CLASSIFICATION OF OPTOMECHANICAL INTERACTION AND THE DISCOVERY OF COHERENT COUPLING
2.4 Purely coherent coupling in a ring cavity system
2.4.1 Cavity modes and the Hamiltonian
The detailed derivation of the total Hamiltonian of the ring cavity system can be found in App. 2.8. Here we only sketch the key steps of the derivation.
Without the membrane, the ring cavity can support degenerate clockwise and counterclockwise modes that propagate independently. The membrane reflection
ˆ a1
<latexit sha1_base64="vIA1T90psPhkzzHyaXh7x/gTR8Q=">AAAB73icbZDLSgNBEEVr4ivGV9Slm8YguAozIugy6MZlBPOAZAg1nU7SpOdhd40QhvyEGxeKuPV33Pk3dpJZaOKFhsOtKrrqBomShlz32ymsrW9sbhW3Szu7e/sH5cOjpolTzUWDxyrW7QCNUDISDZKkRDvRAsNAiVYwvp3VW09CGxlHDzRJhB/iMJIDyZGs1e6OkBj2vF654lbdudgqeDlUIFe9V/7q9mOehiIirtCYjucm5GeoSXIlpqVuakSCfIxD0bEYYSiMn833nbIz6/TZINb2RcTm7u+JDENjJmFgO0OkkVmuzcz/ap2UBtd+JqMkJRHxxUeDVDGK2ex41pdacFITC8i1tLsyPkKNnGxEJRuCt3zyKjQvqp7l+8tK7SaPowgncArn4MEV1OAO6tAADgqe4RXenEfnxXl3PhatBSefOYY/cj5/AEbej3Q=</latexit><latexit sha1_base64="vIA1T90psPhkzzHyaXh7x/gTR8Q=">AAAB73icbZDLSgNBEEVr4ivGV9Slm8YguAozIugy6MZlBPOAZAg1nU7SpOdhd40QhvyEGxeKuPV33Pk3dpJZaOKFhsOtKrrqBomShlz32ymsrW9sbhW3Szu7e/sH5cOjpolTzUWDxyrW7QCNUDISDZKkRDvRAsNAiVYwvp3VW09CGxlHDzRJhB/iMJIDyZGs1e6OkBj2vF654lbdudgqeDlUIFe9V/7q9mOehiIirtCYjucm5GeoSXIlpqVuakSCfIxD0bEYYSiMn833nbIz6/TZINb2RcTm7u+JDENjJmFgO0OkkVmuzcz/ap2UBtd+JqMkJRHxxUeDVDGK2ex41pdacFITC8i1tLsyPkKNnGxEJRuCt3zyKjQvqp7l+8tK7SaPowgncArn4MEV1OAO6tAADgqe4RXenEfnxXl3PhatBSefOYY/cj5/AEbej3Q=</latexit><latexit sha1_base64="vIA1T90psPhkzzHyaXh7x/gTR8Q=">AAAB73icbZDLSgNBEEVr4ivGV9Slm8YguAozIugy6MZlBPOAZAg1nU7SpOdhd40QhvyEGxeKuPV33Pk3dpJZaOKFhsOtKrrqBomShlz32ymsrW9sbhW3Szu7e/sH5cOjpolTzUWDxyrW7QCNUDISDZKkRDvRAsNAiVYwvp3VW09CGxlHDzRJhB/iMJIDyZGs1e6OkBj2vF654lbdudgqeDlUIFe9V/7q9mOehiIirtCYjucm5GeoSXIlpqVuakSCfIxD0bEYYSiMn833nbIz6/TZINb2RcTm7u+JDENjJmFgO0OkkVmuzcz/ap2UBtd+JqMkJRHxxUeDVDGK2ex41pdacFITC8i1tLsyPkKNnGxEJRuCt3zyKjQvqp7l+8tK7SaPowgncArn4MEV1OAO6tAADgqe4RXenEfnxXl3PhatBSefOYY/cj5/AEbej3Q=</latexit><latexit sha1_base64="vIA1T90psPhkzzHyaXh7x/gTR8Q=">AAAB73icbZDLSgNBEEVr4ivGV9Slm8YguAozIugy6MZlBPOAZAg1nU7SpOdhd40QhvyEGxeKuPV33Pk3dpJZaOKFhsOtKrrqBomShlz32ymsrW9sbhW3Szu7e/sH5cOjpolTzUWDxyrW7QCNUDISDZKkRDvRAsNAiVYwvp3VW09CGxlHDzRJhB/iMJIDyZGs1e6OkBj2vF654lbdudgqeDlUIFe9V/7q9mOehiIirtCYjucm5GeoSXIlpqVuakSCfIxD0bEYYSiMn833nbIz6/TZINb2RcTm7u+JDENjJmFgO0OkkVmuzcz/ap2UBtd+JqMkJRHxxUeDVDGK2ex41pdacFITC8i1tLsyPkKNnGxEJRuCt3zyKjQvqp7l+8tK7SaPowgncArn4MEV1OAO6tAADgqe4RXenEfnxXl3PhatBSefOYY/cj5/AEbej3Q=</latexit>
ˆ a<latexit sha1_base64="v4royarsAA+6En0mzOC4oWgTPoE=">AAAB73icbZDLSgNBEEVrfMb4irp00xgEV2EmCLoMunEZwTwgGUJNp5M06XnYXSOEIT/hxoUibv0dd/6NnWQWmnih4XCriq66QaKkIdf9dtbWNza3tgs7xd29/YPD0tFx08Sp5qLBYxXrdoBGKBmJBklSop1ogWGgRCsY387qrSehjYyjB5okwg9xGMmB5EjWandHSAx71V6p7FbcudgqeDmUIVe9V/rq9mOehiIirtCYjucm5GeoSXIlpsVuakSCfIxD0bEYYSiMn833nbJz6/TZINb2RcTm7u+JDENjJmFgO0OkkVmuzcz/ap2UBtd+JqMkJRHxxUeDVDGK2ex41pdacFITC8i1tLsyPkKNnGxERRuCt3zyKjSrFc/y/WW5dpPHUYBTOIML8OAKanAHdWgABwXP8ApvzqPz4rw7H4vWNSefOYE/cj5/AEhij3U=</latexit><latexit sha1_base64="v4royarsAA+6En0mzOC4oWgTPoE=">AAAB73icbZDLSgNBEEVrfMb4irp00xgEV2EmCLoMunEZwTwgGUJNp5M06XnYXSOEIT/hxoUibv0dd/6NnWQWmnih4XCriq66QaKkIdf9dtbWNza3tgs7xd29/YPD0tFx08Sp5qLBYxXrdoBGKBmJBklSop1ogWGgRCsY387qrSehjYyjB5okwg9xGMmB5EjWandHSAx71V6p7FbcudgqeDmUIVe9V/rq9mOehiIirtCYjucm5GeoSXIlpsVuakSCfIxD0bEYYSiMn833nbJz6/TZINb2RcTm7u+JDENjJmFgO0OkkVmuzcz/ap2UBtd+JqMkJRHxxUeDVDGK2ex41pdacFITC8i1tLsyPkKNnGxERRuCt3zyKjSrFc/y/WW5dpPHUYBTOIML8OAKanAHdWgABwXP8ApvzqPz4rw7H4vWNSefOYE/cj5/AEhij3U=</latexit><latexit sha1_base64="v4royarsAA+6En0mzOC4oWgTPoE=">AAAB73icbZDLSgNBEEVrfMb4irp00xgEV2EmCLoMunEZwTwgGUJNp5M06XnYXSOEIT/hxoUibv0dd/6NnWQWmnih4XCriq66QaKkIdf9dtbWNza3tgs7xd29/YPD0tFx08Sp5qLBYxXrdoBGKBmJBklSop1ogWGgRCsY387qrSehjYyjB5okwg9xGMmB5EjWandHSAx71V6p7FbcudgqeDmUIVe9V/rq9mOehiIirtCYjucm5GeoSXIlpsVuakSCfIxD0bEYYSiMn833nbJz6/TZINb2RcTm7u+JDENjJmFgO0OkkVmuzcz/ap2UBtd+JqMkJRHxxUeDVDGK2ex41pdacFITC8i1tLsyPkKNnGxERRuCt3zyKjSrFc/y/WW5dpPHUYBTOIML8OAKanAHdWgABwXP8ApvzqPz4rw7H4vWNSefOYE/cj5/AEhij3U=</latexit><latexit sha1_base64="v4royarsAA+6En0mzOC4oWgTPoE=">AAAB73icbZDLSgNBEEVrfMb4irp00xgEV2EmCLoMunEZwTwgGUJNp5M06XnYXSOEIT/hxoUibv0dd/6NnWQWmnih4XCriq66QaKkIdf9dtbWNza3tgs7xd29/YPD0tFx08Sp5qLBYxXrdoBGKBmJBklSop1ogWGgRCsY387qrSehjYyjB5okwg9xGMmB5EjWandHSAx71V6p7FbcudgqeDmUIVe9V/rq9mOehiIirtCYjucm5GeoSXIlpsVuakSCfIxD0bEYYSiMn833nbJz6/TZINb2RcTm7u+JDENjJmFgO0OkkVmuzcz/ap2UBtd+JqMkJRHxxUeDVDGK2ex41pdacFITC8i1tLsyPkKNnGxERRuCt3zyKjSrFc/y/WW5dpPHUYBTOIML8OAKanAHdWgABwXP8ApvzqPz4rw7H4vWNSefOYE/cj5/AEhij3U=</latexit> 2
