Appl. Phys. A 76, 257–260 (2003)
Applied Physics A
DOI: 10.1007/s00339-002-1447-z
Materials Science & Processing
a. marcinkeviˇcius1 v. mizeikis1 s. juodkazis2 s. matsuo2 h. misawa2,✉
Effect of refractive index-mismatch on laser microfabrication in silica glass 1 Laboratory
of Photonic Nano-Materials, The University of Tokushima, 2-1 Minamijyosanjima, Tokushima 770-8506, Japan 2 Department of Ecosystem Engineering, The University of Tokushima, 2-1 Minamijyosanjima, Tokushima 770-8506, Japan
Received: 3 December 2001/Accepted: 11 April 2002 Published online: 10 September 2002 • © Springer-Verlag 2002
We studied the peculiarities of femtosecond laser microfabrication in silica glass with a refractive index that did not exactly match the value for which the focusing optics is designed. Spherical aberrations resulting from a small refractive index mismatch were found to increase the size and distort the shape of photodamaged regions, thus reducing the spatial resolution of the microfabrication. However, these undesirable effects can be minimized, providing that the focusing depth inside the glass is not too large, and the laser intensity is kept close to the light-induced damage threshold.
ABSTRACT
PACS 61.80.Ba; 41.85.Gy;
1
61.43.Fs
Introduction
Femtosecond laser microfabrication is becoming increasingly competitive with other known microfabrication techniques [1–5]. It utilizes light-induced breakdown, which occurs at the focal spot of a tightly focused femtosecond laser beam. Dielectrics, usually transparent to the laser irradiation, may become strongly absorbing in the focal spot region due to multi-photon absorption and avalanche ionization. The photogenerated electron-hole plasma causes further absorption until material breakdown is reached in this highly localized region, leaving the surrounding material intact. The size of this region may become reduced towards or even below the laser wavelength if high numerical aperture (NA) oil immersion microscope objectives are used for the focusing [6–8]. Most of the commercially available high NA transmission objectives are optimized for the imaging of specimens mounted on a cover glass with a refractive index of n = 1.522 (for λ = 587.56 nm) and a thickness of 0.17 mm. Deviation from this thickness or refractive index value results in a spherical aberration, which decreases the peak intensity of the focused beam, along with shifting and severely extending the focal region in the direction of the beam propagation [9, 10]. Many practical tasks of femtosecond laser microfabrication will invariably require such deviations. First, the fabrication of complex microstructures (e.g. microfluidic de✉ Fax: +81-88/656-7598, E-mail:
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vices [11]) requires sequential scanning of the focal spot position over a broad range of focusing depths (relative to the sample surface). Secondly, in some microstructures, such as photonic crystals, it is necessary to maximize the refractive index contrast between the removed and intact regions, which can only be achieved by using initial materials with a refractive index higher than two [12]. Under such circumstances, it is reasonable to expect that spherical aberration will strongly influence the size and shape of the photodamaged regions and the intensity of the light-induced damage threshold (LIDT). However, to-date this influence has been neglected [1, 13], or microfabrication has been performed in refractive indexmatched materials and at focusing depths for which the microscope objectives were aberration-corrected [3, 6]. In an attempt to fill this gap, in this paper we investigate the shapes of photodamaged regions in glass which were created by tightly focused femtosecond laser pulses in the presence of a small refractive index mismatch between the immersion oil and the sample. From the data acquired in the experiments, and numerical modeling, we identified the influence of spherical aberration on the shape of the photodamaged region. In addition, we show that this influence can be minimized by adjusting the laser intensity close to the LIDT. 2
Description of experiments
First consider the focusing of a laser beam in the presence of a refractive index mismatch between the immersion oil and glass. As shown in Fig. 1, the laser beam propagated along the z-axis direction is focused by the microscope objective lens across the oil–glass interface into the glass. If n 1 = n 2 (no mismatch), laser light converges to the focal point O , as illustrated by straight thick lines. In this case, focusing conditions are independent of the focusing depth d . If n 1 = n 2 , the index mismatch at the oil–glass interface may deflect the laser light along the paths shown by thin solid lines to converge at the point O1 (in the case of n 1 < n 2 ). Thus, the focusing depth becomes shifted by the amount ∆ f along the z -axis, and spherical aberrations arise. It is quite obvious that in this case, the focal shift, the size of the focal spot, and the irradiation peak intensity will depend upon the focusing depth. Based on these considerations, we chose two glass samples with non-matching refractive indices for our investigations, and another sample with a matching refractive index
