ≈1 μm in scale and the laser intensity required correspondingly increased. However, the laser intensity available with our current equipment was not sufficient to cleave such a small taper [21]. 3. Characterization of the tellurite spheres The surface roughness of the tellurite spheres was mapped using Atomic Force Microscopy (AFM) and the result from a sphere fabricated by CO2 laser is shown in Fig. 3(a). The average roughness of the sphere surface was found to be ~1 nm. The spheres fabricated using the “Ω” shape filament showed comparable surface roughness. The smooth surface of these spheres ensures extremely low scattering loss of the spheres. Figure 3(b) shows the experimental setup used to excite and observe the WGMs in the ErYb codoped Te spheres. A tapered SMF-28 fiber with a waist diameter of 1.5 μm was pulled by the splicer and used to couple light into the microsphere and to collect the evanescent field of the WGMs for spectra analysis. The relative positions of the taper and the sphere were monitored from the top using a microscope connected to a CCD camera. A 840 nm short pass filter was used to remove the 975 nm CW pump laser before the output light of the fiber taper was input into the spectrometer. Drops of the solvent were placed on a coverslip, located under the sphere, and spread across the coverslip. The coverslip was lifted up to allow the
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Received 1 Apr 2014; revised 28 Apr 2014; accepted 28 Apr 2014; published 9 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.011995 | OPTICS EXPRESS 11999
sphere to be immersed in the solvent, which changed the refractive index of the environment surrounding the sphere. a nm 10 8 6 4 2 0.9
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9.4μm sphere by CO2 laser and in methanol
Fig. 3. a. AFM image of the surface of a microsphere fabricated using a CO2 laser; b. Experimental setup to measure WGMs of the microspheres. c, d and e are WGMs modulated upconversion spectrum of the Er-Yb codoped spheres in air with 33 μm, 30 μm and 9.4 μm diameter, respectively. f is the WGM spectrum of the 9.4 μm diameter sphere dipped in methanol. The inserted resonance peak at 670.18nm displays Q of 45,000. The integration time for these fluorescence spectra was 1s. The sphere in c was fabricated using a hot filament, and those in d, e and f were made using a CO2 laser.
Figures 3(c) and 3(d) show the upconversion spectra modulated by the WGMs in the spheres with relative large size and located in air. They were fabricated using the filament and CO2 laser, respectively. It can be seen that the WGM spectra of the larger microspheres (over 30μm diameter) were complex and consists of groups of the modes. Each group includes the first and higher orders modes, which are difficult to identify. However, the gap between the two neighbouring groups is constant, and corresponds to free spectral range (FSR) of the measured sphere calculated from ΔλFSR = λ 2 2π ns R,
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(1)
Received 1 Apr 2014; revised 28 Apr 2014; accepted 28 Apr 2014; published 9 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.011995 | OPTICS EXPRESS 12000
where R is the radius of the sphere [1]. The FSR value measured from Fig. 3(c) is 1.42 nm and that in Fig. 3(d) is 1.5 nm, close to the calculated 1.46 nm and 1.58 nm, respectively by using Eq. (1). When the size of the spheres made using a CO2 laser was decreased to 9.4 μm, the WGM spectrum of the sphere became simpler as shown in Fig. 3(e) since fewer modes are allowed due to the increased curvature of the surface. Moreover, the FSR depended inversely on the diameter of the sphere, thereby further reducing the number of the modes within the emission range. When the 9.4 μm diameter sphere was dipped into the organic solvent methanol, only a limited number of low order modes were excited as shown in Fig. 3(f) with most of the higher order modes quenched due to high loss caused by the reduced refractive index contrast between this microsphere and methanol (na = 1.3284) compared to air (na = 1.0). From the resolved modes, the measured Q values at the red upconversion wavelengths for these spheres were up to of 45,000 with variations dependent on the sphere quality (shown at the inset of Fig. 3(f)). It was challenging to align the silica taper to the equatorial plane of the small spheres (around 20 μm diameter) with bent fiber stem fabricated by the filament. This was because the fiber taper in our setup easily slid away from these spheres, particularly in the liquid environment. With straight fiber stems on the spheres fabricated by the CO2 laser, this was not an issue. Thus a 9 μm tellurite sphere made by the CO2 laser was investigated for sensing demonstration described in the following section. 3.1 Resonance shift with changed refractive index contrast To assess potential applications of the high index tellurite spheres for refractometric sensing, the resonance shift of the WGMs as a function of changes in the refractive index na of the surrounding medium of the microspheres was studied for the 9 μm diameter sphere. Three organic solvents with different refractive indices at 580 nm were used: methanol (na = 1.3284), acetone (na = 1.3586) and isopropanol (IPA) (na = 1.3772). Figure 4(a) shows the WGM spectrum of the 9 μm sphere dipped into IPA and methanol, respectively. It can be seen that the mode peaks of the sphere dipped in IPA are shifted towards long wavelength due to reduced refractive index contrast between the sphere and its environment. The wavelength shifts in the two neighboring modes are clearly different, for example, δλTM = 0.55 nm > δλTE = 0.33 nm as shown in Fig. 4(a).
Fig. 4. Resonance shift of the Er-Yb doped spheres in solvents. a. the spectrum of the 9 μm spheres in IPA and methanol, respectively. The mode order numbers are assigned by numerical calculation using the code provided by Oxborrow [22]. b. dependence of the resonance shift δλ on refractive index change δn for the 9 μm tellurite sphere. The solid line is calculated wavelength shift δλ, and the separate points are measured values.
