Micro-resonators have attracted considerable attention as a potential geometry for photonic devices used in multiplexing, memory and switching. These all-optical-resonators allow light at certain wavelengths to build up in intensity allowing nonlinear effects to be seen for much lower input power than in a bulk material. We report here on microspheres made from gallium-lanthanum-sulphide glass. Spheres have been produced with diameters from less than 1 µm up to 450µm, and we demonstrate a first measured quality factor of 8x104 at 1.55µm, for a chalcogenide sphere diameter of 100µm. We also predict an ultimate Q of up to 4x1010 at 3µm.
©2007 Optical Society of America
Although the concept of integrated optical devices using circular micro-resonators was first proposed in 1969 , electrons rather than photons have dominated research and development of integrated circuits. However, in recent years, all-optical networks have become the norm in long distance telecommunications, and there is increasing interest in trying to replace electrical components with their optical counterpart. Resonators are of particular interest for the design of optical components and systems, because of their ability to transmit very specific wavelengths of light and also because the intensity of light inside a resonator can be orders of magnitude higher than the incoming light. These properties could be potentially useful in a number of optical components. Micro resonators have been proposed for the production of a variety of optical components. These include, but are not limited to; logic switches, routing switches (add drop multiplexing) and lasers. The fact that light will propagate through a suitably small resonator at only very specific wavelengths, is a key factor in its exploitation. For example, if broadband light travels through a waveguide next to a resonator, it will couple to the resonator through its evanescent field and a specific wavelength or wavelengths will resonate, while the rest of the broadband light in the waveguide will be unaffected. If the resonator is coupled to a second waveguide, then the resonating light can be coupled out. The same process works in reverse producing an add drop multiplexer or wavelength switch [1–5].
If the resonator is made of a non-linear material, a logic switch can be produced [6–8]. Through nonlinear effects, the refractive index can be changed by the intensity of light in the resonator. This changing refractive index will cause the resonant wavelength to vary, which can then in turn be used to switch a signal on or off, or tune the resonance for use at a specific wavelength.
The natural resonant properties of circular resonators can be utilized as a laser cavity  if the resonator incorporates a gain medium. This eliminates the need for providing the feedback mechanism of the laser cavity with mirrors, because the cavity is inherently resonant. Furthermore, micro-resonator lasers can be used to produce memory devices , by utilizing the difference between the clockwise and anticlockwise modes of circular resonance.
All of these are highly useful applications. However it is quite probable that there are many other useful applications may not yet have been considered. Therefore the study of resonators potentially carries considerable reward.
In this paper evidence is presented of the first chalcogenide microspheres, the quality (Q) values that have currently been measured and the Q-factor that these microspheres could potentially achieve.
Glasses which incorporate any of the chalcogen group of elements (e.g. sulphur) are known as the chalcogenides. These glasses are noted for having high refractive indices and corresponding highly nonlinear properties, and could therefore be used in all-opticalswitching. Their range of transmission reaches from the visible, well into the infrared, beyond the transmission range of more conventional oxide glasses . Some chalcogenides can be readily doped with rare earth elements, making them useful for active optical devices, such as amplifiers and lasers .
This paper focuses on gallium lanthanum sulphide (GLS)/gallium lanthanum sulphide oxide (GLSO) glasses, which are non-toxic (unlike many chalcogenides that contain arsenic), have a high melting temperature and many other useful properties . The refractive index of GLS/GLSO is between 2.2 and 2.4  depending on the composition and through Miller’s Law a high nonlinear index is expected and has been experimentally validated [15,16] This high nonlinearity is in part a motivating factor for the production of high Q GLS/GLSO micro-resonators.
