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Abstract
Optofluidic microlenses are one of the crucial components in many miniature lab-on-chip systems. However, many optofluidic microlenses are fabricated through complex micromachining and tuned by high-precision actuators. We propose a kind of tunable optofluidic microbubble lens that is made by the fuse-and-blow method with a fiber fusion splicer. The optical focusing properties of the microlens can be tuned by changing the refractive index of the liquid inside. The focal spot size is 2.8 µm and the focal length is 13.7 µm, which are better than those of other tunable optofluidic microlenses. The imaging capability of the optofluidic microbubble lens is demonstrated under a resolution test target and the imaging resolution can reach 1 µm. The results indicate that the optofluidic microbubble lens possesses good focusing properties and imaging capability for many applications, such as cell counting, optical trapping, spatial light coupling, beam shaping and imaging.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The synergy of microfluidics and photonics has gained increasing importance for better light-matter interactions on a microchip [1–8]. Optofluidics, as a new research field that integrates light and fluids into a microscale platform, has been developed in various photonic devices, such as microlenses [9,10], microcavity biolasers [11,12], biosensors [13,14] and flow cytometry [15,16]. Among them, the optofluidic microlens is a novel lab-on-chip device due to its easy integration and manipulation of light of miniature size, which has been applied in flow cytometry [9,17], optical coupling [18,19], imaging [20,21] and optical trapping [22,23].
Tunable optofluidic microlenses adaptively reshape the incident light, such as the focal length, light spot size, intensity and even propagation direction [4,24,25]. Therefore, it works as one of the crucial components in many miniature lab-on-chip systems. The tunable optofluidic microlenses studied thus far can be divided into two categories, namely, geometric shape tuning [26–29] and liquid refractive index (RI) tuning [30,31]. For the geometric shape of a lens, a variety of tuning methods can be found in microfluidics, such as tuning a flexible material with pressure [32], hydrodynamics [33,34], electrowetting or other physical effects [26,29]. However, all of these lenses need an actuator for tuning the lens shape, which tends to be influenced by the environmental disturbance. Liquid RI tuning provides another effective approach to tune the focal length. For example, a liquid crystal (LC) tunable lens [30] and a tunable microlens by changing the RI contrast [31] were proposed, respectively. However, the complexity of fabrication and tuning methods limit their application. In addition, the roughness of lens surface will increase the scattering loss and degrade the optical performances as well.
To address the above issues, a novel tunable optofluidic microlens with good tuning ability was proposed. As shown in Fig. 1(a), the microbubble plays the role of a biconvex lens while keeping the hollow channel for liquid input and outlet. The microbubbles were usually used for physical, chemical and biological sensing in the form of optical microcavities [35–38]. To the best of our knowledge, the optofluidic microbubble lens (OMBL) proposed in this study is the first application of microbubbles in a new dimension, and it has both the properties of microfluidic channels and lenses. Unlike the methods that tune focusing properties by changing the RI contrast [31], the effective RI of the microlens itself was changed. With different types or concentrations of liquids, the incident light will be refracted at different positions and different spot sizes, as shown in Figs. 1(b) and (c). The OMBLs with good optical performance and special hollow structures are easily fabricated by the fuse-and-blow method [39]. It is known that the tuning ability depends on both the RI of liquid and microbubble shape. The optical focusing properties of OMBLs were investigated theoretically in Section 2. Then, the tuning ability of the OMBLs were experimentally demonstrated by changing different concentrations of dimethyl sulfoxide (DMSO) solutions from 0-100% in Section 3. A schematic of the experiment is shown in Fig. 1(d). The focal length ranges from 217.4 µm to 13.7 µm, and the focal spot size ranges from 7.0 µm to 2.8 µm, which agrees well with the ABCD matrix theoretical and simulation results, respectively. Finally, it was realized that an imaging resolution of 1 µm in Section 4, which is better than other tunable optofluidic microlenses.
Fig. 1. (a) Optical microscopy image of Microbubbles. (b) Long focal length with a low RI medium. (c) Short focal length with a high RI medium. (d) Schematic of the experiment for the OMBL characteristic analysis: CCD (charge-coupled device), OL (objective lens), OMBLs (optofluidic microbubble lenses), PCFs (photonic crystal fiber lens), and 4-CLS (4-channel laser source). The inset is a microbubble filled with high RI oil during the experiment.
