## Abstract

We address errors found in our recent measurement data for the piezo-optic
coefficients and calculation data for the photoelastic coefficients and the
acousto-optic figures of merit for ${\mathrm{LiKB}}_{4}{\mathrm{O}}_{7}$, ${\mathrm{Li}}_{2}{\mathrm{B}}_{6}{\mathrm{O}}_{10}$, and ${\mathrm{LiCsB}}_{6}{\mathrm{O}}_{10}$ glasses [Appl. Opt. **49**, 5360
(2010)].

© 2014 Optical Society of America

We have found some errors in the piezo-optic coefficients measured for ${\mathrm{LiKB}}_{4}{\mathrm{O}}_{7}$, ${\mathrm{Li}}_{2}{\mathrm{B}}_{6}{\mathrm{O}}_{10}$, and ${\mathrm{LiCsB}}_{6}{\mathrm{O}}_{10}$ glasses in our recent work [1]. The errors arose because a common uniaxial mechanical loading method was applied, leading to the appearance of spatially inhomogeneous stresses inside the glass samples, with unknown coordinate dependences (see, e.g., Ref. [2]). As a result, the stress tensor components and, subsequently, the piezo-optic coefficients were determined with inappropriate errors or even incorrectly. In addition, the contribution of Poisson strain to the total optical retardation determined with the interferometric technique was not accounted for in Ref. [1].

We have reinvestigated the piezo-optic coefficients for ${\mathrm{LiKB}}_{4}{\mathrm{O}}_{7}$, ${\mathrm{Li}}_{2}{\mathrm{B}}_{6}{\mathrm{O}}_{10}$, and ${\mathrm{LiCsB}}_{6}{\mathrm{O}}_{10}$ glasses using an experimental method suggested recently. It is based on a so-called four-point bending technique [3]. The correct piezo-optic coefficients have been obtained, as shown in Table 1. Table 1 also presents the recalculated photoelastic coefficients. Moreover, we have introduced the corrections for the mean-square deviations for the elastic stiffness coefficients.

It follows from the results of our recent work [4] that the optically isotropic glass media are characterized by three different types of acousto-optic (AO) figures of merit and not four as supposed in Ref. [1]. They are concerned with the following experimental geometries:

- (I) AO interaction of a longitudinal acoustic wave propagating along the $X$ axis (the velocity ${v}_{11}$) with an incident optical wave, where the electric induction $D$ is parallel to $Y$ axis;
- (II) AO interaction of a longitudinal acoustic wave (${v}_{11}$) propagating along the $X$ axis with an incident optical wave, where the electric induction lies in the $X\u2013Z$ plane at an angle ${\theta}_{B}$ with respect to the $X$ axis (${D}_{3}=D\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}{\theta}_{B}$ and ${D}_{1}=D\text{\hspace{0.17em}}\mathrm{cos}\text{\hspace{0.17em}}{\theta}_{B}$); and
- (III) AO interaction of a transverse acoustic wave (${v}_{13}$) that propagates along the $X$ axis and is polarized along the $Z$ axis, with an incident optical wave, where the polarization vector lies in the $X\u2013Z$ plane at an angle ${\theta}_{B}$ with respect to the $X$ axis (${D}_{3}=D\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}{\theta}_{B}$ and ${D}_{1}=D\text{\hspace{0.17em}}\mathrm{cos}\text{\hspace{0.17em}}{\theta}_{B}$).

Notice that a fourth, hypothetical, type of AO interaction has also been considered in Ref. [1]. It involves a transverse acoustic wave ${v}_{13}$ and an incident optical wave polarized parallel to the $Y$ axis. However, this interaction cannot be implemented since the relevant elasto-optic coefficient ${p}_{25}$ is equal to zero in all isotropic solid-state media (see Ref. [4]).

The AO figures of merit for all of the three possible types of AO interactions may be written as, ${M}_{2}^{(\mathrm{I})}={n}^{6}{p}_{12}^{2}/\rho {v}_{11}^{3}$, ${M}_{2}^{(\mathrm{II})}={n}^{6}{({p}_{12}\text{\hspace{0.17em}}{\mathrm{sin}}^{2}{\theta}_{B}+{p}_{11}\text{\hspace{0.17em}}{\mathrm{cos}}^{2}{\theta}_{B})}^{2}/\rho {v}_{11}^{3}$, and ${M}_{2}^{(\mathrm{III})}={n}^{6}{({p}_{44}\text{\hspace{0.17em}}{\mathrm{sin}}^{2}{\theta}_{B})}^{2}/\rho {v}_{13}^{3}$ (see Ref. [4]), where ${p}_{44}={p}_{11}-{p}_{12}$, ${p}_{11}$, and ${p}_{12}$ are the photoelastic coefficients, ${v}_{11}$ and ${v}_{13}$ are the velocities of the longitudinal and transverse acoustic waves, respectively, $n$ denotes the refractive index, $\rho $ is the glass density, and ${\theta}_{B}$ is the Bragg angle defined by the relation $\mathrm{sin}\text{\hspace{0.17em}}{\theta}_{B}=\lambda {f}_{a}/2{nv}_{ij}$. Here, the acoustic wave frequency ${f}_{a}$ takes a value of 500 MHz.

The corrected values of the AO figures of merit are gathered in Table 1. Among the borate glasses under analysis, the highest AO figure of merit corresponds to ${\mathrm{LiCsB}}_{6}{\mathrm{O}}_{10}$. It is equal to $(7.443\pm 0.529)\times {10}^{-15}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\mathrm{s}}^{3}/\mathrm{kg}$ rather than, $(201\pm 104)\times {10}^{-15}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\mathrm{s}}^{3}/\mathrm{kg}$ as declared in Ref. [1]. Nonetheless, the ${\mathrm{LiCsB}}_{6}{\mathrm{O}}_{10}$ glass still remains an effective AO material, in compliance with what has been concluded in Ref. [1].

## References

**1. **V. Adamiv, I. Teslyuk, Ya. Dyachok, G. Romanyuk, O. Krupych, O. Mys, I. Martynyuk-Lototska, Ya. Burak, and R. Vlokh, “Synthesis and optical characterization
of LiKB_{4}O_{7}, Li_{2}B_{6}O_{10},
and LiCsB_{6}O_{10} glasses,”
Appl. Opt. **49**, 5360–5365
(2010). [CrossRef]

**2. **Yu. Vasylkiv, O. Kvasnyuk, O. Krupych, O. Mys, O. Maksymuk, and R. Vlokh, “Reconstruction of 3D stress fields
basing on piezo-optic experiment,” Ukr. J.
Phys. Opt. **10**, 22–37
(2009). [CrossRef]

**3. **O. Krupych, V. Savaryn, I. Skab, and R. Vlokh, “Interferometric measurements of
piezo-optic coefficients by means of four-point bending
method,” Ukr. J. Phys. Opt. **12**, 150–159
(2011). [CrossRef]

**4. **O. Mys, M. Kostyrko, M. Smyk, O. Krupych, and R. Vlokh, “Anisotropy of acoustooptic figure of
merit in optically isotropic media,” Appl.
Opt. (to be published).