Fast response varifocal lenses using KTa_1−xNb_xO₃ crystals and a simulation method with electrostrictive calculations

Abstract

We fabricated cylindrical varifocal lenses with fast responses by using the strong Kerr effect of KTa(1-x)Nb(x)O(3) (KTN) single crystals. We observed focus shifts of up to 87 mm with the assistance of a 250 mm focal length lens, which corresponds to a focus shift from infinity to 720 mm by the KTN lens itself. The response time was as fast as 1 μs. We also present a simulation method for calculating refractive index distributions in KTN single crystals, which is essential when designing the lens. The method is characterized by the strain contribution, which has not conventionally been typical of electro-optic simulations. We used this method to explain the refractive index modulations that are characteristic of the varifocal lenses.

Polarization independent varifocal lens using KTN crystals

“…The huge EO effect makes it possible to realize quick and strong control of the refractive index in the KTN crystal by employing electrical signals. We have already confirmed that the KTN lens works properly as a fast response varifocal lens [8]. The KTN lens is especially effective in situations where a transmitted beam is linearly polarized parallel to the direction of an applied electric field.…”

“…(1) [8]. Figure 2(b) shows the calculated optical path distribution, which depends on the y coordinate of the KTN lens.…”

“…Note that the strain caused by the electrostrictive effect induces additional strain in competition with the elasticity of the crystal. The strain e kl , which includes the elastic interaction in the crystal, is no longer described simply as being proportional to the square of the electric field, and it can be calculated by the finite element method with the plane stress model [8,[13][14][15]. Ultimately, the total EO effect of the KTN crystal includes not only the Kerr effect, but also the elasto-optic effects via the electrostrictive effect and the elastic interaction in the crystal.…”

A Varifocal Lens Using an Electrooptic KTa_1&minus;_<i>x</i>Nb_<i>x</i>O₃ Crystal with a Microsecond Order Response Time

“…In fact the strain components must be calculated by regarding the KTN block as an elastic substance strained by the electrostrictive stress as a driving force so that the strain components minimize the total free energy of the block. [6] To calculate the electrostrictive stress, we used the same spatial distributions of E x and E z as those used for Fig. 8.…”

Temperature dependence of Kerr coefficient and quadratic polarized optical coefficient of a paraelectric Mn:Fe:KTN crystal

“…[3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] KTN crystal, a perovskite-type oxide material, well recognized for its excellent EO performance where the index modulation is proportional to the square of the electric field, can realize rapid response, strong control of the refractive index and much lower driving energy comparing to LiNbO 3 for the same change ∆n in the refractive index. For this reason, KTN-based single crystal has been considered as promising materials, and has then been substantially investigated and successfully exploited in such diverse areas as EO deflection, [6][7][8] EO scanner, 9 a fast varifocal lens [10][11][12][13] and so on. 14,16,17 Mn:Fe:KTN crystal doped with both iron and manganese simultaneously are of particular interest because of its two competing subsystems of dipole moments and exhibits faster EO response than single-doped crystal.…”