In order to understand these experimental results, we used a 2D finite element method to simulate the modes in COMSOL with the code provided by Oxborrow [22]. Through this code, the peak wavelength of each mode and their corresponding mode order number can be found. Thus the numbers of the first order TE/TM modes are assigned in Fig. 4(a), and
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Received 1 Apr 2014; revised 28 Apr 2014; accepted 28 Apr 2014; published 9 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.011995 | OPTICS EXPRESS 12001
correspond to those modes with high peak intensity. It can be seen that the shift of the TM mode δλTM (0.55 nm) was bigger than δλTE (0.33 nm) of the TE mode. Arnold et al in Ref [23] presented a first order perturbation approach to calculate the resonance shift caused by a uniform change in the refractive index of the environmental medium by using the perturbed Schroedinger equation. They found that the ratio of the TM shift to the TE shift is greater than unity for the first order modes. Therefore our measurement was consistent with their prediction. The FSR, ΔλFSR, of the two neighboring TM modes was 4.4 nm. The diameter 2R of the sphere calculated from Eq. (1) using the measured ΔλFSR was 9.7 μm, which is close to 9 μm measured using optical microscopy. Figure 4(b) shows the dependence of the resonance shifts (as shown by three points) on the change of the refractive index δn of the surrounding medium for the first order TM mode at λ = 523.5 nm. The mode exhibited detection sensitivity of 7.7 nm/RIU (refractive index unit), compared to 45 nm/RIU sensitivity achieved by others using a dye-doped polystyrene sphere with 10 μm diameter [24]. This difference was attributed to the much higher refractive index of the tellurite glass than that of the polystyrene (ns = 1.59), which results in tighter mode confinement in the high index material, and thus less light available to interact with the environment external to the sphere. The theoretical resonance shift of the 9 μm tellurite sphere was also calculated by using the formula in Ref [25]:
δλ = −
na ζ 2ns 6 + na 2 ns 4 − 4na 4 ns 2 + 2na 6 −2/3 λ2 (2ns 2 − na 2 ) − 1/3l υ , (2) 2 2 2 3/2 2π a ns ( ns − na ) 2 ns 2 ( ns 2 − na 2 )
1 , ζ l denotes the lth zero of the airy function, which is −2.338 for the first 2 order mode and l is the order number of the first order modes labelled in Fig. 4(a). The results are shown as a solid line in Fig. 4(b). It can be seen that our measurements are in good agreement with the calculated values.
where υ = n +
4. Discussions Since spheres with low mode volume are desirable in many practical applications, the impact of the size and refractive index of the spheres on their performance and application are investigated here by theoretical calculations and compared to our measurements. 4.1 Dependence of sensitivity on microsphere size By calculating the wavelength shift δλ/λ of a WGM caused by environmental index change, we can understand how the refractive index of the sphere affects its detection sensitivity for the following two distinct cases: (A) a uniform change in refractive index of the surrounding medium, and (B) a single nanoparticle attached to the sphere surface.
Fig. 5. Predicted sensitivity of the refractometric sensing for the first order TM modes of the microspheres made from tellurite, silica and polystyrene for different sphere radii. The excitation wavelength is 606 nm except the red point at 523.5 nm for the tellurite sphere.
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Received 1 Apr 2014; revised 28 Apr 2014; accepted 28 Apr 2014; published 9 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.011995 | OPTICS EXPRESS 12002
A. Uniform change in refractive index of the surrounding medium The shift δλ/λ of the WGM resonance that occurs due to a small change in the refractive index in the surrounding medium is proportional to the energy of the evanescent field in this medium [23] and dependent on sphere material and excitation wavelength. Figure 5(a) shows the calculated sensitivity of silica and tellurite microspheres as a function of sphere size using Eq. (1) in Section 3. Only the first order TM modes are assumed to be excited and the refractive index na of the surrounding medium used is 1.33. The excitation wavelength is set to 606 nm to enable direct comparison of calculated sensitivity of the 5 μm radius polystyrene sphere to the experimental measurement (black point as shown above the black curve in Fig. 5) from Ref [24]. The low index silica spheres show higher sensitivity than the same size tellurite spheres, and the sensitivity increases exponentially with reduced sphere size. However, when the sphere size becomes smaller, the broadening of their WGMs presents a practical limit for WGM shift detection. As a reasonable trade-off, a sphere with overall quality factor Q of 500 with 1.2 nm linewidth is regarded as the smallest cavity that can be used for practical applications [26]. Q is determined by several mechanisms and can be calculated by adding the different significant contributions, Q−1 = Qrad−1 + Qmat−1, where Qrad−1 is due to purely radiative loss and Qmat−1 results from non-ideal material properties. Since our tellurite spheres have negligible ellipticity, the effect of the sphere shape is not included here. A ray-tracing approach is used to calculate the Qrad values of the first order TM modes of the spheres dipped in the solution [27]. Our calculation shows the tellurite sphere with 1.2 μm radius and the silica sphere with 12.5 μm radius can achieve a Q ~500, and can be the smallest spheres for the sensing applications in aqueous environment. Our calculations show the experimentally measured Q values of the spheres are two to threeorders of magnitude lower than the calculated values. There are two possible reasons for this discrepancy. One reason is the experimental uncertainties based on limited measurements from only three tellurite spheres with different diameter are sufficiently incomplete. Another possible reason could be the ray-tracing approach as it now stands is incomplete or inadequately describes the experiments. Therefore, the practically feasible minimum size which can be used for sensing needs to be experimentally determined in future. b
aa
a
Fig. 6. Calculated wavelength shift δλ (solid lines) as a function of the radii of the spheres for single nanoparticles adsorbed on the surface of the spheres made from (a) tellurite and (b) silica glass. The green dashed lines are the detection limits when a tunable DFB laser and a low noise detector are used for characterisation, and the dark violet dash-dot lines are the RMS noise. The radii of the single nanoparticles are labeled next to their corresponding shift curves on the right hand side. The excitation wavelength is 633 nm unless otherwise stated in the figures.
