Integrated microsphere arrays: light focusing and propagation effects

Arash Darafsheha, Matthew D. Kerra, Kenneth W. Allena, Nathaniel M. Frieda, Andrew N. Antoszykb, Howard S. Yingc, and Vasily N. Astratov*a

aDepartment of Physics and Optical Science, University of North Carolina at Charlotte, 9201

University City Boulevard, Charlotte, North Carolina 28223-0001, USA; bUniformed Services University of the Health Sciences (USUHS), 4301 Jones Bridge Road,

Bethesda, Maryland 20814, Retina Service, Charlotte Eye Ear Nose and Throat Associates, P.A. 6035 Fairview Road, Charlotte, North Carolina 28210;

cWilmer Eye Institute, Johns Hopkins University, 600 N. Wolfe Street, Maumenee 723, Baltimore, Maryland 21287-9277, USA

ABSTRACT

Integration of microspheres inside micro-capillaries or hollow waveguides may allow development of compact focusing tools for a variety of biomedical and photonics applications. However, problems associated with developing focusing microprobes involve the multimodal structure of noncollimated beams delivered by fibers and waveguides. By using numerical ray tracing, it is shown that serial spherical microlenses filter out spatially periodic modes which can be used for obtaining tightly focused beams. Experimental studies are performed for spheres with sizes from 10 to 300 µm with different indices of refraction ranging from 1.47 to 1.9. The chains were assembled inside plastic tubing with bore sizes matching the size of the spheres. By using high index spheres, it is demonstrated that these structures are capable of focusing light in contact with tissue. The beam attenuation properties of such chains are found to be in good agreement with numerical modeling results. Potential applications of integrated microsphere arrays include ultra-precise intraocular and neurosurgical laser procedures, photoporation of cells, and coupling of light into photonic microstructures.

Keywords: microoptics, microlenses, microspheres, focusing, optical microprobes, laser tissue surgery

1. INTRODUCTION

Focusing of light is widely used in optical microprobes where a stable and well-confined beam of photons is scanned or directed over some area of a biological sample or photonic structure. Focusing microprobes may be useful for laser surgery1, optical endoscopy and spectroscopy2, high-density optical data storage3, and photo-induced patterning of thin films. A fundamental principle in diffraction-limited optics4 requires that the spatial resolution of focusing devices be limited by the wavelength of the incident light and by the numerical aperture of the objective lens systems.

Spatial resolution beyond the classical optical diffraction limit can be obtained by using near-field optical phenomena5 or by using special material properties such as fluorescent, nonlinear6 or negative refractive index7 effects. However, these approaches have certain drawbacks in many biomedical and photonic applications due to low transmission of near-field microprobes and difficulties in realizing desirable material properties.

In the past few years, researchers have demonstrated that a small wavelength-scale microsphere with an index of about 1.6 can produce a narrow focused beam, termed a “nanoscale photonic jet”.8-13 The photonic nanojet propagates with little divergence for several wavelengths into the surrounding medium, while maintaining a sub-wavelength transverse beam width. The concept of nanojets is attractive for designing focusing microprobes with high transmission properties. It should be noted, however, that photonic nanojets from single spheres require strictly plane-wave (or conical) illumination which is not readily available in devices using flexible optical delivery systems. As an example, such problem arises in mid-IR laser tissue surgery where hollow fibers with bore sizes larger than 200 μm are used.

* astratov@uncc.edu; phone 1 704 687-8131; fax 1 704 687-8197; http://maxwell.uncc.edu/astratov/astratov.htm

Invited Paper

Optoelectronic Integrated Circuits XII, edited by Louay A. Eldada, El-Hang Lee, Proc. of SPIE Vol. 7605, 76050R · © 2010 SPIE · CCC code: 0277-786X/10/$18 · doi: 10.1117/12.845791

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More recently, periodic focusing of light has been observed in chains of polystyrene microspheres assembled on substrates.14-17 In these chains, the photonic nanojets were quasi-periodically reproduced along the chain giving rise to “nanojet-induced modes” (NIMs). The coupled nanojets decreased in size along the chain, reaching wavelength-scale dimensions, even for non-collimated input beams. The periodicity, spectral transmission properties, and losses of NIMs were studied14,15 for such chains.

