A reply to the comment by van de Nes et al. directed to the paper of “Cylindrical vector beam focusing through a dielectric interface,” by Biss and Brown, Opt. Express, 9 490–497, (2001).
©2004 Optical Society of America
This letter is intended as a reply to the comments of van de Nes et al. directed to our original paper  describing some very interesting phenomena which accompany the focusing of radial and azimuthally polarized beams (cylindrical vector beams) through a planar interface. The problem is of general interest in a variety of areas of microscopy – the particular calculation addressed by van de Nes et al. was directed to focusing in an immersion system with a numerical aperture which extends outside the critical angle.
We, first of all, thank all of the authors for taking an interest in this subject and identifying what was indeed a numerical difficulty in the immersion system. We have verified that, and have noted in the process that these types of beams, because of the ‘doughnut’ apodization contain a very high fraction of energy outside the critical angle. It is well known that, outside the critical angle, the phase shift on refection at an interface changes very rapidly. The error therefore was most evident in the computation of the reflected wave, the movie in the comment by van de Nes et al. shows this very clearly. To summarize, the main error is in the reflected wave computation, with the general character of the beam focused beyond the interface (i.e. the transmitted wave) still very interesting and similar to the results shown in the original paper.
The interest in these results is due to the following: 1) For defocused surfaces extending even 5 or 6 wavelengths beyond the interface, the longitudinal field continues to dominate the lateral size of the focal region and remains relatively unchanged over this range. This serves rather to strengthen, rather than weaken one of the conclusions of the original paper, namely that a focused radial beam can be used in a solid immersion system without the lens necessarily being in intimate contact with the sample – provided the object being probed is within 2 to 6 wavelengths of the interface, resolution better than λ/2 is possible (λ/2 would be the normal limit in an air objective) and 2) The longitudinal field does not suffer from the same polarization-induced asymmetry which is present in the linearly polarized field. Both of these are important conclusions, and we apologize that the numerical error may have obscured this.
We also note that another important case, that of focusing from air to a high index surface such as silicon, was not significantly affected by the numerical error. This case is less sensitive to numerical sampling because there is no critical angle, and the amplitude reflectance is slowly varying for all polarizations. The key result of that calculation is that again, the surface tends to strengthen the longitudinal component such that, for regions near the surface, the energy density is dominated by the longitudinal field. This has important implications for such problems as the scattering of optical energy by particles near a semiconductor surface, a process which is critical to inspection problems in the semiconductor industry.
In summary, we thank all of the participating authors for a stimulating exchange, and look forward to many more papers on this very interesting topic.
References and links
1. D. P. Biss and T. G. Brown, “Cylindrical vector beam focusing through a dielectric interface,” Opt. Express 9, 490–497, (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-10-490. [CrossRef] [PubMed]