B. Nanoparticle detection Considering a single nanoparticle with radius a and refractive index np, the δλ/λ of the WGMs of a microsphere caused by adsorption of this nanoparticle depends on the location of the particle’s binding site on the sphere surface. For an equatorial binding event at a site where
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Received 1 Apr 2014; revised 28 Apr 2014; accepted 28 Apr 2014; published 9 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.011995 | OPTICS EXPRESS 12003
the evanescent field intensity is maximum, the δλ/λ is calculated from the following formula [3]:
δλ / λ ≅ Da 3e − a L / ( R 5 2 ⋅ λ 1 2 ),
(3)
D = 2na 2 ⋅ 2ns ( nnp 2 − na 2 ) / ( ns 2 − na 2 )( nnp 2 + 2na 2 ),
(4)
with na and ns are refractive index of the surrounding medium and sphere material, respectively, L ≈ (λ 4π ) ⋅ ns 2 − na 2 is the evanescent field penetration distance. The δλ/λ is clearly seen to be proportional to R-2/5 and is also strongly dependent on a and L, the latter being determined by the index contrast of the sphere and its surrounding medium. The solid lines in Figs. 6(a) and 6(b) show the calculated shift δλ of the first order TM modes caused by a nanoparticle (np = 1.5) absorbed onto the equator of the tellurite and silica spheres, respectively, as a function of sphere radius at λ = 633nm. The wavelength shift δλ increases with decreasing sphere radii, and increasing nanoparticle size. In practice, the smallest detectable wavelength shift (detection limit) δλmin is determined by noise sources such as thermo-refractive noise, and can be calculated by the formula δλmin/λ = F/Q, where the figure of merit F is typically 1/50-1/100 [28]. The green dashed lines in Figs. 6(a) and 6(b) show the detection limit δλmin calculated by choosing F = 1/100 and the Q of the spheres located in the aqueous solution. The dark violet dash-dot lines are the RMS background noise level of 2 fm when a tunable DFB laser and a low noise detector are used for excitation and signal detection [29]. Thus only when the shift δλ caused by a single nanoparticle adsorption is bigger than δλmin and 2 fm, is this shift detectable. From Fig. 6(a), it can be seen that the tellurite spheres with radius ≥ 2.3 μm can detect a nanoparticle with a radius larger than 5 nm. The silica spheres can detect nanoparticles larger than 20 nm, and the minimum size of the silica sphere required to achieve this needs to bigger than 25 μm. The black point in Fig. 6(b) is the calculated detection limit using the practically measured Q value for a 39 μm radius silica sphere at λ = 763 nm [3], which is overlapped with the shift line of the 50 nm nanoparticle. This means the 39 μm radius silica sphere is predicted to be able to detect a nanoparticle with radius ≥ 50 nm and refractive index np = 1.5. This was confirmed by the authors in Ref [3], which have used this sphere to successfully detect a single InfA virion with a 50 nm radius. This is the smallest nanoparticle reported to be detected by silica spheres. From Fig. 6(b) we can expect that a 39 μm radius silica sphere can detect nanoparticles with radii bigger than 30 nm at λ = 633 nm. The reason that only the 50 nm nanoparticle was detectable at λ = 763 nm by this sphere is due to the practically achieved Q being significantly smaller than the theoretical Q mentioned previously. As discussed above the smallest shift and thus the size of the nanoparticle that a sphere can detect is strongly dependent on the Q value of the sphere. The red point in Fig. 6(a) indicates a detection limit of 40 nm calculated for a 4.5 μm radius Er-Yb tellurite sphere based on its Q value measured when this sphere was dipped in methanol. As we discussed earlier in this section, the pure tellurite sphere could have one order magnitude higher Q with reduced glass loss, thus the same size sphere (4.5 μm radius) of the pure tellurite glass made in-house should permit detection of single nanoparticles as small as 15 nm. Therefore, the high index tellurite spheres have advantage to detect small label-free bionanoparticles such as virus and proteins with their size less than 50 nm compared to low index silica spheres. 4.2 High Q/Vmode for cavity QED, enhancement of spontaneous emission and lasing To explore the dependence of Q/Vmode on sphere size for these specific applications, we calculated Q/Vmode for the tellurite spheres in air at λ = 633 nm. Lorenz-Mie theory [8] is used to calculate Q values of the spheres located in air as these applications usually require, which are more close to the experimental values [1] compared those calculated by the ray-tracing approach for the spheres in the solutions [27]. The mode volumes of the spheres were numerically calculated using two 2D finite element simulations [22]. The Q/Vmode values for
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Received 1 Apr 2014; revised 28 Apr 2014; accepted 28 Apr 2014; published 9 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.011995 | OPTICS EXPRESS 12004
L og ( Q / V m o d e )
L og ( Q / V m o d e )
the silica spheres were also calculated for comparison with their absorption coefficient at 633 nm as 1.5 × 10−4 m −1 [30] and the results are shown in Fig. 7(a). For larger spheres when the material loss is dominant, the Q/Vmode increases with decreasing sphere radius since Q is relatively constant. The Q/Vmode increases with decreasing sphere radius until a critical value of the radius where radiation losses of the sphere become dominant. The Q/Vmode then drops quickly with further decreased sphere size due to increased radiation loss in this region. Thus there exists an optimum radius for a given type of material to achieve the maximum Q/Vmode. This optimum sphere size is 1.75 μm for tellurite spheres and 5.5 μm for silica spheres. With the current loss (0.5 dB/m at 633 nm) achieved in-house for tellurite glass, the tellurite microsphere shows similar Q/Vmode to that of the silica glass microspheres at 633 nm. Assuming the loss of the tellurite glass can be reduced by a factor of 10, which has been achieved by Mori group [31], the tellurite microspheres then show a potential for 2-3 times higher maximum Q/Vmode than the silica microspheres.
Fig. 7. Q Vmode for tellurite and silica microspheres at different wavelengths: (a). 633 nm and (b). 1.9 μm. The losses of the silica glasses used for calculation are the measured values. The losses of tellurite glasses used for calculation in (a) include the currently achieved 0.5 dB/m in-house (solid line) and assumed 10 times improvement in loss (dashed line, achieved by Mori group [31]); in (b) 20 dB/km are assumed at λ = 1.9 μm.
The Q/Vmode of the tellurite and silica spheres is also calculated at the infrared wavelength λ = 1.9 μm and shown in Fig. 7(b). The loss of the silica glass at 1.9 μm was taken as achieved 7.5 dB/km [32]. The lowest, measured loss reported to date at 1.5 µm is 20 dB/km [32]. The predicted minimum loss of the tellurite glass is at λ = 1.9 μm [33]. Thus it is reasonable to assume the loss of the tellurite fiber at 1.9 μm is also 20 dB/km. Based on this assumption, the tellurite sphere shows maximum (Q/Vmode)max with 6.5 μm radius, ≈10 times higher than that achieved by a silica sphere with 20 μm radius due to increased silica loss, and reduced tellurite loss towards the mid-infrared. To achieve low loss (~20 dB/km) of tellurite fibers at 1.9 μm, requires the use of high purity (99.9999%) TeO2 raw materials [31]. As discussed in Section 2, due to low viscosity, it should be possible to fabricate smaller tellurite spheres (less than 5 μm diameter) using a higher intensity CO2 laser spot. Combined with its third-order high nonlinearity and high transparency in the mid-IR range, the tellurite spheres fabricated using the CO2 laser have high potential for generation of IR frequency combs with low pump threshold. They can also be used for detection of nanoparticle adsorption. 5. Conclusion The Er-Yb codoped tellurite spheres with diameters as small as 7.5 μm have been fabricated. WGMs with Q in excess of 45,000 were observed for a 9 μm tellurite sphere in methanol solution. Refractometric sensing using the 9 μm tellurite sphere was demonstrated. Our theoretical calculations show that high index tellurite spheres are better suited for the detection of nanoparticles smaller than 50 nm, while lower index silica spheres are more
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Received 1 Apr 2014; revised 28 Apr 2014; accepted 28 Apr 2014; published 9 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.011995 | OPTICS EXPRESS 12005
suitable for detection of the uniform change of the exterior refractive index and for nanoparticles larger than 50 nm. We also show that a maximum value of Q/Vmode exists for a microsphere made from any given type of material. The potential for enhanced Q factor by further reducing fiber loss and decreasing sphere size by using high power CO2 laser makes the high index microspheres a competitive platform for practical applications in nanoparticle sensing and IR frequency conversion. Acknowledgments The authors acknowledge support from Australian Research Council under DP120100901. This work was performed in part at the Optofab node of the Australian National Fabrication Facility utilizing Commonwealth and SA State Government funding. T. M. Monro acknowledges the support of an ARC Laureate Fellowship.