In this work, we study focusing of multimodal beams propagating through flexible optical delivery systems such as optical fibers or hollow waveguides. These delivery systems provide illumination in a broad cone of directions that result in large sizes of the focused spots well in excess of the diffraction limit. Using ray tracing ZEMAX-EE software18 we show that chains of microspheres have certain advantages over single lenses in such applications. They filter the nanojet-induced modes with the best focusing properties in such structures. This allows reduction in the sizes of the focused beams in such structures to wavelength-scale dimensions while maintaining high optical transmission. Experimental studies are performed for spheres with sizes from 10 to 300 µm with different indices of refraction ranging from 1.47 to 1.9. The chains were assembled inside plastic tubing with bore sizes matching the size of the spheres. Using high index spheres, we demonstrate that these structures are capable of focusing light into tissue or a sample in close proximity to the end sphere. The beam attenuation properties in such chains are found to be in a good agreement with the numerical modeling results. Due to simple integration with flexible fibers and hollow waveguides, sharp focusing of the beam, and the ability to operate in contact with tissue, microsphere arrays can be used in a variety of biomedical and photonics applications as a compact focusing tool.

2. THEORETICAL MODELING

2.1. Focusing effects

In lens-based focusing microprobes a critical factor determining the spatial resolution is represented by the angular distribution of the incident beams, as illustrated in Fig. 1 (a). Due to a broad light acceptance angle of fibers or hollow waveguides the flexible optical delivery systems provide a multi-mode illumination within a certain cone of directions along the axis of the system. In the fiber-based focusing microprobes the ball lens is centered and placed at a fixed

Figure 1. (a) Multimodal beams delivered by fibers or hollow waveguides. (b) Ray tracing of several beams in a single high index (1.97) sphere showing multiple focused spots. This factor leads to a broadening of the focused spot sizes. (c) Ray tracing of several beams in a chain of three high index spheres. It is seen that at the end of the chain only the beam incident along the axis of the system (red) is focused that results in smaller spot sizes. (d) Similar filtering of the axial modes with good focusing properties in a chain of medium index (1.63) spheres.

(b)(a)

(d)

(c)

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distance to the fiber with a metallic holder.2 Illumination with a series of beams incident at different angles leads to formation of multiple focused spots at the focal plane of a spherical lens.19

These multiple beam focusing effects are illustrated in Fig. 1 (b) by numerical ray tracing performed using ZEMAX-EE software18. This approach is applicable for sufficiently large spheres with the radius a>>λ, where λ is the wavelength of light. In our modeling we used spheres with the size a=25 µm and λ=0.53 µm. However, it should be noted that the modeling results scale with the size of the spheres in the limit of large spheres. The index of refraction of the spheres (n) was varied over a wide range from 1.4 to 3.0. The illumination of microspheres was provided by a series of collimated beams propagating in different directions, as shown in Fig. 1 (b). It is well known that in the limit a>>λ the index of refraction of the sphere must be close to 2 to provide maximum intensity of focused light at the “shadow” surface of the sphere.8-10 This is illustrated in Fig. 1 (b) by numerical ray tracing for a single sphere with an index of refraction n=1.97. In the limit of geometrical optics, each spot size is determined by the spherical aberrations. With increasing beam diameters, spherical aberrations degrade beam focusing because light will propagate outside the paraxial regime. According to a more rigorous physical optics approach each focused spot in Fig. 1 (b) should have at least diffraction-limited dimensions.4 If the incident beams have a continuous angular distribution, all the focused spots originating from the individual modes are overlapped near the back surface of the sphere forming a broad intensity distribution with characteristic sizes well in excess of the diffraction limit. Thus, the spatial resolution of optical microprobes based on single spheres is expected to be significantly below the diffraction limit due to multimode illumination and superposition effects for focusing of different modes.

Focusing effects in a chain of microspheres are illustrated by numerical ray tracing in Figs. 1 (c) and 1 (d) for high (1.97) and medium (1.62) index spheres, respectively. Only illumination along the axis leads to efficient coupling of light to optical modes propagating in such chains. The skew beams, depending on their angle, tend to be scattered away from such chains due to reflections of light beams provided at the spherical interfaces. This is illustrated by skew beams at ~16-200 (blue) and at ~300 (green) beams. Propagation effects inside the chain are modeled by taking into account multiple refractions and reflections at the spherical interfaces. Only refracted beams are shown in Fig. 1 to simplify the images. The collimated beams incident along the axis of the system (red) are coupled to modes which are focused inside the structure with the periodicity depending on the index of refraction. For spheres with index 1.97 the period is found to be close to 4a, whereas for spheres with index 1.62 the period is close to 4.5a, as shown in Figs. 1 (c) and 1 (d), respectively. By adjusting the index of refraction and number of spheres focusing can be achieved in close proximity to the end sphere.