2. Theory of chalcogenide micro-resonators
In this section we begin with the basic theory of circular micro-resonators and chalcogenide glass, and present calculations which show the potential of chalcogenide micro-resonators. In a circular body, it is possible for light to propagate in a mode of continuous near total internal reflection, such that the light effectively travels round the perimeter of the circle. When light propagates in this fashion, it is said to exist in a whispering gallery mode (WGM). Whispering gallery modes occur when the effective circumference of the sphere is equal to an integer multiple of wavelengths, allowing the propagating fields to build up constructively. For spheres which are large compared with the wavelength, the effective circumference of the fundamental WGM is close to the physical circumference of the sphere. The resonant interference pattern is shown in Fig. 1, which theoretically describes the intensity dependence of the light within a cavity as a function of wavelength. The more times the light travels round the resonator, the narrower the bandwidth of each spectral peak will become. If one considers the light to be traveling along a one dimensional line that has been curved round to form a ring inside the sphere, then the interference pattern is described by the Airy function;
where k is the wave vector, p is the perimeter of the ring, n is refractive index and F is the coefficient of finesse  defined as
and L is the fractional loss of half one round trip of the ring.
The free spectral range (FSR) is the distance from one peak to the next (Fig. 1) and is governed by the wavelength and the diameter of the ring. The Q-factor is a measure of mode damping in a resonator. A value for the Q of a resonator can be obtained by measuring the full width half maximum (FWHM=Δλ) of each transmission peak as shown in Fig. 1 and comparing it to the resonant wavelength .
The intrinsic quality factor of a resonator is limited by three main factors, the radiation loss due to curved nature of the resonator (Qcurv), the surface scattering (Qsurf), and the internal or material losses (Qmat) this term will include the Rayleigh scattering, electronic absorption and multiphonon absorption. In addition to these three factors, the observed Q will be influenced by interaction with the coupler (Qcoupl). These terms are related as below [18, 19].
Examining the contributions we note that if the diameter of the resonator is sufficiently large then losses due to curvature will be small . The surface quality can be controlled by the production and the impact from this should become minimized with improvements in technique. Therefore as discussed in  for a sufficiently large sphere it may be possible to reach the ultimate limit where only the material loss limit the value of Q.
where n is the refractive index and α is the linear loss or absorption coefficient.
The attenuation of a material can be reduced by purification of the glass, controlling contamination during the melting process and processing the spheres in a clean dry environment. With control of these extrinsic impurities, there comes a point when an ultimate limit for attenuation is reached. This limit is a combination of electronic absorption, multiphonon absorption and Rayleigh scattering. The point at which this ultimate limit on attenuation occurs has been examined in detail for gallium lanthanum sulphide based glasses (GLS/GLSO)  and this data can be used to predict an ultimate Q for GLS and GLSO spheres.
With Eq. (5) and the minimum attenuation data for GLS/GLSO  we can predict a maximum Q value of over 4x1010 possible in GLSO at 3µm and 109 at 1µm (see Fig. 2). The values quoted here for GLS/GLSO are for specific compositions in , but these are typical of GLS/GLSO in general.
In a micro-resonator such values of Q would represent significant enhancement of the circulating intensity, which would in turn significantly reduce the input power needed to observe nonlinear effects.
The minimum attenuation data given in  are calculated values, while these low values of attenuation are theoretically possible, they relate to a glass quality that has not been achieved. The current state of the art for minimum attenuation measured in GLS/GLSO glass fibers is detailed in . The values are lower than that achieved in bulk glass, however optical fiber drawn from bulk glass preforms are processed in an environment and manner not dissimilar to our sphere fabrication methods and are therefore more representative of the true Q which could be experimentally achieved. Using this data to calculate a theoretical maximum Q gives a value of 1.6x107 at 1µm. Later we will discuss Q values taken from measured spectra of microspheres that have been produced as part of this work.
The nature of the measured spectra makes it favorable to identify families of peaks in order to understand the mode structure. A family of peaks is a set of peaks that can be described by a single Airy function. From this the free spectral range can be measured.
If one considers the light in a given mode to be traveling around a ring inside the sphere then it is possible to fit an Airy function to the data. To do this four numbers are required; λp the wavelength at which a peak occurs, N the number of wavelengths that fit into one round trip at wavelength λp, Q and relative intensity. All values are arrived at from an initial estimate via an iterative process, λp and N combine to give the peak position, Q gives the shape of the peak and the relative intensity gives the height.