#208839 - $15.00 USD (C) 2014 OSA
Received 1 Apr 2014; revised 28 Apr 2014; accepted 28 Apr 2014; published 9 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.011995 | OPTICS EXPRESS 12006
Abstract: High index Er-Yb codoped tellurite spheres with diameter of 9 μm and good sphericity were fabricated using a CO2 laser. Upconversion modulated whispering gallery modes with a quality factor of 45,000 were observed in the sphere dipped in methanol. Refractometric sensing with detection sensitivity of 7.7 nm/RIU was demonstrated using a 9 μm diameter sphere. Such high index spheres have the potential to be used for nanoparticle sensing and mid-IR frequency conversion. ©2014 Optical Society of America OCIS codes: (140.4780) Optical resonators; (280.4788) Optical sensing and sensors.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
G. C. Righini, Y. Dumeige, P. Feron, M. Ferrari, G. N. Conti, and D. Ristic, “Whispering gallery mode microresonators: fundamentals and applications,” Riv. Nuovo Cim. 34, 435–488 (2011). B. Gayral, J. M. Gerard, A. Lemaitre, C. Dupuis, L. Manin, and J. L. Pelouard, “High Q wet-etched GaAs microdisks containing InAs quantum boxes,” Appl. Phys. Lett. 75(13), 1908–1910 (1999). F. Vollmer, S. Arnold, and D. Keng, “Single virus detection from the reactive shift of a whispering-gallery mode,” Proc. Natl. Acad. Sci. U.S.A. 105(52), 20701–20704 (2008). T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011). J. Ward and O. Benson, “WGM microresonators: sensing, lasing and fundamental optics with microspheres,” Laser Photonics Rev. 5(4), 553–570 (2011). C. Grivas, C. Li, P. Andreakou, P. Wang, M. Ding, G. Brambilla, L. Manna, and P. Lagoudakis, “Single-mode tunable laser emission in the single-exciton regime from colloidal nanocrystals,” Nat. Commun. 4, 2376 (2013). P. Wang, G. Senthil Murugan, T. Lee, X. Feng, Y. Semenova, Q. Wu, W. Loh, G. Brambilla, J. M. Wilkinson, and G. Farrell, “Lead silicate glass microsphere resonators with absorption-limited Q,” Appl. Phys. Lett. 98(18), 181105 (2011). J. R. Buck and H. J. Kimble, “Optimal sizes of dielectric microspheres for cavity QED with strong coupling,” Phys. Rev. A 67(3), 033806 (2003). P. Wang, T. Lee, M. Ding, A. Dhar, T. Hawkins, P. Foy, Y. Semenova, Q. Wu, J. Sahu, G. Farrell, J. Ballato, and G. Brambilla, “Germanium microsphere high-Q resonator,” Opt. Lett. 37(4), 728–730 (2012). O. Svitelskiy, Y. Li, A. Darafsheh, M. Sumetsky, D. Carnegie, E. Rafailov, and V. N. Astratov, “Fiber coupling to BaTiO3 glass microspheres in an aqueous environment,” Opt. Lett. 36(15), 2862–2864 (2011). C. Grillet, S. N. Bian, E. C. Magi, and B. J. Eggleton, “Fiber taper coupling to chalcogenide microsphere modes,” Appl. Phys. Lett. 92(17), 171109 (2008). F. Vanier, M. Rochette, and Y.-A. Peter, “Raman scattering emission in high Q factor As2S3 microspheres,” CELO 2013, CM1L.8, San Jose, USA. E. Xifré-Pérez, R. Fenollosa, and F. Meseguer, “Low order modes in microcavities based on silicon colloids,” Opt. Express 19(4), 3455–3463 (2011). M. R. Oermann, H. Ebendorff-Heidepriem, D. J. Ottaway, D. G. Lancaster, P. J. Veitch, and T. M. Monro, “Extruded microstructured fiber laser,” IEEE Photon. Lett. 24(7), 578–580 (2012). F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008). A. Berthereau, Y. Le Luyer, R. Olazcuaga, G. Le Flem, M. Couzi, L. Canioni, P. Segonds, L. Sarger, and A. Ducasse, “Nonlinear optical properties of some tellurium (IV) oxide glasses,” Mater. Res. Bull. 29(9), 933–941 (1994). J. Wu, S. Jiang, T. Qua, M. Kuwata-Gonokami, and N. Peyghambarian, “2 μm lasing from highly thulium doped tellurite glass microsphere,” Appl. Phys. Lett. 87(21), 211118 (2005). X. Peng, F. Song, M. Kuwata-Gonokami, S. Jiang, and N. Peyghambarian, “Er-doped tellurite glass microsphere laser: optical properties, coupling scheme, and lasing characteristics,” Opt. Eng. 44, 034202 (2005). S. D. Conzone, U. O. Häfeli, D. E. Day, and G. J. Ehrhardt, “Preparation and properties of radioactive rhenium glass microspheres intended for in vivo radioembolization therapy,” J. Biomed. Mater. Res. 42(4), 617–625 (1998).
