1. Introduction

Femtosecond laser micro-machining has attracted increasing interest due to its unique 3D structuring capabilities in transparent materials. Many different kinds of structures including optical waveguides, light couplers and 3D optical storage inside glasses [1–12] and photoresist polymers such as PMMA and photopolymerizable resin [13–15] have been created. When femtosecond laser pulses of sufficient energy are tightly focused in the bulk of a transparent material, the high intensity at the focus causes a nonlinear absorption (typically multi-photon absorption) and leads to a range of modifications due to optical breakdown or structural and chemical changes in the material. Several research groups have studied the refractive index change within the irradiated area in glass and polymeric materials and found values in the range of 1×^-2 to 1×^-4 [1–12, 15]. Since the absorption is strongly nonlinear, the index change inside the bulk materials is generally localized in the focal volume, leaving the surrounding area unaffected. By translation of the bulk sample with respect to the laser focal point, fabrication of different 3D structures can be realized. Recently, much larger index of refraction changes have been produced by femtosecond pulse irradiation in glasses that have been doped with semiconductor materials [16, 17]. In those reports, the large index increase was attributed to a phase separation, leading to formation of semiconductor microcrystallites.

Femtosecond lasers used in micro-machining can be operated over a wide range of parameters, from low-repetition-rates (10 Hz to 1MHz) with pulse energies of microjoules to millijoules [1–6], to high-repetition-rates (>1MHz) femtosecond lasers with pulse energies typically of the order of nanojoules [7–12]. For low-repetition-rate femtosecond lasers, the excitation density is usually well above the material nonlinear absorption threshold, and because the thermal diffusion time is much shorter than the time interval between the adjacent laser pulses, usually each pulse is responsible for the change of the focal volume and the modification region is often within the focal volume. Under some focusing conditions, these high energy pulses may lead to micro-machined structures with asymmetric modification profiles. In the other hand, when high-repetition-rate femtosecond lasers are used, heat accumulation plays a more important role in the laser-material interaction. In this case, the thermal diffusion time is longer than the time interval between the laser pulses, and the absorbed laser energy can accumulate within the focal volume and increase the laser-material interaction temperature [18, 19]. Usually as a result, the size of the modification region will increase and a more symmetric structure may be formed. For high-repetition rate femtosecond lasers, generally the pulse energy is much lower than that of the low-repetition-rate femtosecond lasers. Since material nonlinear multi-photon absorption is highly peak powerdependent, at low pulse energies it is possible that only the center part of the pulse has enough power to exceed the nonlinear absorption threshold and introduce modifications. Therefore with the combined effects of multi-photon absorption and heat accumulation, the structures that high-repetition-rate, low-pulse-energy femtosecond lasers create can still be of the order of the focus size, or within the focal volume [7, 9].

In this paper, we report the fabrication of optical diffraction gratings inside several silicone-based and non-silicone-based hydrogel materials by using a high-repetition-rate, lowpulse-energy femtosecond laser. The principal difference between our work and the previous work is that the femtosecond micromachining in our experiment is done in an aqueous environment and there is no photoinitiator inside of these polymers for photopolymerization. Since these hydrogel polymers substantially absorb water and dry quickly in an air environment, the fabrication and measurements are always performed within the aqueous solution. By measuring the diffraction efficiency of the gratings, we find relatively large average refractive index changes ranging from 0.03±0.005 to as large as 0.06±0.005 in lines of roughly 1 micron width, 3 microns depth at 5 microns spacing.

2. Experiment setup

The femtosecond laser micro-machining experiment setup is shown in Fig. 1. The laser source is a Kerr-lens mode-locked Ti:Sapphire laser (K-M Labs) pumped by 4 W of green light from a frequency-doubled Nd:YVO₄ laser. The laser generates pulses of 300 mW average power, 30-fs pulsewidth and 93MHz repetition rate at 800 nm. The measured average laser power at the objective focus on the material is about 120mW, corresponding to a pulse energy of about 1.3 nJ. We use two SF10 prisms in a double-pass configuration at 37.5cm separation distance between the prisms to compensate the dispersion of the microscope objective. A collinear autocorrelator using 3^rd order harmonic generation is employed to measure the pulse width at the objective focus. A concave mirror pair is added into the optical path in order to adjust the beam size to optimally fill the objective aperture. We used third order surface harmonic generation (THG) autocorrelation to characterize the pulse width at the focus of the high-numerical-aperture objectives because of its simplicity, high signal to noise ratio and lack of material dispersion that second harmonic generation (SHG) crystals usually introduce [20, 21]. The THG signal is generated at the interface of air and an ordinary cover slip (Corning No. 0211 Zinc Titania glass), and measured with a photomultiplier and a lock-in amplifier. We tested a set of different high-numerical-aperture objectives while carefully adjusting the separation distance between the two prisms and the amount of glass inserted. We found that a nearly transform-limited 30-fs duration pulse can be obtained at the focus of a 60X 0.70NA Olympus LUCPlanFLN long-working-distance objective. Three Newport VP-25XA linear servo stages with 100 nm resolution form a 3D scanning platform which is controlled and programmed by computer. Since they are DC servo-motor driven stages, they can move smoothly between adjacent steps. In addition, a CCD camera along with a monitor is used beside the objective to real-time monitor the micro-machining process.

