We fabricated the Fresnel zone plate by embedding voids in silica glass. We investigated the focusing properties by launching a He-Ne laser beam into the zone plate. The spot size of the primary focal point was 7.0 μm and agreed with the theoretical value of 6.1 μm. The diffraction efficiency was 2.0 %. This technique enables us to make alignment free micro-scale lenses inside bulk materials.
©2002 Optical Society of America
In recent years, micromachining by femtosecond laser pulses in transparent materials has received much attention. When femtosecond laser pulses are focused inside the bulk of a transparent material, the intensity in the focal volume can become high enough to cause nonlinear absorption, which leads to localized modification in the focal volume, while leaving the surface unaffected. The modification enables us to fabricate a variety of photonic devices in glass, such as waveguides [1–8], couplers [9–12], gratings [13,14], and three-dimensional binary data storage [15–18].
Tightly focusing femtosecond laser pulses with high numerical-aperture (NA) lenses produce submicron-damage inside a wide variety of transparent materials including glass, crystal, and plastics [15,16]. The damage appears as cavities or voids with diameters of only 200 nm to 1μm, surrounded by densified material. An important feature of the void is the large difference of refractive-index change between a cavity and the surrounding region. Glezer et al. fabricated periodic arrays of voids and measured the diffraction pattern to estimate the refractive-index change . Although many researchers have fabricated the microscopic optical elements in transparent materials described above, fabrication of a lens has not been reported. If one can make lenses in the bulk of a material, the integration of the micro-scale optical elements will be possible inside a small area of the materials. In addition, once the lenses in the sample are fabricated, it is not necessary to align the optical elements.
To the best of our knowledge, we are presenting in this paper the first report of the fabrication of a lens by embedding voids inside silica glass. We fabricated a Fresnel zone plate and investigated the focusing properties. The Fresnel zone plate, with a size of 400 μm × 400 μm, was made by embedding voids in silica glass. When a He-Ne laser beam was launched into the zone plate, we investigated the focusing properties. The spot size of the primary focal point was 7.0 μm and agreed with the theoretical value of 6.1 μm. The diffraction efficiency was 2.0 %.
2. Design of Fresnel Zone Plate
Figure 1 shows the schematic of the designed Fresnel lens. Fresnel zone plate consists of a series of disks centered at one point with a radius of s1, s1 + λ/2, s1 + λ, s1 +3 λ/2, and so forth, where s1 is the radius of the first odd zone and λ is the wavelength . When we block either all the even or all the odd zones, this zone plate has a focusing property. In our layout, light passes through only the odd zones in the zone plate, and light cannot transmit in the even zones. Even zones are fabricated by embedding the array of the voids to block light. Under plane-wave illumination, we have peaks in the intensity along the optical axis at a distance of f1, f1 / 3, f1 / 5, and so on, from the zone plate. The zone plate with the converging property acts as a thin lens. The primary focal length f1 is related to the radius of the first odd zone s1 as follows:
Our designed Fresnel lens has the primary focal length f1 of 3 mm at the wavelength of 632.8 nm. From Eq. (1), the radius of the first odd zone was designed to be 43.5 μm. The size of the zone plate was 400 μm × 400 μm. In this condition, the radius of the outer zone is 200 μm. In the radius of 200 μm, the included number of the odd zone plate N is eleven. The resolution in the primary focal point R is defined as,
where ∆ sN is the width of the outer zone plate and satisfies the following equation:
3. Fabrication of Fresnel Zone Plate
The fabrication of the zone plate was performed by use of a chirped pulse amplifier of the Ti:sapphire laser system, which produces 130-fs, 800-nm pulses at 1 kHz. The optical setup is shown in Fig. 2. The output beam from the laser system was magnified by a concave lens L1with a focal length of negative 60 mm and an achromatic convex lens L2 (focal length, 300 mm). The central part of the beam passes through a circular aperture (diameter; 5 mm) to give uniform spatial profile. The linearly-polarized laser pulses were tightly focused by an objective lens OB with a NA of 0.55 (Olympus, ULWD Mplan 50) to create the voids inside silica glass, which was 3 mm thick. Suppose that the laser pulses propagate along the optical axis (+z direction). We fabricated the Fresnel zone plate by embedding voids at the depth of 300 μm beneath the sample of silica glass. To modify the structural change, we did not induce the refractive-index change, but created voids, which are cavities surrounded by densified material. The energy to create a void was 0.4 μJ/pulse when we observed through the transmitted optical microscope. When we increased the energy, two voids are created along the optical axis. In the following experiment, we set the energy to be 0.4 μJ/pulse to produce one layer of the zone plate by embedding voids. The sample was displaced dot by dot in the xy-plane perpendicular to the laser propagation axis by steps of 1 μm with a computer-controlled motor stage.