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Received 1 Apr 2014; revised 28 Apr 2014; accepted 28 Apr 2014; published 9 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.011995 | OPTICS EXPRESS 11995
20. T. Kishi, T. Kumagai, T. Yano, and S. Shibata, “On-chip fabrication of air-bubble-containing Nd3 + -dopedd tellurite glass microsphere for laser emission,” AIP Adv. 2(4), 042169 (2012). 21. K. Boyd, H. Ebendorff-Heidepriem, T. M. Monro, and J. Munch, “Surface tension and viscosity measurement of optical glasses using a scanning CO2 laser,” Opt. Mater. Express 2(8), 1101–1110 (2012). 22. M. Oxborrow, “Traceable 2D finite element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microw. Theory Tech. 55(6), 1209–1218 (2007). 23. I. Teraoka, S. Arnold, and F. Vollmer, “Perturbation approach to resonance shifts of whispering-gallery modes in a dielectric microsphere as a probe of a surrounding medium,” J. Opt. Soc. Am. B 20(9), 1937–1946 (2003). 24. A. François, K. J. Rowland, and T. Monro, “Highly efficient excitation and detection of whispering gallery modes in a dye-doped microsphere using a microstructured optical fiber,” Appl. Phys. Lett. 99(14), 141111 (2011). 25. N. M. Hanumegowda, C. J. Stica, B. C. Patel, I. White, and X. Fan, “Refractometric sensors based on microsphere resonators,” Appl. Phys. Lett. 87(20), 201107 (2005). 26. A. Weller, F. C. Liu, R. Dahint, and M. Himmelhaus, “Whispering gallery mode biosensors in the low-Q limit,” Appl. Phys. B 90(3–4), 561–567 (2008). 27. T. Ioppolo, N. Das, and M. V. Ötügen, “Whispering gallery modes of microspheres in the presence of a changing surrounding medium: A new ray-tracing analysis and sensor experiment,” J. Appl. Phys. 107(10), 103105 (2010). 28. F. Vollmer and L. Yang, “Label-free detection with high-Q microcavities: a review of biosensing mechanisms for integrated devices,” Nanophotonics 1(3–4), 267–291 (2012). 29. V. R. Dantham, S. Holler, V. Kolchenko, Z. Wan, and S. Arnold, “Taking whispering gallery-mode single virus detection and sizing to the limit,” Appl. Phys. Lett. 101(4), 043704 (2012). 30. M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, “Ultimate Q of optical microsphere resonators,” Opt. Lett. 21(7), 453–455 (1996). 31. A. Mori, “Tellurite-based fibers and their applications to optical communication networks,” J. Ceram. Soc. Jpn. 116(1358), 1040–1051 (2008). 32. N. Uchida and N. Uesugi, “Infrared optical loss increase in silica fibers due to hydrogen,” J. Lightwave Technol. 4(8), 1132–1138 (1986). 33. J. S. Wang, E. M. Vogel, and E. Snitzer, “Tellurite glass: a new candidate for fiber devices,” Opt. Mater. 3(3), 187–203 (1994).
1. Introduction The quality factor Q and mode volume Vmode are useful parameters in characterizing the performance of resonators. A high Q/Vmode ratio is desirable in many resonator applications such as lasers, biochemical sensing, frequency combs, and cavity quantum electrodynamics (cavity QED) [1], and the Purcell enhancement factor for the spontaneous emission rate of atoms in a single photon source scales as (Q/Vmode) [2]. Whispering gallery modes (WGMs) supported within silica microspheres have been widely investigated for applications ranging from sensing [3] to frequency conversion [4]. They are relatively easy to fabricate by thermal flow from standard optical fibers [1]. By heating the distal tip of a silica fiber, the glass reflows to form a spherical shape under the influence of surface tension. Q factors of up to 109 have been achieved for a 750 μm diameter silica sphere enabled by the smooth surface of the sphere produced under reflow conditions, low material absorption and low ellipticity [1]. The ellipticity e is defined as e = ( a 2 − c 2 ) c 2 , where a is the equatorial radius of the sphere and c is polar radius, and cω2), was then used to further taper the region to a diameter dt2. (c) The CO2 laser cut the region of diameter dt2, and the beam was then aligned at a length x2 from the cut section using the alignment HeNe Laser. The section was then irradiated with a spot size of 2ω3 giving (d) a microsphere of diameter ds.
Figures 1(c) and 1(d) show the Er-Yb doped tellurite spheres fabricated by this setup with diameters of 36 μm and 7.5 μm, respectively. The latter is the minimum size of the tellurite spheres achieved to date using this setup (but not characterised so far). Compared to Figs. 1(a) and 1(b), it can be clearly seen that the CO2 laser setup, which relied on the fiber weight to pull the fiber taper, significantly improved the sphere sphericity and centrality of the sphere positioned on the top of the fiber stem without any bending. The ellipticity in one plane of the spheres was measured as less than 1% using direct dimension measurement. The requirement for low ellipticity is particularly important for the spheres with diameter less than 10 μm. It allows them to maintain simply degenerate modes with their total quality factor Q that is not significantly affected by the resonator shape [8], as required for sensing applications discussed below. To decrease the sphere size further, the diameter of the fiber taper needs to be decreased significantly to ≈1 μm in scale and the laser intensity required correspondingly increased. However, the laser intensity available with our current equipment was not sufficient to cleave such a small taper [21]. 3. Characterization of the tellurite spheres The surface roughness of the tellurite spheres was mapped using Atomic Force Microscopy (AFM) and the result from a sphere fabricated by CO2 laser is shown in Fig. 3(a). The average roughness of the sphere surface was found to be ~1 nm. The spheres fabricated using the “Ω” shape filament showed comparable surface roughness. The smooth surface of these spheres ensures extremely low scattering loss of the spheres. Figure 3(b) shows the experimental setup used to excite and observe the WGMs in the ErYb codoped Te spheres. A tapered SMF-28 fiber with a waist diameter of 1.5 μm was pulled by the splicer and used to couple light into the microsphere and to collect the evanescent field of the WGMs for spectra analysis. The relative positions of the taper and the sphere were monitored from the top using a microscope connected to a CCD camera. A 840 nm short pass filter was used to remove the 975 nm CW pump laser before the output light of the fiber taper was input into the spectrometer. Drops of the solvent were placed on a coverslip, located under the sphere, and spread across the coverslip. The coverslip was lifted up to allow the
#208839 - $15.00 USD (C) 2014 OSA
Received 1 Apr 2014; revised 28 Apr 2014; accepted 28 Apr 2014; published 9 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.011995 | OPTICS EXPRESS 11999
sphere to be immersed in the solvent, which changed the refractive index of the environment surrounding the sphere. a nm 10 8 6 4 2 0.9
b Spectrometer 1.0 0.7
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9.4μm sphere by CO2 laser and in methanol
Fig. 3. a. AFM image of the surface of a microsphere fabricated using a CO2 laser; b. Experimental setup to measure WGMs of the microspheres. c, d and e are WGMs modulated upconversion spectrum of the Er-Yb codoped spheres in air with 33 μm, 30 μm and 9.4 μm diameter, respectively. f is the WGM spectrum of the 9.4 μm diameter sphere dipped in methanol. The inserted resonance peak at 670.18nm displays Q of 45,000. The integration time for these fluorescence spectra was 1s. The sphere in c was fabricated using a hot filament, and those in d, e and f were made using a CO2 laser.