ˆ c1
<latexit sha1_base64="od96gtjmHvFgcd46UTjOKe85tpg=">AAAB73icbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8cK9gPaUCbbTbt0s4m7G6GE/gkvHhTx6t/x5r9x0+agrQ8GHu/NMDMvSATXxnW/ndLa+sbmVnm7srO7t39QPTxq6zhVlLVoLGLVDVAzwSVrGW4E6yaKYRQI1gkmt7nfeWJK81g+mGnC/AhHkoecorFStz9GQ+jAG1Rrbt2dg6wSryA1KNAcVL/6w5imEZOGCtS657mJ8TNUhlPBZpV+qlmCdIIj1rNUYsS0n83vnZEzqwxJGCtb0u7P1d8TGUZaT6PAdkZoxnrZy8X/vF5qwms/4zJJDZN0sShMBTExyZ8nQ64YNWJqCVLF7a2EjlEhNTaiig3BW355lbQv6p7l95e1xk0RRxlO4BTOwYMraMAdNKEFFAQ8wyu8OY/Oi/PufCxaS04xcwx/4Hz+AEnqj3Y=</latexit><latexit sha1_base64="od96gtjmHvFgcd46UTjOKe85tpg=">AAAB73icbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8cK9gPaUCbbTbt0s4m7G6GE/gkvHhTx6t/x5r9x0+agrQ8GHu/NMDMvSATXxnW/ndLa+sbmVnm7srO7t39QPTxq6zhVlLVoLGLVDVAzwSVrGW4E6yaKYRQI1gkmt7nfeWJK81g+mGnC/AhHkoecorFStz9GQ+jAG1Rrbt2dg6wSryA1KNAcVL/6w5imEZOGCtS657mJ8TNUhlPBZpV+qlmCdIIj1rNUYsS0n83vnZEzqwxJGCtb0u7P1d8TGUZaT6PAdkZoxnrZy8X/vF5qwms/4zJJDZN0sShMBTExyZ8nQ64YNWJqCVLF7a2EjlEhNTaiig3BW355lbQv6p7l95e1xk0RRxlO4BTOwYMraMAdNKEFFAQ8wyu8OY/Oi/PufCxaS04xcwx/4Hz+AEnqj3Y=</latexit><latexit sha1_base64="od96gtjmHvFgcd46UTjOKe85tpg=">AAAB73icbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8cK9gPaUCbbTbt0s4m7G6GE/gkvHhTx6t/x5r9x0+agrQ8GHu/NMDMvSATXxnW/ndLa+sbmVnm7srO7t39QPTxq6zhVlLVoLGLVDVAzwSVrGW4E6yaKYRQI1gkmt7nfeWJK81g+mGnC/AhHkoecorFStz9GQ+jAG1Rrbt2dg6wSryA1KNAcVL/6w5imEZOGCtS657mJ8TNUhlPBZpV+qlmCdIIj1rNUYsS0n83vnZEzqwxJGCtb0u7P1d8TGUZaT6PAdkZoxnrZy8X/vF5qwms/4zJJDZN0sShMBTExyZ8nQ64YNWJqCVLF7a2EjlEhNTaiig3BW355lbQv6p7l95e1xk0RRxlO4BTOwYMraMAdNKEFFAQ8wyu8OY/Oi/PufCxaS04xcwx/4Hz+AEnqj3Y=</latexit><latexit sha1_base64="od96gtjmHvFgcd46UTjOKe85tpg=">AAAB73icbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8cK9gPaUCbbTbt0s4m7G6GE/gkvHhTx6t/x5r9x0+agrQ8GHu/NMDMvSATXxnW/ndLa+sbmVnm7srO7t39QPTxq6zhVlLVoLGLVDVAzwSVrGW4E6yaKYRQI1gkmt7nfeWJK81g+mGnC/AhHkoecorFStz9GQ+jAG1Rrbt2dg6wSryA1KNAcVL/6w5imEZOGCtS657mJ8TNUhlPBZpV+qlmCdIIj1rNUYsS0n83vnZEzqwxJGCtb0u7P1d8TGUZaT6PAdkZoxnrZy8X/vF5qwms/4zJJDZN0sShMBTExyZ8nQ64YNWJqCVLF7a2EjlEhNTaiig3BW355lbQv6p7l95e1xk0RRxlO4BTOwYMraMAdNKEFFAQ8wyu8OY/Oi/PufCxaS04xcwx/4Hz+AEnqj3Y=</latexit>
ˆ c<latexit sha1_base64="6oS+HEuzK2meT6PIisnfbFHFs6k=">AAAB73icbVBNS8NAEJ34WetX1aOXxSJ4KkkR9Fj04rGC/YA2lMl20y7dbOLuRiihf8KLB0W8+ne8+W/ctDlo64OBx3szzMwLEsG1cd1vZ219Y3Nru7RT3t3bPzisHB23dZwqylo0FrHqBqiZ4JK1DDeCdRPFMAoE6wST29zvPDGleSwfzDRhfoQjyUNO0Vip2x+jIXRQH1Sqbs2dg6wSryBVKNAcVL76w5imEZOGCtS657mJ8TNUhlPBZuV+qlmCdIIj1rNUYsS0n83vnZFzqwxJGCtb0u7P1d8TGUZaT6PAdkZoxnrZy8X/vF5qwms/4zJJDZN0sShMBTExyZ8nQ64YNWJqCVLF7a2EjlEhNTaisg3BW355lbTrNc/y+8tq46aIowSncAYX4MEVNOAOmtACCgKe4RXenEfnxXl3Phata04xcwJ/4Hz+AEtuj3c=</latexit><latexit sha1_base64="6oS+HEuzK2meT6PIisnfbFHFs6k=">AAAB73icbVBNS8NAEJ34WetX1aOXxSJ4KkkR9Fj04rGC/YA2lMl20y7dbOLuRiihf8KLB0W8+ne8+W/ctDlo64OBx3szzMwLEsG1cd1vZ219Y3Nru7RT3t3bPzisHB23dZwqylo0FrHqBqiZ4JK1DDeCdRPFMAoE6wST29zvPDGleSwfzDRhfoQjyUNO0Vip2x+jIXRQH1Sqbs2dg6wSryBVKNAcVL76w5imEZOGCtS657mJ8TNUhlPBZuV+qlmCdIIj1rNUYsS0n83vnZFzqwxJGCtb0u7P1d8TGUZaT6PAdkZoxnrZy8X/vF5qwms/4zJJDZN0sShMBTExyZ8nQ64YNWJqCVLF7a2EjlEhNTaisg3BW355lbTrNc/y+8tq46aIowSncAYX4MEVNOAOmtACCgKe4RXenEfnxXl3Phata04xcwJ/4Hz+AEtuj3c=</latexit><latexit sha1_base64="6oS+HEuzK2meT6PIisnfbFHFs6k=">AAAB73icbVBNS8NAEJ34WetX1aOXxSJ4KkkR9Fj04rGC/YA2lMl20y7dbOLuRiihf8KLB0W8+ne8+W/ctDlo64OBx3szzMwLEsG1cd1vZ219Y3Nru7RT3t3bPzisHB23dZwqylo0FrHqBqiZ4JK1DDeCdRPFMAoE6wST29zvPDGleSwfzDRhfoQjyUNO0Vip2x+jIXRQH1Sqbs2dg6wSryBVKNAcVL76w5imEZOGCtS657mJ8TNUhlPBZuV+qlmCdIIj1rNUYsS0n83vnZFzqwxJGCtb0u7P1d8TGUZaT6PAdkZoxnrZy8X/vF5qwms/4zJJDZN0sShMBTExyZ8nQ64YNWJqCVLF7a2EjlEhNTaisg3BW355lbTrNc/y+8tq46aIowSncAYX4MEVNOAOmtACCgKe4RXenEfnxXl3Phata04xcwJ/4Hz+AEtuj3c=</latexit><latexit sha1_base64="6oS+HEuzK2meT6PIisnfbFHFs6k=">AAAB73icbVBNS8NAEJ34WetX1aOXxSJ4KkkR9Fj04rGC/YA2lMl20y7dbOLuRiihf8KLB0W8+ne8+W/ctDlo64OBx3szzMwLEsG1cd1vZ219Y3Nru7RT3t3bPzisHB23dZwqylo0FrHqBqiZ4JK1DDeCdRPFMAoE6wST29zvPDGleSwfzDRhfoQjyUNO0Vip2x+jIXRQH1Sqbs2dg6wSryBVKNAcVL76w5imEZOGCtS657mJ8TNUhlPBZuV+qlmCdIIj1rNUYsS0n83vnZFzqwxJGCtb0u7P1d8TGUZaT6PAdkZoxnrZy8X/vF5qwms/4zJJDZN0sShMBTExyZ8nQ64YNWJqCVLF7a2EjlEhNTaisg3BW355lbTrNc/y+8tq46aIowSncAYX4MEVNOAOmtACCgKe4RXenEfnxXl3Phata04xcwJ/4Hz+AEtuj3c=</latexit> 2