2. Theoretical and simulation results
2.1 ABCD matrix theory
To completely study the focusing properties of the OMBLs, we built an ABCD matrix from the photonic crystal fiber lens (PCFs) to the OMBL, as shown in Fig. 2(a) [40,41]. The ABCD matrix of the PCFs can be written as
When a Gaussian beam transports from Plane A to G along the optical axis, the change in the transmission parameters can be obtained through the radius of complex curvature by the ABCD matrix
where q(z) is related to the beam parameters,R(z) is the radius of the wave front curvature, λ is the center wavelength, ω(z) is the beam spot radius, and n is the effective RI. Combining the R(a)=R(g)=∞ with (4) and (5), we can obtain
Fig. 2. (a) Schematic of theory model for the ABCD matrix. (b) - (d) Focusing electric field intensity distribution for n =1.33, 1.53 and 1.73, respectively. (e) Focal length and focal spot size changing relationship with the liquid RI. (f) Electric field intensity distribution along the optical axis.
By solving (6), the focal length and focal spot size in Plane G can be calculated. The result is shown in section 3.
2.2 Numerical simulation
As shown in Figs. 2(b) - (d), a physical optics model was built to systematically analyze the optical field transmission after an OMBL with the commercial finite element method software (COMSOL Multiphysics 5.4). The electromagnetic waves, beam envelope method and the wavelength domain in the wave optics module were used. In the model, the focal length was the distance between the focal spot and back surface of the microbubbles when light is refracted out of it along the optical axis. The focal spot size is the full width at half maximum (FWHM) of the intensity distribution on the cross section. Although the key impact factors were the liquid types and concentrations because the size and wall thickness will be fixed once the microbubble was fabricated, the influence of every possible factor was studied as well, which has guiding significance for the experimental design. It is worth noting that the parallel beam was set as the incident light in this section, which is different from the Gaussian beam used in the experiments. Therefore, the simulation results are better than the experiment. As shown in Fig. 2(a), the Gaussian beam was also simulated as the incident light, in which case the simulation results are in good accordance with the experiment. Details can be found in Section 3.
2.2.1 Tunability of the OMBLs with different liquid concentrations
According to Snell's law, the refraction becomes stronger with the increasing RI, resulting in a shorter focal length. The radius of a microbubble was set as 90 µm, the thickness of the microbubble wall was set as 10 µm, the surrounding medium was set as air, the wavelength of incident light was set as 830 nm and the incident light radius was set as 30 µm. Figures 2(b) - (d) represent the electric field distribution for liquid RIs of 1.33, 1.53 and 1.73, respectively. It is obvious that the focal length becomes shorter with the increasing RI. In addition, it was also found that the divergence angle after focusing becomes larger with the increasing RI, which indicates a smaller focal spot size. Note that the interference fringes of the incident light and reflected light was weak because of a small RI difference between the OMBL and surrounding medium. The relationship between the focal length and RI is shown in Fig. 2(e) with a red line, and the relationship between the focal spot size and RI is shown in Fig. 2(e) with a blue line, from which the tuning ranged from 92.1 µm to 11.3 µm for the focal length and the tuning ranged from 2.9 µm to 1.5 µm for the spot size. The electric field strength distribution along the optical axis is shown in Fig. 2(f), which can fully present the focusing properties from the intensity and focal length.
2.2.2 Tunability of the OMBLs with different microbubble sizes
According to Snell’s law, the refraction becomes weaker with the decreasing lens radius of curvature. The liquid RI was set as 1.48, and the other parameters were the same as in Section 2.2.1. As shown in Fig. 3(a) with the red line, the focal length increases with the increasing microbubble radius. When the size of microbubbles is 170 µm, the focal length was as small as 40.8 µm. In contrast, when the size of microbubbles was 390 µm, the focal length was as large as 103.5 µm. The increase in focal length was mainly due to the weak refraction of the small lens radius of curvature. In addition, the relationship between the focal spot size and lens radius is shown in Fig. 3(a) with a blue line, from which the tuning ranges of the focal spot size change from 1.9 µm to 4.3 µm. From Figs. 3(c) - (e), one can observe the electric field distribution of different microbubble sizes.
Fig. 3. Focusing properties of the OMBL with different sizes. (a) Focal length and focal spot size changing relationship with the microbubble radius. (b) Focal length and focal spot size changing relationship with the microbubble wall thickness. (c) - (e) Focusing electric field intensity distribution for R = 85 µm, 145 µm and 185 µm, respectively.