The advantages of chains of microspheres over a single sphere stem from the following factors. First, the structure plays the part of a filter of the modes with the best focusing properties. This allows simple integration of chains of spheres with flexible delivery systems such as fibers or waveguides. Second, microprobes for some of the biomedical optics applications require short focusing depths in a fluid or tissue. For example, this is necessary in some types of ultra-precise laser surgeries performed in contact with tissue. It is well known, however, that the focusing properties of microprobes based on single lenses are limited in a fluid due to its high index of refraction.2 In contrast, the chains of microprobes can be enclosed in a tube, so that all the beads except the last sphere are completely isolated from the fluid, as illustrated in Fig. 2. The periodical focusing effects occur inside the chain similar to the air situation illustrated in Fig. 1 (c). Only the last sphere is exposed to fluid (or tissue) with index 1.33, as illustrated in Fig. 2. It is observed that the

Figure 2. Ray tracing of several beams in a chain of three high index (1.97) spheres enclosed in a light absorbing tube. The end sphere is exposed into a medium with index 1.33.

n=1.33

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focusing effects are preserved in a fluid despite of its index of refraction. This opens up the possibility of using similar focusing structures in a liquid or in direct contact with tissue.

Although the advantages of chains of microspheres over single lenses can be understood by simple ray tracing arguments, detailed study of the focused beams’ sizes involves taking into account the diffraction effects. This task requires a rigorous solution of Maxwell’s equations without assumptions used in geometrical optics, which goes beyond the scope of the present work. It should be noted, however, that spot sizes comparable to the wavelength of light were observed14 in chains of 3 µm polystyrene microspheres coupled to multimodal light sources (dye-doped spheres).

It should also be noted that using long chains leads to certain disadvantages in light focusing applications. First, the spherical aberrations are accumulated in such structures from sphere to sphere and lead to a gradual increase of the focused spot size along the chain. These effects are determined by the beam apertures used in our modeling. The results presented in Fig. 1 were obtained with apertures comparable to a. They demonstrate that in relatively short chains (<10 spheres) the spherical aberrations are tolerable; however they become an important factor determining the spot sizes in longer chains. Another factor is connected with the optical losses in such structures considered in the next Section 2.2.

2.2. Propagation properties

Light source properties such as directionality determine coupling losses in the first few spheres. Coupling is most efficient for collimated beams incident along the axis of the chain. In our modeling, we selected a source which is sub- optimal in terms of coupling to nanojet induced modes. We used a spherical light source placed in a contact position at one end of the chain, as illustrated in the inset of Fig. 3. This source was selected to describe our experiments with dye-doped fluorescent microspheres presented in Section 3, and generally leads to extensive coupling losses due to the mode filtering processes in the first few spheres. It should be noted, however, that propagation effects deep inside these chains are expected to be determined by the properties of the chains themselves rather than by the light source properties used in modeling.

Figure 3. Transmitted intensity in chains of spheres coupled to a spherical source of light in a contact position. The index of refraction of the microspheres is varied from 1.47 to 1.9. In the inset: Source of light obtained by using point light emitters uniformly distributed inside a “fluorescent” microsphere and a light detector with a variable position inside the chain.

0 2 4 6 8 10 12 14 16 18 200.01

0.1

1

Tran

smitt

ed p

ower

(a.u

.)

Sphere number, N

1.47 1.59 1.7 1.78 1.9

Source Detector1 2 N=8. . . . . .

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The spherical light source with size equal to the size of the spheres in the chain was obtained by using a large number of point light emitters uniformly distributed throughout its volume. The emission properties of such sources mimic the properties of fluorescent microspheres, where the role of the point light sources is played by dye molecules.

The optical power transmitted through the chain was measured by using a detector shaped as a disk with variable position inside the chain. The disk size was equal to the size of the spheres in the chain to collect all of the transmitted power, but to prevent collection of light scattered away from the structure. The detector was placed perpendicular to the axis of the chain at positions where the spheres touch. In the limit of geometrical optics the transmitted power is determined by the number of rays reaching the detector. By moving the detector along the chain it was possible to calculate the attenuation of power along the chains. The power was normalized at a level determined after the first sphere in the chain, the position indicated 1 in the inset of Fig. 2. We modeled the multiple refractions and reflections by the spherical interfaces inside the chain using the ZEMAX-EE software. Only the rays reaching the detector were traced by the program. The scattered rays were allowed to leak, as illustrated in the inset of Fig. 2.

