We successfully developed an arbitrary micro-patterning method with femtosecond pulses using a multi-level phase type diffractive optical element (DOE) and a focusing objective lens. The large chromatic dispersion effects of DOE resulting from the spectral bandwidth of femtosecond pulses can be reduced with the appropriate DOE focal length and the proper distance between the DOE and the focusing lens. The method was verified through optical and processing experiments. A partial periodic structure was formed at the designated position. Microstructures were precisely formed on the SiO2 glass surface and inside the glass by irradiating the constructed beam. The points were evenly dispersed with a separation of 5 μm.
©2004 Optical Society of America
Recently research and development into femtosecond laser microprocessing has progressed considerably allowing the fabrication of optical waveguides [1,2] and periodical structures such as gratings [3,4] or photonic crystals [5,6]. Focused femtosecond pulses achieve a high energy density at the focal point. This causes a multiphoton absorption, thus transparent materials can be processed at the focal point. Generally a femtosecond laser beam is simply focused into or on transparent materials and scanned through the materials to form the structure. The advantage of this method is that it can fabricate complicate microstructures, however it takes a significant amount of time to form large-scale structures and the energy efficiency is poor because the laser beam is not used effectively. Moreover, the focal shape is difficult to control.
In order to solve these difficulties, holographic techniques such as multibeam interference methods have been investigated for making periodical structures such as gratings  or photonic crystal structures [8,9] inside SiO2 glass using femtosecond pulses. These methods have the advantage of being able to make large-scale structures, however, it is difficult to control the shape and position of each interference area. Moreover the optical setup for the interference pattern is extremely complicate and hard to align.
On the other hand, DOEs (diffractive optical elements) have excellent control over spot array generation, image reconstruction, and the construction of focal shapes, such as a top hut shape . Tunable devices, such as liquid crystal spatial light modulators, are applicable for laser micromachining . These methods are also used in femtosecond laser irradiation, for example, fan-out multi-beam generation  and fabrication of long period fiber Bragg gratings with phase masks . However, these approaches were used for simple periodical patterns like 1-dimensional grating structures or multi-beam generation, and not applied in making microstructures on the order of several microns.
In this paper, we propose an arbitrary micropatterning method using a DOE for femtosecond laser irradiation. This method is simple but has the advantage of forming complicate microstructures, moreover the DOE patterns and irradiation system is easy to control the design.
2. Optical design
When a DOE is used in the irradiation of ultra-short pulses such as femtosecond pulses, excessive chromatic dispersion becomes a problem because of its wide spectral bandwidth. Chromatic dispersion causes both lateral and longitudinal aberrations and results in a distorted beam spot . The dispersion of DOE follows the relation,
where fb is the focal length of the DOE, λ is the center wavelength of the laser pulse and Δλ and Δfb are the derivatives of λ and fb, respectively. Equation (1) gives a large negative chromatic dispersion compared to ordinary glass lenses. If a femtosecond laser beam, which has a wide spectral width, is focused using only the DOE, this chromatic dispersion makes for a looser focus and as a result, resolution become worse. For example, when Δλ = 40 nm for a λ = 800 nm, equation (1) gives a change of focal length, fb, of 5 %, and this give 500 μm for an fb=10 mm. Other problems also exist when using only a DOE setup, for example Numerical Aperture (NA) of a DOE is not very high. This prevents microprocessing. Another problem is that a special design for the DOE and optical system is required. Therefore in order to decrease the chromatic dispersion, increase the NA and simplify the optical design, we used a DOE with a long focal length and inserted an objective lens after the DOE. The objective lens reduces the effective focal length of the total system and the effective NA becomes higher. As a result, the change of focal shift by λ is reduced as well. This method is simple but extremely effective for reducing the chromatic dispersion and simplifying the design of the optical system.
Figure 1 shows the configuration for the femtosecond laser irradiation with the DOE. The focal point of the DOE without the lens is at point P’. The focal length is fb and the imaging height is M. The focal point moves to point P when the lens with a focal length of f is inserted after the DOE. The focal length becomes Zm and the imaging height becomes y. From the geometrical optical analysis in paraxial regime, the height, y and length, Zm, are obtained by using the distance, x, between the DOE and the focusing lens. The parameters, x, f, and fb are the critical parameters for determining the degree of chromatic dispersion. To decrease the chromatic aberration, the conditions, fb ≫ f, fb > x, f > M should be satisfied. By using these relationships and neglecting the terms of f2/fb2, the equations below are obtained:
From Eqs. (2) and (3), fb and M are roughly reduced to f/fb of the image. Therefore we can make arbitral focal patterns from the set of many focal points by changing the value of fb and M in the DOE. This method simplifies the optical design. From Eqs. (4) and (5), the magnitude of the aberration can be estimated. To prevent focal elongation by Δλ, the ΔZm value should be comparable to the focal depth of the focusing lens. In this case, Δf becomes an important parameter, because, if Δf is designed as
then ΔZm can be reduced to 0.