x<latexit sha1_base64="IArQpDG4Gw7Ax+5Wri9CZWKD4Bo=">AAAB6HicbZBNS8NAEIYn9avWr6pHL4tF8FQSEfRY9OKxBfsBbSib7aRdu9mE3Y1YQn+BFw+KePUnefPfuG1z0NYXFh7emWFn3iARXBvX/XYKa+sbm1vF7dLO7t7+QfnwqKXjVDFssljEqhNQjYJLbBpuBHYShTQKBLaD8e2s3n5EpXks780kQT+iQ8lDzqixVuOpX664VXcusgpeDhXIVe+Xv3qDmKURSsME1brruYnxM6oMZwKnpV6qMaFsTIfYtShphNrP5otOyZl1BiSMlX3SkLn7eyKjkdaTKLCdETUjvVybmf/VuqkJr/2MyyQ1KNniozAVxMRkdjUZcIXMiIkFyhS3uxI2oooyY7Mp2RC85ZNXoXVR9Sw3Liu1mzyOIpzAKZyDB1dQgzuoQxMYIDzDK7w5D86L8+58LFoLTj5zDH/kfP4A5juM/A==</latexit><latexit sha1_base64="IArQpDG4Gw7Ax+5Wri9CZWKD4Bo=">AAAB6HicbZBNS8NAEIYn9avWr6pHL4tF8FQSEfRY9OKxBfsBbSib7aRdu9mE3Y1YQn+BFw+KePUnefPfuG1z0NYXFh7emWFn3iARXBvX/XYKa+sbm1vF7dLO7t7+QfnwqKXjVDFssljEqhNQjYJLbBpuBHYShTQKBLaD8e2s3n5EpXks780kQT+iQ8lDzqixVuOpX664VXcusgpeDhXIVe+Xv3qDmKURSsME1brruYnxM6oMZwKnpV6qMaFsTIfYtShphNrP5otOyZl1BiSMlX3SkLn7eyKjkdaTKLCdETUjvVybmf/VuqkJr/2MyyQ1KNniozAVxMRkdjUZcIXMiIkFyhS3uxI2oooyY7Mp2RC85ZNXoXVR9Sw3Liu1mzyOIpzAKZyDB1dQgzuoQxMYIDzDK7w5D86L8+58LFoLTj5zDH/kfP4A5juM/A==</latexit><latexit sha1_base64="IArQpDG4Gw7Ax+5Wri9CZWKD4Bo=">AAAB6HicbZBNS8NAEIYn9avWr6pHL4tF8FQSEfRY9OKxBfsBbSib7aRdu9mE3Y1YQn+BFw+KePUnefPfuG1z0NYXFh7emWFn3iARXBvX/XYKa+sbm1vF7dLO7t7+QfnwqKXjVDFssljEqhNQjYJLbBpuBHYShTQKBLaD8e2s3n5EpXks780kQT+iQ8lDzqixVuOpX664VXcusgpeDhXIVe+Xv3qDmKURSsME1brruYnxM6oMZwKnpV6qMaFsTIfYtShphNrP5otOyZl1BiSMlX3SkLn7eyKjkdaTKLCdETUjvVybmf/VuqkJr/2MyyQ1KNniozAVxMRkdjUZcIXMiIkFyhS3uxI2oooyY7Mp2RC85ZNXoXVR9Sw3Liu1mzyOIpzAKZyDB1dQgzuoQxMYIDzDK7w5D86L8+58LFoLTj5zDH/kfP4A5juM/A==</latexit><latexit sha1_base64="IArQpDG4Gw7Ax+5Wri9CZWKD4Bo=">AAAB6HicbZBNS8NAEIYn9avWr6pHL4tF8FQSEfRY9OKxBfsBbSib7aRdu9mE3Y1YQn+BFw+KePUnefPfuG1z0NYXFh7emWFn3iARXBvX/XYKa+sbm1vF7dLO7t7+QfnwqKXjVDFssljEqhNQjYJLbBpuBHYShTQKBLaD8e2s3n5EpXks780kQT+iQ8lDzqixVuOpX664VXcusgpeDhXIVe+Xv3qDmKURSsME1brruYnxM6oMZwKnpV6qMaFsTIfYtShphNrP5otOyZl1BiSMlX3SkLn7eyKjkdaTKLCdETUjvVybmf/VuqkJr/2MyyQ1KNniozAVxMRkdjUZcIXMiIkFyhS3uxI2oooyY7Mp2RC85ZNXoXVR9Sw3Liu1mzyOIpzAKZyDB1dQgzuoQxMYIDzDK7w5D86L8+58LFoLTj5zDH/kfP4A5juM/A==</latexit>
L1
<latexit sha1_base64="sCX6gf2o5hPydr1JpewW3X4FVX4=">AAAB6nicbZA9SwNBEIbn4leMX1FLm8UgWIU7EWIZtLGwiGg+IDnC3mYuWbK3d+zuCeHIT7CxUMTWX2Tnv3GTXKGJLyw8vDPDzrxBIrg2rvvtFNbWNza3itulnd29/YPy4VFLx6li2GSxiFUnoBoFl9g03AjsJAppFAhsB+ObWb39hErzWD6aSYJ+RIeSh5xRY62Hu77XL1fcqjsXWQUvhwrkavTLX71BzNIIpWGCat313MT4GVWGM4HTUi/VmFA2pkPsWpQ0Qu1n81Wn5Mw6AxLGyj5pyNz9PZHRSOtJFNjOiJqRXq7NzP9q3dSEV37GZZIalGzxUZgKYmIyu5sMuEJmxMQCZYrbXQkbUUWZsemUbAje8smr0LqoepbvLyv16zyOIpzAKZyDBzWowy00oAkMhvAMr/DmCOfFeXc+Fq0FJ585hj9yPn8AyJuNdA==</latexit><latexit sha1_base64="sCX6gf2o5hPydr1JpewW3X4FVX4=">AAAB6nicbZA9SwNBEIbn4leMX1FLm8UgWIU7EWIZtLGwiGg+IDnC3mYuWbK3d+zuCeHIT7CxUMTWX2Tnv3GTXKGJLyw8vDPDzrxBIrg2rvvtFNbWNza3itulnd29/YPy4VFLx6li2GSxiFUnoBoFl9g03AjsJAppFAhsB+ObWb39hErzWD6aSYJ+RIeSh5xRY62Hu77XL1fcqjsXWQUvhwrkavTLX71BzNIIpWGCat313MT4GVWGM4HTUi/VmFA2pkPsWpQ0Qu1n81Wn5Mw6AxLGyj5pyNz9PZHRSOtJFNjOiJqRXq7NzP9q3dSEV37GZZIalGzxUZgKYmIyu5sMuEJmxMQCZYrbXQkbUUWZsemUbAje8smr0LqoepbvLyv16zyOIpzAKZyDBzWowy00oAkMhvAMr/DmCOfFeXc+Fq0FJ585hj9yPn8AyJuNdA==</latexit><latexit sha1_base64="sCX6gf2o5hPydr1JpewW3X4FVX4=">AAAB6nicbZA9SwNBEIbn4leMX1FLm8UgWIU7EWIZtLGwiGg+IDnC3mYuWbK3d+zuCeHIT7CxUMTWX2Tnv3GTXKGJLyw8vDPDzrxBIrg2rvvtFNbWNza3itulnd29/YPy4VFLx6li2GSxiFUnoBoFl9g03AjsJAppFAhsB+ObWb39hErzWD6aSYJ+RIeSh5xRY62Hu77XL1fcqjsXWQUvhwrkavTLX71BzNIIpWGCat313MT4GVWGM4HTUi/VmFA2pkPsWpQ0Qu1n81Wn5Mw6AxLGyj5pyNz9PZHRSOtJFNjOiJqRXq7NzP9q3dSEV37GZZIalGzxUZgKYmIyu5sMuEJmxMQCZYrbXQkbUUWZsemUbAje8smr0LqoepbvLyv16zyOIpzAKZyDBzWowy00oAkMhvAMr/DmCOfFeXc+Fq0FJ585hj9yPn8AyJuNdA==</latexit><latexit sha1_base64="sCX6gf2o5hPydr1JpewW3X4FVX4=">AAAB6nicbZA9SwNBEIbn4leMX1FLm8UgWIU7EWIZtLGwiGg+IDnC3mYuWbK3d+zuCeHIT7CxUMTWX2Tnv3GTXKGJLyw8vDPDzrxBIrg2rvvtFNbWNza3itulnd29/YPy4VFLx6li2GSxiFUnoBoFl9g03AjsJAppFAhsB+ObWb39hErzWD6aSYJ+RIeSh5xRY62Hu77XL1fcqjsXWQUvhwrkavTLX71BzNIIpWGCat313MT4GVWGM4HTUi/VmFA2pkPsWpQ0Qu1n81Wn5Mw6AxLGyj5pyNz9PZHRSOtJFNjOiJqRXq7NzP9q3dSEV37GZZIalGzxUZgKYmIyu5sMuEJmxMQCZYrbXQkbUUWZsemUbAje8smr0LqoepbvLyv16zyOIpzAKZyDBzWowy00oAkMhvAMr/DmCOfFeXc+Fq0FJ585hj9yPn8AyJuNdA==</latexit>