The calculated relative transmitted power is presented in Fig. 3 as a function of the position along the chain represented by the number of spheres (N). The attenuation in the first 3-4 spheres is very similar (around 1.2 dB/sphere) for all chains formed by spheres with indices from 1.47 to 1.9. This is determined by the mode filtering effects in the chain in the vicinity of a spherical light source. Away from the source the attenuation gradually decreases for all chains. At long distances from the source (>10 spheres) the magnitude of attenuation becomes strongly dependent on the index of refraction, which is clearly observed due to the diverging behavior of the attenuation curves in Fig. 3. The general trend is that the attenuation is larger for spheres with higher index, however, the attenuation experiences strong variations in the region of 1.7<n<1.8.

This behavior is illustrated in a more detailed way by the dependence of the attenuation per one sphere calculated as a function of the index of refraction in Fig. 4. This dependence was obtained for a segment of the chain separated by more than 15 spheres from the spherical source (from 15th to 20th sphere). The amplitude coefficients of partial reflections by the spheres are proportional to the refractive indices of the spheres due to Fresnel’s equations4. This should result in higher attenuation for larger index spheres and is generally reproduced by the results of numerical modeling in Fig. 4. It should be noted, however, that the strong non-monotonic variations in the region of 1.7<n<1.8 do

1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

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0.4

0.6

0.8

1.0

1.2

1.4

Atte

nuat

ion

(dB

/sph

ere)

Index of spheres, n

Figure 4. Light attenuation calculated in a segment of chains (from 15th to 20th sphere) well separated from the spherical light source. The general trend of an increase in attenuation with a corresponding increase in the index of refraction can be explained by higher reflections produced by spherical interfaces in accordance with Fresnel’s equations. Strong variations of the attenuation at 1.7<n<1.8 can be related to additional effects introduced by the spatial period of the modes matching some of the geometrical parameters of the chain.

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not follow this trend. This behavior can be explained by additional factors introduced by the spatially periodic nature of the focused beams in the structure. For example, the minimum at n=1.78 takes place in the case when the distance between the focused spots is equal to 4a. The attenuation should be minimized under these conditions due to the fact that the beams are tightly focused in the vicinity of touching points of spheres.15

3. EXPERIMENTAL RESULTS

Chains of microspheres made from borosilicate glass (n=1.47), soda-lime glass (n=1.50), polystyrene (n=1.59), and barium titanate glass (n=1.9) were assembled inside plastic and glass microcapillaries as well as inside hollow waveguides. Infiltration was performed using micromanipulation and micro-pneumatic propelling of spheres with diameters from 10 to 300 µm. In order to provide tight packing of microspheres, while keeping the chains straight and symmetric along the long central axis of the cylindrical structure, the size of microspheres should match the hole size in the microcapillary tube, as shown in Fig. 5 (a) for 50 μm polystyrene microspheres inside a microcapillary.

The light attenuation properties of chains of microspheres inside capillary tubing were investigated by imaging through the sidewall using scattered light, as illustrated for 50 μm polystyrene beads in Fig. 5 (b). The studies were performed using dye-doped fluorescent (FL) polystyrene spheres with the same 50 μm size as local light sources. Several dye-doped spheres were assembled inside the microcapillary at one end of the chain of undoped spheres. The FL excitation was provided at 460-500 nm by a mercury lamp with an intensity below the threshold for lasing whispering gallery modes (WGMs). Under these conditions only a small fraction (not more than a few percent, since the beads are dye doped throughout the volume) of the total FL intensity is coupled to WGMs. Most of the power is emitted into radiative modes with a broad (500-570 nm) spectrum. A part of this power is coupled to modes propagating in the chain away from the source. These propagation effects were visualized with an inverted IX-71 Olympus microscope due to light scattering away from the axis of the chain. The images illustrating propagation effects were registered by a CCD video camera with variable exposure time and 12 bit dynamic range, as shown in Fig. 5 (b). In order to eliminate any possibility of detecting excitation at 460-500 nm the images were obtained through a spectral filter at λ > 510 nm.

Figure 5. (a) Packing of 50 µm polystyrene spheres inside a microcapillary. (b) Scattering image illustrating optical transport. (c) Measured (circles) and calculated (squares) attenuation of light.

0 5 10 15 200.01

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.u.)

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Model. Exp.

