Appendix I
$$\begin{aligned} \begin{aligned} {\left\{ \begin{array}{ll} &{}\chi _{0}=i\omega \left( t-\frac{y sin \theta _{0}-z cos \theta _{0}}{c_{0}}\right) ,~~~~ \chi _{1}=i\omega \left( t-\frac{y sin \theta _{1}-z cos \theta _{1}}{c_{1}}\right) , ~~~~ \chi _{2}=i\omega \left( t-\frac{y sin \theta _{2}-z cos \theta _{2}}{c_{2}}\right) \\ &{}\chi _{3}=\left\{ i\omega \left( t-\frac{y sin \theta _{3}-z cos \theta _{3}}{c_{3}}\right) \right\} , ~~ \chi _{4}=\left\{ i\omega \left( t-\frac{y sin \theta _{4}-z cos \theta _{4}}{c_{4}}\right) \right\} ,~ \chi _{5}=\left\{ i\omega \left( t-\frac{y sin \theta _{5}+z cos \theta _{5}}{c_{5}}\right) \right\} \\ &{}\chi _{6}=\left\{ i\omega \left( t-\frac{y sin \theta _{6}+z cos \theta _{6}}{c_{6}}\right) \right\} ,~~ \chi _{7}=\left\{ i\omega \left( t-\frac{y sin \theta _{7}+z cos \theta _{7}}{c_{7}}\right) \right\} ,~ \chi _{8}=\left\{ i\omega \left( t-\frac{y sin \theta _{8}+z cos \theta _{8}}{c_{8}}\right) \right\} \\ &{}\chi _{9}=\left\{ i\omega \left( t-\frac{y sin \theta _{9}-z cos \theta _{9}}{c_{9}}\right) \right\} , \chi _{10}=\left\{ i\omega \left( t-\frac{y sin \theta _{10}-z cos \theta _{10}}{c_{10}}\right) \right\} , \chi _{11}=\left\{ i\omega \left( t-\frac{y sin \theta _{11}-z cos \theta _{11}}{c_{11}}\right) \right\} ,\\ &{}\chi _{12}=\left\{ i\omega \left( t-\frac{y sin \theta _{12}-z cos \theta _{12}}{c_{12}}\right) \right\} , ~\chi _{1n}^{\pm }=\left\{ i\omega \left( t-\frac{y sin \theta _{1n}^{\pm }-z cos \theta _{1n}^{\pm }}{c_{1}}\right) \right\} ,\\ &{}\chi _{2n}^{\pm }=\left\{ i\omega \left( t-\frac{y sin \theta _{2n}^{\pm }-z cos \theta _{2n}^{\pm }}{c_{2}}\right) \right\} , ~\chi _{3n}^{\pm }=\left\{ i\omega \left( t-\frac{y sin \theta _{3n}^{\pm }-z cos \theta _{3n}^{\pm }}{c_{3}}\right) \right\} ,\\ &{}\chi _{4n}^{\pm }=\left\{ i\omega \left( t-\frac{y sin \theta _{4n}^{\pm }-z cos \theta _{4n}^{\pm }}{c_{4}}\right) \right\} , ~\chi _{5n}^{\pm }=\left\{ i\omega \left( t-\frac{y sin \theta _{5n}^{\pm }+z cos \theta _{5n}^{\pm }}{c_{5}}\right) \right\} ,\\ &{}\chi _{6n}^{\pm }=\left\{ i\omega \left( t-\frac{y sin \theta _{6n}^{\pm }+z cos \theta _{6n}^{\pm }}{c_{6}}\right) \right\} , ~\chi _{7n}^{\pm }=\left\{ i\omega \left( t-\frac{y sin \theta _{7n}^{\pm }+z cos \theta _{7n}^{\pm }}{c_{7}}\right) \right\} ,\\ &{}\chi _{8n}^{\pm }=\left\{ i\omega \left( t-\frac{y sin \theta _{8n}^{\pm }+z cos \theta _{8n}^{\pm }}{c_{8}}\right) \right\} , ~\chi _{9n}^{\pm }=\left\{ i\omega \left( t-\frac{y sin \theta _{9n}^{\pm }-z cos \theta _{9n}^{\pm }}{c_{9}}\right) \right\} ,\\ &{}\chi _{10n}^{\pm }=\left\{ i\omega \left( t-\frac{y sin \theta _{10n}^{\pm }-z cos \theta _{10n}^{\pm }}{c_{10}}\right) \right\} , ~\chi _{11n}^{\pm }=\left\{ i\omega \left( t-\frac{y sin \theta _{11n}^{\pm }-z cos \theta _{11n}^{\pm }}{c_{11}}\right) \right\} ,\\ &{}\chi _{12n}^{\pm }=\left\{ i\omega \left( t-\frac{y sin \theta _{12n}^{\pm }-z cos \theta _{12n}^{\pm }}{c_{12}}\right) \right\} \end{array}\right. } \end{aligned} \end{aligned}$$
$$\begin{aligned} U_{0}&=\frac{M_{0}}{\rho _{1} c_{0}^{2}-L_{0}}=\frac{\rho _{1}c_{0}^{2}-N_{0}}{M_{0}}, ~~ U_{1}=\frac{M_{1}}{\rho _{1} c_{1}^{2}-L_{1}}=\frac{\rho _{1}c_{1}^{2}-N_{1}}{M_{1}}, ~~\\ U_{2}&=\frac{M_{2}}{\rho _{1} c_{2}^{2}-L_{2}}=\frac{\rho _{1}c_{2}^{2}-N_{2}}{M_{2}}, \\ U_{3}&=\frac{M_{3}}{\rho _{2} c_{3}^{2}-L_{3}}=\frac{\rho _{2}c_{3}^{2}-N_{3}}{M_{3}}, ~~ U_{4}=\frac{M_{4}}{\rho _{2} c_{4}^{2}-L_{4}}=\frac{\rho _{2}c_{4}^{2}-N_{4}}{M_{4}}, ~~\\ U_{5}&=\frac{M_{5}}{\rho _{2} c_{5}^{2}-L_{5}}=\frac{\rho _{2}c_{5}^{2}-N_{5}}{M_{5}},\\ U_{6}&=\frac{M_{6}}{\rho _{2} c_{6}^{2}-L_{6}}=\frac{\rho _{2}c_{6}^{2}-N_{6}}{M_{6}}, ~~ U_{7}=\frac{M_{7}}{\rho _{2} c_{7}^{2}-L_{7}}=\frac{\rho _{2}c_{7}^{2}-N_{7}}{M_{7}}, ~~\\ U_{8}&=\frac{M_{8}}{\rho _{2} c_{8}^{2}-L_{8}}=\frac{\rho _{2}c_{8}^{2}-N_{8}}{M_{8}}, \\ U_{9}&=\frac{M_{9}}{\rho _{3} c_{9}^{2}-L_{9}}=\frac{\rho _{3}c_{9}^{2}-N_{9}}{M_{9}},~ U_{10}=\frac{M_{10}}{\rho _{3} c_{10}^{2}-L_{10}}=\frac{\rho _{3}c_{10}^{2}-N_{10}}{M_{10}},\\ U_{11}&=\frac{M_{11}}{\rho _{3} c_{11}^{2}-L_{11}}=\frac{\rho _{3}c_{11}^{2}-N_{11}}{M_{11}},\\ U_{12}&=\frac{M_{12}}{\rho _{3} c_{12}^{2}-L_{12}}=\frac{\rho _{3}c_{12}^{2}-N_{12}}{M_{12}},~~ U^{\pm }_{1n}=\frac{M^{\pm }_{1n}}{\rho _{1} c_{1}^{2}-L^{\pm }_{1n}}=\frac{\rho _{1}c_{1}^{2}-N^{\pm }_{1n}}{M^{\pm }_{1n}},\\ U^{\pm }_{2n}&=\frac{M^{\pm }_{2n}}{\rho _{1} c_{2}^{2}-L^{\pm }_{2n}}=\frac{\rho _{1}c_{2}^{2}-N^{\pm }_{2n}}{M^{\pm }_{2n}},\\ U^{\pm }_{3n}&=\frac{M^{\pm }_{3n}}{\rho _{2} c_{3}^{2}-L^{\pm }_{3n}}=\frac{\rho _{2}c_{3}^{2}-N^{\pm }_{3n}}{M^{\pm }_{3n}},~ U^{\pm }_{4n}=\frac{M^{\pm }_{4n}}{\rho _{2} c_{4}^{2}-L^{\pm }_{4n}}=\frac{\rho _{2}c_{4}^{2}-N^{\pm }_{4n}}{M^{\pm }_{4n}},\\ U^{\pm }_{5n}&=\frac{M^{\pm }_{5n}}{\rho _{2} c_{5}^{2}-L^{\pm }_{5n}}=\frac{\rho _{2}c_{5}^{2}-N^{\pm }_{5n}}{M^{\pm }_{5n}},\\ U^{\pm }_{6n}&=\frac{M^{\pm }_{6n}}{\rho _{2} c_{6}^{2}-L^{\pm }_{6n}}=\frac{\rho _{2}c_{6}^{2}-N^{\pm }_{6n}}{M^{\pm }_{6n}},~ U^{\pm }_{7n}=\frac{M^{\pm }_{7n}}{\rho _{2} c_{7}^{2}-L^{\pm }_{7n}}=\frac{\rho _{2}c_{7}^{2}-N^{\pm }_{7n}}{M^{\pm }_{7n}},\\ U^{\pm }_{8n}&=\frac{M^{\pm }_{8n}}{\rho _{2} c_{8}^{2}-L^{\pm }_{8n}}=\frac{\rho _{2}c_{8}^{2}-N^{\pm }_{8n}}{M^{\pm }_{8n}},\\ U^{\pm }_{9n}&=\frac{M^{\pm }_{9n}}{\rho _{3} c_{9}^{2}-L^{\pm }_{9n}}=\frac{\rho _{3}c_{9}^{2}-N^{\pm }_{9n}}{M^{\pm }_{9n}},U^{\pm }_{10n}=\frac{M^{\pm }_{10n}}{\rho _{3} c_{10}^{2}-L^{\pm }_{10n}}=\frac{\rho _{3}c_{10}^{2}-N^{\pm }_{10n}}{M^{\pm }_{10n}},\\ U^{\pm }_{11n}&=\frac{M^{\pm }_{11n}}{\rho _{3} c_{11}^{2}-L^{\pm }_{11n}}=\frac{\rho _{3}c_{11}^{2}-N^{\pm }_{11n}}{M^{\pm }_{11n}},\\ U^{\pm }_{12n}&=\frac{M^{\pm }_{12n}}{\rho _{3}c_{12}^{2}-L^{\pm }_{12n}}=\frac{\rho _{3}c_{12}^{2}-N^{\pm }_{12n}}{M^{\pm }_{12n}} \\ \end{aligned}$$
$$\begin{aligned} L_{0}&=C_{22}sin^{2}\theta _{0}+C_{44}cos^{2}\theta _{0}-2C_{24}sin \theta _{0}cos\theta _{0},~~~\\ M_{0}&=C_{24}sin^{2}\theta _{0}+C_{44}cos^{2}\theta _{0}-(C_{23}+C_{44})sin \theta _{0}cos\theta _{0},\\ N_{0}&=C_{44}sin^{2}\theta _{0}+C_{33}cos^{2}\theta _{0}-2C_{34}sin \theta _{0}cos\theta _{0},~~\\ M_{1}&=C_{24}sin^{2}\theta _{1}+C_{44}cos^{2}\theta _{1}-(C_{23}+C_{44})sin \theta _{1}cos\theta _{1},\\ L_{1}&=C_{22}sin^{2}\theta _{1}+C_{44}cos^{2}\theta _{1}-2C_{24}sin \theta _{1}cos\theta _{1},~~~~\\ N_{1}&=C_{44}sin^{2}\theta _{1}+C_{33}cos^{2}\theta _{1}-2C_{34}sin \theta _{1}cos\theta _{1}, \\ L_{2}&=C_{22}sin^{2}\theta _{2}+C_{44}cos^{2}\theta _{2}-2C_{24}sin \theta _{2}cos\theta _{2},~~~~\\ M_{2}&=C_{24}sin^{2}\theta _{2}+C_{44}cos^{2}\theta _{2}-(C_{23}+C_{44})sin \theta _{2}cos\theta _{2},\\ N_{2}&=C_{44}sin^{2}\theta _{2}+C_{33}cos^{2}\theta _{2}-2C_{34}sin \theta _{2}cos\theta _{2},~~ L_{3}=C_{24}sin^{2}\theta _{3}+C_{44}cos^{2}\theta _{3},\\ M_{3}&=(C_{23}+C_{44})sin \theta _{3}cos\theta _{3},~ N_{3}=C_{44}sin^{2}\theta _{3}+C_{33}cos^{2}\theta _{3}-2C_{34}sin \theta _{3}cos\theta _{3},\\ L_{4}&=C_{24}sin^{2}\theta _{4}+C_{44}cos^{2}\theta _{4},~ M_{4}=(C_{23}+C_{44})sin \theta _{4}cos\theta _{4},\\ N_{4}&=C_{44}sin^{2}\theta _{4}+C_{33}cos^{2}\theta _{4}-2C_{34}sin \theta _{4}cos\theta _{4},\\ L_{5}&=C_{24}sin^{2}\theta _{5}+C_{44}cos^{2}\theta _{5}, M_{5}=(C_{23}+C_{44})sin \theta _{5}cos\theta _{5},\\ N_{5}&=C_{44}sin^{2}\theta _{5}+C_{33}cos^{2}\theta _{5}-2C_{34}sin \theta _{5}cos\theta _{5},\\ L_{6}&=C_{24}sin^{2}\theta _{6}+C_{44}cos^{2}\theta _{6},~ M_{6}=(C_{23}+C_{44})sin \theta _{6}cos\theta _{6}, ~\\ N_{6}&=C_{44}sin^{2}\theta _{6}+C_{33}cos^{2}\theta _{6}-2C_{34}sin \theta _{6}cos\theta _{6},\\ L_{7}&=C_{24}sin^{2}\theta _{7}+C_{44}cos^{2}\theta _{7},~ M_{7}=(C_{23}+C_{44})sin \theta _{7}cos\theta _{7},\\ N_{7}&=C_{44}sin^{2}\theta _{7}+C_{33}cos^{2}\theta _{7}-2C_{34}sin \theta _{7}cos\theta _{7},\\ L_{8}&=C_{24}sin^{2}\theta _{8}+C_{44}cos^{2}\theta _{8},~M_{8}=(C_{23}+C_{44})sin \theta _{8}cos\theta _{8},\\ N_{8}&=C_{44}sin^{2}\theta _{8}+C_{33}cos^{2}\theta _{8}-2C_{34}sin \theta _{8}cos\theta _{8}, \\ L_{9}&=C_{22}sin^{2}\theta _{9}+C_{44}cos^{2}\theta _{9}-2C_{24}sin \theta _{9}cos\theta _{9},~\\ M_{9}&=C_{24}sin^{2}\theta _{9}+C_{44}cos^{2}\theta _{9}-(C_{23}+C_{44})sin \theta _{9}cos\theta _{9},\\ N_{9}&=C_{44}sin^{2}\theta _{0}+C_{33}cos^{2}\theta _{9}-2C_{34}sin \theta _{9}cos\theta _{9},~~\\ L_{10}&=C_{22}sin^{2}\theta _{10}+C_{44}cos^{2}\theta _{10}-2C_{24}sin \theta _{10}cos\theta _{10},\\ M_{10}&=C_{24}sin^{2}\theta _{10}+C_{44}cos^{2}\theta _{10}-(C_{23}+C_{44})sin \theta _{10}cos\theta _{10},\\ N_{10}&=C_{44}sin^{2}\theta _{10}+C_{33}cos^{2}\theta _{10}-2C_{34}sin \theta _{10}cos\theta _{10},\\ L_{11}&=C_{22}sin^{2}\theta _{11}+C_{44}cos^{2}\theta _{11}-2C_{24}sin \theta _{11}cos\theta _{11},\\ M_{11}&=C_{24}sin^{2}\theta _{11}+C_{44}cos^{2}\theta _{11}-(C_{23}+C_{44})sin \theta _{11}cos\theta _{11},\\ N_{11}&=C_{44}sin^{2}\theta _{11}+C_{33}cos^{2}\theta _{11}-2C_{34}sin \theta _{11}cos\theta _{11},\\ \end{aligned}$$
$$\begin{aligned} M_{12}&=C_{24}sin^{2}\theta _{12}+C_{44}cos^{2}\theta _{12}-(C_{23}+C_{44})sin \theta _{12}cos\theta _{12},\\ L^{\pm }_{1n}&=C_{22}sin^{2}\theta ^{\pm }_{1n}+C_{44}cos^{2}\theta ^{\pm }_{1n} -2C_{24}sin\theta ^{\pm }_{1n}cos\theta ^{\pm }_{1n},~\\ N^{\pm }_{1n}&=C_{44}sin^{2}\theta ^{\pm }_{1n}+C_{33}cos^{2}\theta ^{\pm }_{1n}-2C_{34}sin \theta ^{\pm }_{1n}cos\theta ^{\pm }_{1n},\\ M^{\pm }_{1n}&=C_{24}sin^{2}\theta ^{\pm }_{1n}+C_{44}cos^{2}\theta ^{\pm }_{1n}-(C_{23}+C_{44})sin \theta ^{\pm }_{1n}cos\theta ^{\pm }_{1n},\\ L^{\pm }_{2n}&=C_{22}sin^{2}\theta ^{\pm }_{2n}+C_{44}cos^{2}\theta ^{\pm }_{2n} -2C_{24}sin\theta ^{\pm }_{2n}cos\theta ^{\pm }_{2n},\\ N^{\pm }_{2n}&=C_{44}sin^{2}\theta ^{\pm }_{2n}+C_{33}cos^{2}\theta ^{\pm }_{2n}-2C_{34}sin \theta ^{\pm }_{2n}cos\theta ^{\pm }_{2n},\\ M^{\pm }_{2n}&=C_{24}sin^{2}\theta ^{\pm }_{2n}+C_{44}cos^{2}\theta ^{\pm }_{2n}-(C_{23}+C_{44})sin\theta ^{\pm }_{2n}cos\theta ^{\pm }_{2n},\\ L^{\pm }_{3n}&=C_{24}sin^{2}\theta ^{\pm }_{3n}+C_{44}cos^{2}\theta ^{\pm }_{3n},~\\ M^{\pm }_{3n}&=(C_{23}+C_{44})sin^{2}\theta ^{\pm }_{3n}+C_{44}cos^{2}\theta ^{\pm }_{3n}-(C_{23}+C_{44})sin\theta ^{\pm }_{3n}cos\theta ^{\pm }_{3n},\\ N^{\pm }_{3n}&=C_{44}sin^{2}\theta ^{\pm }_{3n}+C_{33}cos^{2}\theta ^{\pm }_{3n}-2C_{34}sin \theta ^{\pm }_{3n}cos\theta ^{\pm }_{3n},\\ L^{\pm }_{4n}&=C_{24}sin^{2}\theta ^{\pm }_{4n}+C_{44}cos^{2}\theta ^{\pm }_{4n},\\ M^{\pm }_{4n}&=(C_{23}+C_{44})sin^{2}\theta ^{\pm }_{4n}+C_{44}cos^{2}\theta ^{\pm }_{4n}-(C_{23}+C_{44})sin\theta ^{\pm }_{4n}cos\theta ^{\pm }_{4n},\\ N^{\pm }_{4n}&=C_{44}sin^{2}\theta ^{\pm }_{4n}+C_{33}cos^{2}\theta ^{\pm }_{4n}-2C_{34}sin \theta ^{\pm }_{4n}cos\theta ^{\pm }_{4n}, \\ L^{\pm }_{5n}&=C_{24}sin^{2}\theta ^{\pm }_{5n}+C_{44}cos^{2}\theta ^{\pm }_{5n},~\\ M^{\pm }_{5n}&=(C_{23}+C_{44})sin^{2}\theta ^{\pm }_{5n}+C_{44}cos^{2}\theta ^{\pm }_{5n}-(C_{23}+C_{44})sin\theta ^{\pm }_{5n}cos\theta ^{\pm }_{5n},\\ N^{\pm }_{5n}&=C_{44}sin^{2}\theta ^{\pm }_{5n}+C_{33}cos^{2}\theta ^{\pm }_{5n}-2C_{34}sin \theta ^{\pm }_{5n}cos\theta ^{\pm }_{5n},\\ L^{\pm }_{6n}&=C_{24}sin^{2}\theta ^{\pm }_{6n}+C_{44}cos^{2}\theta ^{\pm }_{6n},\\ M^{\pm }_{6n}&=(C_{23}+C_{44})sin^{2}\theta ^{\pm }_{6n}+C_{44}cos^{2}\theta ^{\pm }_{6n}-(C_{23}+C_{44})sin\theta ^{\pm }_{6n}cos\theta ^{\pm }_{6n},\\ N^{\pm }_{6n}&=C_{44}sin^{2}\theta ^{\pm }_{6n}+C_{33}cos^{2}\theta ^{\pm }_{6n}-2C_{34}sin \theta ^{\pm }_{6n}cos\theta ^{\pm }_{6n},\\ L^{\pm }_{7n}&=C_{24}sin^{2}\theta ^{\pm }_{7n}+C_{44}cos^{2}\theta ^{\pm }_{7n},~\\ M^{\pm }_{7n}&=(C_{23}+C_{44})sin^{2}\theta ^{\pm }_{7n}+C_{44}cos^{2}\theta ^{\pm }_{7n}-(C_{23}+C_{44})sin\theta ^{\pm }_{7n}cos\theta ^{\pm }_{7n},\\ N^{\pm }_{3n}&=C_{44}sin^{2}\theta ^{\pm }_{7n}+C_{33}cos^{2}\theta ^{\pm }_{7n}-2C_{34}sin \theta ^{\pm }_{7n}cos\theta ^{\pm }_{7n},\\ L^{\pm }_{8n}&=C_{24}sin^{2}\theta ^{\pm }_{8n}+C_{44}cos^{2}\theta ^{\pm }_{8n},\\ M^{\pm }_{8n}&=(C_{23}+C_{44})sin^{2}\theta ^{\pm }_{8n}+C_{44}cos^{2}\theta ^{\pm }_{8n}-(C_{23}+C_{44})sin\theta ^{\pm }_{8n}cos\theta ^{\pm }_{8n},\\ N^{\pm }_{8n}&=C_{44}sin^{2}\theta ^{\pm }_{8n}+C_{33}cos^{2}\theta ^{\pm }_{8n}-2C_{34}sin \theta ^{\pm }_{8n}cos\theta ^{\pm }_{8n},\\ L^{\pm }_{9n}&=C_{22}sin^{2}\theta ^{\pm }_{9n}+C_{44}cos^{2}\theta ^{\pm }_{9n}-2C_{24}sin\theta ^{\pm }_{9n}cos\theta ^{\pm }_{9n},~\\ N^{\pm }_{9n}&=C_{44}sin^{2}\theta ^{\pm }_{9n}+C_{33}cos^{2}\theta ^{\pm }_{9n}-2C_{34}sin \theta ^{\pm }_{9n}cos\theta ^{\pm }_{9n}, \\ \end{aligned}$$
$$\begin{aligned} M^{\pm }_{9n}&=C_{24}sin^{2}\theta ^{\pm }_{9n}+C_{44}cos^{2}\theta ^{\pm }_{9n}-(C_{23}+C_{44})sin \theta ^{\pm }_{9n}cos\theta ^{\pm }_{9n},\\ L^{\pm }_{10n}&=C_{22}sin^{2}\theta ^{\pm }_{10n}+C_{44}cos^{2}\theta ^{\pm }_{10n}-2C_{24}sin \theta ^{\pm }_{10n}cos\theta ^{\pm }_{10n},\\ N^{\pm }_{10n}&=C_{44}sin^{2}\theta ^{\pm }_{10n}+C_{33}cos^{2}\theta ^{\pm }_{10n}-2C_{34}sin \theta ^{\pm }_{10n}cos\theta ^{\pm }_{10n},\\ M^{\pm }_{10n}&=C_{24}sin^{2}\theta ^{\pm }_{10n}+C_{44}cos^{2}\theta ^{\pm }_{10n}-(C_{23}+C_{44})sin \theta ^{\pm }_{10n}cos\theta ^{\pm }_{10n},\\ L^{\pm }_{11n}&=C_{22}sin^{2}\theta ^{\pm }_{11n}+C_{44}cos^{2}\theta ^{\pm }_{11n}-2C_{24}sin \theta ^{\pm }_{11n}cos\theta ^{\pm }_{11n},\\ N^{\pm }_{11n}&=C_{44}sin^{2}\theta ^{\pm }_{11n}+C_{33}cos^{2}\theta ^{\pm }_{11n}-2C_{34}sin \theta ^{\pm }_{11n}cos\theta ^{\pm }_{11n},\\ M^{\pm }_{11n}&=C_{24}sin^{2}\theta ^{\pm }_{11n}+C_{44}cos^{2}\theta ^{\pm }_{11n}-(C_{23}+C_{44})sin \theta ^{\pm }_{11n}cos\theta ^{\pm }_{11n},\\ L^{\pm }_{12n}&=C_{22}sin^{2}\theta ^{\pm }_{12n}+C_{44}cos^{2}\theta ^{\pm }_{12n}-2C_{24}sin \theta ^{\pm }_{12n}cos\theta ^{\pm }_{12n},\\ N^{\pm }_{12n}&=C_{44}sin^{2}\theta ^{\pm }_{12n}+C_{33}cos^{2}\theta ^{\pm }_{12n}-2C_{34}sin \theta ^{\pm }_{12n}cos\theta ^{\pm }_{12n},\\ M^{\pm }_{12n}&=C_{24}sin^{2}\theta ^{\pm }_{12n}+C_{44}cos^{2}\theta ^{\pm }_{12n}-(C_{23}+C_{44})sin \theta ^{\pm }_{12n}cos\theta ^{\pm }_{12n}, \end{aligned}$$
Appendix II
$$\begin{aligned} l_{0}&=(U_{0}c_{24}+c_{44})P_{0}-(U_{0}c_{44}+c_{34})R_{0},~~~l_{1}=(U_{1}c_{24}+c_{44})P_{0}+(U_{1}c_{44}+c_{34})R_{1},\\ l_{2}&=(U_{2}c_{24}+c_{44})P_{0}+(U_{2}c_{44}+c_{34})R_{2},~~~l_{3}=c_{44}P_{0}-U_{3}c_{44}R_{3},\\ l_{4}&=c_{44}P_{0}-U_{4}c_{44}R_{4},~~~m_{0}=(U_{0}c_{23}+c_{34})P_{0}-(U_{0}c_{34}+c_{33})R_{0},\\ m_{1}&=(U_{1}c_{23}+c_{34})P_{0}+(U_{1}c_{34}+c_{33})R_{1},~~~m_{2}=(U_{2}c_{23}+c_{34})P_{0}+(U_{2}c_{34}+c_{33})R_{2},\\ m_{3}&=U_{3}c_{23}P_{0}-c_{33}R_{3},~~~m_{4}=U_{4}c_{23}P_{0}-c_{33}R_{4}\\ f^{\mp }_{1}&=i\zeta _{{\mp }_{n}}\left[ -R_{0}U_{0}+R_{1}U_{1}\frac{A_{3}}{B_{0}}+R_{2}U_{2}\frac{B_{3}}{B_{0}}+R_{3}U_{3}\frac{C_{3}}{B_{0}}+R_{4}U_{4}\frac{D_{3}}{B_{0}}\right] ,\\ f^{\mp }_{2}&=i\zeta _{{\mp }_{n}}\left[ -R_{0}+R_{1}\frac{A_{3}}{B_{0}}+R_{2}\frac{B_{3}}{B_{0}}+R_{3}\frac{C_{3}}{B_{0}}+R_{4}\frac{D_{3}}{B_{0}}\right] ,\\ f^{\mp }_{3}&=i\left[ g^{\mp }_{0}+g^{\mp }_{1}\frac{A_{3}}{B_{0}}+g^{\mp }_{2}\frac{B_{3}}{B_{0}}-g^{\mp }_{3}\frac{C_{3}}{B_{0}}-g^{\mp }_{4}\frac{D_{3}}{B_{0}}\right] ,\\ f^{\mp }_{4}&=i\left[ h^{\mp }_{0}+h^{\mp }_{1}\frac{A_{3}}{B_{0}}+h^{\mp }_{2}\frac{B_{3}}{B_{0}}-h^{\mp }_{3}\frac{C_{3}}{B_{0}}-h^{\mp }_{4}\frac{D_{3}}{B_{0}}\right] ,\\ g^{\mp }_{0}&=[\{\mp (c_{23}-c_{22})npP_{0}+c_{24}P_{0}R_{0}\pm (c_{34}-c_{24})npR_{0}-c_{44}R_{0}^{2}\}U_{0}\pm (c_{33}-c_{23})npR_{0}\\&\quad -c_{34}R_{0}^{2}\mp (c_{34}-c_{24})npP_{0}+c_{44}P_{0}R_{0}]\zeta _{{\mp }_{n}},\\ g^{\mp }_{1}&=[\{\mp (c_{23}-c_{22})npP_{0}+c_{24}P_{0}R_{1}\pm (c_{34}-c_{24})npR_{1}-c_{44}R_{1}^{2}\}U_{1}\pm (c_{33}-c_{23})npR_{1}\\&\quad -c_{34}R_{1}^{2}\mp (c_{34}-c_{24})npP_{0}+c_{44}P_{0}R_{1}]\zeta _{{\mp }_{n}},\\ g^{\mp }_{2}&=[\{\mp (c_{23}-c_{22})npP_{0}+c_{24}P_{0}R_{2}\pm (c_{34}-c_{24})npR_{2}-c_{44}R_{2}^{2}\}U_{2}\pm (c_{33}-c_{23})npR_{2}\\&\quad -c_{34}R_{2}^{2}\mp (c_{34}-c_{24})npP_{0}+c_{44}P_{0}R_{2}]\zeta _{{\mp }_{n}},\\ g^{\mp }_{3}&=[\{\mp (c_{23}-c_{22})npP_{0}-c_{24}R_{3}\}U_{3}\pm (c_{33}-c_{23})npR_{3}-c_{44}P_{0}]\zeta _{{\mp }_{n}},\\ g^{\mp }_{4}&=[\{\mp (c_{23}-c_{22})npP_{0}-c_{24}R_{4}\}U_{4}\pm (c_{33}-c_{23})npR_{4}-c_{44}P_{0}]\zeta _{{\mp }_{n}},\\ g^{\mp }_{5}&=-[\{c_{44}R^{\pm }_{1n} \mp +c_{24}(P_{0}\pm np)\}U^{\pm }_{1n}+c_{34}R^{\pm }_{1n}+c_{44}(P_{0}\pm np)],\\ g^{\mp }_{6}&=-[\{c_{44}R^{\pm }_{2n} \mp +c_{24}(P_{0}\pm np)\}U^{\pm }_{2n}+c_{34}R^{\pm }_{2n}+c_{44}(P_{0}\pm np)],\\ g^{\mp }_{7}&=[\{c_{44}R^{\pm }_{3n}+(c_{23}-c_{22})np(P_{0}\pm np)\}U^{\pm }_{3n}+(c_{33}-c_{23})npR^{\pm }_{3n}-c_{44}(P_{0}\pm np)],\\ g^{\mp }_{8}&=[\{c_{44}R^{\pm }_{4n}+(c_{23}-c_{22})np(P_{0}\pm np)\}U^{\pm }_{4n}+(c_{33}-c_{23})npR^{\pm }_{4n}-c_{44}(P_{0}\pm np)],\\ h^{\mp }_{0}&=[\{c_{23}P_{0}R_{0}\pm 2c_{24}npP_{0}-c_{34}R_{0}^{2}-2c_{44}npR_{0}\}U_{0}\\&\quad -c_{33}R_{0}^{2}\mp 2c_{34}npR_{0}-c_{34}P_{0}R_{0}\pm 2c_{44}npP_{0}]\zeta _{{\mp }_{n}},\\ h^{\mp }_{1}&=[\{c_{23}P_{0}R_{1}\pm 2c_{24}npP_{0}-c_{34}R_{1}^{2}-2c_{44}npR_{1}\}U_{1}\\&\quad -c_{33}R_{1}^{2}\mp 2c_{34}npR_{1}-c_{34}P_{0}R_{1}\pm 2c_{44}npP_{0}]\zeta _{{\mp }_{n}},\\ h^{\mp }_{2}&=[\{c_{23}P_{0}R_{2}\pm 2c_{24}npP_{0}-c_{34}R_{2}^{2}-2c_{44}npR_{2}\}U_{2}\\&\quad -c_{33}R_{2}^{2}\mp 2c_{34}npR_{2}-c_{34}P_{0}R_{2}\pm 2c_{44}npP_{0}]\zeta _{{\mp }_{n}},\\ \end{aligned}$$
$$\begin{aligned} h^{\mp }_{3}&=[\{c_{23}P_{0}- 2c_{44}npR_{3}\}U_{3}+c_{33}R_{3}- 2c_{44}npP_{0}]\zeta _{{\mp }_{n}},\\ h^{\mp }_{4}&=[\{c_{23}P_{0}- 2c_{44}npR_{4}\}U_{4}+c_{33}R_{4}- 2c_{44}npP_{0}]\zeta _{{\mp }_{n}},\\ h^{\mp }_{5}&=[\{c_{23}(P_{0}\pm np)+c_{34}R^{\pm }_{1n}\}U^{\pm }_{1n}+c_{33}R^{\pm }_{1n}-c_{34}(P_{0}\pm np)],\\ h^{\mp }_{6}&=[\{c_{23}(P_{0}\pm np)+c_{34}R^{\pm }_{2n}\}U^{\pm }_{2n}+c_{33}R^{\pm }_{2n}-c_{34}(P_{0}\pm np)],\\ h^{\mp }_{7}&=[\{c_{23}(P_{0}\pm np)-2c_{44}npR^{\pm }_{3n}\}U^{\pm }_{3n}+c_{33}R^{\pm }_{3n}-2c_{44}np(P_{0}\pm np)],\\ h^{\mp }_{8}&=[\{c_{23}(P_{0}\pm np)-2c_{44}npR^{\pm }_{4n}\}U^{\pm }_{4n}+c_{33}R^{\pm }_{4n}-2c_{44}np(P_{0}\pm np)]\\ l_{5}&=\{c_{44}P_{0}-U_{5}c_{44}R_{5} \}e^{i(R_{5}+R_{3})H},~~~l_{6}=\{c_{44}P_{0}+U_{6}c_{44}R_{6}\}e^{i(R_{6}+R_{3})H},\\ l_{9}&=\{(U_{9}c_{24}+c_{44})P_{0}-(U_{9}c_{44}+c_{34})R_{9} \}e^{i(-R_{9}+R_{3})H}, ~~m_{5}=\{U_{5}c_{23}P_{0}-c_{33}R_{5} \}e^{i(R_{5}+R_{3})H}, \\ l_{10}&=\{(U_{10}c_{24}+c_{44})P_{0}-(U_{10}c_{44}+c_{34})R_{10}\}e^{i(-R_{10}+R_{3})H},~~m_{6}=\{U_{6}c_{23}P_{0}-c_{33}R_{6}\}e^{i(R_{6}+R_{3})H},\\ m_{9}&=\{(U_{9}c_{24}+c_{44})P_{0}-(U_{9}c_{44}+c_{34})R_{9} \}e^{i(-R_{9}+R_{3})H},\\ m_{10}&=\{(U_{10}c_{24}+c_{44})P_{0}-(U_{10}c_{44}+c_{34})R_{10}\}e^{i(-R_{10}+R_{3})H} \\ f^{\mp }_{5}&=i\zeta _{{\mp }_{n}}\left[ -R_{3}U_{3}+R_{5}U_{5}\frac{E_{3}}{C_{3}}e^{i(R_{5}+R_{3})H}+R_{6}U_{6}\frac{F_{3}}{C_{3}}e^{i(R_{6}+R_{3})H}+R_{9}U_{9}\frac{G_{3}}{C_{3}}e^{i(-R_{9}+R_{3})H}\right. \\&\quad \left. +R_{10}U_{10}\frac{H_{3}}{C_{3}}e^{i(-R_{10}+R_{3})H}\right] ,\\ f^{\mp }_{6}&=i\zeta _{{\mp }_{n}}\left[ -R_{3}+R_{5}\frac{E_{3}}{C_{3}}e^{i(R_{5}+R_{3})H} +R_{6}\frac{F_{3}}{C_{3}}e^{i(R_{6}+R_{3})H}+R_{9}\frac{G_{3}}{C_{3}}e^{i(-R_{9}+R_{3})H}\right. \\&\quad \left. +R_{10}\frac{H_{3}}{C_{3}}e^{i(-R_{10}+R_{3})H}\right] ,\\ f^{\mp }_{7}&=i\left[ g^{\mp }_{9}+g^{\mp }_{10}\frac{E_{3}}{C_{3}}+g^{\mp }_{11}\frac{F_{3}}{C_{3}} -g^{\mp }_{12}\frac{G_{3}}{C_{3}}-g^{\mp }_{13}\frac{H_{3}}{C_{3}}\right] ,\\ f^{\mp }_{8}&=i\left[ h^{\mp }_{9}+h^{\mp }_{10}\frac{E_{3}}{C_{3}}+h^{\mp }_{11}\frac{F_{3}}{C_{3}} -h^{\mp }_{12}\frac{G_{3}}{C_{3}}-h^{\mp }_{13}\frac{H_{3}}{C_{3}}\right] \end{aligned}$$
$$\begin{aligned} g^{\mp }_{9}&=[\{\mp (c_{23}-c_{22})npP_{0}+c_{44}R_{3}\}U_{3}\pm (c_{23}-c_{22})npR_{3}+c_{44}P_{0}]\zeta _{{\mp }_{n}}e^{-iR_{3}H},\\ g^{\mp }_{10}&=[\{\mp (c_{23}-c_{22})npP_{0}+c_{44}R_{5}\}U_{5}\pm (c_{23}-c_{22})npR_{5}+c_{44}P_{0}]\zeta _{{\mp }_{n}}e^{iR_{5}H},\\ g^{\mp }_{11}&=[\{\mp (c_{23}-c_{22})npP_{0}+c_{44}R_{6}\}U_{6}\pm (c_{23}-c_{22})npR_{6}+c_{44}P_{0}]\zeta _{{\mp }_{n}}e^{iR_{6}H},\\ g^{\mp }_{12}&=[\{\mp (c_{23}-c_{22})npP_{0}+c_{24}P_{0}R_{9}\}U_{9}\pm (c_{34}-c_{24})npP_{0}+c_{44}P_{0}R_{9}\\&\quad \mp (c_{33}-c_{23})npR_{9}+c_{34}R_{9}^{2} ]\zeta _{{\mp }_{n}}e^{-R_{9}H},\\ g^{\mp }_{13}&=[\{\mp (c_{23}-c_{22})npP_{0}+c_{24}P_{0}R_{10}\}U_{10}\pm (c_{34}-c_{24})npP_{0}+c_{44}P_{0}R_{10}\\&\quad \mp (c_{33}-c_{23})npR_{10}+c_{34}R_{10}^{2} ]\zeta _{{\mp }_{n}}e^{-R_{10}H},\\ g^{\mp }_{14}&=[\{c_{44}R^{\pm }_{5n}+(c_{23}-c_{22})np(P_{0}\pm np)\}U^{\pm }_{5n}+(c_{33}-c_{23})npR^{\pm }_{5n}-c_{44}(P_{0}\pm np)]e^{R^{\pm }_{5n}H},\\ g^{\mp }_{15}&=[\{c_{44}R^{\pm }_{6n}+(c_{23}-c_{22})np(P_{0}\pm np)\}U^{\pm }_{6n}+(c_{33}-c_{23})npR^{\pm }_{6n}-c_{44}(P_{0}\pm np)]e^{R^{\pm }_{6n}H},\\ g^{\mp }_{16}&=[\{c_{44}R^{\pm }_{9n}+c_{24}(P_{0}\pm np)\}U^{\pm }_{9n}+c_{34}R^{\pm }_{9n}-c_{44}(P_{0}\pm np)]e^{-R^{\pm }_{9n}H},\\ g^{\mp }_{17}&=[\{c_{44}R^{\pm }_{10n}+c_{24}(P_{0}\pm np)\}U^{\pm }_{10n}+c_{34}R^{\pm }_{10n}-c_{44}(P_{0}\pm np)]e^{-R^{\pm }_{10n}H},\\ h^{\mp }_{9}&=[\{c_{23}P_{0}-2c_{44}npR_{3}\}U_{3}+c_{33}R_{3}-2c_{44}npP_{0}]\zeta _{{\mp }_{n}}e^{-iR_{3}H},\\ h^{\mp }_{10}&=[\{c_{23}P_{0}-2c_{44}npR_{5}\}U_{5}+c_{33}R_{5}-2c_{44}npP_{0}]\zeta _{{\mp }_{n}}e^{iR_{5}H},\\ h^{\mp }_{11}&=[\{c_{23}P_{0}-2c_{44}npR_{6}\}U_{6}+c_{33}R_{6}-2c_{44}npP_{0}]\zeta _{{\mp }_{n}}e^{iR_{6}H},\\ h^{\mp }_{12}&=[\{c_{23}P_{0}R_{9}-2c_{24}npP_{0}-c_{34}R_{9}^{2}-2c_{44}npR_{9}\}U_{9}-c_{33}R_{9}^{2}\mp 2c_{34}npR_{9}-c_{34}P_{0}R_{9}\\&\quad \pm 2c_{44}npP_{0}]\zeta _{{\mp }_{n}}e^{-R_{9}H},\\ h^{\mp }_{13}&=[\{c_{23}P_{0}R_{9}\pm 2c_{24}npP_{0}-c_{34}R_{10}^{2}-2c_{44}npR_{10}\}U_{10}-c_{33}R_{10}^{2}\mp 2c_{34}npR_{10}-c_{34}P_{0}R_{10}\\&\quad \pm 2c_{44}npP_{0}]\zeta _{{\mp }_{n}}e^{-R_{10}H},\\ h^{\mp }_{14}&=[\{c_{23}(P_{0}\pm np)-2c_{44}R^{\pm }_{5n}\}U^{\pm }_{5n}+c_{33}R^{\pm }_{5n}-2c_{44}(P_{0}\pm np)]e^{R^{\pm }_{5n}H},\\ h^{\mp }_{15}&=[\{c_{23}(P_{0}\pm np)-2c_{44}R^{\pm }_{6n}\}U^{\pm }_{6n}+c_{33}R^{\pm }_{6n}-2c_{44}(P_{0}\pm np)]e^{R^{\pm }_{6n}H},\\ h^{\mp }_{16}&=[\{c_{23}(P_{0}\pm np)+c_{34}R^{\pm }_{9n}\}U^{\pm }_{9n}+c_{33}R^{\pm }_{9n}-c_{34}(P_{0}\pm np)]e^{-R^{\pm }_{9n}H},\\ h^{\mp }_{17}&=[\{c_{23}(P_{0}\pm np)+c_{34}R^{\pm }_{10n}\}U^{\pm }_{10n}+c_{33}R^{\pm }_{10n}-c_{34}(P_{0}\pm np)]e^{-R^{\pm }_{10n}H}\\ l_{7}&=\{c_{44}P_{0}+U_{7}c_{44}R_{7}\}e^{i(R_{7}+R_{4})H},~~l_{8}=\{c_{44}P_{0}+U_{8}c_{44}R_{8}\}e^{i(R_{8}+R_{4})H},\\ l_{11}&=\{(U_{11}c_{24}+c_{44})P_{0}-(U_{11}c_{44}+c_{34})R_{11}\}e^{i(-R_{11}+R_{4})H},\\ l_{12}&=\{(U_{12}c_{24}+c_{44})P_{0}-(U_{12}c_{44}+c_{34})R_{12} \}e^{i(-R_{12}+R_{4})H},\\ m_{7}&=\{U_{7}c_{23}P_{0}-c_{33}R_{7} \}e^{i(R_{7}+R_{4})H},~~~m_{8}=\{U_{8}c_{23}P_{0}-c_{33}R_{8}\}e^{i(R_{8}+R_{4})H},\\ m_{11}&=\{(U_{11}c_{24}+c_{44})P_{0}-(U_{11}c_{44}+c_{34})R_{11} \}e^{i(-R_{11}+R_{4})H},\\ m_{12}&=\{(U_{12}c_{24}+c_{44})P_{0}-(U_{12}c_{44}+c_{34})R_{12}\}e^{i(-R_{12}+R_{4})H} \\ \end{aligned}$$
$$\begin{aligned} f^{\mp }_{9}&=i\zeta _{{\mp }_{n}}\left[ -R_{4}U_{4}+R_{7}U_{7}\frac{I_{3}}{D_{3}}e^{i(R_{7}+R_{4})H}+R_{8}U_{8}\frac{J_{3}}{D_{3}}e^{i(R_{8}+R_{4})H}+R_{11}U_{11}\frac{K_{3}}{D_{3}}e^{i(-R_{11}+R_{4})H}\right. \\&\quad \left. +R_{12}U_{12}\frac{S_{3}}{D_{3}}e^{i(-R_{12}+R_{4})H}\right] ,\\ f^{\mp }_{10}&=i\zeta _{{\mp }_{n}} \left[ -R_{4}+R_{7}\frac{I_{3}}{D_{3}}e^{i(R_{7}+R_{4})H}+R_{8}\frac{J_{3}}{D_{3}}e^{i(R_{8} +R_{4})H}+R_{11}\frac{K_{3}}{D_{3}}e^{i(-R_{11}+R_{4})H}\right. \\&\quad \left. +R_{12}\frac{S_{3}}{D_{3}}e^{i(-R_{12}+R_{4})H}\right] ,\\ f^{\mp }_{11}&=i\left[ g^{\mp }_{18}+g^{\mp }_{19}\frac{I_{3}}{D_{3}}+g^{\mp }_{20}\frac{J_{3}}{D_{3}}-g^{\mp }_{21}\frac{K_{3}}{D_{3}}-g^{\mp }_{22}\frac{S_{3}}{D_{3}}\right] ,\\ f^{\mp }_{12}&=i\left[ h^{\mp }_{18}+h^{\mp }_{19}\frac{I_{3}}{D_{3}}+h^{\mp }_{20}\frac{J_{3}}{D_{3}}-h^{\mp }_{21}\frac{K_{3}}{D_{3}}-h^{\mp }_{22}\frac{S_{3}}{D_{3}}\right] ,\\ g^{\mp }_{18}&=[\{\mp (c_{23}-c_{22})npP_{0}+c_{44}R_{4}\}U_{4}\pm (c_{23}-c_{22})npR_{4}+c_{44}P_{0}]\zeta _{{\mp }_{n}}e^{-R_{4}H},\\ g^{\mp }_{19}&=[\{\mp (c_{23}-c_{22})npP_{0}+c_{44}R_{7}\}U_{7}\pm (c_{23}-c_{22})npR_{7}+c_{44}P_{0}]\zeta _{{\mp }_{n}}e^{-R_{7}H},\\ g^{\mp }_{20}&=[\{\mp (c_{23}-c_{22})npP_{0}+c_{44}R_{8}\}U_{8}\pm (c_{23}-c_{22})npR_{8}+c_{44}P_{0}]\zeta _{{\mp }_{n}}e^{-R_{8}H},\\ g^{\mp }_{21}&=[\{\mp (c_{23}-c_{22})npP_{0}+c_{24}P_{0}R_{11}\}U_{11}\pm (c_{34}-c_{24})npP_{0}+c_{44}P_{0}R_{11}\\&\quad \mp (c_{33}-c_{23})npR_{11}+c_{34}R_{11}^{2} ]\zeta _{{\mp }_{n}}e^{-R_{11}H},\\ g^{\mp }_{22}&=[\{\mp (c_{23}-c_{22})npP_{0}+c_{24}P_{0}R_{12}\}U_{12}\pm (c_{34}-c_{24})npP_{0}+c_{44}P_{0}R_{12}\\&\quad \mp (c_{33}-c_{23})npR_{12}+c_{34}R_{12}^{2} ]\zeta _{{\mp }_{n}}e^{-R_{12}H},\\ g^{\mp }_{23}&=[\{c_{44}R^{\pm }_{7n}+(c_{23}-c_{22})np(P_{0}\pm np)\}U^{\pm }_{7n}+(c_{33}-c_{23})npR^{\pm }_{7n}-c_{44}(P_{0}\pm np)]e^{-R^{\pm }_{7n}H},\\ g^{\mp }_{24}&=[\{c_{44}R^{\pm }_{8n}+(c_{23}-c_{22})np(P_{0}\pm np)\}U^{\pm }_{8n}+(c_{33}-c_{23})npR^{\pm }_{8n}-c_{44}(P_{0}\pm np)]e^{-R^{\pm }_{8n}H},\\ g^{\mp }_{25}&=[\{c_{44}R^{\pm }_{11n}+c_{24}(P_{0}\pm np)\}U^{\pm }_{11n}+c_{34}R^{\pm }_{11n}-c_{44}(P_{0}\pm np)]e^{-R^{\pm }_{11n}H},\\ g^{\mp }_{26}&=[\{c_{44}R^{\pm }_{12n}+c_{24}(P_{0}\pm np)\}U^{\pm }_{12n}+c_{34}R^{\pm }_{12n}-c_{44}(P_{0}\pm np)]e^{-R^{\pm }_{12n}H},\\ h^{\mp }_{18}&=[\{c_{23}P_{0}-2c_{44}npR_{4}\}U_{4}+c_{33}R_{4}-2c_{44}npP_{0}]\zeta _{{\mp }_{n}}e^{R_{4}H},\\ h^{\mp }_{19}&=[\{c_{23}P_{0}-2c_{44}npR_{7}\}U_{7}+c_{33}R_{7}-2c_{44}npP_{0}]\zeta _{{\mp }_{n}}e^{R_{7}H},\\ h^{\mp }_{20}&=[\{c_{23}P_{0}-2c_{44}npR_{8}\}U_{8}+c_{33}R_{8}-2c_{44}npP_{0}]\zeta _{{\mp }_{n}}e^{R_{8}H},\\ h^{\mp }_{21}&=[\{c_{23}P_{0}R_{11}-2c_{24}npP_{0}-c_{34}R_{11}^{2}-2c_{44}npR_{11}\}U_{11}-c_{33}R_{11}^{2}\mp 2c_{34}npR_{11}-c_{34}P_{0}R_{11}\\&\quad \pm 2c_{44}npP_{0}]\zeta _{{\mp }_{n}}e^{-R_{11}H},\\ h^{\mp }_{24}&=[\{c_{23}(P_{0}\pm np)-2c_{44}R^{\pm }_{8n}\}U^{\pm }_{8n}+c_{33}R^{\pm }_{8n}-2c_{44}(P_{0}\pm np)]e^{R^{\pm }_{8n}H},\\ h^{\mp }_{25}&=[\{c_{23}(P_{0}\pm np)+c_{34}R^{\pm }_{11n}\}U^{\pm }_{11n}+c_{33}R^{\pm }_{11n}-c_{34}(P_{0}\pm np)]e^{-R^{\pm }_{11n}H},\\ h^{\mp }_{26}&=[\{c_{23}(P_{0}\pm np)+c_{34}R^{\pm }_{12n}\}U^{\pm }_{12n}+c_{33}R^{\pm }_{12n}-c_{34}(P_{0}\pm np)]e^{-R^{\pm }_{12n}H} \end{aligned}$$
Appendix III
$$\begin{aligned} {\left\{ \begin{array}{ll} &{}Q_{1}=l_{1}P_{0}+m_{1}R_{1},~~Q_{2}=l_{2}P_{0}+m_{2}R_{2},~~Q_{3}=l_{3}P_{0}+m_{3}R_{3},~~Q_{4}=l_{4}P_{0}+m_{4}R_{4},\\ &{}Q_{5}=l_{5}P_{0}+m_{5}R_{5},~~Q_{6}=l_{6}P_{0}+m_{6}R_{6},~~Q_{7}=l_{7}P_{0}+m_{7}R_{7},~~Q_{8}=l_{8}P_{0}+m_{8}R_{8},\\ &{}Q_{9}=l_{9}P_{0}+m_{9}R_{9},~~Q_{10}=l_{10}P_{0}+m_{10}R_{10},~~Q_{11}=l_{11}P_{0}+m_{11}R_{11},~~Q_{12}=l_{12}P_{0}+m_{12}R_{12},\\ &{}Q^{\pm }_{1n}=l^{\pm }_{1n}P_{0}+m^{\pm }_{1n}R^{\pm }_{1n},~Q^{\pm }_{2n}=l^{\pm }_{2n}P_{0}+m^{\pm }_{2n}R^{\pm }_{2n},~Q^{\pm }_{3n}=l^{\pm }_{3n}P_{0}+m^{\pm }_{3n}R^{\pm }_{3n},~Q^{\pm }_{4n}=l^{\pm }_{4n}P_{0}+m^{\pm }_{4n}R^{\pm }_{4n},\\ &{}Q^{\pm }_{5n}=l^{\pm }_{5n}P_{0}+m^{\pm }_{5n}R^{\pm }_{5n},~Q^{\pm }_{6n}=l^{\pm }_{6n}P_{0}+m^{\pm }_{6n}R^{\pm }_{6n},~Q^{\pm }_{7n}=l^{\pm }_{7n}P_{0}+m^{\pm }_{7n}R^{\pm }_{7n},~Q^{\pm }_{8n}=l^{\pm }_{8n}P_{0}+m^{\pm }_{8n}R^{\pm }_{8n},\\ &{}Q^{\pm }_{9n}=l^{\pm }_{9n}P_{0}+m^{\pm }_{9n}R^{\pm }_{9n},~~Q^{\pm }_{10n}=l^{\pm }_{10n}P_{0}+m^{\pm }_{10n}R^{\pm }_{10n},~~Q^{\pm }_{11n}=l^{\pm }_{11n}P_{0}+m^{\pm }_{11n}R^{\pm }_{11n},\\ &{}Q^{\pm }_{12n}=l^{\pm }_{12n}P_{0}+m^{\pm }_{12n}R^{\pm }_{12n}, \\ &{}l^{\pm }_{1n}=(U^{\pm }_{1n}c_{24}+c_{44})P_{0}-(U^{\pm }_{1n}c_{44}+c_{34})R^{\pm }_{1n},~~m^{\pm }_{1n}=(U^{\pm }_{1n}c_{23}+c_{34})P_{0}+(U^{\pm }_{1n}c_{34}+c_{33})R^{\pm }_{1n},\\ &{}l^{\pm }_{2n}=(U^{\pm }_{2n}c_{24}+c_{44})P_{0}-(U^{\pm }_{2n}c_{44}+c_{34})R^{\pm }_{2n},~~m^{\pm }_{2n}=(U^{\pm }_{2n}c_{23}+c_{34})P_{0}+(U^{\pm }_{2n}c_{34}+c_{33})R^{\pm }_{2n},\\ &{}l^{\pm }_{3n}=c_{44}P_{0}-U^{\pm }_{3n}c_{44}R^{\pm }_{3n},~~~m^{\pm }_{3n}=U^{\pm }_{3n}c_{23}P_{0}-c_{33}R^{\pm }_{3n},\\ &{}l^{\pm }_{4n}=c_{44}P_{0}-U^{\pm }_{4n}c_{44}R^{\pm }_{4n},~~~m^{\pm }_{4n}=U^{\pm }_{4n}c_{23}P_{0}-c_{33}R^{\pm }_{4n}, \\ &{}l^{\pm }_{5n}=\{c_{44}P_{0}-U^{\pm }_{5n}c_{44}R^{\pm }_{5n} \}e^{-iR^{\pm }_{3n}H},~m^{\pm }_{5n}=\{U^{\pm }_{5n}c_{23}P_{0}-c_{33}R^{\pm }_{5n}\}e^{-i(R^{\pm }_{5n}+R^{\pm }_{3n})H},\\ &{}l^{\pm }_{6n}=\{c_{44}P_{0}+U^{\pm }_{6n}c_{44}R^{\pm }_{6n}\}e^{iR^{\pm }_{6n}H},~~m^{\pm }_{6n}=\{U^{\pm }_{6n}c_{23}P_{0}-c_{33}R^{\pm }_{6n} \}e^{-iR^{\pm }_{5n}H},\\ &{}l^{\pm }_{7n}=\{c_{44}P_{0}+U^{\pm }_{7n}c_{44}R^{\pm }_{7n}\}e^{iR^{\pm }_{7n}H},~~~m^{\pm }_{7n}=\{U^{\pm }_{7n}c_{23}P_{0}-c_{33}R^{\pm }_{7n}\}e^{-iR^{\pm }_{6n}H},\\ &{}l^{\pm }_{8n}=\{(U^{\pm }_{8n}c_{24}+c_{44})P_{0}-(U^{\pm }_{8n}c_{44}+c_{34})R^{\pm }_{8n}\}e^{-iR^{\pm }_{8n}H},\\ &{}m^{\pm }_{8n}=\{(U^{\pm }_{8n}c_{24}+c_{44})P_{0}-(U^{\pm }_{8n}c_{44}+c_{34})R^{\pm }_{8n} \}e^{-iR^{\pm }_{8n}H},\\ &{}l^{\pm }_{9n}=\{(U^{\pm }_{9n}c_{24}+c_{44})P_{0}-(U^{\pm }_{9n}c_{44}+c_{34})R^{\pm }_{9n} \}e^{-iR^{\pm }_{9n}H},\\ &{}m^{\pm }_{9n}=\{(U^{\pm }_{9n}c_{24}+c_{44})P_{0}-(U^{\pm }_{9n}c_{44}+c_{34})R^{\pm }_{9n}\}e^{-iR^{\pm }_{9n}H}, \end{array}\right. } \end{aligned}$$