L2
<latexit sha1_base64="Qhpyf+b7iCvT0ehvl3+d2Pg8qzw=">AAAB6nicbZA9SwNBEIbn4leMX1FLm8UgWIW7IGgZtLGwiGg+IDnC3mYuWbK3d+zuCeHIT7CxUMTWX2Tnv3GTXKGJLyw8vDPDzrxBIrg2rvvtFNbWNza3itulnd29/YPy4VFLx6li2GSxiFUnoBoFl9g03AjsJAppFAhsB+ObWb39hErzWD6aSYJ+RIeSh5xRY62Hu36tX664VXcusgpeDhXI1eiXv3qDmKURSsME1brruYnxM6oMZwKnpV6qMaFsTIfYtShphNrP5qtOyZl1BiSMlX3SkLn7eyKjkdaTKLCdETUjvVybmf/VuqkJr/yMyyQ1KNniozAVxMRkdjcZcIXMiIkFyhS3uxI2oooyY9Mp2RC85ZNXoVWrepbvLyr16zyOIpzAKZyDB5dQh1toQBMYDOEZXuHNEc6L8+58LFoLTj5zDH/kfP4Ayh+NdQ==</latexit><latexit sha1_base64="Qhpyf+b7iCvT0ehvl3+d2Pg8qzw=">AAAB6nicbZA9SwNBEIbn4leMX1FLm8UgWIW7IGgZtLGwiGg+IDnC3mYuWbK3d+zuCeHIT7CxUMTWX2Tnv3GTXKGJLyw8vDPDzrxBIrg2rvvtFNbWNza3itulnd29/YPy4VFLx6li2GSxiFUnoBoFl9g03AjsJAppFAhsB+ObWb39hErzWD6aSYJ+RIeSh5xRY62Hu36tX664VXcusgpeDhXI1eiXv3qDmKURSsME1brruYnxM6oMZwKnpV6qMaFsTIfYtShphNrP5qtOyZl1BiSMlX3SkLn7eyKjkdaTKLCdETUjvVybmf/VuqkJr/yMyyQ1KNniozAVxMRkdjcZcIXMiIkFyhS3uxI2oooyY9Mp2RC85ZNXoVWrepbvLyr16zyOIpzAKZyDB5dQh1toQBMYDOEZXuHNEc6L8+58LFoLTj5zDH/kfP4Ayh+NdQ==</latexit><latexit sha1_base64="Qhpyf+b7iCvT0ehvl3+d2Pg8qzw=">AAAB6nicbZA9SwNBEIbn4leMX1FLm8UgWIW7IGgZtLGwiGg+IDnC3mYuWbK3d+zuCeHIT7CxUMTWX2Tnv3GTXKGJLyw8vDPDzrxBIrg2rvvtFNbWNza3itulnd29/YPy4VFLx6li2GSxiFUnoBoFl9g03AjsJAppFAhsB+ObWb39hErzWD6aSYJ+RIeSh5xRY62Hu36tX664VXcusgpeDhXI1eiXv3qDmKURSsME1brruYnxM6oMZwKnpV6qMaFsTIfYtShphNrP5qtOyZl1BiSMlX3SkLn7eyKjkdaTKLCdETUjvVybmf/VuqkJr/yMyyQ1KNniozAVxMRkdjcZcIXMiIkFyhS3uxI2oooyY9Mp2RC85ZNXoVWrepbvLyr16zyOIpzAKZyDB5dQh1toQBMYDOEZXuHNEc6L8+58LFoLTj5zDH/kfP4Ayh+NdQ==</latexit><latexit sha1_base64="Qhpyf+b7iCvT0ehvl3+d2Pg8qzw=">AAAB6nicbZA9SwNBEIbn4leMX1FLm8UgWIW7IGgZtLGwiGg+IDnC3mYuWbK3d+zuCeHIT7CxUMTWX2Tnv3GTXKGJLyw8vDPDzrxBIrg2rvvtFNbWNza3itulnd29/YPy4VFLx6li2GSxiFUnoBoFl9g03AjsJAppFAhsB+ObWb39hErzWD6aSYJ+RIeSh5xRY62Hu36tX664VXcusgpeDhXI1eiXv3qDmKURSsME1brruYnxM6oMZwKnpV6qMaFsTIfYtShphNrP5qtOyZl1BiSMlX3SkLn7eyKjkdaTKLCdETUjvVybmf/VuqkJr/yMyyQ1KNniozAVxMRkdjcZcIXMiIkFyhS3uxI2oooyY9Mp2RC85ZNXoVWrepbvLyr16zyOIpzAKZyDB5dQh1toQBMYDOEZXuHNEc6L8+58LFoLTj5zDH/kfP4Ayh+NdQ==</latexit>
M<latexit sha1_base64="n92bh9T9EeNW2TxJoE4z2HHDAL4=">AAAB6nicbZBNS8NAEIYn9avWr6pHL4tF8FQSEeqx6MWLUNF+QBvKZjtpl242YXcjlNCf4MWDIl79Rd78N27bHLT1hYWHd2bYmTdIBNfGdb+dwtr6xuZWcbu0s7u3f1A+PGrpOFUMmywWseoEVKPgEpuGG4GdRCGNAoHtYHwzq7efUGkey0czSdCP6FDykDNqrPVw13f75Ypbdeciq+DlUIFcjX75qzeIWRqhNExQrbuemxg/o8pwJnBa6qUaE8rGdIhdi5JGqP1svuqUnFlnQMJY2ScNmbu/JzIaaT2JAtsZUTPSy7WZ+V+tm5rwys+4TFKDki0+ClNBTExmd5MBV8iMmFigTHG7K2EjqigzNp2SDcFbPnkVWhdVz/L9ZaV+ncdRhBM4hXPwoAZ1uIUGNIHBEJ7hFd4c4bw4787HorXg5DPH8EfO5w/InY10</latexit><latexit sha1_base64="n92bh9T9EeNW2TxJoE4z2HHDAL4=">AAAB6nicbZBNS8NAEIYn9avWr6pHL4tF8FQSEeqx6MWLUNF+QBvKZjtpl242YXcjlNCf4MWDIl79Rd78N27bHLT1hYWHd2bYmTdIBNfGdb+dwtr6xuZWcbu0s7u3f1A+PGrpOFUMmywWseoEVKPgEpuGG4GdRCGNAoHtYHwzq7efUGkey0czSdCP6FDykDNqrPVw13f75Ypbdeciq+DlUIFcjX75qzeIWRqhNExQrbuemxg/o8pwJnBa6qUaE8rGdIhdi5JGqP1svuqUnFlnQMJY2ScNmbu/JzIaaT2JAtsZUTPSy7WZ+V+tm5rwys+4TFKDki0+ClNBTExmd5MBV8iMmFigTHG7K2EjqigzNp2SDcFbPnkVWhdVz/L9ZaV+ncdRhBM4hXPwoAZ1uIUGNIHBEJ7hFd4c4bw4787HorXg5DPH8EfO5w/InY10</latexit><latexit sha1_base64="n92bh9T9EeNW2TxJoE4z2HHDAL4=">AAAB6nicbZBNS8NAEIYn9avWr6pHL4tF8FQSEeqx6MWLUNF+QBvKZjtpl242YXcjlNCf4MWDIl79Rd78N27bHLT1hYWHd2bYmTdIBNfGdb+dwtr6xuZWcbu0s7u3f1A+PGrpOFUMmywWseoEVKPgEpuGG4GdRCGNAoHtYHwzq7efUGkey0czSdCP6FDykDNqrPVw13f75Ypbdeciq+DlUIFcjX75qzeIWRqhNExQrbuemxg/o8pwJnBa6qUaE8rGdIhdi5JGqP1svuqUnFlnQMJY2ScNmbu/JzIaaT2JAtsZUTPSy7WZ+V+tm5rwys+4TFKDki0+ClNBTExmd5MBV8iMmFigTHG7K2EjqigzNp2SDcFbPnkVWhdVz/L9ZaV+ncdRhBM4hXPwoAZ1uIUGNIHBEJ7hFd4c4bw4787HorXg5DPH8EfO5w/InY10</latexit><latexit sha1_base64="n92bh9T9EeNW2TxJoE4z2HHDAL4=">AAAB6nicbZBNS8NAEIYn9avWr6pHL4tF8FQSEeqx6MWLUNF+QBvKZjtpl242YXcjlNCf4MWDIl79Rd78N27bHLT1hYWHd2bYmTdIBNfGdb+dwtr6xuZWcbu0s7u3f1A+PGrpOFUMmywWseoEVKPgEpuGG4GdRCGNAoHtYHwzq7efUGkey0czSdCP6FDykDNqrPVw13f75Ypbdeciq+DlUIFcjX75qzeIWRqhNExQrbuemxg/o8pwJnBa6qUaE8rGdIhdi5JGqP1svuqUnFlnQMJY2ScNmbu/JzIaaT2JAtsZUTPSy7WZ+V+tm5rwys+4TFKDki0+ClNBTExmd5MBV8iMmFigTHG7K2EjqigzNp2SDcFbPnkVWhdVz/L9ZaV+ncdRhBM4hXPwoAZ1uIUGNIHBEJ7hFd4c4bw4787HorXg5DPH8EfO5w/InY10</latexit> 0