A long focal length, fb, for the DOE is good for small chromatic aberration. However, if fb is more than 2000 mm, a difficulty arises when designing and fabricating it. Since a long focal length results in a very small phase modulation, smaller pitch multilevel quantization is required in constructing the required wavefront. A smaller ΔZm can be achieved by decreasing the focal length value, f, however, the entrance pupil also gets smaller as the value of f decreases. As a result, the narrow pupil may eclipse the image formed by the DOE. By taking these considerations into account, we chose f = 10 mm, fb = 1600 mm, and x = 500 mm. We could not obtain the Δf value, so we assumed that the absolute value of Δf was less than 2.5 μm. This would result from a focal depth for objective lens with numerical aperture (NA) of 0.4. The absolute value of Δλ and M were also assumed to be less than 20 nm and 2.2 mm respectively. Then the absolute values of ΔZm and Δy are estimated to be less than 6 μm and 1 μm, respectively. This value is much smaller than if only the DOE, which has a focal length of 10 mm, was used.
3. Experimental setup
Figure 2 shows the experimental setup for femtosecond laser irradiation with the DOE. The DOE was mounted before the objective lens at a distance of 500 mm. We used Ti:sapphire multi-pass amplifier (FEMTOPOWER compact PRO, FEMTOLASERS) which had a 400 fs pulse duration (at 1 kHz), a center wavelength of 800 nm and 40 nm of bandwidth. The beam cross-section was slightly elliptical. Since the amplifier was designed to provide ultrafast pulses of less than 30 fs, the beam mode was poor. M2 was about 2. The laser beam passed through the DOE and was focused by the objective lens (M Plan NIR 20x, Mitutoyo), which had a focal length of 10 mm and an NA of 0.4. A SiO2 glass sample was mounted on a XYZ-translation stage and irradiated by the modified laser pulses. The coordinate system is shown in Fig. 2. The focused laser beam profile was observed by using a beam profiler with a near-IR 100x objective lens mounted on the same XYZ stage. Pulse energy before the DOE was 5.7 μJ and 50 pulses were shot into the glass.
A DOE, which consisted of 22 focal points with a partial periodic structure, was designed. The DOE had a long focal length of 1600 mm. The focal shape of the DOE is shown in Fig. 3(a). The cross-sectional focal area was about 4 mm by 4 mm. This pattern was reduced by about 1/100 by the objective lens. The reduced image was easily calculated from Eq. (2) and (3) and is shown in Fig. 3(b). The DOE was made of SiO2 glass (with a 1/4 inch thickness) and an effective area of 8 mm by 8 mm. A Computer Generated Hologram (CGH) method was used to design the pattern. The elements had 4 phase levels and were designed with a wavelength of 800 nm. The CGH element was designed and made at Dai Nippon Printing Co., Ltd.
4. Results and discussion
Figure 4(a) shows the beam profile before and after the focal plane with the DOE. The original Z point was roughly set to the minimum point of the beam waist. This figure shows that the periodic structure of the focal points were precisely formed at Z=0 μm and were in a same plane. The points were evenly separated and spaced. Noise, degradation of beam spots and intensity distribution were also seen in the image. However, with adequate design of the DOE, we believe these degradations can be improved. Figure 4(b) shows the beam profile around the focal point without the DOE. The focal point difference between the configurations, with and without the DOE, was 87 μm. This value is in good agreement with the calculated difference of 90 μm. The out of focused beam was elliptical, and the major axis of the beam before and after focusing was orthogonal each other. This result indicates astigmatism in the focused beam. The error is thought to be mainly caused from the degraded beam quality (M2 ~ 2) of the Ti:sapphire multi-pass amplifier. As we can see in this figure, the diameter of each spot formed with the DOE was not as long as those focused without the DOE.