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an oil immersion objective lens (Plan-Neofluar ×100, NA = 1.3, Zeiss), with a maximum lateral resolution of ∆rlat = 230 nm. The confocal pinhole diameter was set to 19.2% of the Airy disk intensity distribution, which corresponds to ∆z ax = 680 nm axial resolution. In all measurements we examined the side view images of the photomodified regions, which allowed us to minimize the influence of spherical aberration during examination of the fabricated samples. 3
FIGURE 1 Focusing of light by oil immersion microscope lens into the glass in the presence of refractive index mismatch (n 2 < n 1 ) between the oil immersion and glass
as a reference. We measured and compared LIDT dependencies on focusing depth for these three samples in an attempt to identify the influence of the spherical aberration. Next, we experimentally investigated conditions under which the influence of spherical aberration is minimized. This was done by direct observation under a confocal laser microscope of glass regions that were photodamaged at different laser intensities. Finally, to clarify the role of spherical aberration in our findings, we performed numerical calculations based on a simple but adequate model. The two glass samples with non-matching refractive indices were dry v-SiO2 , EDC brand from Nippon Silica Glass Co. (n = 1.473 (for λ = 587.56 nm), with a thickness of (140± 20) µm), and VIOSIL brand silica glass from the ShinEtsu Chemical Co. (n = 1.4534 (for λ = 587.56 nm), with a thickness of (250 ± 20) µm). The side surfaces of the samples were polished to allow a side view of the photodamaged regions. The reference sample with matching refractive index used for the LIDT measurements was a microslide from Matsunami Glass Ind. (n = 1.522 (for λ = 587.56 nm), with a thickness of 1 mm) made of the same glass as the cover glass plates optimized for the oil immersion objective used in this work. The microfabrication laser source was a modelocked Ti:sapphire laser oscillator with a regenerative amplifier (pulse duration 140 fs, central wavelength 800 nm, pulse repetition rate 1 kHz). The laser irradiation was focused by an oil-immersion objective lens (Universal Plan Apochromat ×100, NA = 1.35, Olympus) in an inverted-type microscope Olympus IX70. In the experiments we used oil with the refractive index n = 1.515 (for λ = 587.56 nm). The pulse energy at the entrance of the microscope was adjusted between 5 nJ and 1 µJ by a neutral density filter attenuator. Transmission of the microscope and the objective lens was 0.56 at 800 nm. A computer-controlled 2D translation stage with 0.1 µm resolution was used for the sample translation in the x – y plane, synchronized with the arrival of the laser pulses to obtain ordered arrays of damage spots. Fabricated arrays were examined later using a confocal laser scanning microscope (Zeiss, LSM-410), operated in reflection mode. Under the confocal microscope, the sample was illuminated by an argon ion laser 488 nm line through
Results and discussion
Before measuring the dependencies of LIDT on the focusing depth, it is necessary to define the criteria and techniques used for determination of LIDT. We define single-shot LIDT as the energy level at which 75% of laser shots leave damage that is observable as optical contrast changes in the glass. Experimental determination of LIDT was performed from direct in situ optical observation of the sample under condenser white light illumination. Assuming NA = 1.35 and the illumination central wavelength is 550 nm, the lateral size of the smallest observable region is about 250 nm. The focusing depth was measured from the top surface of the samples, and was changed by the mechanical movement of the microscope objective. Experimental dependencies of the LIDT thus defined on the focusing depth are presented in Fig. 2. As can be seen, in both index-mismatched (EDC and VIOSIL) glasses the LIDT increases nearly linearly with the focusing depth, such that an increase in the depth by 100 µm results in a two-fold increase in the LIDT. In our opinion, the measured dependencies directly indicate that, as pointed out at the beginning of the previous section, the volume of the photodamaged focal spot region increases with the focusing depth, presumably as a result of the spherical aberration. For comparison, in the index-matched microslide glass (Fig. 2b, filled circles), LIDT is almost constant with the focusing depth, exhibiting just a slight minimum around 130 µm, followed by a moderate gradual increase above 170 µm. It is helpful to bear in mind that an increase of the LIDT starts at a depth that is equal to the