 

Fig. 1. Experimental setup for femtosecond micro-machining

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3. Experiment result and discussion

Three different polymers have been initially studied in our experiments. They are amorphous hydrogels with degradation temperature of about 250 °C. PV2526-164 is a silicone-containing hydrogel that can absorb 36% water by weight. RD1817 is a hydrogel based on a copolymer of 2-hydroxyethyl methacrylate and N-1-vinyl-pyrrolidinone that absorbs 80% water by weight, and its refractive index when hydrated is very close to the index of water. HEMA B is a hydrogel based on 2-hydroxyethyl methacrylate that absorbs 38% water by weight. Its refractive index is the highest among these three materials. Table 1 shows the parameters of the three polymers. We measured the refractive indices in a hydrated state by ellipsometry. Figure 2 shows the transmission spectra of these materials measured by an Ocean Optics HR4000 Spectrometer.

Table 1. Parameters of different hydrogel polymers

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Fig. 2. Transmission spectra of PV2526-164, RD1817 and HEMA B

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The hydrogel samples are mounted horizontally on the scanning platform, and the femtosecond laser is focused with a high-numerical-aperture objective through a cover slip inside the sample (Fig. 3).

 

Fig. 3. Samples are placed in a hydrating solution between two microscope slides and irradiated with 30 fs pulses. The sample holder is translated continuously.

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The hydrogel samples are maintained in a solution (Bausch and Lomb “Renu” solution) in room temperature to maintain their water-content during micro-machining and subsequent optical measurements. The thickness of these hydrogel samples in the solution is about 700µm, and the laser is typically focused ~100µm beneath the top surface of the sample. Periodic gratings structures were fabricated with a scanning speed of 0.4µm/s in an X-Y plane perpendicular to the laser beam. Figure 4 shows the differential interference contrast (DIC) and phase contrast (PC) images of plan views of the gratings that we made inside these three materials. We use an Olympus BX51 Model microscope for these pictures.

 

Figs. 4. (a) and (b). (a). and 4 (b). DIC and PC images of a grating in PV2526-164

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Figs. 4. (c) and (d) (c). and 4 (d). DIC and PC images of a grating in RD1817

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Figs. 4. (e) and (f) (e). and 4. (f). DIC and PC images of a grating in HEMA B

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These images show periodic structures with a 5-µm spacing were fabricated inside the samples. The structures are difficult to see in bright-field microscope, indicating that these structures exhibit very low scattering loss. We estimate that the width of the grating lines is approximately 1 µm, which is significantly smaller than the laser focus diameter 2.5 µm that we measured using a knife-edge method in air. We investigated the cross sectional images of the lines by cutting the material with a razor blade mounted on a xyz translation stage perpendicular to the lines. Figure 5(a) shows a DIC image of the cross section of a grating line formed inside the PV2526-164 polymer. We notice that the cross section has an elliptical shape. From these photos, we estimate that the thickness of the line is approximately 3 µm. In a transverse writing configuration, the laser modification region is typically found to be extended in the longitudinal direction [22]. In particular, we note that spherical aberration caused by the refractive index mismatch between the air, cover slip and polymer can strongly influence the cross section [23]. The Olympus focusing objective that we use has a variable cover slip correction covering a variation in thickness ranging from 0.1 to 1.3 millimeters. By carefully adjusting the cover slip correction of the objective, we are able to compensate the spherical aberration of the focusing laser beam even when the focus is deep inside of the bulk polymer materials, to achieve the result shown in Fig. 5(a). In contrast, Fig. 5(b) shows the cross section of a line formed inside PV2526-164 without any spherical aberration correction, where the longitudinal axis is 10 microns long.