Figures 3(c) and 3(d) show the upconversion spectra modulated by the WGMs in the spheres with relative large size and located in air. They were fabricated using the filament and CO2 laser, respectively. It can be seen that the WGM spectra of the larger microspheres (over 30μm diameter) were complex and consists of groups of the modes. Each group includes the first and higher orders modes, which are difficult to identify. However, the gap between the two neighbouring groups is constant, and corresponds to free spectral range (FSR) of the measured sphere calculated from ΔλFSR = λ 2 2π ns R,
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(1)
Received 1 Apr 2014; revised 28 Apr 2014; accepted 28 Apr 2014; published 9 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.011995 | OPTICS EXPRESS 12000
where R is the radius of the sphere [1]. The FSR value measured from Fig. 3(c) is 1.42 nm and that in Fig. 3(d) is 1.5 nm, close to the calculated 1.46 nm and 1.58 nm, respectively by using Eq. (1). When the size of the spheres made using a CO2 laser was decreased to 9.4 μm, the WGM spectrum of the sphere became simpler as shown in Fig. 3(e) since fewer modes are allowed due to the increased curvature of the surface. Moreover, the FSR depended inversely on the diameter of the sphere, thereby further reducing the number of the modes within the emission range. When the 9.4 μm diameter sphere was dipped into the organic solvent methanol, only a limited number of low order modes were excited as shown in Fig. 3(f) with most of the higher order modes quenched due to high loss caused by the reduced refractive index contrast between this microsphere and methanol (na = 1.3284) compared to air (na = 1.0). From the resolved modes, the measured Q values at the red upconversion wavelengths for these spheres were up to of 45,000 with variations dependent on the sphere quality (shown at the inset of Fig. 3(f)). It was challenging to align the silica taper to the equatorial plane of the small spheres (around 20 μm diameter) with bent fiber stem fabricated by the filament. This was because the fiber taper in our setup easily slid away from these spheres, particularly in the liquid environment. With straight fiber stems on the spheres fabricated by the CO2 laser, this was not an issue. Thus a 9 μm tellurite sphere made by the CO2 laser was investigated for sensing demonstration described in the following section. 3.1 Resonance shift with changed refractive index contrast To assess potential applications of the high index tellurite spheres for refractometric sensing, the resonance shift of the WGMs as a function of changes in the refractive index na of the surrounding medium of the microspheres was studied for the 9 μm diameter sphere. Three organic solvents with different refractive indices at 580 nm were used: methanol (na = 1.3284), acetone (na = 1.3586) and isopropanol (IPA) (na = 1.3772). Figure 4(a) shows the WGM spectrum of the 9 μm sphere dipped into IPA and methanol, respectively. It can be seen that the mode peaks of the sphere dipped in IPA are shifted towards long wavelength due to reduced refractive index contrast between the sphere and its environment. The wavelength shifts in the two neighboring modes are clearly different, for example, δλTM = 0.55 nm > δλTE = 0.33 nm as shown in Fig. 4(a).
Fig. 4. Resonance shift of the Er-Yb doped spheres in solvents. a. the spectrum of the 9 μm spheres in IPA and methanol, respectively. The mode order numbers are assigned by numerical calculation using the code provided by Oxborrow [22]. b. dependence of the resonance shift δλ on refractive index change δn for the 9 μm tellurite sphere. The solid line is calculated wavelength shift δλ, and the separate points are measured values.
In order to understand these experimental results, we used a 2D finite element method to simulate the modes in COMSOL with the code provided by Oxborrow [22]. Through this code, the peak wavelength of each mode and their corresponding mode order number can be found. Thus the numbers of the first order TE/TM modes are assigned in Fig. 4(a), and
#208839 - $15.00 USD (C) 2014 OSA
Received 1 Apr 2014; revised 28 Apr 2014; accepted 28 Apr 2014; published 9 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.011995 | OPTICS EXPRESS 12001
correspond to those modes with high peak intensity. It can be seen that the shift of the TM mode δλTM (0.55 nm) was bigger than δλTE (0.33 nm) of the TE mode. Arnold et al in Ref [23] presented a first order perturbation approach to calculate the resonance shift caused by a uniform change in the refractive index of the environmental medium by using the perturbed Schroedinger equation. They found that the ratio of the TM shift to the TE shift is greater than unity for the first order modes. Therefore our measurement was consistent with their prediction. The FSR, ΔλFSR, of the two neighboring TM modes was 4.4 nm. The diameter 2R of the sphere calculated from Eq. (1) using the measured ΔλFSR was 9.7 μm, which is close to 9 μm measured using optical microscopy. Figure 4(b) shows the dependence of the resonance shifts (as shown by three points) on the change of the refractive index δn of the surrounding medium for the first order TM mode at λ = 523.5 nm. The mode exhibited detection sensitivity of 7.7 nm/RIU (refractive index unit), compared to 45 nm/RIU sensitivity achieved by others using a dye-doped polystyrene sphere with 10 μm diameter [24]. This difference was attributed to the much higher refractive index of the tellurite glass than that of the polystyrene (ns = 1.59), which results in tighter mode confinement in the high index material, and thus less light available to interact with the environment external to the sphere. The theoretical resonance shift of the 9 μm tellurite sphere was also calculated by using the formula in Ref [25]:
δλ = −
na ζ 2ns 6 + na 2 ns 4 − 4na 4 ns 2 + 2na 6 −2/3 λ2 (2ns 2 − na 2 ) − 1/3l υ , (2) 2 2 2 3/2 2π a ns ( ns − na ) 2 ns 2 ( ns 2 − na 2 )
1 , ζ l denotes the lth zero of the airy function, which is −2.338 for the first 2 order mode and l is the order number of the first order modes labelled in Fig. 4(a). The results are shown as a solid line in Fig. 4(b). It can be seen that our measurements are in good agreement with the calculated values.
where υ = n +
4. Discussions Since spheres with low mode volume are desirable in many practical applications, the impact of the size and refractive index of the spheres on their performance and application are investigated here by theoretical calculations and compared to our measurements. 4.1 Dependence of sensitivity on microsphere size By calculating the wavelength shift δλ/λ of a WGM caused by environmental index change, we can understand how the refractive index of the sphere affects its detection sensitivity for the following two distinct cases: (A) a uniform change in refractive index of the surrounding medium, and (B) a single nanoparticle attached to the sphere surface.