To obtain good optical performances of the OMBL, the influence of wall thickness was also evaluated. The model was the same as Section 2.2.1 while changing the wall thickness from 5 µm to 15 µm. Compared to the liquid core of microbubbles, the wall only occupies a small part, which indicates that the effective RI of OMBL is mainly determined by the inner liquid. As shown in Fig. 3(b), the influence of microbubble wall thickness on focal length was only approximately 10 µm, and the changing ranges of focal spot size were approximately 0.2 µm, indicating that the influence of wall thickness is negligible for the experiment.
2.2.3 Comparison of the OMBL with microsphere and planoconvex lenses
Thee different types of lenses were comprehensively compared, such as the microsphere lens, the plano-convex lens and the OMBL. The parameter was the same as in Section 2.2.1, and the RI of the microsphere and planoconvex was also set as 1.48 for comparison. From Figs. 4(a) - (c), we can clearly find that the planoconvex lens has worse focusing properties than a microsphere or an OMBL. Two spherical surfaces of the OMBL or microsphere lens leads to twice refraction in the front and back surface. However, the incident light is refracted once in the back surface of the planoconvex lens, as shown in Figs. 4(a) - (c). The refraction difference between the OMBL or microsphere lens and the planoconvex lens indicates a better focusing properties of the OMBL or microsphere lens. To specify the differences of the three types of microlenses accurately, the relationship between the focusing characteristics and lens size was calculated, as shown in Figs. 4(d) and (e). Compared with the planoconvex lens and microsphere lens, the OMBL provides better focusing property and tunability.
Fig. 4. Focusing properties for different microlenses. (a) - (c) Focusing electric field intensity distribution for the OMBL, microsphere and planoconvex lens. (d) Focal length changing relationship with the microlens radius for three different types of microlenses. (f) Focal spot size changing relationship with the microlens radius for three different types of microlenses.
2.2.4 Focusing properties under off-axis incidence of beam
The OMBL can still maintain a good optical focusing performance although the incident beam does not enter the maximum radius of the microbubble. As shown in Fig. 5, the focusing electric field intensity distribution of the OMBL with the off-axis positions of -20 µm to 20 µm were analyzed. The incident beam at different off-axis positions is focused on nearly the same plane. In addition, the effect of off-axis incidence on the spot size is also weak. Therefore, the OMBL possesses good tolerance to the off-axis incidence.
Fig. 5. The focusing properties under the incidence light deviates away from the optical axis of (a) 20 µm, (b) 10 µm, (c) 5 µm, (d) 0 µm. (e) Focal length and focal spot size as a function of off-axis position.
3. Characterization of the OMBL
To experimentally prove the tuning ability and focusing properties of the OMBL, two different sizes of microbubbles, 180 µm and 285 µm were prepared, respectively. During the fabrication process of an OMBL, we can control the microbubble geometry by using the fiber fusion splicer. A spherical microbubble could be fabricated through the combination of relatively low pressure and multiple heating and blowing operations to guarantee that the microbubble geometry meets the experimental requirements. For different microbubble geometries, the optical focusing performance is also different. For example, a spherical microbubble lens can lead to a circular focusing spot while a non-spherical one can lead to an elongated focusing spot. Because of the spherical shape of a microbubble lens, the spherical aberration occurs. To further reduce the spherical aberration, a collimated Gaussian beam generated by the PCFs was set as the incident light [41]. As shown in Figs. 6(a) and (b), the spot size is approximately 30 µm and the effective working distance is approximately 1 mm.
Fig. 6. (a), (b) Light spot of the Gaussian waist for the PCFs. (c) RI changing relationship with different concentrations of DMSO. (d), (e) Curves of the focal length and focal spot size for different liquid RIs. (f) Repeatable and reversible optical tuning properties for the OMBL.
The experimental setup is shown in Fig. 1(d). A 4-channel laser source (4-CLS, MCLS1, Thorlabs) with a center wavelength of 830 nm was transmitted into the PCFs, and then the light from the PCFs was perpendicularly incident on one side of the microbubble. Details can be clearly seen in Fig. 2(a). To study the focusing properties of the OMBL precisely, a 20x objective lens (OL, NA = 0.45) was used to observe the size of the focusing spot and imaged by a charge-coupled device (CCD) camera in real time. In the experiment, a three-dimensional Picomotor Piezo Linear Stage (Accuracy: ∼21 nm, 9063-XYZ-PPP-M, New Focus) was used to precisely control the horizontal and vertical positions of the microbubbles. Firstly, the incident light irradiates the central area of the microbubbles vertically by adjusting the position of the OMBL in the horizontal direction, thereby effectively reducing the spherical aberration. Secondly, the distance between the microbubble and the objective lens in the vertical direction was continuously adjusted until the focal position of the microbubble coincided with the focal position of the objective lens. The focal length can be obtained by converting the steps of the three-dimensional Picomotor Piezo Linear Stage into the distance. At the same time, the focusing spot can be monitored by a CCD camera because the imaging spot of the microscope is the converging spot of the OMBL. All of the experiments were performed at room temperature.