 

Fig. 5. Cross section of one grating line formed inside PV2526-164 (a) with spherical aberration correction, (b) without spherical aberration correction

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We investigated these gratings by focusing an unpolarized He-Ne laser beam with a wavelength of 632.8nm on these gratings and monitoring the diffraction pattern. The diffraction angles showed good agreement with the diffraction equation:

where m is the diffraction order, λ is the wavelength of the incident laser beam which here is 632.8nm, and d is the grating period. Figure 6 shows the diffraction patterns of these three gratings.

 

Fig. 6. (a). Diffraction pattern of the grating fabricated in PV2526-164

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Fig. 6. (b). Diffraction pattern of the grating fabricated in RD1817

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Fig. 6. (c). Diffraction pattern of the grating fabricated in HEMA B

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Diffracted light from 0^th order to 2^nd order can be easily seen in these images. The diffraction efficiency of the grating can be measured, and since the efficiency is a function of the refractive index change, we can use it to calculate the refractive index change in the laser irradiation region. Considering the grating as a phase grating, its transmittance function can be written as:

where a is the grating linewidth, d is the groove spacing, ϕ ₂ and ϕ ₁ are the phase delays through the lines and ambient region respectively: ${\varphi }_2=2\pi \times \frac{(n+\Delta n)\times b}{\lambda }$ and ${\varphi }_1=2\pi \times \frac{n\times b}{\lambda }$ . b is the thickness of the grating line, n is the average refractive index of the material, Δn is the average refractive index change in the grating lines, and λ is the incident light wavelength of the measurement (632.8nm). Here, the grating linewidth we are using is 1 µm and the thickness is 3 µm. We assume a uniform (‘top-hat’ shape) index change within the lasereffected region. The convolution theorem can be used to calculate the spectrum of the grating such as:

Then, the intensity distribution of the grating diffraction pattern is:

From this formula, the intensities of the 0^th, 1^st and 2^nd order diffraction light are:

and

By comparing the light intensities of 1^st, 2^nd and 0^th diffraction orders, we can determine the refractive index change within the grating lines. Figure 7 shows the ratio of intensity of the 1^st diffraction order to 0^th order of the grating in PV2526-164 is 0.1374, and the corresponding refractive index change determined by the analysis is about 0.06. Using the ratio of intensity of the 2^nd diffraction order to 0^th order of the grating, the calculated refractive index change is virtually identical. We note that several factors could affect this result, such as the accuracy of measurement of the different diffraction order intensities, and the measurements of grating linewidth and thickness. To reduce measurement error of the diffraction order intensities, we usually took several measurements and averaged the results. In principle, the refractive index change is not a uniform top-hat function, rather we suspect that it is a gradient-index structure on a small scale. From the cross-section pictures (Fig. 5), we can see that the affected region is reasonably well-defined. For the purposes of the present investigation, we assume that the index profile is uniform, and considering our measurement accuracy of the parameters as discussed, we calculate an error bar on the refractive index change of±0.005. Using the same method, we determine the average refractive index change in RD1817 and HEMA B are 0.05±0.005 and 0.03±0.005.

 

Fig. 7. Using 1st order diffraction efficiency to calculate refractive index change in PV2526-164

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4. Discussion and conclusions

The index of refraction changes that we observe in these experiments are much larger than those that have been observed in ordinary glasses or other polymer materials. We can speculate on the origin of the optical effects. We believe that the action of the femtosecond pulses is principally to cause a phase separation similar to that discussion by Takeshima [16, 17], except that instead of the phase separation causing a precipitation of semiconductor microcrystallites, in our case, there may be a densification of the polymer material such that water is locally excluded from the line regions, leading to a large change in refractive index. We note that, in principle, the index change could be positive or negative, and the diffraction grating experiments would not elucidate the difference, however if the change is due to a material densification, we would expect the change to be positive. We have performed preliminary experiments on waveguide fabrication in these materials under nearly identical conditions, and these results suggest that the index change is positive. These results will be reported elsewhere.

We found large refractive index change in hydrogel polymers induced by a high-repetition rate, low-pulse-energy femtosecond laser. The modified regions are as small as 1µm×3µm, and the average refractive index changes as large as 0.06±0.005 at room temperature are observed. We are further investing fabrication of more complex three-dimensional optical structures and the dependence of the refractive index change on the different pulse energy and temperature, and these results will be reported in the future.