M<latexit sha1_base64="lr4z9kR9Bg3urt6KlGmUwT+ROEU=">AAAB6nicbZBNS8NAEIYn9avWr6pHL4tF8FQSEeqx6MWLUNF+QBvKZjtpl242YXcjlNCf4MWDIl79Rd78N27bHLT1hYWHd2bYmTdIBNfGdb+dwtr6xuZWcbu0s7u3f1A+PGrpOFUMmywWseoEVKPgEpuGG4GdRCGNAoHtYHwzq7efUGkey0czSdCP6FDykDNqrPVw1/f65Ypbdeciq+DlUIFcjX75qzeIWRqhNExQrbuemxg/o8pwJnBa6qUaE8rGdIhdi5JGqP1svuqUnFlnQMJY2ScNmbu/JzIaaT2JAtsZUTPSy7WZ+V+tm5rwys+4TFKDki0+ClNBTExmd5MBV8iMmFigTHG7K2EjqigzNp2SDcFbPnkVWhdVz/L9ZaV+ncdRhBM4hXPwoAZ1uIUGNIHBEJ7hFd4c4bw4787HorXg5DPH8EfO5w/KIY11</latexit><latexit sha1_base64="lr4z9kR9Bg3urt6KlGmUwT+ROEU=">AAAB6nicbZBNS8NAEIYn9avWr6pHL4tF8FQSEeqx6MWLUNF+QBvKZjtpl242YXcjlNCf4MWDIl79Rd78N27bHLT1hYWHd2bYmTdIBNfGdb+dwtr6xuZWcbu0s7u3f1A+PGrpOFUMmywWseoEVKPgEpuGG4GdRCGNAoHtYHwzq7efUGkey0czSdCP6FDykDNqrPVw1/f65Ypbdeciq+DlUIFcjX75qzeIWRqhNExQrbuemxg/o8pwJnBa6qUaE8rGdIhdi5JGqP1svuqUnFlnQMJY2ScNmbu/JzIaaT2JAtsZUTPSy7WZ+V+tm5rwys+4TFKDki0+ClNBTExmd5MBV8iMmFigTHG7K2EjqigzNp2SDcFbPnkVWhdVz/L9ZaV+ncdRhBM4hXPwoAZ1uIUGNIHBEJ7hFd4c4bw4787HorXg5DPH8EfO5w/KIY11</latexit><latexit sha1_base64="lr4z9kR9Bg3urt6KlGmUwT+ROEU=">AAAB6nicbZBNS8NAEIYn9avWr6pHL4tF8FQSEeqx6MWLUNF+QBvKZjtpl242YXcjlNCf4MWDIl79Rd78N27bHLT1hYWHd2bYmTdIBNfGdb+dwtr6xuZWcbu0s7u3f1A+PGrpOFUMmywWseoEVKPgEpuGG4GdRCGNAoHtYHwzq7efUGkey0czSdCP6FDykDNqrPVw1/f65Ypbdeciq+DlUIFcjX75qzeIWRqhNExQrbuemxg/o8pwJnBa6qUaE8rGdIhdi5JGqP1svuqUnFlnQMJY2ScNmbu/JzIaaT2JAtsZUTPSy7WZ+V+tm5rwys+4TFKDki0+ClNBTExmd5MBV8iMmFigTHG7K2EjqigzNp2SDcFbPnkVWhdVz/L9ZaV+ncdRhBM4hXPwoAZ1uIUGNIHBEJ7hFd4c4bw4787HorXg5DPH8EfO5w/KIY11</latexit><latexit sha1_base64="lr4z9kR9Bg3urt6KlGmUwT+ROEU=">AAAB6nicbZBNS8NAEIYn9avWr6pHL4tF8FQSEeqx6MWLUNF+QBvKZjtpl242YXcjlNCf4MWDIl79Rd78N27bHLT1hYWHd2bYmTdIBNfGdb+dwtr6xuZWcbu0s7u3f1A+PGrpOFUMmywWseoEVKPgEpuGG4GdRCGNAoHtYHwzq7efUGkey0czSdCP6FDykDNqrPVw1/f65Ypbdeciq+DlUIFcjX75qzeIWRqhNExQrbuemxg/o8pwJnBa6qUaE8rGdIhdi5JGqP1svuqUnFlnQMJY2ScNmbu/JzIaaT2JAtsZUTPSy7WZ+V+tm5rwys+4TFKDki0+ClNBTExmd5MBV8iMmFigTHG7K2EjqigzNp2SDcFbPnkVWhdVz/L9ZaV+ncdRhBM4hXPwoAZ1uIUGNIHBEJ7hFd4c4bw4787HorXg5DPH8EfO5w/KIY11</latexit> 1
M2
<latexit sha1_base64="pQ6Jmzgt42DS+iC5N8Cd2c/O+Ow=">AAAB6nicbZBNS8NAEIYn9avWr6pHL4tF8FSSIuix6MWLUNF+QBvKZjtpl242YXcjlNCf4MWDIl79Rd78N27bHLT1hYWHd2bYmTdIBNfGdb+dwtr6xuZWcbu0s7u3f1A+PGrpOFUMmywWseoEVKPgEpuGG4GdRCGNAoHtYHwzq7efUGkey0czSdCP6FDykDNqrPVw16/1yxW36s5FVsHLoQK5Gv3yV28QszRCaZigWnc9NzF+RpXhTOC01Es1JpSN6RC7FiWNUPvZfNUpObPOgISxsk8aMnd/T2Q00noSBbYzomakl2sz879aNzXhlZ9xmaQGJVt8FKaCmJjM7iYDrpAZMbFAmeJ2V8JGVFFmbDolG4K3fPIqtGpVz/L9RaV+ncdRhBM4hXPw4BLqcAsNaAKDITzDK7w5wnlx3p2PRWvByWeO4Y+czx/LpY12</latexit><latexit sha1_base64="pQ6Jmzgt42DS+iC5N8Cd2c/O+Ow=">AAAB6nicbZBNS8NAEIYn9avWr6pHL4tF8FSSIuix6MWLUNF+QBvKZjtpl242YXcjlNCf4MWDIl79Rd78N27bHLT1hYWHd2bYmTdIBNfGdb+dwtr6xuZWcbu0s7u3f1A+PGrpOFUMmywWseoEVKPgEpuGG4GdRCGNAoHtYHwzq7efUGkey0czSdCP6FDykDNqrPVw16/1yxW36s5FVsHLoQK5Gv3yV28QszRCaZigWnc9NzF+RpXhTOC01Es1JpSN6RC7FiWNUPvZfNUpObPOgISxsk8aMnd/T2Q00noSBbYzomakl2sz879aNzXhlZ9xmaQGJVt8FKaCmJjM7iYDrpAZMbFAmeJ2V8JGVFFmbDolG4K3fPIqtGpVz/L9RaV+ncdRhBM4hXPw4BLqcAsNaAKDITzDK7w5wnlx3p2PRWvByWeO4Y+czx/LpY12</latexit><latexit sha1_base64="pQ6Jmzgt42DS+iC5N8Cd2c/O+Ow=">AAAB6nicbZBNS8NAEIYn9avWr6pHL4tF8FSSIuix6MWLUNF+QBvKZjtpl242YXcjlNCf4MWDIl79Rd78N27bHLT1hYWHd2bYmTdIBNfGdb+dwtr6xuZWcbu0s7u3f1A+PGrpOFUMmywWseoEVKPgEpuGG4GdRCGNAoHtYHwzq7efUGkey0czSdCP6FDykDNqrPVw16/1yxW36s5FVsHLoQK5Gv3yV28QszRCaZigWnc9NzF+RpXhTOC01Es1JpSN6RC7FiWNUPvZfNUpObPOgISxsk8aMnd/T2Q00noSBbYzomakl2sz879aNzXhlZ9xmaQGJVt8FKaCmJjM7iYDrpAZMbFAmeJ2V8JGVFFmbDolG4K3fPIqtGpVz/L9RaV+ncdRhBM4hXPw4BLqcAsNaAKDITzDK7w5wnlx3p2PRWvByWeO4Y+czx/LpY12</latexit><latexit sha1_base64="pQ6Jmzgt42DS+iC5N8Cd2c/O+Ow=">AAAB6nicbZBNS8NAEIYn9avWr6pHL4tF8FSSIuix6MWLUNF+QBvKZjtpl242YXcjlNCf4MWDIl79Rd78N27bHLT1hYWHd2bYmTdIBNfGdb+dwtr6xuZWcbu0s7u3f1A+PGrpOFUMmywWseoEVKPgEpuGG4GdRCGNAoHtYHwzq7efUGkey0czSdCP6FDykDNqrPVw16/1yxW36s5FVsHLoQK5Gv3yV28QszRCaZigWnc9NzF+RpXhTOC01Es1JpSN6RC7FiWNUPvZfNUpObPOgISxsk8aMnd/T2Q00noSBbYzomakl2sz879aNzXhlZ9xmaQGJVt8FKaCmJjM7iYDrpAZMbFAmeJ2V8JGVFFmbDolG4K3fPIqtGpVz/L9RaV+ncdRhBM4hXPw4BLqcAsNaAKDITzDK7w5wnlx3p2PRWvByWeO4Y+czx/LpY12</latexit>