It should be noted that the largest numerical aperture (NA) was calculated theoretically before the start of the experiment to ensure that the objective lens can effectively collect the incident light condensed by the OMBL. The NA for the OMBL can be calculated by (7)
where the output spot of the microbubble surface (s1), the focal spot size (s2) and the focal length (f) are obtained by the electric field distribution. n is the RI of the medium around the microbubble, and α is the convergence angle of the exiting spot. In our experiment, the NA of the selected objective lens is 0.45, which is larger than the calculated maximum numerical aperture (NA = 0.44), as shown in Table 1.
Table 1. The results of NA for different RI
Liquids of different concentrations were extracted into the microbubble through a Teflon tube, and the diameter of the microbubble was 180 µm. In the experiment, DMSO solutions of different volume concentrations were diluted with the deionized water. The relationship between the RI and the concentration of DMSO solution is shown in Fig. 6(c), from which the RI of DMSO increases with the increasing concentration. The focal length and focal spot size of different RIs were studied experimentally, and the results are shown in Figs. 6(d) and (e), respectively, which is the average of three measurements. From Fig. 6(d), the focal length decreases from 97.5 µm to 13.7 µm, which is mainly due to the increase in RI leading to the refraction enhancement. Notably, a RI of 1.7 was realized by oil droplets in the experiment, as shown in the inset of Fig. 1(d). A focal spot size as small as 2.8 µm was realized, which indicates the good optical focusing performance of the OMBL, as shown in Fig. 6(e). By the combination of the ABCD matrix theory and numerical simulation, the experimental results are in good agreement with the theoretical results. The deviation between the experiment and theoretical calculation is mainly due to the aberration. During the imaging of microbubbles, there are always aberrations by the microscope, so the position of the microbubble wall will always slightly deviate in each test. Moreover, the focal length was measured by repeatedly alternating the deionized water and 50% DMSO in the microbubbles, which proved that the OMBL has good repeatability and reversibility, as shown in Fig. 6(f). The deviation from each measurement mainly results from the measurement error during the imaging of the OMBL.
The OMBLs with different sizes have different focusing characteristics. Theoretically, the refraction becomes stronger with the increasing OMBL curvature. The focusing properties of the OMBLs with diameters of 180 µm and 285 µm were studied, which are shown in Figs. 7(a) and (b). The focal length and focal spot size decrease with the increasing liquid RI while increasing with the increasing OMBL radius. The tuning ranges were realized from 13.7 µm to 217.4 µm for the focal length and from 2.8 µm to 7.0 µm for the focal spot. The images of focal spots for the microbubbles with diameters of 180 µm are shown in Figs. 7(c) - (f), where (c) - (f) are RIs of 1, 1.33, 1.48 and 1.7, respectively. It is obvious that the focusing properties are enhanced with the increasing RI. Furthermore, the OMBL is made of silica microcapillary and fixed on a glass scaffold, which has a stable structure. By the combination of microfluidic technology, the medium in the microbubble can be easily changed. Therefore, the OMBL can maintain a good optical performance and stability for a long time.
Fig. 7. Focusing properties of different microbubble size. (a) Focal length changing curves for 180 µm and 285 µm. (b) Focal spot size changing curves for 180 µm and 285 µm. (c)-(f) Optical microscopy images of focusing spots for different RIs with diameters of 180 µm.
