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We describe a microoptical planar waveguide solid immersion mirror with high optical throughput, and show that it can focus light to spot sizes of ~90 nm at a wavelength of 413 nm. Scanning near field optical microscope images of the light within the device are in good agreement with a simple theoretical model. This device is accurately mass-produced with lithographic and thin film deposition techniques known from modern integrated circuit processing.
©2005 Optical Society of America
1. Introduction
A variety of high resolution optical systems have been developed for various applications, several of which are pictured in Fig. 1. Some systems make use of apertures at the tip of a tapered optical fiber [1] or silicon cantilever [2] to illuminate or collect light from an area much smaller than a wavelength. This is the basis for many scanning near field optical microscopes, which are commercially available today with an optical resolution of 100 nm or better. The optical throughput of subwavelength apertures, however, is generally extremely small [3]. For example, the transmission coefficient [4] through a tapered fiber with a 100 nm opening is ~10-5. This optical throughput is much too small for practical application in optical recording for which the optical system must transmit a sufficient amount of light to the recording medium to heat the medium by ~200 C or more. The small optical throughput also restricts the minimum aperture size and resolution in microscopy applications to that which provides sufficient light for an acceptable image quality.
Fig. 1. Some techniques for achieving high optical resolution: (a) an aperture of opaque metal at the tip of a Si cantilever or a tapered optical fiber, (b) a solid immersion mirror, (c) a solid immersion lens, and (d) a superSIL.
A solid immersion lens (SIL) [5], shown in Fig. 1(c), has also been used to obtain high resolution but with high optical throughput. The focused spot size of a SIL can be estimated from scalar diffraction theory. An approximate relation between the full width at half maximum (FWHM) of the spot at the focal point of a SIL, d, the wavelength, λ, and numerical aperture, NA, of the lens when uniformly illuminated is given by
The NA is the product of the index of refraction of the material in which the light is brought to focus with the sine of the half angle of the focused cone of light. Hence, an aberration-free SIL with an NA of 2.0 can focus light to about a quarter wavelength [6,7]. Although this is a lower resolution than that possible with near field apertures, in principle nearly all of the incident light can be brought to the focal point, which is an important advantage in many applications [8–10].
However, there are several problems with SIL’s that have limited their usefulness. The fabrication of SIL’s with sufficient accuracy to achieve diffraction-limited performance is extremely difficult [11,12] and expensive because these lenses are highly curved and their surface geometry must be accurate to a fraction of a wavelength. The bottom surface of the SIL must be precisely located at the focal point to minimize spherical aberration. Furthermore, it is a challenge to mount the SIL without blocking the high angle rays important for high resolution. A high NA objective is also required as part of the complete optical system to focus light into the SIL. For a given focusing objective, the SuperSIL geometry [7], shown in Fig. 1(d), provides a larger effective NA and smaller focused spot size than that of a hemispherical SIL, but the position of the focal point along the optical axis of the SuperSIL is a function of its index of refraction and thus varies with wavelength.
Mirrors can often perform functions similar to those of lenses, so it is pertinent to consider parabolic solid immersion mirrors (SIM) [13] as an alternative to SIL’s. A SIM, like a SIL, focuses all of the incident light and, therefore, has a high optical throughput. Unlike a SIL, a SIM uses reflection to focus the light and is essentially free of chromatic aberration. However, the parabolic curvature of a SIM is even more difficult to polish than the spherical curvature of a SIL.
Fig. 2. (a) FWHM of field intensity for the TE0 mode vs. core thickness for the waveguide described in the text. The best light confinement occurs at the minimum. (b) Normalized field intensity perpendicular to plane of waveguide for a core thickness of 70 nm. The light intensity decays quickly in the outer cladding layers.
2. PSIM theory
It is well known that light can be highly confined in one dimension within planar dielectric waveguides [14]. This suggests that a microoptical structure consisting of a planar SIM (PSIM) etched into a planar waveguide may effectively confine and focus a propagating beam of light with high optical throughput into a spot much smaller than the wavelength of the incident light. The simplest planar waveguide consists of a high index dielectric core laminated on both sides with lower index claddings. A large difference between the refractive indices of the core and cladding is desirable to provide the highest degree of confinement of the light energy within the waveguide. The thickness of the core layer also determines the degree of confinement. In Fig. 2(a) the FWHM of the |E|2 light intensity for the TE0 mode is plotted for a symmetric waveguide with a core index of 2.1 and cladding indices of 1.6 at a wavelength of 413 nm as a function of core thickness. The theoretical FWHM extent of the field intensity for this particular waveguide with a core thickness of 70 nm is only 97 nm, less than a quarter wavelength. The spatial distribution of the field intensity normal to the plane of the waveguide is shown in Fig. 2(b). The field intensity decays quickly outside of the core layer, which must be considered when attempting to directly measure the field distribution within the waveguide.