In order to compare the Z dependence of focal profiles, we defined full width of half maximum (FWHM) in Z dependence of focal profiles as focal depth. The focal depths of the spots were measured as more than 16 μm in the spots formed with DOE and 10 μm in the spot formed without DOE, respectively. The focal depth of the spots formed with the DOE was much deeper than that without the DOE. As we calculated in the previous section, the absolute value of the ΔZm for the spectral width of 40 nm was less than 6 μm. This value has the same order of magnitude as the difference between measured focal depth with and without the DOE. The sizes of beam waists were also measured in the spots formed with and without DOE. They were about 3.5 μm (with DOE) and 2.5 μm (without DOE), respectively. As we calculated in the previous section, the absolute value of the Δy for the spectral width of 40 nm was less than 1 μm. This value has the same order of magnitude as the difference between measured beam size with and without the DOE. Therefore we consider these focal depth and beam size degradations were mainly due to chromatic aberration of the total system. Another possibility is that it may also be due to DOE and objective lens wavefront errors. These degradations could not be accurately estimated, however, since we limited the focusing area to the paraxial regime, they were minimized. If necessary, error correction can be performed through optical design.
Using the same configuration, modified beams were irradiated on the surfaces of SiO2 glass. Microstructures were formed on the surface of the glass. Figure 5 shows the processed areas where the focal plane was adjusted along the Z direction. Z = 0 μm indicates a focal plane was on the glass surface. As we can see in this figure, SiO2 glass surface ablation occurred in a 12 μm region of focal plane shift. Debris was also seen around the ablated holes. The focal pattern was precisely reflected into the processed structure when Z = 0 μm. These results indicate that micropatterning using a DOE can be achieved using femtosecond laser irradiation. The diameters of the processed spots were less than 2 μm, which are smaller than the focal spot sizes. However, the spot sizes varied widely, which are thought to be due to the beam intensity distribution caused by imperfections of the image formed by the DOE. Therefore design of the DOE is very important in achieving uniform, precise processing.
We also irradiated the interior of SiO2 glass with the modified beam. As a result, we succeeded in forming a microstructure inside the glass. Figure 6 shows the processed area inside the glass. Figure 6(a) shows the spots processed with the DOE in the focal plane. As we can see in Fig. 6(a), the focal pattern was also precisely reflected into processed structures. Figure 6(b) shows a side view of the processed spots using the DOE. Although each spot was elongated, they were processed inside the glass. The length of the spot was about 77 μm. The processed spot lengths were about six times longer than the focal depth of the beam. Since a similar elongation of the processed area was observed by using low NA objective lenses in previous reports [15,16], these phenomena are considered to be related to the self-focusing of the pulse. Additionally, as the elongation of the focal depth shown in Fig.4 resulted in a decrease of effective NA, it is speculated that our results were affected by similar nonlinear effects. Compared to the cross-sectional view of the processed spots, the side view is unclear. We believe that they consist of cavities or a change in refractive index areas or damaged areas, which have their absorption originating from some structural defects or color centers.
From the above results, we demonstrated that an arbitrary focal shape can be constructed and that microprocessing can be performed not only on the surface but also inside the glass by using a femtosecond laser irradiation system.
We proposed an arbitral focal pattern forming method using a DOE in femtosecond laser irradiation. The proposed system with a DOE and a focusing lens was designed not only to reduce chromatic aberration resulting from the spectral bandwidth of a femtosecond pulse while maintaining a high NA but also to simplify the optical design. The method was verified through optical and processing experiments with laser pulses from a Ti:sapphire multi-pass amplifier, which had a 400 fs duration and a 40 nm bandwidth. A partial periodic structure of focused points was observed and its focal depth was much smaller than that of the DOE only value. By irradiating the constructed beam, a microstructure was formed precisely on and inside the SiO2 glass. The focal pattern was precisely reflected into the processed structures. Degradations of focal depth were also observed. This was mainly due to the beam quality of the femtosecond laser (M2 ~ 2) and the chromatic aberration of the total system. Since these degradations resulted in a decrease of effective NA, spot elongation took place.
Our method, which can be used not only with an amplified laser beam but also with a non-amplified laser oscillator, increases the flexibility and controllability of material processing and has an advantage when used for micro-processing applications inside transparent materials such as optical waveguides, periodical structures such as grating, photonic crystals, where the precise control of structural shapes and patterns is needed.
This work was carried out in the Nanotechnology Glass Project as part of the Nanotechnology Materials Program supported by the New Energy and Industrial Technology Development Organization (NEDO).
The authors wish to thank Dai Nippon Printing Co., Ltd for the design and fabrication of the CGH element, and Marubun Corporation for building the laser irradiation system.
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