From the definition of free spectral range for a thin ring;
Where λp and λ p-1 are the wavelengths of two consecutive peaks and N is the number of wavelengths fitting into the ring at λp. Once a family of peaks has been identified the values of wavelength are extracted from the data, a value of N can be calculated. N and λp are the only values that determine the position of the peaks.
From Eq. (5) Q can be given as
Where k is the wave vector, p is the perimeter of the ring, n is refractive index and L is loss of half one round trip of the ring. Using the definition of the wave vector and the condition for constructive interference in a thin ring one arrives at,
Note that λp will be a constant while λ will be a variable. If λp≈λ then
This can then be used to match the data. A multiplication factor is applied to take account of the relative intensity of different families of peaks.
3. Experimental Method
Microspheres can be made by a number of methods, these include polishing, chemical etching and rapid quenching of liquid droplets. Individual microspheres can also be formed by melting the tip of an optical fiber  and allowing surface tension to pull the molten glass into a sphere, which remains attached to the fiber. However this approach means that only one microsphere can be produced at a time and the size is determined by the fiber size. Microspheres made in this way from optical fibers will have an additional heating step in the production process, compared to microspheres produced directly from bulk glass. Therefore, this introduces another point at which contamination can occur, for these reasons the chalcogenide microspheres reported here, are made from crushed bulk glass in a single step.
The method of microsphere production used here was to drop crushed glass through a vertical furnace purged with an inert gas, typically argon. Early trials were performed on an optical fiber drawing tower, which provided proof of principle after which a dedicated vertical furnace, with a longer hot zone and more precise gas flow was utilized. In the fabrication process, the crushed glass melts as it drops through the furnace, surface tension pulls it into a sphere which quenches into an amorphous state as it drops to the cooler region below the hot zone.
Two glass compositions were considered in this study Ga:La:S, composed of Ga2S3 and La2S3, with a few percent of La2O3 added to improve the glass formation, and the Ga:La:S:O, where La2S3 content is entirely substituted by La2O3. Sulphide precursors are not commercially available with the necessary purity, thus they were synthesized in house from high purity precursors. Batches of powders were thoroughly mixed and loaded in a silicalined furnace; glass melting was performed inside vitreous carbon crucibles at 1150°C; melts were quenched to room temperature and subsequently annealed at 20°C below their respective glass transition temperatures (Tg). Trace level analysis of transition metal impurities was performed by glow discharge mass spectroscopy (GDMS): Fe was the main impurity (0.8ppm), whereas other elements such as Cr, Ni, Ti were all lower than 0.1ppm.
Due to the reactive nature of molten chalcogenide glass melting must take place in an inert atmosphere. If GLS is melted in an air atmosphere it will react with the oxygen and water in the air, which will produce a poor surface and increase attenuation . Therefore chalcogenide microspheres are produced in a continually purged inert atmosphere.
Bulk glass synthesized as above was crushed to a suitable size and uniformity before microsphere production. The glass was crushed with a pestle and mortar, and sieved to achieve glass particles of the required size.
In order to assert control over the size of microspheres produced, crushed particles are separated according to size before they are put into the furnace. It has been found that small particles of GLS are strongly attracted to surfaces and each other, however when placed in solvent (isopropanol or methanol) this problem is over come. Large particles can be separated by sieving, but for small particles sieving was found to be impractical. As an alternative, a process of sedimentation has been used, taking advantage of the slow terminal velocity of small particles in liquids. Our best results were obtaining using a method of particle separation which combines sedimentation and sieving. The smallest particles are separated by sedimentation, the larger particles of crushed glass can then be sieved.
The terminal velocity of small particles also has an influence in the sphere formation process within the furnace. Due to the chimney effect associated with having a tube running vertically through a furnace it is necessary to have the inert gas running vertically upwards in order to avoid turbulence. However according to Stoke’s law small particles will be buoyant in this gas flow. Therefore to make the smallest spheres it is necessary to introduce the GLS with the gas at the bottom of the tube and collect at the top.