FIGURE 2 Experimental dependencies of the LIDT on the focusing depth in a EDC glass, b VIOSIL glass (solid squares), and microslide glass (solid circles). The solid lines are the results of numerical simulations (see explanation in the text). The LIDT is expressed in units of laser pulse energy measured at the entrance to the microscope
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Effect of refractive index-mismatch on laser microfabrication
thickness of the cover slip for which the microscope objective is aberration-corrected. Next, we recorded arrays of damage spots to be directly observed with the confocal laser-scanning microscope. Figure 3 shows side images of the photodamaged regions in EDC glass at two focusing depths (30 µm (Fig. 3a–c) and 100 µm (Fig. 3d–f)) and three different light intensities measured in terms of LIDT (about 1.5×LIDT (Fig. 3a and d), 2 × LIDT (Fig. 3b and e), and 4 × LIDT (Fig. 3c and f)). In all images the pulses propagated along the z -axis. We stress here that, according to the data in Fig. 2, LIDT depends upon the focusing depth. Thus, achieving the same intensity in the units of LIDT at different focusing depths requires different pulse energies beforehand, at the entrance of the microscope. Focusing at the 30 µm depth yields nearly spherical photodamaged regions with a diameter of about 600 nm if the intensity is close to a single LIDT (see Fig. 3a). We note that with the microscope objective used in the experiments, the attainable diffraction-limited beam diameter at the focus was 0.722 µm. By increasing the intensity, the photodamaged regions begin to extend along the z -axis, reaching 800 nm and 1 µm (see Fig. 3b and c)). At the same time, their transverse diameter along the x -axis remains unaffected. Although at the highest intensities the photodamaged regions became nonspherical, we did not detect their splitting along the direction of beam propagation into several smaller regions. Focusing at the 100 µm depth at intensity close to a single LIDT also yields nearly spherical photodamaged regions with a diameter of about 630 nm (see Fig. 3d). At 2 × LIDT, noticeable axial elongation to about 940 nm occurs, and a splitoff photodamaged region develops at about 1.3 µm distance
µ
µ
FIGURE 3 Confocal side images of photodamaged regions obtained in reflection and displayed as contour plots. The photodamage was induced at two different depths and three different pulse energies, indicated in the plots. In all experiments the beam propagated along the z-axis. Scale bar 1 µm
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from the focal point (see Fig. 3e). Increasing the intensity to 4 × LIDT further extends the photodamaged region along the z -axis to an area about 2.2 µm in length, and increases the distance to the split-off region to about 2 µm (Fig. 3f). For this focusing depth, the transverse diameters of the first and second nearly spherical regions are unaffected by intensity, and remain close to 630 nm. To interpret the experimental results, we calculated the intensity distributions near the focus of a high NA objective in the presence of the refractive index mismatch. For the situation sketched in Fig. 1, the electric field distribution in glass for the paraxial approximation can be expressed as [10, 14] φ E(, z) =
√
cos ϕ1 sin ϕ1 (τs + τ p cos ϕ2 )J0 (k0 n 1 sin ϕ1 )
0
× exp(iΦ + ik0 zn 2 cos ϕ2 )dϕ1 ,
(1)
where φ is the half angle of the light convergence cone, k0 = 2π/λ is the wave number in a vacuum, and = x 2 + y2 , ϕ1 and ϕ2 are the angles of the ray convergence in the first and second media, respectively, which are related to each other through Snell’s law: n1 ϕ2 = sin−1 sin ϕ1 . (2) n2 The coefficients τs and τ p are the Fresnel transmission coefficients for s and p polarizations, and are functions of n 1 , n 2 , ϕ1 , ϕ2 [15]. The function Φ is the spherical aberration function [10, 16] that describes the effect of the refractive index mismatch: Φ = −k0 d(n 1 cos ϕ1 − n 2 cos ϕ2 ),
(3)
where d is the distance between sample surface and diffraction-limited focus (see Fig. 1). The radial and axial coordinates and z are defined with respect to the diffraction-limited focus in the absence of the second medium. Using (1)–(3), we calculated the intensity distribution in the x –z plane for NA = 1.35, irradiation wavelength λ = 800 nm, n 1 = 1.515, and the value of n 2 pertaining to EDC or VIOSIL glass. The primary goal of the numerical simulations was to determine whether the spherical aberrations are responsible for the observed dependence of the LIDT on the focusing depth. Therefore, we calculated the axial intensity distributions |E(0, z)|2 in both samples for focusing depths in the range from 0 – 250 µm. Some of the most informative results are presented in Fig. 4, which shows the calculated intensity distributions in EDC glass for three focusing depths. The data makes it evident that the central maximum of the focused beam intensity distribution spreads along the propagation direction with increasing focusing depth. In the calculations, given that the incident power was fixed, the intensity decreases are due to the increase in the area of the focused beam. The position of the main maximum, which is associated with the focal spot, shifts towards to sample surface (from about 1.8 µm at 30 µm to about 4.4 µm at 100 µm), and the peak intensity drops about two times. In the case of d = 100 µm, the axial width of the central maximum and the position of
