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Experiments were carried out to study the focusing properties of radially polarized light. By direct recording of the focal pattern in photoresist, the intensity distribution in the vicinity of the beam focus was measured, and the non-propagating longitudinal component (z-component) was clearly demonstrated. Comparison with corresponding theory shows good agreement.
©2007 Optical Society of America
1. Introduction
A variety of spatially variant polarization states have been proposed and studied in recent years. Due to their inherent symmetry, radial and azimuthal polarization states have attracted particular attention. Their focusing properties have been studied extensively using both theoretical and experimental methods [1-9]. One of the most intriguing characteristics of this form of polarization is exhibited by its longitudinal polarization component (z-component). When radially polarized light is focused with a high-numerical-aperture optical system, the longitudinal component can be much stronger and its cross-sectional size smaller than that of the transverse component. Various applications have been proposed to take advantage of this unusual property. For example, in Ref. [4], a method of creating a flat-top intensity distribution in high NA systems has been put forward, by balancing the z-component and the transverse component in the focal plane. However because of the non-propagating nature of the z-component in the vicinity of the focal point, experimental observation and measurement of the z-component is confined only to near-field techniques. A variety of indirect methods have recently been employed such as the use of knife-edge scanning [2], photoluminescence molecules [5], fiber-tip NSOM [6], nano-particle scattering [8], and the quantum-well heterostructure photodetector [9]. In this paper, we report on a direct observation of the z-component of polarization using conventional photoresist to record the intensity shape of the focal spot of radially polarized light. This method has the advantages of being easy to implement and is directly related to focusing and beam shaping applications under high numerical aperture such as optical recording and microlithography.
2. Generation of radially polarized light and experimental setup
To carry out the measurement, the first step was to generate the radially polarized light. Many ways are available with different experimental requirements and complexity. In our experiment, we followed the method introduced by Zhan and Leger [4] because of the flexibility it offers. This method easily changes the polarization from azimuthal to radial, which was required in our experiment. The wavelength of the laser was chosen to expose a conventional g-line (436nm) photoresist (Shipley 1805) in an optimal manner. By studying the wavelength response curve, we decided to use an Argon laser operating at a wavelength of 457.9nm.
The experimental setup is shown in Fig. 1. After beam expansion and spatial filtering by L1 and L2, the linear polarization from the Argon laser is converted to a circular polarization state by a quarter-wave plate. This light is incident on a commercially available radial analyzer, [10]. The function of the radial analyzer is to convert the beam from circular polarization into radial or azimuthal polarization depending on the specific properties of the radial analyzer. Our radial analyzer blocks the radial component of polarization and passes the azimuthal component. The following two half-wave plates work as a polarization rotator [4, 11] independent of the initial polarization state. Radially polarized light can be obtained by rotating the azimuthal polarization by 90°.
After the two half-wave plates, the light possesses the proper polarization state; in the process, however, it takes on a spirally varying phase (often called the Pancharatnam-Berry phase) due to the geometrical properties of the polarization conversion [12]. The last element in Fig. 1 controls the final beam phase front by introducing an additional spiral phase. Depending on the chirality of this spiral phase element, the Pancharatnam-Berry phase is either cancelled (resulting in a topological charge of zero) or doubled (a topological charge of two). Thus, the resulting phase profile is given by exp(i ℓ φ), ℓ = 0 or 2 and φ is the azimuth angle in polar coordinates ranging from 0 to 2π. In the past, we have fabricated this kind of phase plate using variable-dose e-beam lithography to pattern the resist into an appropriate shape; in the current experiment, however, we made use of a computer-generated hologram (CGH) to realize the same function.
3. Focal position control and exposure of photoresist
After the spiral phase plate in Fig. 1, the beam bears the desired radial polarization with either topological charge zero or two. This beam was focused onto a photoresist-coated plate using a microscope objective lens. Numerical modeling shows that a high-numerical-aperture lens is required to generate an appreciable z-component. In our experiment, we chose to use a well-corrected microscope objective lens with NA=0.8 (Nikon CF Plan EPI, DIC, 50X / 0.80, WD=0.54). The depth-of-focus of this lens is very short and control of the focal position is therefore extremely critical. As an aid to establishing proper focus, we devised a knife-edge test to measure focal error and locate the proper focal plane. Figure 2 shows schematically the focal position control setup.
Fig. 2. Focal position control by knife-edge technique. The mask plate contains a knife-edge pattern. Photoresist is spun on top of the mask plate. The position is accurately controlled by the micro actuator.
We started by depositing a sharp chrome strip with a thickness of approximately 100 nm on a transparent fused silica substrate using standard e-beam mask fabrication techniques. Shipley 1805 photoresist was spun on top of the mask with thickness of about 500 nm, and the coated mask was placed near the back focal plane of the microscope objective lens. The position of the mask plate was accurately controlled by a piezo-driven micro-actuator with a nominal precision of about 30nm. The chrome strip was used as a knife-edge to find the focal plane precisely as shown in the top-view of the mask in Fig. 2. Then the mask plate was translated laterally by about 15 micrometers using the piezo-electric stage to expose the photoresist without illuminating the chrome. Because of the lateral movement, the mask plate had the potential to go out-of focus by a small amount. We remedied this effect by recording multiple focal patterns with slightly different longitudinal (z) positions, allowing us to select the one that corresponded to best focus after development. This recording procedure was repeated on the same plate for a variety of exposure times, while keeping the initial laser intensity constant. The entire plate was then developed using Shipley 351 developer (diluted in water by a ratio of 1:5).