The parabolic shape of the PSIM is designed to focus the light within a waveguide. A truncated parabola that is 100 μm long, 50 μm wide at its top opening, and 6 μm wide at the bottom surface is shown in Fig. 3. Light enters this PSIM from the top parallel to its optical axis. Due to the truncation, a portion of the central part of the beam does not strike the parabolic edge of the PSIM and does not get focused but exits the bottom of the structure without changing direction. Light rays a little farther from the central axis reflect off the edge of the PSIM near the bottom corner and are incident onto the focal point at high angles. These rays are particularly important in reducing the focused spot size and, unlike SIL optical systems, are easily captured in the SIM geometry. Light rays entering the PSIM near the upper right or left edges are reflected towards the focal point at smaller angles of incidence. The range of angles of the incident light rays at the focal point for the PSIM design in this figure varies from 14° to 90°.
Fig. 3. Diagram of the light rays within the PSIM. The dimensions shown correspond to the fabricated devices.
The stationary phase approximation was first used by Wolf and Richards [15,16] to calculate the field intensity in the focal plane of an aplanatic lens, and can also be applied to the PSIM. TE0 waveguide modes are summed for angles of incidence of 14° to 90° in increments of 1° from both sides of the PSIM. To ensure energy conservation for the incident beam, the waveguide mode for each angular increment is multiplied by the appropriate factor for PSIM’s,
Amplitude changes and phase shifts from reflection at the sidewalls are not included in the model. The calculated field intensity in the vicinity of the focal point is shown in Fig. 4. Interference between the various waveguide modes creates a light intensity pattern composed of bright filaments converging on the focal point with less intense rings of light circling the focal point. The calculated FWHM spot size in the plane of the PSIM is about a quarter wavelength.
Fig. 4. Calculation of light intensity within the plane of a PSIM by superposition of TE0 waveguide modes. White dashed lines indicate the geometry of the experimental dual-PSIM. An interference pattern is visible with a focal spot size of about a quarter wavelength.
3. Fabrication of the devices
We have fabricated two types of PSIM’s in order to obtain scanning near field optical microscope (SNOM) images of the light intensity near the focal point. Both types of PSIM’s have parabolic dimensions given by Fig. 3. A diffraction grating was etched into the waveguide above the top edge of each PSIM to efficiently couple light into the waveguide.
An image of the electric field intensity within the plane of the PSIM is useful for understanding the manner in which light reflects from the sidewalls and is brought to a focus. However, the field intensity decays quickly outside of the core layer as shown in Fig. 2(b). For a waveguide with thick cladding layers, the field intensity outside of the cladding is too small to be detected by the SNOM. Therefore, an asymmetric waveguide was fabricated on silicon substrates using a thick thermal silicon dioxide layer as the low index inner cladding, a tantalum pentoxide layer as the core, and an outer cladding of air to allow the SNOM tip to directly scan the field intensity at the top surface of the core. Electron beam lithography was used to define the parabolic shape of the PSIM in photoresist to an accuracy of a few tens of nanometers. Light propagating to the focus of a single PSIM generates both reflections and scattered light at the focal plane edge that make the field intensity distribution within the PSIM more complicated to understand. Therefore, each fabricated device consisted of two PSIM’s fabricated back-to-back and joined at their focal planes as shown in Fig. 5(a). The PSIM’s were direct extensions of the planar waveguide. A diffraction grating (not shown) was also etched into the waveguide about 1 cm in front of the device. The grating was used to couple laser light into the waveguide. The light propagated with a flat wavefront to the first PSIM in the direction shown by the red arrows in Fig. 5(a). The light was then reflected through the focal plane of the first PSIM into the second PSIM. The second PSIM had two diffraction gratings etched into it to act as output couplers for the laser light. By viewing the brightness of the output gratings it was possible to determine when the incident laser beam was successfully coupled into the waveguide and into the first PSIM.
Standard techniques were used to etch the sidewalls of the PSIM’s that were optically smooth and vertical for coherent reflection of light. The sidewalls were uncoated in this device because a theory of reflection from waveguide edges [17] shows that total internal reflection should occur along the entire length of both sides of this PSIM design. The quality of the sidewalls is also evident in Fig. 5(a) from the minimal scattering of the light at the walls. Essentially all of the light entering the first PSIM was reflected through the focus into the second PSIM and then scattered by the two gratings at the end of that PSIM.
The confinement of the focused spot perpendicular to the plane of the waveguide can also be measured at the bottom surface of the PSIM if the waveguide has a thick dielectric cladding on both sides of the core to keep the cantilever tip of the SNOM from falling off the edge of the waveguide. Therefore, a second type of PSIM was fabricated as shown in Fig. 5(b) from a symmetric waveguide film stack. The sidewalls of this PSIM were made reflective by a coating of aluminum. For this device the low index cladding material was alumina, the high index core was again tantalum pentoxide, and the films were deposited onto ceramic substrates. The wafers were then sliced, lapped to the focal point of each PSIM parabola, and diced to obtain individual devices. The lapping process can be controlled to several tens of nanometers and produces very smooth surfaces.