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µ µ
µ FIGURE 4 Calculated axial intensity distribution of the laser radiation, focused through the immersion oil into a slightly index-mismatched EDC glass by an NA = 1.35 objective. The beam propagation direction is shown by the arrow. Different curves correspond to different focusing depths, as indicated in the plot
the secondary maximum are about 3 µm and 2.2 µm, respectively. Using the numerical simulation, we fitted the experimental data in Fig. 2a and b (the fits are shown as solid lines). Fairly good correspondence between the experimental and calculated dependencies clearly indicates that LIDT increases with focusing depth, mainly due to the spherical aberration that results from the refractive index mismatch. Deviation of the experimental dependencies from the numerical ones are most likely caused by the propagation effects of the ultra-short pulses in our optical setup; namely, by the time delay between the pulse front and the phase front in the focal plane. As follows from (1), such effects were neglected. A better insight into the calculated data can be gained by considering the intensity distributions in the x –z plane. Such dependencies are shown in Fig. 5 for EDC glass at two focusing depths. The appearance of additional intensity maxima, which become more pronounced for larger focusing depths, is evident. Finally, it is useful to briefly examine the relation between shapes of the experimentally damaged regions from Fig. 3 and the calculated spatial intensity distributions from Fig. 5. Because plasma only forms around the main peak at intensities close to LIDT, aberration-related weaker side wings (Fig. 5) do not induce noticeable damage. When the intensity significantly exceeds the LIDT (i.e. when the pulse energy > 1 µJ), critical density plasma is at first excited at the focus by the leading edge of the laser pulse. Since this region becomes highly reflective for the remainder of the laser pulse, the excited region subsequently spreads backwards, towards the area strongly affected by spherical aberration. From a micromachining perspective, it is clear that the highest spatial resolution is achieved when such phenomena are minimized, i.e. when the intensity is close to the LIDT and focusing depth is reasonably low. 4
Conclusions
We have found that even a small refractive index mismatch between the immersion oil and transparent medium can cause a significant loss of resolution in laser microfabrication experiments as a result of spherical aberration. For the typical pulse energies used in microfabrication, secondary intensity maxima in the intensity distribution may result in substantially elongated photodamaged regions.
FIGURE 5 Calculated spatial intensity distribution in the x–z plane at two different focusing depths: a d = 30 µm, b d = 100 µm
Based on experimental data and numerical analysis, we show that these undesirable effects can be minimized by keeping the laser irradiation level close to the light-induced damage threshold. REFERENCES 1 H. Misawa, H. Sun, S. Juodkazis, M. Watanabe, S. Matsuo: Proc. SPIE 3933, 246 (2000) 2 M. Miwa, S. Juodkazis, T. Kawakami, S. Matsuo, H. Misawa: Appl. Phys. A 73, 561 (2001) 3 C.B. Schaffer, A. Brodeur, E. Mazur: Meas. Sci. Technol. 12, 1784 (2001) 4 K.M. Davis, K. Miura, N. Sugimoto, K. Hirao: Opt. Lett. 21, 1729 (1996) 5 E.N. Glezer, M. Milosavljevic, L. Huang, R.J. Finlay, T.-H. Her, J.P. Callan, E. Mazur: Opt. Lett. 21, 2023 (1996) 6 Ch.B. Schaffer, A. Brodeur, J.F. Garcia, E. Mazur: Opt. Lett. 26, 93 (2001) 7 S. Juodkazis, M. Watanabe, H.B. Sun, S. Matsuo, J. Nishii, H. Misawa: Appl. Surf. Sci. 154–155, 696 (2000) 8 M. Horiyama, H.-B. Sun, M. Miwa, S. Matsuo, H. Misawa: Jpn. J. Appl. Phys. 38, L212 (1999) 9 C.J.R. Sheppard: Appl. Opt. 39, 6366 (2000) 10 M. Gu, D. Day, O. Nakamura, S. Kawata: J. Opt. Soc. Am. A 18, 2002 (2001) 11 A. Marcinkeviˇcius, S. Juodkazis, M. Watanabe, M. Miwa, S. Matsuo, H. Misawa, J. Nishii: Opt. Lett. 26, 277 (2001) 12 V. Mizeikis, S. Juodkazis, A. Marcinkeviˇcius, S. Matsuo, H. Misawa: J. Photochem. Photobiol. C: Photochem. Rev. 2, 35 (2001) 13 W. Watanabe, T. Toma, K. Yamada, J. Nishii, K. Hayashi, K. Itoh: Proc. SPIE 4088, 44 (2000) 14 A.C. Dogariu, R. Rajagopalan: Langmiur 16, 2770 (2000) 15 M. Born, E. Wolf: Principles of Optics (Cambridge University Press, Cambridge 1999) 16 P. Török, P. Varga, Z. Laczik, G.R. Booker: J. Opt. Soc. Am. A 12, 325 (1995)