Fig. 5. Predicted sensitivity of the refractometric sensing for the first order TM modes of the microspheres made from tellurite, silica and polystyrene for different sphere radii. The excitation wavelength is 606 nm except the red point at 523.5 nm for the tellurite sphere.
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Received 1 Apr 2014; revised 28 Apr 2014; accepted 28 Apr 2014; published 9 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.011995 | OPTICS EXPRESS 12002
A. Uniform change in refractive index of the surrounding medium The shift δλ/λ of the WGM resonance that occurs due to a small change in the refractive index in the surrounding medium is proportional to the energy of the evanescent field in this medium [23] and dependent on sphere material and excitation wavelength. Figure 5(a) shows the calculated sensitivity of silica and tellurite microspheres as a function of sphere size using Eq. (1) in Section 3. Only the first order TM modes are assumed to be excited and the refractive index na of the surrounding medium used is 1.33. The excitation wavelength is set to 606 nm to enable direct comparison of calculated sensitivity of the 5 μm radius polystyrene sphere to the experimental measurement (black point as shown above the black curve in Fig. 5) from Ref [24]. The low index silica spheres show higher sensitivity than the same size tellurite spheres, and the sensitivity increases exponentially with reduced sphere size. However, when the sphere size becomes smaller, the broadening of their WGMs presents a practical limit for WGM shift detection. As a reasonable trade-off, a sphere with overall quality factor Q of 500 with 1.2 nm linewidth is regarded as the smallest cavity that can be used for practical applications [26]. Q is determined by several mechanisms and can be calculated by adding the different significant contributions, Q−1 = Qrad−1 + Qmat−1, where Qrad−1 is due to purely radiative loss and Qmat−1 results from non-ideal material properties. Since our tellurite spheres have negligible ellipticity, the effect of the sphere shape is not included here. A ray-tracing approach is used to calculate the Qrad values of the first order TM modes of the spheres dipped in the solution [27]. Our calculation shows the tellurite sphere with 1.2 μm radius and the silica sphere with 12.5 μm radius can achieve a Q ~500, and can be the smallest spheres for the sensing applications in aqueous environment. Our calculations show the experimentally measured Q values of the spheres are two to threeorders of magnitude lower than the calculated values. There are two possible reasons for this discrepancy. One reason is the experimental uncertainties based on limited measurements from only three tellurite spheres with different diameter are sufficiently incomplete. Another possible reason could be the ray-tracing approach as it now stands is incomplete or inadequately describes the experiments. Therefore, the practically feasible minimum size which can be used for sensing needs to be experimentally determined in future. b
aa
a
Fig. 6. Calculated wavelength shift δλ (solid lines) as a function of the radii of the spheres for single nanoparticles adsorbed on the surface of the spheres made from (a) tellurite and (b) silica glass. The green dashed lines are the detection limits when a tunable DFB laser and a low noise detector are used for characterisation, and the dark violet dash-dot lines are the RMS noise. The radii of the single nanoparticles are labeled next to their corresponding shift curves on the right hand side. The excitation wavelength is 633 nm unless otherwise stated in the figures.
B. Nanoparticle detection Considering a single nanoparticle with radius a and refractive index np, the δλ/λ of the WGMs of a microsphere caused by adsorption of this nanoparticle depends on the location of the particle’s binding site on the sphere surface. For an equatorial binding event at a site where
#208839 - $15.00 USD (C) 2014 OSA
Received 1 Apr 2014; revised 28 Apr 2014; accepted 28 Apr 2014; published 9 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.011995 | OPTICS EXPRESS 12003
the evanescent field intensity is maximum, the δλ/λ is calculated from the following formula [3]:
δλ / λ ≅ Da 3e − a L / ( R 5 2 ⋅ λ 1 2 ),
(3)
D = 2na 2 ⋅ 2ns ( nnp 2 − na 2 ) / ( ns 2 − na 2 )( nnp 2 + 2na 2 ),
(4)
with na and ns are refractive index of the surrounding medium and sphere material, respectively, L ≈ (λ 4π ) ⋅ ns 2 − na 2 is the evanescent field penetration distance. The δλ/λ is clearly seen to be proportional to R-2/5 and is also strongly dependent on a and L, the latter being determined by the index contrast of the sphere and its surrounding medium. The solid lines in Figs. 6(a) and 6(b) show the calculated shift δλ of the first order TM modes caused by a nanoparticle (np = 1.5) absorbed onto the equator of the tellurite and silica spheres, respectively, as a function of sphere radius at λ = 633nm. The wavelength shift δλ increases with decreasing sphere radii, and increasing nanoparticle size. In practice, the smallest detectable wavelength shift (detection limit) δλmin is determined by noise sources such as thermo-refractive noise, and can be calculated by the formula δλmin/λ = F/Q, where the figure of merit F is typically 1/50-1/100 [28]. The green dashed lines in Figs. 6(a) and 6(b) show the detection limit δλmin calculated by choosing F = 1/100 and the Q of the spheres located in the aqueous solution. The dark violet dash-dot lines are the RMS background noise level of 2 fm when a tunable DFB laser and a low noise detector are used for excitation and signal detection [29]. Thus only when the shift δλ caused by a single nanoparticle adsorption is bigger than δλmin and 2 fm, is this shift detectable. From Fig. 6(a), it can be seen that the tellurite spheres with radius ≥ 2.3 μm can detect a nanoparticle with a radius larger than 5 nm. The silica spheres can detect nanoparticles larger than 20 nm, and the minimum size of the silica sphere required to achieve this needs to bigger than 25 μm. The black point in Fig. 6(b) is the calculated detection limit using the practically measured Q value for a 39 μm radius silica sphere at λ = 763 nm [3], which is overlapped with the shift line of the 50 nm nanoparticle. This means the 39 μm radius silica sphere is predicted to be able to detect a nanoparticle with radius ≥ 50 nm and refractive index np = 1.5. This was confirmed by the authors in Ref [3], which have used this sphere to successfully detect a single InfA virion with a 50 nm radius. This is the smallest