^{1,a)}, Zhi-qiang Shen

^{1}, Cheng-ping Huang

^{1}, Shi-ning Zhu

^{1,a)}and Yong-yuan Zhu

^{1}

### Abstract

Propagation of phononpolaritons in a nonaxial aligned one-dimensional piezoelectricsuperlattice is studied theoretically. Because of the piezoelectric effect, both transverse and longitudinal superlattice vibrations are induced by one transverse polarized electromagnetic wave. Due to the coupling effect, two orthogonal modes of elliptically polarized polaritons are present with different propagation properties and can be tuned by the rotation angle.

This work is supported by the National Natural Science Foundation of China (Grant Nos. 60578034 and 10534020) and by the National Key Projects for Basic Researches of China (Grant Nos. 2006CB921804 and 2004CB619003).

I. INTRODUCTION

II. THEORETICAL TREATMENT

III. RESULTS AND DISCUSSION

IV. CONCLUSION

### Key Topics

- Polaritons
- 41.0
- Acoustic waves
- 27.0
- Superlattices
- 22.0
- Electric fields
- 9.0
- Dielectrics
- 8.0

## Figures

(a) Schematic of a 1D PSL with the periodically poled ferroelectric domains arranged along the axis and domain walls parallel to the axis. The new set of rectangular coordinates , , and from the standard rectangular coordinates , , and by a rotation in the plane, where the relative orientation of the two sets of axes is described by the angle . Two types of superlattice vibrations, and , as longitudinal and transverse, respectively, are induced by the axis propagated electric field. (b) Two elliptically polarized electric fields and for ordinary and extraordinary polaritons, respectively, are caused by the coupling effect. The long axes of these two ellipses are orthogonal with each other and the one corresponding to the ordinary polariton is rotated by an angle about the axis.

(a) Schematic of a 1D PSL with the periodically poled ferroelectric domains arranged along the axis and domain walls parallel to the axis. The new set of rectangular coordinates , , and from the standard rectangular coordinates , , and by a rotation in the plane, where the relative orientation of the two sets of axes is described by the angle . Two types of superlattice vibrations, and , as longitudinal and transverse, respectively, are induced by the axis propagated electric field. (b) Two elliptically polarized electric fields and for ordinary and extraordinary polaritons, respectively, are caused by the coupling effect. The long axes of these two ellipses are orthogonal with each other and the one corresponding to the ordinary polariton is rotated by an angle about the axis.

(a) Calculated dielectric functions and (b) first-order polariton dispersion curves for transverse superlattice vibration. (c) and (d) correspond to longitudinal vibrations. The insets in (b) and (d) show the discontinuity of polariton dispersion near the frequency . A group of proper damping constants, and , are chosen in the calculation.

(a) Calculated dielectric functions and (b) first-order polariton dispersion curves for transverse superlattice vibration. (c) and (d) correspond to longitudinal vibrations. The insets in (b) and (d) show the discontinuity of polariton dispersion near the frequency . A group of proper damping constants, and , are chosen in the calculation.

Variation curves of the tilt angles of elliptically polarized ordinary (black) and extraordinary (red) polaritons (a) and angles of ellipticity (b) for transverse superlattice vibration. (c) and (d) correspond to longitudinal vibrations. The ellipticity of first-order transverse vibrations is positive, which means that the electric field rotates right handed, while for first-order longitudinal vibrations, it is negative.

Variation curves of the tilt angles of elliptically polarized ordinary (black) and extraordinary (red) polaritons (a) and angles of ellipticity (b) for transverse superlattice vibration. (c) and (d) correspond to longitudinal vibrations. The ellipticity of first-order transverse vibrations is positive, which means that the electric field rotates right handed, while for first-order longitudinal vibrations, it is negative.

(a) Real and (b) imaginary parts of dielectric functions for five-order longitudinal polaritons. Both ordinary (black) and extraordinary (blue) polaritons have dielectric abnormality near the resonance. (c) Tilt angle and angle of ellipticity for ordinary polaritons with the frequency.

(a) Real and (b) imaginary parts of dielectric functions for five-order longitudinal polaritons. Both ordinary (black) and extraordinary (blue) polaritons have dielectric abnormality near the resonance. (c) Tilt angle and angle of ellipticity for ordinary polaritons with the frequency.

Variation in the electric fields [(a) and (d)], magnetic fields [(b) and (e)], and the PFD [(c) and (f)] of -(black solid) and -(red dash dotted) polarized light for transverse and longitudinal vibrations. Here the original incident light is -polarized. A distinct transmission valley due to the dielectric abnormality is located at the frequency of . We choose the transmission distance .

Variation in the electric fields [(a) and (d)], magnetic fields [(b) and (e)], and the PFD [(c) and (f)] of -(black solid) and -(red dash dotted) polarized light for transverse and longitudinal vibrations. Here the original incident light is -polarized. A distinct transmission valley due to the dielectric abnormality is located at the frequency of . We choose the transmission distance .

Variation in the electric fields [(a) and (d)], magnetic fields [(b) and (e)], and the PFD [(c) and (f)] of -(black solid) and -(red dash dotted) polarized light for transverse and longitudinal vibrations. Here the original incident light is -polarized. A distinct transmission valley due to the dielectric abnormality is located at the frequency of . We choose the transmission distance .

(a) Variation curves of resonance frequency (black solid), the largest tilt angle frequency (red dashed), and the right edge frequency (green dash dotted) for first-order transverse vibration polariton. (b) Variation curves of resonance frequency (black solid), the largest tilt angle frequency (red dashed) and the right edge frequency of ordinary (, green dash dotted) and extraordinary (, blue dotted) first-order longitudinal vibration polaritons. The inset in (b) shows the detail variations near the intersection.

(a) Variation curves of resonance frequency (black solid), the largest tilt angle frequency (red dashed), and the right edge frequency (green dash dotted) for first-order transverse vibration polariton. (b) Variation curves of resonance frequency (black solid), the largest tilt angle frequency (red dashed) and the right edge frequency of ordinary (, green dash dotted) and extraordinary (, blue dotted) first-order longitudinal vibration polaritons. The inset in (b) shows the detail variations near the intersection.

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