4. Measurement of the focal shape and comparison with theory
Because the z-component is only significant at high numerical apertures, the focal spot recorded in the photoresist is necessarily small. We used an atomic force microscope (AFM) to measure the surface profile of the various focal spots. The response of the photoresist depth vs. exposure was then carefully calibrated to infer the intensity distribution in the focal plane from the measured depth profile. Due to slight changes in photoresist response and development from one plate to another, a separate photoresist calibration was carried out for each plate. The developing conditions such as developer concentration and developing time were also critically monitored and controlled. The photoresist and developer were chosen specifically to provide a relatively linear relationship between exposure and photoresist depth after development. Figure 3 shows an example of a typical calibration curve. Under our experimental conditions, the calibration curve shows a highly linear dependence between the final depth and exposure. Based on this calibration curve, the intensity distribution near the focus could be inferred.
A theoretical calculation of the light intensity distribution in the focal plane of the objective lens has been performed by Youngworth and Brown [3] using the vectorial diffraction theory developed by Richards and Wolf [13]. In our experiment, light was focused into a dense medium (the photoresist), requiring an extension of this method [14, 15] to take into account the influence of the medium. Figure 4 shows the geometry of the focusing together with the system parameters. Adopting a similar notation as in ref. 14, we have the following formulas for the electric field components close to the focus of a radially polarized light beam:
where tp is the Fresnel coefficient at the interface,
and
is the aberration function (d is the thickness of the photoresist). A is a constant which can be set to unity, and r is the polar coordinate in the image plane. Jn(x) in the above integrals is the first kind Bessel function of order n. From the formula, it is evident that the electric field has only Er and Ez components in the focal plane, in agreement with previously established results [4, 7]. The total electric field intensity I= |Er|2+|Ez|2 can be calculated using the above formulas in a given plane. Because the photoresist has a finite thickness (about 500 nm), we integrated the electric field intensity along the longitudinal (z) direction to take into account the volumetric recording effect. Our simulation showed that the integrated electric field intensity distribution did not deviate from the focal plane intensity distribution significantly. This is because the thickness of the photoresist is within the depth of focus of the recording system, allowing a direct measurement of focal point intensity as long as the position of the focal plane is found accurately.
Fig. 4. Geometry of focusing in photoresist. The Gaussian focal point is at z=0 and the thickness of the photoresist is d. The air-photoresist interface lies in z= -d/2
Figure 5(a) shows the theoretical curve and experimental results near the focus of the radially polarized light. They agree reasonably well with one another. The non-zero center is contributed by the z-component. From the figure, we can see that the z-component is comparable with the surrounding transverse component. For comparison, we also recorded the focal pattern of radially polarized light with topological charge two. The topologoical charge was easily changed from zero to two by rotating the quarter-wave plate by 90°. After the rotation, the handedness of the circular polarization changes. The new Pancharatnam-Berry phase now adds to the phase of the spiral phase element, resulting in an overall topological charge of two. In this case, the electric field components in the focal plane become:
where tp and Ψ have the same definitions as in Eq. (3) and Eq. (4). It should be noted that in this case, Eϕ is no longer zero. This is one major effect of the topological charge. A second effect is that the total intensity, including the z-component, is zero at the center of the focal spot, as is evident from Fig. 5(b). Again, the experiments agree well with the theoretical results. We attribute the slight asymmetry in each pattern to residual aberrations present in the radial analyzer. Indeed, the wavefront aberrations were observed in the system testing by noticing the point spread function degradation.
Fig. 5. Intensity distribution recorded by the photoresist placed in the focal plane of radially polarized light, NA=0.8 (a) no topological charge, (b) topological charge 2.
Comparing Fig. 5 (a) and Fig. 5 (b), we can easily conclude that, although the z-component is non-propagating, it is accurately recorded in the photoresist. The reason to include the charge-two case is twofold. One is to demonstrate the effect of topological charge on the z-component; the other is to keep the Fresnel reflection coefficient constant between the two experiments to allow an accurate comparison of the two cases.
5. Discussion and Conclusion
Previously, Zhan and Leger [4] proposed the concept of beam shaping using generalized cylindrical vector beam which employs a linear superposition of radial and azimuthal polarizations. It was shown that for an optical system focusing radially polarized light with very high NA, the z-component is often much larger than the transverse component. In these cases, the overall focal spot takes on a Gaussian-like shape. To produce a flat-top focal spot, the z-component needs to be attenuated to exactly fill in the hole produced by the doughnut-shaped transverse component. This was achieved by rotating the radial polarization by an angle φ0 from its original orientation. For NA=0.8, φ0 was shown to be 24° to achieve a flattop-shaped focus. Note that the result in ref [4] was obtained for focusing in air. In this paper, where focusing is in the medium, the NA needs to be greater than one to achieve a flat-top focus. Thus, extensions of our experiment with oil-immersion or solid-immersion optics should be able to demonstrate this flat-top beam shaping in photoresist.
In summary, the focusing properties of radially polarized light with topological charge zero and two have been studied experimentally by recording the focused beams in conventional photoresist and inferring the resulting intensity with a calibrated atomic force microscope. The experimental results clearly demonstrate the existence of the non-propagating z-component and the experimental measurements agree well with theory. This method provides a new and easy way of quantifying the light intensity distribution in the focal plane and can be generalized to study focusing properties of other spatially variant polarization beams. For the intriguing z-component in the focus of the radially polarized light, this method provides a good experimental tool to directly study its intensity and shape, and its interaction with materials.
Acknowledgments
The authors gratefully acknowledge Cymer Inc.for their support of this work.
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