Fig. 5. (a) Dual PSIM’s etched into a Ta2O5 / thermal SiO2 stack on a Si wafer. Red light was launched into the PSIM’s as shown by the arrows. The surface of the PSIM’s was scanned by the SNOM near their intersection to obtain the interference pattern and the focal spot size. The scale bar is 50 μm. (b) PSIM etched into an Al2O3 / Ta2O5 / Al2O3 stack on a ceramic substrate. This device was further processed to make the truncated part of the PSIM accessible for SNOM measurements.
4. Results
The focused spot size was measured with a Witec Alpha SNOM having an optical resolution specified to be 100 nm or better. The asymmetric waveguide PSIM samples as shown in Fig. 5(a) were mounted horizontally on the SNOM. Collimated laser radiation at a wavelength of 650 nm was incident onto the coupling grating via an optical fiber and ball lens. The angle of incidence was adjusted to launch a TE0 waveguide mode into the PSIM. The outer surface of the core layer of the PSIM was scanned beneath the cantilever tip. Light transmitted through the aperture in the cantilever tip was reimaged through confocal optics to eliminate stray light and onto a photomultiplier tube to acquire the scanned image of the light propagating within the PSIM shown in Fig. 6. Although the light detected by the SNOM is due to a complex interaction between the cantilever tip and the fields in the PSIM, the good qualitative agreement between this image and the theoretical result in Fig. (4) indicates that the SNOM image is closely related to the |E|2 field intensity at the surface of the waveguide and that the approximations in the theoretical model are reasonable.
Fig. 6. SNOM image of light focused by a PSIM with an asymmetric waveguide. The interference pattern resembles the calculated one shown in Fig. 4. The scale bar is 3 μm.
The symmetric waveguide PSIM devices as shown in Fig. 5(b) were mounted vertically on the SNOM. A collimated laser beam with a wavelength of 413 nm was incident upon the coupling grating to launch light into the PSIM. The surface of the PSIM at its focal point was scanned beneath the SNOM cantilever tip. Fig 7(a) shows an image of the spot for a PSIM that was slightly underlapped and exhibited strong side lobes on either side of the central peak. A line scan across the focused spot for a correctly lapped PSIM, shown in Figs. 7(b) and 7(c), gives a FWHM vertical spot size for the central peak of 230 nm and a FWHM horizontal spot size of ~90 nm (with some uncertainty due to noise) and small side lobes. Of course, the measured spot size is actually a convolution of the instrumental function with the focused spot intensity. The aperture in the cantilever pickup of the SNOM is primarily sensitive to light polarized in the focal plane of the PSIM and is relatively insensitive to light polarized normal to this plane. This is also evident from a contour plot of the theoretical |Ex|2 and |Ey|2 intensities for a symmetric waveguide of the previously given dimensions shown in Figs. 8(a) and (b), respectively.
Fig. 7. (a) SNOM image of spot at bottom surface of a PSIM with a symmetric waveguide slightly out of focus to exhibit side lobes. The scale bar is 0.5 μm. Scan of light intensity across the focused spot in vertical (b), and horizontal (c) directions showing width of central peak and side lobes. The wavelength is 413 nm.
Fig. 8. Theoretical field intensities in the focal plane of the PSIM for (a) light polarized parallel to the bottom surface of the PSIM and (b) light polarized normal to this surface. Dashed lines indicate position of waveguide core. The FWHM contour is also shown for |Ex|2.
5. Conclusion
There are many potential applications for devices capable of focusing light with high throughput into spots much smaller than a wavelength. We have shown that PSIM’s can be fabricated with standard lithographic techniques to the necessary tolerances to achieve diffraction-limited performance in an easily reproducible process. The parabolic design reflects light energy at high angles of incidence onto the focal point to achieve a large effective NA. The measured spot size for the PSIM’s is ~90 nm FWHM at a wavelength of 413 nm, which is comparable to or better than results reported for SIL’s [7]. PSIM’s unlike SuperSIL’s, make use of reflection rather than refraction and are essentially free of chromatic aberration. Optical quality thin films can be deposited with a wide range of refractive indices and thicknesses designed to optimise the PSIM’s at the chosen wavelength(s). Potentially the greatest advantage of the PSIM is that the fabrication process is not significantly different from techniques in routine use for integrated optics. Therefore, it is expected that such devices can be mass-produced at low cost and thereby enable new applications in microscopy, lithography, and data storage.
Acknowledgments
The authors would like to thank J. Hohlfeld, E. Gage, E. Svedberg and F. Erden for critical reading of the manuscript and A. Itagi, T. Rausch, K. Sendur and K. Mountfield for their support of this work and many helpful discussions. This work was performed for the INSIC HAMR ATP program under the support of the U. S. Department of Commerce, National Institute of Standards and Technology, Cooperative Agreement Number 70NANB1H3056.
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