nanoparticle reported to be detected by silica spheres. From Fig. 6(b) we can expect that a 39 μm radius silica sphere can detect nanoparticles with radii bigger than 30 nm at λ = 633 nm. The reason that only the 50 nm nanoparticle was detectable at λ = 763 nm by this sphere is due to the practically achieved Q being significantly smaller than the theoretical Q mentioned previously. As discussed above the smallest shift and thus the size of the nanoparticle that a sphere can detect is strongly dependent on the Q value of the sphere. The red point in Fig. 6(a) indicates a detection limit of 40 nm calculated for a 4.5 μm radius Er-Yb tellurite sphere based on its Q value measured when this sphere was dipped in methanol. As we discussed earlier in this section, the pure tellurite sphere could have one order magnitude higher Q with reduced glass loss, thus the same size sphere (4.5 μm radius) of the pure tellurite glass made in-house should permit detection of single nanoparticles as small as 15 nm. Therefore, the high index tellurite spheres have advantage to detect small label-free bionanoparticles such as virus and proteins with their size less than 50 nm compared to low index silica spheres. 4.2 High Q/Vmode for cavity QED, enhancement of spontaneous emission and lasing To explore the dependence of Q/Vmode on sphere size for these specific applications, we calculated Q/Vmode for the tellurite spheres in air at λ = 633 nm. Lorenz-Mie theory [8] is used to calculate Q values of the spheres located in air as these applications usually require, which are more close to the experimental values [1] compared those calculated by the ray-tracing approach for the spheres in the solutions [27]. The mode volumes of the spheres were numerically calculated using two 2D finite element simulations [22]. The Q/Vmode values for
#208839 - $15.00 USD (C) 2014 OSA
Received 1 Apr 2014; revised 28 Apr 2014; accepted 28 Apr 2014; published 9 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.011995 | OPTICS EXPRESS 12004
L og ( Q / V m o d e )
L og ( Q / V m o d e )
the silica spheres were also calculated for comparison with their absorption coefficient at 633 nm as 1.5 × 10−4 m −1 [30] and the results are shown in Fig. 7(a). For larger spheres when the material loss is dominant, the Q/Vmode increases with decreasing sphere radius since Q is relatively constant. The Q/Vmode increases with decreasing sphere radius until a critical value of the radius where radiation losses of the sphere become dominant. The Q/Vmode then drops quickly with further decreased sphere size due to increased radiation loss in this region. Thus there exists an optimum radius for a given type of material to achieve the maximum Q/Vmode. This optimum sphere size is 1.75 μm for tellurite spheres and 5.5 μm for silica spheres. With the current loss (0.5 dB/m at 633 nm) achieved in-house for tellurite glass, the tellurite microsphere shows similar Q/Vmode to that of the silica glass microspheres at 633 nm. Assuming the loss of the tellurite glass can be reduced by a factor of 10, which has been achieved by Mori group [31], the tellurite microspheres then show a potential for 2-3 times higher maximum Q/Vmode than the silica microspheres.
Fig. 7. Q Vmode for tellurite and silica microspheres at different wavelengths: (a). 633 nm and (b). 1.9 μm. The losses of the silica glasses used for calculation are the measured values. The losses of tellurite glasses used for calculation in (a) include the currently achieved 0.5 dB/m in-house (solid line) and assumed 10 times improvement in loss (dashed line, achieved by Mori group [31]); in (b) 20 dB/km are assumed at λ = 1.9 μm.
The Q/Vmode of the tellurite and silica spheres is also calculated at the infrared wavelength λ = 1.9 μm and shown in Fig. 7(b). The loss of the silica glass at 1.9 μm was taken as achieved 7.5 dB/km [32]. The lowest, measured loss reported to date at 1.5 µm is 20 dB/km [32]. The predicted minimum loss of the tellurite glass is at λ = 1.9 μm [33]. Thus it is reasonable to assume the loss of the tellurite fiber at 1.9 μm is also 20 dB/km. Based on this assumption, the tellurite sphere shows maximum (Q/Vmode)max with 6.5 μm radius, ≈10 times higher than that achieved by a silica sphere with 20 μm radius due to increased silica loss, and reduced tellurite loss towards the mid-infrared. To achieve low loss (~20 dB/km) of tellurite fibers at 1.9 μm, requires the use of high purity (99.9999%) TeO2 raw materials [31]. As discussed in Section 2, due to low viscosity, it should be possible to fabricate smaller tellurite spheres (less than 5 μm diameter) using a higher intensity CO2 laser spot. Combined with its third-order high nonlinearity and high transparency in the mid-IR range, the tellurite spheres fabricated using the CO2 laser have high potential for generation of IR frequency combs with low pump threshold. They can also be used for detection of nanoparticle adsorption. 5. Conclusion The Er-Yb codoped tellurite spheres with diameters as small as 7.5 μm have been fabricated. WGMs with Q in excess of 45,000 were observed for a 9 μm tellurite sphere in methanol solution. Refractometric sensing using the 9 μm tellurite sphere was demonstrated. Our theoretical calculations show that high index tellurite spheres are better suited for the detection of nanoparticles smaller than 50 nm, while lower index silica spheres are more
#208839 - $15.00 USD (C) 2014 OSA
Received 1 Apr 2014; revised 28 Apr 2014; accepted 28 Apr 2014; published 9 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.011995 | OPTICS EXPRESS 12005
suitable for detection of the uniform change of the exterior refractive index and for nanoparticles larger than 50 nm. We also show that a maximum value of Q/Vmode exists for a microsphere made from any given type of material. The potential for enhanced Q factor by further reducing fiber loss and decreasing sphere size by using high power CO2 laser makes the high index microspheres a competitive platform for practical applications in nanoparticle sensing and IR frequency conversion. Acknowledgments The authors acknowledge support from Australian Research Council under DP120100901. This work was performed in part at the Optofab node of the Australian National Fabrication Facility utilizing Commonwealth and SA State Government funding. T. M. Monro acknowledges the support of an ARC Laureate Fellowship.
#208839 - $15.00 USD (C) 2014 OSA
Received 1 Apr 2014; revised 28 Apr 2014; accepted 28 Apr 2014; published 9 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.011995 | OPTICS EXPRESS 12006