4. Application of the OMBL
The imaging performance of the OMBL was further studied due to its good optical focusing properties. Firstly, the resolution test target (USAF 1951, maximum resolution: 512 LP/mm) was imaged by 20x and 100x objective lenses, respectively, as shown in Figs. 8(a) and (b). The minimum line pairs of nearly 1 µm cannot be resolved by a 20x objective lens. Then, we systematically studied the imaging performance by introducing the OMBL between the resolution test target and 20x objective lens. In the experiment, the transmission mode of the microscope was adopted. Then, a clear image for different RIs of liquid was obtained by adjusting the distance between the OMBL and the resolution teat target, which could be observed in real time under a microscope. The experimental results are shown in Figs. 8(c) and (d), which present the imaging of the resolution test target with the microbubble diameters of 210 µm and 345 µm, respectively. As the RI increases, the magnification factor increases gradually from (c1) - (c3) or (d1) - (d3), where (c1) - (c3) or (d1) - (d3) represent RIs of 1.33, 1.48 and 1.7, respectively. In addition, the magnification factor further increases as the radius of the microbubble decreases. Notably, for a microbubble with a diameter of 210 µm, the maximum magnification is 7.2x when the RI of liquid is 1.7, which is equivalent to a magnification effect of a 100x objective lens. Finally, we further studied the imaging quality of the OMBL. By processing the image with grayscale, the intensity distribution of the 512 LP/mm line pairs was extracted from Figs. 8(c3) and (d3). The adjacent line pairs can be clearly distinguished with the OMBL, which is much larger than the Rayleigh resolution range, as shown in Figs. 8(e) and (f). Therefore, the OMBL has good imaging resolution for small structures. To better explain the phenomenon, the finite element method was applied to the theoretically analysis. As shown in Figs. 8(g) - (i), we calculate the effective resolution of the OMBL by σ=1.22λ/(2NA), from which it was found that the effective resolution for a RI of 1.48 was approximately 1 µm at the wavelength of 550 nm, which was the reason for the effective resolution of the 512 LP/mm line pairs in Fig. 8(c2). When the RI increased to 1.7, the resolution further increased to 700 nm. Therefore, the line pairs of 512 LP/mm can be distinguished more clearly, as shown in Fig. 8(c3).
Fig. 8. Imaging capability of the OMBL. (a), (b) Imaging of the resolution test target under 20x and 100x objective lenses. (c) Imaging of the resolution test target by the OMBL with a diameter of 210 µm under a 20x objective lens, where (c1) - (c3) represent RIs of 1.33, 1.48 and 1.7, respectively. (d) Imaging of the resolution test target by the OMBL with a diameter of 345 µm under a 20x objective lens, where (d1) - (d3) represent RIs of 1.33, 1.48 and 1.7, respectively. (e), (f) Grayscale value of the 512 LP/mm line pairs from c3 and d3. (g) - (i) The theoretical calculation methods of NA and resolution for the OMBL.
The OMBL is of a homogenous material. Therefore, the chromatic aberration could not be eliminated. Because of different RIs, the chromatic aberration results in separated focal points associated with different wavelength. In the next step, we will focus on eliminating the chromatic aberration by adjusting the refractive index ratio in the OMBL. The imaging resolution of different types of optofluidic microlenses were also summarized, as shown in Table 2. Compared with other optofluidic microlenses, the optical focusing properties are further enhanced by the OMBL, and a good resolution as small as 1 µm was verified, which is better than those of other tunable optofluidic microlenses. In addition, the OMBLs were easily fabricated and flexible for the focusing property tuning without complex structures, which was another advantage among the current tunable optofluidic microlenses.
Table 2. Imaging resolution for different optofluidic microlenses
5. Conclusion
Breaking the traditional usage of microbubbles for the optical microcavities, we proposed the first application of microbubbles on optofluidic microlenses. Due to the hollow structure of the microbubbles, the tunability of focusing properties can be achieved by a combination of the microfluidic technology. With the help of the finite element method, we theoretically proved the possibility and good optical tuning properties of the OMBLs. Then, we fabricated the microbubbles with sizes of 180 µm and 285 µm to verify the tuning properties experimentally. The focal length varied from 13.7 µm to 217.4 µm and the focal spot sizes varied from 2.8 µm to 7.0 µm, which was in good accordance with the theoretical results. Additionally, the good focusing properties and tuning ability imply the potential imaging capability of OMBL. We studied the imaging ability with a resolution test target and an imaging resolution of 1 µm was realized. The optical focusing properties and imaging capability are better than those of other optofluidic microlenses. In the further work, we will optimize the fabrication method and choose smaller silica microcapillaries to reduce the OMBL size for better optical performances.
Funding
Natural Science Foundation of Shanghai (21ZR1407400); National Natural Science Foundation of China (62175035).
Acknowledgments
Xuyang Zhao also sincerely thanks Shimei Wu for her support and encouragement during writing.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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