M<latexit sha1_base64="crANvVgGivIiDMWlFPoP+QRYTmE=">AAAB6HicbZBNS8NAEIYn9avWr6pHL4tF8FQSEfRY9OJFaMF+QBvKZjtp1242YXcjlNBf4MWDIl79Sd78N27bHLT1hYWHd2bYmTdIBNfGdb+dwtr6xuZWcbu0s7u3f1A+PGrpOFUMmywWseoEVKPgEpuGG4GdRCGNAoHtYHw7q7efUGkeywczSdCP6FDykDNqrNW475crbtWdi6yCl0MFctX75a/eIGZphNIwQbXuem5i/Iwqw5nAaamXakwoG9Mhdi1KGqH2s/miU3JmnQEJY2WfNGTu/p7IaKT1JApsZ0TNSC/XZuZ/tW5qwms/4zJJDUq2+ChMBTExmV1NBlwhM2JigTLF7a6EjaiizNhsSjYEb/nkVWhdVD3LjctK7SaPowgncArn4MEV1OAO6tAEBgjP8ApvzqPz4rw7H4vWgpPPHMMfOZ8/pQ+M0Q==</latexit><latexit sha1_base64="crANvVgGivIiDMWlFPoP+QRYTmE=">AAAB6HicbZBNS8NAEIYn9avWr6pHL4tF8FQSEfRY9OJFaMF+QBvKZjtp1242YXcjlNBf4MWDIl79Sd78N27bHLT1hYWHd2bYmTdIBNfGdb+dwtr6xuZWcbu0s7u3f1A+PGrpOFUMmywWseoEVKPgEpuGG4GdRCGNAoHtYHw7q7efUGkeywczSdCP6FDykDNqrNW475crbtWdi6yCl0MFctX75a/eIGZphNIwQbXuem5i/Iwqw5nAaamXakwoG9Mhdi1KGqH2s/miU3JmnQEJY2WfNGTu/p7IaKT1JApsZ0TNSC/XZuZ/tW5qwms/4zJJDUq2+ChMBTExmV1NBlwhM2JigTLF7a6EjaiizNhsSjYEb/nkVWhdVD3LjctK7SaPowgncArn4MEV1OAO6tAEBgjP8ApvzqPz4rw7H4vWgpPPHMMfOZ8/pQ+M0Q==</latexit><latexit sha1_base64="crANvVgGivIiDMWlFPoP+QRYTmE=">AAAB6HicbZBNS8NAEIYn9avWr6pHL4tF8FQSEfRY9OJFaMF+QBvKZjtp1242YXcjlNBf4MWDIl79Sd78N27bHLT1hYWHd2bYmTdIBNfGdb+dwtr6xuZWcbu0s7u3f1A+PGrpOFUMmywWseoEVKPgEpuGG4GdRCGNAoHtYHw7q7efUGkeywczSdCP6FDykDNqrNW475crbtWdi6yCl0MFctX75a/eIGZphNIwQbXuem5i/Iwqw5nAaamXakwoG9Mhdi1KGqH2s/miU3JmnQEJY2WfNGTu/p7IaKT1JApsZ0TNSC/XZuZ/tW5qwms/4zJJDUq2+ChMBTExmV1NBlwhM2JigTLF7a6EjaiizNhsSjYEb/nkVWhdVD3LjctK7SaPowgncArn4MEV1OAO6tAEBgjP8ApvzqPz4rw7H4vWgpPPHMMfOZ8/pQ+M0Q==</latexit><latexit sha1_base64="crANvVgGivIiDMWlFPoP+QRYTmE=">AAAB6HicbZBNS8NAEIYn9avWr6pHL4tF8FQSEfRY9OJFaMF+QBvKZjtp1242YXcjlNBf4MWDIl79Sd78N27bHLT1hYWHd2bYmTdIBNfGdb+dwtr6xuZWcbu0s7u3f1A+PGrpOFUMmywWseoEVKPgEpuGG4GdRCGNAoHtYHw7q7efUGkeywczSdCP6FDykDNqrNW475crbtWdi6yCl0MFctX75a/eIGZphNIwQbXuem5i/Iwqw5nAaamXakwoG9Mhdi1KGqH2s/miU3JmnQEJY2WfNGTu/p7IaKT1JApsZ0TNSC/XZuZ/tW5qwms/4zJJDUq2+ChMBTExmV1NBlwhM2JigTLF7a6EjaiizNhsSjYEb/nkVWhdVD3LjctK7SaPowgncArn4MEV1OAO6tAEBgjP8ApvzqPz4rw7H4vWgpPPHMMfOZ8/pQ+M0Q==</latexit>
f<latexit sha1_base64="86pTBsw+eU/nGyQFCB3wX7bjE6w=">AAAB73icbZBNS8NAEIYn9avWr6pHL4tF8FQSEfRY9OKxgmkLbSib7aZdutnE3YlQQv+EFw+KePXvePPfuG1z0NYXFh7emWFn3jCVwqDrfjultfWNza3ydmVnd2//oHp41DJJphn3WSIT3Qmp4VIo7qNAyTup5jQOJW+H49tZvf3EtRGJesBJyoOYDpWIBKNorU5vRJFEfa9frbl1dy6yCl4BNSjU7Fe/eoOEZTFXyCQ1puu5KQY51SiY5NNKLzM8pWxMh7xrUdGYmyCf7zslZ9YZkCjR9ikkc/f3RE5jYyZxaDtjiiOzXJuZ/9W6GUbXQS5UmiFXbPFRlEmCCZkdTwZCc4ZyYoEyLeyuhI2opgxtRBUbgrd88iq0Luqe5fvLWuOmiKMMJ3AK5+DBFTTgDprgAwMJz/AKb86j8+K8Ox+L1pJTzBzDHzmfP058j3k=</latexit><latexit sha1_base64="86pTBsw+eU/nGyQFCB3wX7bjE6w=">AAAB73icbZBNS8NAEIYn9avWr6pHL4tF8FQSEfRY9OKxgmkLbSib7aZdutnE3YlQQv+EFw+KePXvePPfuG1z0NYXFh7emWFn3jCVwqDrfjultfWNza3ydmVnd2//oHp41DJJphn3WSIT3Qmp4VIo7qNAyTup5jQOJW+H49tZvf3EtRGJesBJyoOYDpWIBKNorU5vRJFEfa9frbl1dy6yCl4BNSjU7Fe/eoOEZTFXyCQ1puu5KQY51SiY5NNKLzM8pWxMh7xrUdGYmyCf7zslZ9YZkCjR9ikkc/f3RE5jYyZxaDtjiiOzXJuZ/9W6GUbXQS5UmiFXbPFRlEmCCZkdTwZCc4ZyYoEyLeyuhI2opgxtRBUbgrd88iq0Luqe5fvLWuOmiKMMJ3AK5+DBFTTgDprgAwMJz/AKb86j8+K8Ox+L1pJTzBzDHzmfP058j3k=</latexit><latexit sha1_base64="86pTBsw+eU/nGyQFCB3wX7bjE6w=">AAAB73icbZBNS8NAEIYn9avWr6pHL4tF8FQSEfRY9OKxgmkLbSib7aZdutnE3YlQQv+EFw+KePXvePPfuG1z0NYXFh7emWFn3jCVwqDrfjultfWNza3ydmVnd2//oHp41DJJphn3WSIT3Qmp4VIo7qNAyTup5jQOJW+H49tZvf3EtRGJesBJyoOYDpWIBKNorU5vRJFEfa9frbl1dy6yCl4BNSjU7Fe/eoOEZTFXyCQ1puu5KQY51SiY5NNKLzM8pWxMh7xrUdGYmyCf7zslZ9YZkCjR9ikkc/f3RE5jYyZxaDtjiiOzXJuZ/9W6GUbXQS5UmiFXbPFRlEmCCZkdTwZCc4ZyYoEyLeyuhI2opgxtRBUbgrd88iq0Luqe5fvLWuOmiKMMJ3AK5+DBFTTgDprgAwMJz/AKb86j8+K8Ox+L1pJTzBzDHzmfP058j3k=</latexit><latexit sha1_base64="86pTBsw+eU/nGyQFCB3wX7bjE6w=">AAAB73icbZBNS8NAEIYn9avWr6pHL4tF8FQSEfRY9OKxgmkLbSib7aZdutnE3YlQQv+EFw+KePXvePPfuG1z0NYXFh7emWFn3jCVwqDrfjultfWNza3ydmVnd2//oHp41DJJphn3WSIT3Qmp4VIo7qNAyTup5jQOJW+H49tZvf3EtRGJesBJyoOYDpWIBKNorU5vRJFEfa9frbl1dy6yCl4BNSjU7Fe/eoOEZTFXyCQ1puu5KQY51SiY5NNKLzM8pWxMh7xrUdGYmyCf7zslZ9YZkCjR9ikkc/f3RE5jYyZxaDtjiiOzXJuZ/9W6GUbXQS5UmiFXbPFRlEmCCZkdTwZCc4ZyYoEyLeyuhI2opgxtRBUbgrd88iq0Luqe5fvLWuOmiKMMJ3AK5+DBFTTgDprgAwMJz/AKb86j8+K8Ox+L1pJTzBzDHzmfP058j3k=</latexit>ˆ1
fˆ2