Figure 3 shows an optical image of the fabricated Fresnel zone plate by embedding the two-dimensional array of voids. The image was observed under halogen lamp illumination. The voids were embedded only in the even zones. You can see that light transmitted in the odd zones.
Figure 4 shows the magnified image of a part of the zone plate obtained by a 50× objective. Because we embedded voids in increments of 1 μm apart, the voids were not written periodically and the even zones were modified by the structural change. The interfaces between odd zones and even zones were not smooth and looked like quasi-digitized structures.
4. Focusing Properties
We investigated the focusing properties of the fabricated Fresnel zone plate. The beam incident on the lens is diffracted and converges in on the primary focal spot on the optical axis. Figure 5 shows an intensity distribution in the primary focal point when a cw-He-Ne laser beam at the wavelength of 632.8 nm was incident on the zone plate. The He-Ne laser beam was launched into the zone plate and a diffracted beam was focused on the surface of a CCD (charge-coupled device) camera by use of a 50× objective. Just after the rear surface of the sample, the beam was focused at the primary focal point. The primary focal point was located in air. The measured spot size was 7.0 μm and agreed with the theoretical value of 6.1 μm. The measured diffraction efficiency was 2.0 %.
Under plane-wave illumination, the zone plate has multiple peaks in the intensity along the optical axis from the zone plate. The theoretical diffraction efficiency at the primary focal point is 1/π2 ~ 10.1 % at maximum when the number of the zone plate is assumed to be infinite . Because we embedded voids in increments of 1 μm apart, the quasi-digitized structures at the interfaces also caused the loss of diffraction efficiency. It is necessary to discuss how close to the diffraction efficiency considering the non-ideal nature of the micro-machining of the zone plate. Such comparison, however, falls beyond the scope of this paper because the positional accuracy of the embedded voids is not estimated as shown in Fig. 4. Therefore, we just compared the theoretical value and experimental results. When the beam intensity incident on the zone plate is enough, the zone plate is used as a focusing lens and an imaging lens even though the diffraction efficiency is only a few percent.
For practical applications, we need to enhance the diffraction efficiency. An increase in the number of zone plates and embedding voids in multiple layers will increase the diffraction efficiency. Alternatively, a phase-reversal zone plate by retarding their phase by π instead of blocking out every other zone will increase the diffraction efficiency. The phase-reversal zone plate can be fabricated by the induction of refractive index change with femtosecond laser pulses.
The gratings can be fabricated inside glass by two-beam interference of a femtosecond laser pulse . By use of two-beam interference, much shorter periods can be achieved. However, it is difficult to control the depth profile of the modified region by two-beam interference. In our method, we can control the depth of the modified region by stacking voids in multiple layers.
Note that the zone plate has extensive chromatic aberration as suggested from Eq. (1); however, the technique to fabricate lenses inside glass will have potential applications in the alignment-free integration of a variety of micro optical elements inside a small bulk of the materials.
We fabricated the Fresnel zone plate, which size was 400 μm × 400 μm by embedding voids in silica glass. The collimated He-Ne laser beam was launched into the zone plate and investigated the focusing properties. The spot size of the primary focal point was 7.0 μm and agreed well with the theoretical value of 6.1 μm. The diffraction efficiency was 2.0 %. This technique enables us to make alignment free micro-scale lenses inside bulk materials.
A portion of the experiments reported in this paper was conducted at the Venture Business Laboratory, Osaka University. The authors thank K. Yamada of Department of Material and Life Science, Graduate School of Engineering, Osaka University for helpful discussion.
References and links
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