Lateral gradient index microlenses written in ophthalmic hydrogel polymers by femtosecond laser micromachining

Lisen Xu; Wayne H. Knox

doi:10.1364/OME.1.001416

1. Introduction

Femtosecond laser micromachining has been widely used to write microstructures in materials such as glass or polymers [1–6], due to the unique three-dimensional structuring capability. When femtosecond laser pulses are tightly focused inside transparent material, the intensity at the tiny focus is high enough to cause nonlinear absorption in the material, modifying the material locally while leaving the surrounding material unaffected. There have been some studies on the refractive index change inside glass induced by femtosecond laser micromachining, and various optical devices have been created using this mechanism, such as optical waveguides, light couplers, and three-dimensional optical storage [7–11]. The refractive index changes were generally in the range of 1 × 10⁻⁴ to 1 × 10⁻² [1–11].

In 2006, Ding et al. reported the fabrication of optical diffraction gratings inside several silicone-based and non-silicone-based hydrogel polymers using a high-repetition-rate low-pulse-energy femtosecond laser [12]. Compared to previous work, larger refractive index changes as high as 0.06 was obtained, based on multi-photon absorption and heat accumulation effects. In this work, the fabrication and measurement were both done in ophthalmic polymers in an aqueous environment. The largest refractive index changes were obtained only at writing speeds that were extremely slow (~0.4 μm/s) [12]. This slow scanning speed limited any practical applications of this technique. Later on, it was found that, by doping dyes such as Fluorescein or Coumarin which significantly enhance two-photon absorption, the results of femtosecond laser micromachining could be greatly improved, with larger refractive index changes and much faster (by 1000X) scanning speed [13]. The largest refractive index change was 0.08 ± 0.005 for Akreos® doped with Coumarin and 0.065 ± 0.005 for Balaficon doped with Fluorescein. These two dyes were known to have large two photon absorption (TPA) cross section at the laser wavelength 800nm, so that the nonlinear absorption in the focal volume was greatly enhanced with these dopings. The capability of writing large refractive index changes at fast scanning speeds has made femtosecond laser micromachining potentially important for ophthalmic applications, such as customized aberration or vision correction in contact lenses, intra-ocular lenses, or other ophthalmic devices.

In this paper, we report studies of femtosecond laser micromachining in Akreos® (Bausch & Lomb, Inc.) doped with “X-monomer”, which is an FDA-approved UV absorber that is used in intraocular lenses (IOL). We first calibrate the refractive index change with respect to the scanning speed. Then, a theoretical model is given in order to predict the result of inscribed refractive structures based on the refractive index change. Finally, we will present experimental results and analysis of a gradient-index refractive structure written inside a flat Akreos® polymer sample.

2. Experimental setup

The femtosecond laser micromachining system is shown in Fig. 1 . We use a commercial mode-locked Ti:Sapphire laser (MaiTai-HP from Newport Corporation), which generates pulses of 100 fs pulse width, 80 MHz repetition rate and a tunable spectrum of 690 to 1040 nm. The average output power of Mai Tai HP at 800 nm is as high as 2.5 W, with a peak power of 310 kW. After passing through a broadband isolator, the laser is first attenuated by a high energy zero-order attenuator, which consists of a half-wave plate and a polarizer. With proper beam shaping, the laser beam is delivered to a metallic variable attenuator and finally focused into the polymer sample through a high numerical aperture objective (LUCPlanFLN, 60X, NA0.70, Olympus). The objective is set to compensate spherical aberration at different depths below the sample surface, so as to create a nearly diffraction-limited focal spot. The average power at the objective focus is typically attenuated to be ~400 mW, corresponding to pulse energies of ~5 nJ. The polymer sample is sandwiched between a glass slide and a #1 coverslip, and mounted on a stacked three-dimensional linear motor stage system, consisting of three DC motor stages in XYZ configuration (VP-25XA, Newport Corporation, 0.1 μm resolution) and two closed-loop linear piezo stages in XY configuration (M-663, Physik Instrumente GmbH & Co. KG, 0.1 μm resolution). The three-dimensional VP-25XA stages are used for coarse control while the two-dimensional M-663 stages are used for fast scanning (up to 500 mm/s) with 19 mm travel range. This combination of 2D precision stages on top of 3D coarse stages ensures the maximum flexibility of writing three-dimensional refractive structures. The entire micromachining process is also monitored in real time by a CCD camera viewing the side-scattered light. A phase contrast microscope (BX51, Olympus) is used after the micromachining procedure for imaging purpose. For the refractive index calibration process, a custom-built scatterometer captures the diffraction patterns of phase diffraction gratings written by this technique. Finally, a Shack-Hartmann wavefront sensor is used to measure the wavefront aberration induced in the region where the refractive structure is inscribed.