<latexit sha1_base64="2HoX89nWNs3L3Rqlv8wVqFEV8/0=">AAAB73icbZBNS8NAEIYn9avWr6pHL4tF8FSSIuix6MVjBfsBbSib7aZdutmkuxOhhP4JLx4U8erf8ea/cdvmoK0vLDy8M8POvEEihUHX/XYKG5tb2zvF3dLe/sHhUfn4pGXiVDPeZLGMdSeghkuheBMFSt5JNKdRIHk7GN/N6+0nro2I1SNOE+5HdKhEKBhFa3V6I4ok7Nf65YpbdRci6+DlUIFcjX75qzeIWRpxhUxSY7qem6CfUY2CST4r9VLDE8rGdMi7FhWNuPGzxb4zcmGdAQljbZ9CsnB/T2Q0MmYaBbYzojgyq7W5+V+tm2J442dCJSlyxZYfhakkGJP58WQgNGcopxYo08LuStiIasrQRlSyIXirJ69Dq1b1LD9cVeq3eRxFOINzuAQPrqEO99CAJjCQ8Ayv8OZMnBfn3flYthacfOYU/sj5/AFQAI96</latexit><latexit sha1_base64="2HoX89nWNs3L3Rqlv8wVqFEV8/0=">AAAB73icbZBNS8NAEIYn9avWr6pHL4tF8FSSIuix6MVjBfsBbSib7aZdutmkuxOhhP4JLx4U8erf8ea/cdvmoK0vLDy8M8POvEEihUHX/XYKG5tb2zvF3dLe/sHhUfn4pGXiVDPeZLGMdSeghkuheBMFSt5JNKdRIHk7GN/N6+0nro2I1SNOE+5HdKhEKBhFa3V6I4ok7Nf65YpbdRci6+DlUIFcjX75qzeIWRpxhUxSY7qem6CfUY2CST4r9VLDE8rGdMi7FhWNuPGzxb4zcmGdAQljbZ9CsnB/T2Q0MmYaBbYzojgyq7W5+V+tm2J442dCJSlyxZYfhakkGJP58WQgNGcopxYo08LuStiIasrQRlSyIXirJ69Dq1b1LD9cVeq3eRxFOINzuAQPrqEO99CAJjCQ8Ayv8OZMnBfn3flYthacfOYU/sj5/AFQAI96</latexit><latexit sha1_base64="2HoX89nWNs3L3Rqlv8wVqFEV8/0=">AAAB73icbZBNS8NAEIYn9avWr6pHL4tF8FSSIuix6MVjBfsBbSib7aZdutmkuxOhhP4JLx4U8erf8ea/cdvmoK0vLDy8M8POvEEihUHX/XYKG5tb2zvF3dLe/sHhUfn4pGXiVDPeZLGMdSeghkuheBMFSt5JNKdRIHk7GN/N6+0nro2I1SNOE+5HdKhEKBhFa3V6I4ok7Nf65YpbdRci6+DlUIFcjX75qzeIWRpxhUxSY7qem6CfUY2CST4r9VLDE8rGdMi7FhWNuPGzxb4zcmGdAQljbZ9CsnB/T2Q0MmYaBbYzojgyq7W5+V+tm2J442dCJSlyxZYfhakkGJP58WQgNGcopxYo08LuStiIasrQRlSyIXirJ69Dq1b1LD9cVeq3eRxFOINzuAQPrqEO99CAJjCQ8Ayv8OZMnBfn3flYthacfOYU/sj5/AFQAI96</latexit><latexit sha1_base64="2HoX89nWNs3L3Rqlv8wVqFEV8/0=">AAAB73icbZBNS8NAEIYn9avWr6pHL4tF8FSSIuix6MVjBfsBbSib7aZdutmkuxOhhP4JLx4U8erf8ea/cdvmoK0vLDy8M8POvEEihUHX/XYKG5tb2zvF3dLe/sHhUfn4pGXiVDPeZLGMdSeghkuheBMFSt5JNKdRIHk7GN/N6+0nro2I1SNOE+5HdKhEKBhFa3V6I4ok7Nf65YpbdRci6+DlUIFcjX75qzeIWRpxhUxSY7qem6CfUY2CST4r9VLDE8rGdMi7FhWNuPGzxb4zcmGdAQljbZ9CsnB/T2Q0MmYaBbYzojgyq7W5+V+tm2J442dCJSlyxZYfhakkGJP58WQgNGcopxYo08LuStiIasrQRlSyIXirJ69Dq1b1LD9cVeq3eRxFOINzuAQPrqEO99CAJjCQ8Ayv8OZMnBfn3flYthacfOYU/sj5/AFQAI96</latexit>
ˆ e<latexit sha1_base64="8iacsLI0NuQz6Pzzumah6XGsYWQ=">AAAB73icbZDLSgNBEEVrfMb4irp00xgEV2EmCLoMunEZwTwgGUJPp5I06XnYXSOEIT/hxoUibv0dd/6NnWQWmnih4XCriq66QaKkIdf9dtbWNza3tgs7xd29/YPD0tFx08SpFtgQsYp1O+AGlYywQZIUthONPAwUtoLx7azeekJtZBw90CRBP+TDSA6k4GStdnfEiWGv2iuV3Yo7F1sFL4cy5Kr3Sl/dfizSECMSihvT8dyE/IxrkkLhtNhNDSZcjPkQOxYjHqLxs/m+U3ZunT4bxNq+iNjc/T2R8dCYSRjYzpDTyCzXZuZ/tU5Kg2s/k1GSEkZi8dEgVYxiNjue9aVGQWpigQst7a5MjLjmgmxERRuCt3zyKjSrFc/y/WW5dpPHUYBTOIML8OAKanAHdWiAAAXP8ApvzqPz4rw7H4vWNSefOYE/cj5/AE56j3k=</latexit><latexit sha1_base64="8iacsLI0NuQz6Pzzumah6XGsYWQ=">AAAB73icbZDLSgNBEEVrfMb4irp00xgEV2EmCLoMunEZwTwgGUJPp5I06XnYXSOEIT/hxoUibv0dd/6NnWQWmnih4XCriq66QaKkIdf9dtbWNza3tgs7xd29/YPD0tFx08SpFtgQsYp1O+AGlYywQZIUthONPAwUtoLx7azeekJtZBw90CRBP+TDSA6k4GStdnfEiWGv2iuV3Yo7F1sFL4cy5Kr3Sl/dfizSECMSihvT8dyE/IxrkkLhtNhNDSZcjPkQOxYjHqLxs/m+U3ZunT4bxNq+iNjc/T2R8dCYSRjYzpDTyCzXZuZ/tU5Kg2s/k1GSEkZi8dEgVYxiNjue9aVGQWpigQst7a5MjLjmgmxERRuCt3zyKjSrFc/y/WW5dpPHUYBTOIML8OAKanAHdWiAAAXP8ApvzqPz4rw7H4vWNSefOYE/cj5/AE56j3k=</latexit><latexit sha1_base64="8iacsLI0NuQz6Pzzumah6XGsYWQ=">AAAB73icbZDLSgNBEEVrfMb4irp00xgEV2EmCLoMunEZwTwgGUJPp5I06XnYXSOEIT/hxoUibv0dd/6NnWQWmnih4XCriq66QaKkIdf9dtbWNza3tgs7xd29/YPD0tFx08SpFtgQsYp1O+AGlYywQZIUthONPAwUtoLx7azeekJtZBw90CRBP+TDSA6k4GStdnfEiWGv2iuV3Yo7F1sFL4cy5Kr3Sl/dfizSECMSihvT8dyE/IxrkkLhtNhNDSZcjPkQOxYjHqLxs/m+U3ZunT4bxNq+iNjc/T2R8dCYSRjYzpDTyCzXZuZ/tU5Kg2s/k1GSEkZi8dEgVYxiNjue9aVGQWpigQst7a5MjLjmgmxERRuCt3zyKjSrFc/y/WW5dpPHUYBTOIML8OAKanAHdWiAAAXP8ApvzqPz4rw7H4vWNSefOYE/cj5/AE56j3k=</latexit><latexit sha1_base64="8iacsLI0NuQz6Pzzumah6XGsYWQ=">AAAB73icbZDLSgNBEEVrfMb4irp00xgEV2EmCLoMunEZwTwgGUJPp5I06XnYXSOEIT/hxoUibv0dd/6NnWQWmnih4XCriq66QaKkIdf9dtbWNza3tgs7xd29/YPD0tFx08SpFtgQsYp1O+AGlYywQZIUthONPAwUtoLx7azeekJtZBw90CRBP+TDSA6k4GStdnfEiWGv2iuV3Yo7F1sFL4cy5Kr3Sl/dfizSECMSihvT8dyE/IxrkkLhtNhNDSZcjPkQOxYjHqLxs/m+U3ZunT4bxNq+iNjc/T2R8dCYSRjYzpDTyCzXZuZ/tU5Kg2s/k1GSEkZi8dEgVYxiNjue9aVGQWpigQst7a5MjLjmgmxERRuCt3zyKjSrFc/y/WW5dpPHUYBTOIML8OAKanAHdWiAAAXP8ApvzqPz4rw7H4vWNSefOYE/cj5/AE56j3k=</latexit> 2
ˆ e1
