## Abstract

In our publication [Opt. Express, 20(7), 8055–8070 (2012)] a convergence issue resulted in a discrepancy between the relative photothermal signal of two models: the paraxial scalar diffraction model and the accurate vectorial generalized multilayer Lorenz-Mie scattering theory which served as a reference. The resolution yields the expected agreement.

© 2013 OSA

## Discrepancy by a factor of order unity between the two models in Fig. (4) and the discussion following Eq. (21)

Unfortunately, the discretizations of the thermal lens scatterer *n*(*r*) used in the GLMT calculations of our article [1] were not carried out to large enough sizes, i.e. the outmost layer was not chosen sufficiently large as compared to the probing beam waist. As a result, in Fig. 4 of Ref. [1], and in the discussions based on these plots, an unexpected discrepancy by a factor of the order *𝒪* (1) was found between the results of the diffraction and the GLMT model. The problem resides in a convergence issue of the signal in the GLMT model [3]: the thermal lens must be discretized up to a size of about *r _{L}* > 5

*ω*

_{0}, see Fig. 1. If this is done, the expected equivalence between both approaches is realized for weak and even moderate focusing, see the new Fig. 2 correcting former Fig. (4) of the article. This also corrects the discrepancy of Fig. (5) of Ref. [1], i.e. giving the same picture but without the scaling by a factor 1.6. Now, the solution to the paraxial approximation of the Helmholtz equation, i.e. Fresnel diffraction, and the exact solution for a focused beam which approximates the Gaussian beam (the Davis beam) match perfectly as they should. Expectedly, minor discrepancies remain for large numerical apertures or inverse apertures, see the new Fig. 2d).

## Simplification of Eq. (7)

Eq. (7) of Ref. [1] is correct but can be simplified further to first order in the perturbation Δ*n/n*
_{0}, see also Ref. [2, 3] on photonic Rutherford scattering:

## Typo in Eq. (19)

Eq. (19) in Ref. [1] has a typo. The factor (−1)* ^{n}* should read (−1)

^{n}^{+1}, i.e. the correct equation reads [3]:

*θ*

_{min}= 0. The calculations in Ref. [1] were all done using this correct equation. In view of practicability, we here also provide a more compact form [3] for Gaussian (zero-order Davis) beams based on the Gaussian intensity profile:

## References and links

**1. **M. Selmke, M. Braun, and F. Cichos, “Nano-lens diffraction around a single heated nano particle,” Opt. Express **20**(7), 8055–8070 (2012). [CrossRef]

**2. **M. Selmke and F. Cichos, “Photothermal single particle Rutherford scattering microscopy,” Phys. Rev. Lett. **110**, 103901 (2013). [CrossRef]

**3. **M. Selmke, “Photothermal single particle detection in theory & experiments,” Dissertation, Universität Leipzig, Institute for experimental physics I, (2013).