Fig. 1 Experimental setup for femtosecond laser micromachining.

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3. Experimental procedure, results and discussion

The polymer sample used in this study was Akreos® (Bausch & Lomb, Inc.), one of the IOL materials used on the market. The 1-mm thick sample was labeled so that the anterior surface was always facing upwards during both the micromachining and subsequent measurement. The sample was stored in Balanced Salt Solution (BSS, Bausch & Lomb, Inc.) overnight at room temperature before any experiment was performed. We measured the transmission spectrum of Akreos® sample using an Ocean Optics spectrometer (HR4000), as shown in Fig. 2 . We can see that the sample is almost transparent at 800 nm while having strong absorption below 400 nm.

Fig. 2 Transmission spectrum of Akreos® sample (Bausch & Lomb).

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The sample was sandwiched between a glass slide and #1 coverslip, and maintained in BSS solution during both the micromachining and metrology procedures. Then the sandwich structure was mounted horizontally on the three-dimensional scanning stage platform, and the laser pulses were focused through a high numerical aperture objective into the hydrogel sample at a depth ~150 μm from the anterior surface (Fig. 1). For calibration purpose, periodic phase gratings at various scanning speeds were inscribed inside the Akreos® sample at the same laser parameters (laser wavelength 800 nm, repetition rate of 80 MHz, and average power 400 mW or pulse energy of 5 nJ). The scanning speeds were ranged from 5 mm/s to 400 mm/s. For the grating written at < 5 mm/s, we observe some localized damage along the periodic grating lines, which occurs when there is excess laser energy deposited within the focal volume inside the polymer sample [14]. For any given scanning speed, laser induced damage can be eliminated by maintaining the laser power below a certain threshold. In the present study, we calibrate the resulting refractive index changes versus scanning speed at the given laser parameters. We find that the threshold for damage is extremely sharp.

In Fig. 3 , we show phase-contrast microscope images of diffraction gratings with 5 micron spacing written at 5mm/s (A) and 70 mm/s (B). The grating in Fig. 3A is written at the transition speed and clearly shows some scattered damages. In Fig. 3B, the grating at 70 mm/s is very uniform, without any damage at all. We tested scanning speeds from 5 to 400 mm/s. Each grating was written in an area 4 mm long and 1 mm wide. The grating far-field scattering was measured in a scatterometer and the refractive index change was extracted from the measured first order diffraction efficiency [12]. The resulting extracted refractive index changes are plotted as a function of scanning speed in Fig. 4 . As seen in the plot, the refractive index change decreases sharply as the scanning speed increases. At 400 mW average power, the largest refractive index change is 0.05 ± 0.001; and below 5 mm/s, we observe damage spots along the grating lines, in the form of isolated black carbon spots [14]. As the scanning speed is further decreased, the localized damage becomes continuous carbonized damage along the grating lines, as we have discussed previously [14]. The smallest refractive index change was 0.007 ± 0.0001 at a scanning speed of 400 mm/s. We use this calibration procedure for fabrication of lateral gradient index microlenses.