The material that has passed through the furnace will typically contain a mixture of particles that have melted into spheres and particles that have not (see Fig. 3). This material can be separated according to the quality of the spheres by repeatedly rolling the material down progressively shallower slopes. This was achieved by placing the spheres in a glass container such as a Petri dish, tilting the container and allowing the spheres to roll. Each time the material is rolled down a slope, the non-spherical material will be left behind, the steepness of the slope will determine how precisely spherical the particle has to be in order to roll down the slope. The GLS particles stick to the dry glass surface therefore they were immersed in isopropanol to insure that the spheres are able to roll freely.
As described in the previous section the quality of resonators such as microspheres is quantified by the Q-factor. The experimental apparatus used to observe the WGMs is shown in Fig. 4. A sphere of 100µm diameter, produced by the method previously explained was attached to a fibre taper with UV curable resin (with a refractive index of 1.42) so that its position could be controlled across the waveguide. The taper was made from standard telecoms fibre and its only purpose was as a positioning device.
An ion-exchanged channel waveguide in BK-7 glass, monomode at 1550nm and with a substrate index of 1.50 and a peak core index of 1.52, was used to evanescently couple the light into a microsphere. The microsphere was placed on top of the waveguide with the aid of the positioning fibre and the position of the sphere was observed from the side and top using microscopes equipped with CCD cameras. The top microscope also housed an InGaAs detector to measure the scattered power directly. WGMs were excited using a narrow-line tunable laser source (1440–1640nm) at 8dBm, coupled into the waveguide with TM polarization using a polarization maintaining single mode fibre. The throughput of the waveguide was measured with another InGaAs detector. The sphere was placed in contact with the substrate and moved horizontally along the surface perpendicular to the waveguide to achieve the required separation between sphere and waveguide.
4. Results and Discussion
The method of blowing small particles into the furnace has successfully produced a range of sphere sizes down to approximately 1µm in diameter (see Fig. 3). The failure to confirm spheres of a smaller size than this owes more to the equipment used to analyze the samples rather than a lack of spheres themselves. At the other end of the scale spheres have been produced up to 450µm in diameter (see Fig. 5).
This maximum size is limited by the experimental apparatus. According to Stoke’s law, as the diameter of particle increases, its terminal velocity will increase according to its diameter squared. Therefore, to melt larger particles of crushed glass, a longer hot zone is required.
The separation of spherical particles from non-spherical particles by the rolling method described earlier has been demonstrated (see Fig. 6). Some spherical particles have become trapped by the non-spherical particles, but the spheres that have been successfully rolled can be shown to be spherical.
The spheres shown in Fig. 6, were on the order of 100µm in diameter and fabricated from GLSO glass. From these a representative sphere was selected for the Q measurement. The sphere was selected by hand using an optical microscope, therefore no quantitative assessment of surface quality or impurities was made prior to the Q measurement. It is likely that from amongst all the suitable spheres, a range of Q values would be achieved and such a study is part of our ongoing work.
Spectra were taken with the apparatus in Fig. 4, the sphere was held in two different positions, a strongly coupled position where the sphere was placed directly on top of the waveguide and a weaker coupled position, where the sphere was moved to one side of the waveguide to increase coupling distance and therefore reduce evanescent coupling. Due to the attractive forces between the sphere and the substrate/waveguide surface it was not possible to accurately position the sphere away from the surface, therefore it was moved across the surface away from the waveguide in order to achieve the required coupling.
A set of Airy functions have been fitted to the spectra (Fig. 7, Fig. 8) by the method described earlier in order to clarify the mode ‘family’ structure. The data that makes up the calculated curve are tabulated in the Table 1 and Table 2, and from this data, a diameter is calculated for each Airy function. The Airy function diameter is a result of only the measured values of N and lambda. The Q factor works in conjunction with the relative intensity of the families and the Vernier effect between them to define the shape of the calculated spectra. It was found that an accuracy of more than one significant figure in Q was unnecessary as small variation in any of the other parameters would dominate over this small variation in Q.