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The positions of bright spots observed in Fig. 5 (b) with focusing at the equatorial plane of spheres through the transparent wall of the microcapillary correspond to the areas at the spherical surfaces near the touching points of the neighboring spheres. These spots appear due to reflection or scattering of a small fraction of the propagating electromagnetic power into the microscope objective. Since the conditions of collection of scattered light were fixed along the chain, one can assume that the power contained in the bright spots should be proportional to the power of modes propagating inside the chain at the cross sections determined by the spheres’ contact points. In order to estimate the total power contained in the bright spots, the intensity distribution was integrated within each spot. Similar to the theoretical power distributions in Fig. 3, the experimental data was normalized on the power level determined after the first sphere in the chain, the position indicated 1 in Fig. 5 (b).

The experimental power distribution along the chain determined by the technique described above is represented by red dots in Fig. 5 (c). It is in reasonable agreement with the results of numerical ray tracing presented at the same plot. A slight difference between the results of measurements and modeling can be explained by the role of the partially reflecting walls of the microcapillary which was not taken into account in our calculations. Similar results were obtained for chains formed by the borosilicate (n=1.47) and soda-lime glasses (n=1.50). For chains formed by high index (n=1.9) barium titanate glass spheres the experimentally measured transmission was less than the theoretical values due to absorption of light by the material of microspheres at 510-570 nm.

In order to test the focusing properties of the microprobe in the presence of a tissue-like medium, a gel was used, as illustrated in Fig. 6 (a). The structure formed by barium titanate glass microspheres with a=62.5 µm was completely embedded in a gel, so that the surface of the end sphere was in contact with the medium with index around 1.4 similar to the case considered earlier by theoretical modeling in Fig. 2. The illumination was provided at λ=630 nm by the single mode fiber inserted in a capillary tube holding the chain of microspheres. The gel makes visible the beam inside such a “tissue”, due to light scattering properties, as shown in Fig. 6 (b). The beam is focused in the vicinity of the surface of the end sphere with the beam waist measuring about 5 µm. Due to significant beam divergence the intensity distribution has a small depth of ~ 10-20 µm. Thus, such structures are capable of focusing light into tissue in contact mode and may provide laser interaction with the tissue in close proximity to the end sphere.

4. CONCLUSIONS

Focusing microprobes are used in biomedical and photonics applications commonly requiring: (i) high spatial resolution, (ii) high optical transmission, and (iii) integration with flexible delivery systems provided by fibers or waveguides. These requirements, however, are contradictory since multimodal imperfect beams delivered by fibers or waveguides cannot be focused down to small spot sizes with high efficiency. Conventional single lens-based microprobes can focus light to spot sizes which are a priory significantly larger than the diffraction limited dimensions. This is a fundamental problem which cannot be solved using conventional imaging systems. In such systems the resolution can be increased only at the expense of the transmitted power due to filtering of modes which can be focused more efficiently. An example of such a process is given by spatial filters which are commonly used to create well collimated beams or to “clean up” the output of lasers.

In this work we demonstrate that a trade-off between focused spot sizes and transmitted power can be conveniently controlled in microprobes by using chains of microspheres. Increasing the number of spheres in such chains generally

50µm

Tissue

(b)(a)

Figure 6. (a) Microprobe inserted into a tissue-mimicking gel with an index of 1.4. (b) Focusing at λ=0.63 µm with the microcapillary tube in contact with tissue.

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provides smaller focused spot sizes at the expense of transmitted power. It should be noted, however, that excessively long chains (more than 10 spheres) have significant spherical aberrations. The chains of microspheres can be assembled directly inside the cores of hollow waveguides or simply integrated with the fibers. Such structures with appropriately designed parameters allow tight focusing of the beams in the proximity of the end sphere. This focusing can be sustained in the presence of a fluid or under tissue contact conditions. We show that such structures allow one to obtain focused beams with spot sizes of several wavelengths and with a treatment depth of approximately 10-20 μm in tissue. As a result of simple integration with flexible fibers and hollow waveguides, sharp focusing of the beam, and the ability to operate in contact mode with tissue, microsphere arrays can be used in a variety of biomedical and photonics devices. Potential applications include ultra-precise intraocular and neurosurgical laser procedures, photoporation of cells, and coupling of light into photonic nanostructures. We are currently pursuing this research for development of a novel optical scalpel for ultra-precise ophthalmic laser surgery.

Acknowledgments

The authors thank M. A. Fiddy for stimulating discussions. We gratefully acknowledge support for our work from the U.S. Army Research Office (ARO) under Contract No. W911NF-09-1-0450 (J. T. Prater) and from the National Science Foundation (NSF) under grant ECCS-0824067. This work was also partially supported by funds provided by The University of North Carolina at Charlotte. The authors also wish to thank Mo-Sci and Thermo Fisher Scientific Corporations for donating microspheres for this research.

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