Fig. 3 Phase contrast image of gratings written at 5mm/s (A) and 70 mm/s (B). Other parameters are: laser wavelength 800 nm, pulse width ~100 fs, average power ~400 mW, repetition rate 80 MHz, and depth of grating from front surface ~150 μm.

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Fig. 4 Plot of refractive index change induced by femtosecond laser micromachining as a function of scanning speed (mm/s).

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With the calibration procedure described above, we can then write an optical device based on the refractive index change profile. For a gradient index structure, we need to know the refractive index, or effectively the refractive index change relative to the untreated bulk material, at each coordinate of the structure. Since a specific refractive index change corresponds to a particular scanning speed at given experimental conditions, we need to know the relationship between the scanning speed and the coordinates inside the structure. This can be obtained in two steps. Firstly, the plot in Fig. 4 is reversed to get a relationship of scanning speed with respect to refractive index change. With the data acquired from experiment, an analytic function could be fitted so as to obtain scanning speed at any desired refractive index change. Secondly, a theoretical analysis of a thin lens structure allows us to design a refractive index profile for a thin lens with given focal lengths or powers (in diopter) [15]. A thin lens model is regarded as phase transformation from wave-optics point of view, with the thickness function illustrated in Fig. 5A . As a lens with constant refractive index but varying thickness, the total phase delay by light wave passing through the lens is,

φ (x, y) = k n Δ (x, y) + k [Δ_{0} - Δ (x, y)]

where k is the wavenumber in free space, n is the refractive index of the base polymer, x & y are coordinates in the plane normal to the incident wave, ∆(x,y) is the lens thickness at coordinates (x,y), and ∆₀ is the maximum lens thickness at center. The lens transformation is then,

t (x, y) = e^{j k n Δ_{0}} e^{- j k \frac{x^{2} + y^{2}}{2 f}}

where

f = {[(n - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})]}^{- 1}

is defined as the focal length of the lens, and R₁ and R₂ are the radii of the anterior and posterior surfaces, respectively.

Fig. 5 (A): A thin lens model with constant refractive index but curvature on both surfaces. The phase transformation leads to the lens power [15]; (B): Our lateral gradient index structure within a flat polymer sample. The refractive index change region inside the sample has a layered gradient index profile that consists of gradient index layers that are parallel to the material surfaces.

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Starting from the definition of focal length of a thin lens from wave-optics point of view, we can then propose a gradient index structure with certain focal length based on refractive index change purely induced by femtosecond laser micromachining, as shown in Fig. 5B. The bulk Akreos® sample has flat surfaces on both sides and uniform refractive index n₀, thus has no refractive power. The proposed gradient index structure is buried inside the bulk material and also has flat surfaces; however, the refractive index is not constant and varies as n₁(x,y) = n₀ + ∆n(x,y). Similarly, the phase delay and total lens transformation through the gradient index structure are as follows,

φ^{'} (x, y) = k n_{0} (Δ_{0} - t) + k n_{1} (x, y) t

t^{'} (x, y) = e^{j k n_{0} Δ_{0}} e^{j k Δ n (x, y) t}

where ∆n(x,y) and t are the refractive index change relative to that of the bulk material and the thickness of the gradient index structure, which are both determined by the femtosecond laser micromachining process. In order for the gradient index structure to work as an optical device, the refractive index change is proposed to behave as,

Δ n (x, y) = \frac{1 - (x^{2} + y^{2})}{2 f t}

so that the lens transformation of the gradient index structure becomes,

t^{'} (x, y) = e^{j k n_{0} Δ_{0}} e^{j \frac{k}{2 f}} e^{- j k \frac{x^{2} + y^{2}}{2 f}}

where

e^{- j k \frac{x^{2} + y^{2}}{2 f}}

renders a focal length of

f

for the gradient index structure, x and y are coordinates in the plane perpendicular to the incident light wave with origin at the center of gradient index structure, and ∆n(x,y) is a parabolic profile and depends on coordinates x & y, desired focal length f and the structure thickness t.