The periodic nature of the spectra is visible, although the number of peaks corresponding to several of the possible whispering gallery modes does complicate the picture. The weaker coupled spectrum (Fig. 7) has narrower peaks, implying higher Q values than the same sphere in the stronger coupled position (Fig. 8). This is because the component of Eq. 4 due to coupling (Qcoup) is dominating the observed Q. Light will also be coupled into the substrate, as the sphere remains in contact with the surface, as mentioned earlier.
The Airy functions approximate the path of light as a one dimensional loop. This will not be the case in a sphere, but it is a reasonable first approximation as all fitted peaks coincide with their fitted counterparts to within experimental tolerances of 0.25nm. Here N is an approximation of the azimuthal mode number, however the Airy function takes no account of the shape of the sphere or other mode numbers. This leads to several modes having the same azimuthal mode number and slightly different values of diameter (Table 1, Table 2). In reality these modes could differ in either the radial or angular direction, but in this model that difference is only absorbed into the diameter of the ring. The Airy function diameter must vary in order to take account of the position and free spectral range of the families of peaks.
The highest order modes will be those with the largest radius, with a reduction in radius representing a reduction in mode order.
The actual diameter of the spheres as measured by the microscope is within the bounds of accuracy of the Airy function diameters, this is to be expected as the modes will be circulating close to the surface of the sphere. The different modes will have a Q associated them individually, this relates to the various causes of degradation interacting with them differently. For example the high order modes will be closest to the surface will therefore scatter from the surface more strongly.
The highest value of Q used in the fit of Fig. 7 was 8x104. This is several orders of magnitude lower than the ultimate value of 7x109 at 1.55µm which does not take into account material loss and surface scattering introduced during fabrication. It has been observed through scanning electron microscope images that some surface roughness exists on these spheres, this will degrade the potential Q of the sphere. It will be further degraded by the resin and tapered fibre on its surface which will cause scattering. Moreover, the glass used was not of the high standard used in optical fiber production, where the utmost purity is required. It is therefore likely that incremental improvements to all aspects of this experimental work will be mirrored by improved of the measured Q.
It would also be preferred that evaluation of the Q factor takes place using spheres that have been produced minutes or hours earlier, as has been the case in studies made on spheres in other materials . However in this study this was not practical and the spheres were produced weeks or months before their Q values were measured. In this time they were stored in solvent to prevent contamination from the air, but it is still likely that some degradation will have occurred.
Finally it is possible that there will is a significant mode mismatch between the BK-7 waveguide used in Q measurements and the sphere. The exact extent of this is not known as the effect of the sphere production process on the refractive index is not known. It is likely that some elements in the glass will have partially evaporated while molten, thus altering the refractive index.
Production of GLS microspheres over a considerable range of sizes has been demonstrated. Whispering gallery modes have been observed and the peak value of Q was found to be 8x104 at 1.55µm. It has been shown that it is theoretically possible to achieve a Q up to three orders of magnitude higher, at a wavelength of 1µm, with GLSO glass that has previously been produced. It has also been shown that with improvements in the quality of bulk glass it would be possible to produce spheres with a Q over 4x1010 at 3µm and 109 at 1µm. There exist flaws in the production process of GLS/GLSO microspheres and these would need to be addressed before such high Q values could be achieved.
Separation of particles according to size and spherical quality has been demonstrated. These techniques have not yet been explored to their natural limits and it is likely they would work for a larger range of sizes than has been shown here.
The combination of the high Q presented here and high nonlinearity known to exist in GLS/GLSO make production of an all optical chalcogenide switch using microspheres a very real possibility.
The authors would like to thank Yuwapat Panitchob, Mikhail Zervas, Elizabeth Tull and Phil Bartlett for helpful discussions; and Kenton Knight, Fei Xu, Andrew Webb and Edwin Wetherby for technical support.
Gregor Elliott would like to thank EPSRC for a PhD studentship. All authors acknowledge EPSRC for funding this work through GR/S96500/01 Integrated Microsphere Planar Lightwave Circuits and in part by EP/C515668/1 Portfolio Partnership in Photonics.
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