This letter is intended as a Reply to the Comment by Iglesias and Sáenz directed to one previous paper [1] proposing the use of radial polarization to trap metallic Rayleigh particles. Better understanding of the optical forces acting on metallic nanoparticles is very important and of great interests to the community considering its numerous potential applications.

First of all, I would like to thank the authors for taking interests in the subject. Two characteristics of highly focused radial polarization were exploited in [1] in an effort to improve the trapping efficiency of metallic nanoparticles. A sharper focus produces higher gradient trapping force. The focal field also features a donut shape power density distribution that is spatially delocalized from the energy density distribution. Using a dipole approximation for the optical force on Rayleigh particles, the spatial separation between the power density and energy density indicates a spatial separation of the trapping force (proportional to the gradient of electric energy density) and the destabilizing radiation pressure forces (proportional to the power density), leading to the expectation of significantly improved trapping stability of metallic nanoparticles using radial polarization. This dipole approximation model for optical force calculation was widely used to estimate the forces and interpret experimental results including the trapping of metallic Rayleigh particles [2].

In their Comment, Iglesias and Sáenz pointed out that a recently discovered additional scattering force term (so-called light spin force) [3], also known as an “unnamed third term” reported previously by Wong and Ratner [4], should also be included. This term is normally negligible compared to the gradient force and the radiation pressure force and little attention has been paid to it. However, owing to the unique vector field distributions of the highly focused radial polarization, this term becomes comparable to the radiation pressure force unexpectedly. The additional light spin force does not have the donut shape spatial distribution to minimize the axial scattering force as required in [1]. With this term considered, the authors calculated total scattering force for radial and linear polarization and found that the radial polarization does not offer a reduced axial scattering force [5]. Hence, the destabilizing force is underestimated in [1] and the advantage of using radial polarization over linear polarization to minimize the scattering force would be significantly reduced.

However, unlike the well-understood gradient trapping force and optical pressure force, the nature and magnitude of this light spin force needs further understanding and experimental confirmation. It may be too early to conclude that the radial polarization does not offer advantages in improving the trapping efficiency of metallic nanoparticles over spatially homogeneous polarization. The same arguments offered in [1] and in the Comment apply to dielectric particles including those with very high refractive index. Experimental work on the improvement of axial trapping stiffness for dielectric particles using radial polarization has been reported [6]. T-matrix method calculation also demonstrates that radially polarized beam allows the improved trapping of spherical particles, including particles of quite high relative refractive index that also experience large scattering force [7]. The advantage of using radial polarization to improve axial trapping of metallic nanoparticles is predicted by FDTD calculations using the Maxwell’s stress tensor [8]. Preliminary experimental results reported in [9] also indicate the improved trapping stability of gold nanoparticles using radial polarization at a much shorter wavelength (633 nm). Furthermore, one important reason for the strong interests in trapping metallic nanoparticles is to exploit the associated phenomena such as plasmonic excitation and local field enhancement. Unique plasmonic effects of various metallic nano-objects under radial polarization excitation have been reported [10–12]. Thus, it is still of great importance to investigate optical trapping of metallic Rayleigh particles with radial polarization. In fact, detailed experimental studies on metallic nanoparticle trapping with radial polarization may just provide the kind of experimental validation of the light spin force discussed in [3].

In summary, I appreciate the authors for the stimulating exchange. I am glad to see that the original work has inspired research interests and discussions that advance our understanding of the optical forces on metallic Rayleigh particles. The new force term described by the authors are very important for better understanding of the interactions between light fields and nanoparticles. With the consideration of the light spin force, the benefits of using radial polarization to minimize the scattering force appear to be reduced. However, radial polarization may still offer advantages of linear polarization due to the minimization of radiation pressure force along the optical axis as indicated by other computational methods [7, 8] and experimental works [6, 9]. More importantly, the use of vector beams could eventually allow us to shape the vector focal field distribution and tailor the optical force distributions to suit for the specific needs of different applications.