With the refractive index change calibration and design of gradient index structure described above, we now have a matrix of scanning speed as a function of refractive index change, which is also a function of coordinates and depends on presumed focal length and structure thickness. Thus, these calibration data can be then incorporated into the experimental scanning algorithms in order to write such a gradient index structure which works as an optical device. The first optical device that we write is a cylindrical lens written in a flat polymer sample (as illustrated in Fig. 6A ). The refractive index change only varies along one axis in the manner of a parabolic profile, while remaining constant along the other axis. This was achieved by raster scanning the laser focus inside the sample at a constant speed along y axis and at a varying speed along x axis (with a fashion derived from Eq. (5)). Each grating line (as shown in Fig. 3B) has a lateral width of ~1 μm. Three layers of gradient index layers are written at 150, 140, 130 μm depths from the anterior surface of sample. Each gradient index layer is ~1.84 mm wide and ~6 mm long. By raster scanning, each layer is written line-by-line with a spacing of ~0.7 μm. As a result of the high NA (~0.7) focusing, each layer is about 3 microns thick [12].

Fig. 6 (A): Experimental design of a cylindrical lens induced by femtosecond laser micromachining. Refractive index change is constant along y axis, and varies in a parabolic manner on x axis. The refractive index change is maximum in center and minimum at two edges on x axis. (B): Diagram illustrating wavefront measurement of the cylindrical lens. A pupil diameter of 1.5 mm is used, with pupil separation of 0.5 mm for measuring at different locations inside the cylindrical lens.

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In order to measure this device optically, we performed two types of procedures: wavefront measurement and interferometry. The first method is wavefront measurement using a standard Shack-Hartmann wavefront sensor system. To properly measure the cylindrical lens inside a bulk polymer sample, we chose a pupil diameter of 1.5 mm, which was nearly the width of the cylindrical lens (Fig. 6B). Since the lens was written by raster scanning the three-dimensional stage back and forth and the local refractive index change depended on scanning speed, we did expect some variation along the longitudinal direction as a result of imperfections in the scanning system accuracy. With a pupil step size of 0.5 mm, we could also evaluate the variations of this cylindrical lens. After we obtained all the Zernike coefficients from the Shack-Hartmann sensor, we could then extract the astigmatism in diopters using the following formula [16]

A s t i g m a t i s m = - \frac{1}{r_{0}^{2}} 4 \sqrt{6} \sqrt{c_{1}^{2} + c_{2}^{2}}

where

r_{0}^{}

is the pupil radius,

c_{1}^{}

and

c_{2}^{}

are astigmatism coefficients in horizontal and vertical directions. We also measured at a number of locations outside the cylindrical lens in the bulk polymer sample with the same parameters. With the background aberration subtracted, the astigmatism induced by the femtosecond laser micromachining process was measured to be as high as + 0.8 diopters with an average of + 0.64 diopters and standard deviation of 0.17. We wrote two cylindrical lens samples with identical design, and the average dioptric power was identical to within 0.07 diopters.

We then use our second method to have a qualitative measurement of the cylindrical lens: a Twyman-Green interferometer. It is a double-pass interferometer that can detect small phase variations when the light passes through the sample. The interferogram was taken with the bulk sample containing the rectangular cylindrical lens area (Fig. 7 ). As shown in Fig. 7, the bulk sample generates uniform fringes with smooth trend. When it comes to the cylindrical lens, shown in the rectangular area, there is an obvious phase jump from the bulk sample fringes. Yet, it is not uniform phase retardation from the optical path length (OPL) that the laser beam experiences through bulk sample. As expected, it gradually rises from one edge, reaches maximum in center, reduces down at the other edge and merges to the bulk fringes. This matches the experimental design with a parabolic phase structure. Since it is a gradient index lens, it is difficult to extract the astigmatism information from this interferogram; however, it gives an intuitive, straightforward way to visualize this type of device made of parabolic phase structure.

Fig. 7 Interferogram of polymer sample (Akreos®) with cylindrical lens written in the rectangular area. The solid curve represent the trend of fringes of the bulk sample. The additional curve in rectangular area shows additional parabolic phase added to the bulk sample fringes.

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For applications in vision correction, it is important to know whether the induced refractive index changes in Akreos polymer created by femtosecond micromachining are long-lived. We compared the structures as-written and after a 30 month period. Figure 8 shows the differential interference contrast microscope images for the Akreos® sample. There is no detectable change in the pattern after a ~30 month period, indicating that microlenses that are written into the materials should have good longevity.

Fig. 8 Differential interference contrast mode images of Akreos® sample doped with X-Monomer, showing no substantial change of the grating over a >30 month period. (A): The Akreos® sample with grating written on 10/31/2008 (as-written); (B): The same sample re-measured on 06/06/2011 (2 years, 7 months, 6 days later).

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4. Conclusion

We have demonstrated the ability to change the refractive index up to ~0.05 in a widely used ophthalmological polymer material, by using high-repetition-rate low-pulse-energy femtosecond lasers. An experimental calibration of the femtosecond laser micromachining conditions enables us to fully control the refractive index change profile, which is critical for fabricating large scale optical devices. We have designed, fabricated and characterized a cylindrical lens that can be written inside a bulk ophthalmic polymer sample. An average of 0.64 diopters of astigmatism has been achieved in the cylindrical lens region. An interferometric direct measurement of the lens shows parabolic wavefront, as expected. This work is significant in the sense that we can customize the power or aberration in clinically used intraocular lenses (IOL) either prior to or after implantation for cataract surgery. With improvement of programming and optical modeling, we can achieve at least a few diopters of power change and customize the IOL’s aberrations according to patients’ need.

By optimizing the laser, gradient index design, scanning and material parameters, we expect to be able to produce structures within the range of −3 to + 3 diopters of custom vision correction. With our recent work on exogenous and endogenous enhancement of Intra-tissue Refractive Index Shaping (IRIS) in living corneal tissue [17], we hope to be able to directly write gradient index structures into live cornea as well, which could result in a significant advance in vision correction.

Acknowledgments

This research was supported by grants from Bausch & Lomb, Inc. and the CEIS program (project number 5-29375) at the University of Rochester. The authors would like to thank Len Zheleznyak for metrology support with a Shack-Hartmann wavefront sensor, John Bowen for metrology support with Twyman Green Interferometer measurements, Dharmendra Jani for materials support, and Yuhong Yao for help on diffraction measurement during the calibration process.

References and links

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12. L. Ding, R. Blackwell, J. F. Künzler, and W. H. Knox, “Large refractive index change in silicone-based and non-silicone-based hydrogel polymers induced by femtosecond laser micro-machining,” Opt. Express 14(24), 11901–11909 (2006). [CrossRef] [PubMed]

13. L. Ding, D. Jani, J. Linhardt, J. F. Künzler, S. Pawar, G. Labenski, T. Smith, and W. H. Knox, “Large enhancement of femtosecond laser micromachining speed in dye-doped hydrogel polymers,” Opt. Express 16(26), 21914–21921 (2008). [CrossRef] [PubMed]

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17. L. Xu, W. H. Knox, and K. R. Huxlin, “Exogenous and endogenous two-photon absorption for Intra-tissue Refractive Index Shaping (IRIS) in live corneal tissue [Invited],” Opt. Mater. Express 1, 1159–1164 (2011) (feature issue on nonlinear optics).

Lateral gradient index microlenses written in ophthalmic hydrogel polymers by femtosecond laser micromachining

Abstract

1. Introduction

2. Experimental setup

3. Experimental procedure, results and discussion

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (8)

Equations (7)

Optical Materials Express