<latexit sha1_base64="4qI8g9w04WwuJH4Q2j9s5Gj9Aso=">AAAB73icbZDLSgNBEEVr4ivGV9Slm8YguAozIugy6MZlBPOAZAg9nUrSpOdhd40QhvyEGxeKuPV33Pk3dpJZaOKFhsOtKrrqBomShlz32ymsrW9sbhW3Szu7e/sH5cOjpolTLbAhYhXrdsANKhlhgyQpbCcaeRgobAXj21m99YTayDh6oEmCfsiHkRxIwcla7e6IE8Oe1ytX3Ko7F1sFL4cK5Kr3yl/dfizSECMSihvT8dyE/IxrkkLhtNRNDSZcjPkQOxYjHqLxs/m+U3ZmnT4bxNq+iNjc/T2R8dCYSRjYzpDTyCzXZuZ/tU5Kg2s/k1GSEkZi8dEgVYxiNjue9aVGQWpigQst7a5MjLjmgmxEJRuCt3zyKjQvqp7l+8tK7SaPowgncArn4MEV1OAO6tAAAQqe4RXenEfnxXl3PhatBSefOYY/cj5/AEz2j3g=</latexit><latexit sha1_base64="4qI8g9w04WwuJH4Q2j9s5Gj9Aso=">AAAB73icbZDLSgNBEEVr4ivGV9Slm8YguAozIugy6MZlBPOAZAg9nUrSpOdhd40QhvyEGxeKuPV33Pk3dpJZaOKFhsOtKrrqBomShlz32ymsrW9sbhW3Szu7e/sH5cOjpolTLbAhYhXrdsANKhlhgyQpbCcaeRgobAXj21m99YTayDh6oEmCfsiHkRxIwcla7e6IE8Oe1ytX3Ko7F1sFL4cK5Kr3yl/dfizSECMSihvT8dyE/IxrkkLhtNRNDSZcjPkQOxYjHqLxs/m+U3ZmnT4bxNq+iNjc/T2R8dCYSRjYzpDTyCzXZuZ/tU5Kg2s/k1GSEkZi8dEgVYxiNjue9aVGQWpigQst7a5MjLjmgmxEJRuCt3zyKjQvqp7l+8tK7SaPowgncArn4MEV1OAO6tAAAQqe4RXenEfnxXl3PhatBSefOYY/cj5/AEz2j3g=</latexit><latexit sha1_base64="4qI8g9w04WwuJH4Q2j9s5Gj9Aso=">AAAB73icbZDLSgNBEEVr4ivGV9Slm8YguAozIugy6MZlBPOAZAg9nUrSpOdhd40QhvyEGxeKuPV33Pk3dpJZaOKFhsOtKrrqBomShlz32ymsrW9sbhW3Szu7e/sH5cOjpolTLbAhYhXrdsANKhlhgyQpbCcaeRgobAXj21m99YTayDh6oEmCfsiHkRxIwcla7e6IE8Oe1ytX3Ko7F1sFL4cK5Kr3yl/dfizSECMSihvT8dyE/IxrkkLhtNRNDSZcjPkQOxYjHqLxs/m+U3ZmnT4bxNq+iNjc/T2R8dCYSRjYzpDTyCzXZuZ/tU5Kg2s/k1GSEkZi8dEgVYxiNjue9aVGQWpigQst7a5MjLjmgmxEJRuCt3zyKjQvqp7l+8tK7SaPowgncArn4MEV1OAO6tAAAQqe4RXenEfnxXl3PhatBSefOYY/cj5/AEz2j3g=</latexit><latexit sha1_base64="4qI8g9w04WwuJH4Q2j9s5Gj9Aso=">AAAB73icbZDLSgNBEEVr4ivGV9Slm8YguAozIugy6MZlBPOAZAg9nUrSpOdhd40QhvyEGxeKuPV33Pk3dpJZaOKFhsOtKrrqBomShlz32ymsrW9sbhW3Szu7e/sH5cOjpolTLbAhYhXrdsANKhlhgyQpbCcaeRgobAXj21m99YTayDh6oEmCfsiHkRxIwcla7e6IE8Oe1ytX3Ko7F1sFL4cK5Kr3yl/dfizSECMSihvT8dyE/IxrkkLhtNRNDSZcjPkQOxYjHqLxs/m+U3ZmnT4bxNq+iNjc/T2R8dCYSRjYzpDTyCzXZuZ/tU5Kg2s/k1GSEkZi8dEgVYxiNjue9aVGQWpigQst7a5MjLjmgmxEJRuCt3zyKjQvqp7l+8tK7SaPowgncArn4MEV1OAO6tAAAQqe4RXenEfnxXl3PhatBSefOYY/cj5/AEz2j3g=</latexit>
zx
<latexit sha1_base64="q9kqZlPLRngIqst0U1bsvB1sD0w=">AAAB6nicdVDLSgMxFM34rPVVdekmWARXQ2Zsp3VXdOOyon1AO5RMmmlDM5khyYh16Ce4caGIW7/InX9j+hBU9MCFwzn3cu89QcKZ0gh9WEvLK6tr67mN/ObW9s5uYW+/qeJUEtogMY9lO8CKciZoQzPNaTuRFEcBp61gdDH1W7dUKhaLGz1OqB/hgWAhI1gb6fq+d9crFJGNSmW3jCCyT6uuhzxDPO/MqbjQsdEMRbBAvVd47/ZjkkZUaMKxUh0HJdrPsNSMcDrJd1NFE0xGeEA7hgocUeVns1Mn8NgofRjG0pTQcKZ+n8hwpNQ4CkxnhPVQ/fam4l9eJ9Vh1c+YSFJNBZkvClMOdQynf8M+k5RoPjYEE8nMrZAMscREm3TyJoSvT+H/pOnajuFXpWLtfBFHDhyCI3ACHFABNXAJ6qABCBiAB/AEni1uPVov1uu8dclazByAH7DePgHiFo4x</latexit><latexit sha1_base64="q9kqZlPLRngIqst0U1bsvB1sD0w=">AAAB6nicdVDLSgMxFM34rPVVdekmWARXQ2Zsp3VXdOOyon1AO5RMmmlDM5khyYh16Ce4caGIW7/InX9j+hBU9MCFwzn3cu89QcKZ0gh9WEvLK6tr67mN/ObW9s5uYW+/qeJUEtogMY9lO8CKciZoQzPNaTuRFEcBp61gdDH1W7dUKhaLGz1OqB/hgWAhI1gb6fq+d9crFJGNSmW3jCCyT6uuhzxDPO/MqbjQsdEMRbBAvVd47/ZjkkZUaMKxUh0HJdrPsNSMcDrJd1NFE0xGeEA7hgocUeVns1Mn8NgofRjG0pTQcKZ+n8hwpNQ4CkxnhPVQ/fam4l9eJ9Vh1c+YSFJNBZkvClMOdQynf8M+k5RoPjYEE8nMrZAMscREm3TyJoSvT+H/pOnajuFXpWLtfBFHDhyCI3ACHFABNXAJ6qABCBiAB/AEni1uPVov1uu8dclazByAH7DePgHiFo4x</latexit><latexit sha1_base64="q9kqZlPLRngIqst0U1bsvB1sD0w=">AAAB6nicdVDLSgMxFM34rPVVdekmWARXQ2Zsp3VXdOOyon1AO5RMmmlDM5khyYh16Ce4caGIW7/InX9j+hBU9MCFwzn3cu89QcKZ0gh9WEvLK6tr67mN/ObW9s5uYW+/qeJUEtogMY9lO8CKciZoQzPNaTuRFEcBp61gdDH1W7dUKhaLGz1OqB/hgWAhI1gb6fq+d9crFJGNSmW3jCCyT6uuhzxDPO/MqbjQsdEMRbBAvVd47/ZjkkZUaMKxUh0HJdrPsNSMcDrJd1NFE0xGeEA7hgocUeVns1Mn8NgofRjG0pTQcKZ+n8hwpNQ4CkxnhPVQ/fam4l9eJ9Vh1c+YSFJNBZkvClMOdQynf8M+k5RoPjYEE8nMrZAMscREm3TyJoSvT+H/pOnajuFXpWLtfBFHDhyCI3ACHFABNXAJ6qABCBiAB/AEni1uPVov1uu8dclazByAH7DePgHiFo4x</latexit><latexit sha1_base64="q9kqZlPLRngIqst0U1bsvB1sD0w=">AAAB6nicdVDLSgMxFM34rPVVdekmWARXQ2Zsp3VXdOOyon1AO5RMmmlDM5khyYh16Ce4caGIW7/InX9j+hBU9MCFwzn3cu89QcKZ0gh9WEvLK6tr67mN/ObW9s5uYW+/qeJUEtogMY9lO8CKciZoQzPNaTuRFEcBp61gdDH1W7dUKhaLGz1OqB/hgWAhI1gb6fq+d9crFJGNSmW3jCCyT6uuhzxDPO/MqbjQsdEMRbBAvVd47/ZjkkZUaMKxUh0HJdrPsNSMcDrJd1NFE0xGeEA7hgocUeVns1Mn8NgofRjG0pTQcKZ+n8hwpNQ4CkxnhPVQ/fam4l9eJ9Vh1c+YSFJNBZkvClMOdQynf8M+k5RoPjYEE8nMrZAMscREm3TyJoSvT+H/pOnajuFXpWLtfBFHDhyCI3ACHFABNXAJ6qABCBiAB/AEni1uPVov1uu8dclazByAH7DePgHiFo4x</latexit>
z = 0
<latexit sha1_base64="9NPZW731DiDGc9zsVU/sDXdDHE0=">AAAB6nicdVDLSgMxFM34rPVVdekmWARXQ2Zsp3UhFN24rGgf0A4lk2ba0ExmSDJCHfoJblwo4tYvcuffmD4EFT1w4XDOvdx7T5BwpjRCH9bS8srq2npuI7+5tb2zW9jbb6o4lYQ2SMxj2Q6wopwJ2tBMc9pOJMVRwGkrGF1O/dYdlYrF4laPE+pHeCBYyAjWRrq5P0e9QhHZqFR2ywgi+7TqesgzxPPOnIoLHRvNUAQL1HuF924/JmlEhSYcK9VxUKL9DEvNCKeTfDdVNMFkhAe0Y6jAEVV+Njt1Ao+N0odhLE0JDWfq94kMR0qNo8B0RlgP1W9vKv7ldVIdVv2MiSTVVJD5ojDlUMdw+jfsM0mJ5mNDMJHM3ArJEEtMtEknb0L4+hT+T5qu7Rh+XSrWLhZx5MAhOAInwAEVUANXoA4agIABeABP4Nni1qP1Yr3OW5esxcwB+AHr7RNBTI3H</latexit><latexit sha1_base64="9NPZW731DiDGc9zsVU/sDXdDHE0=">AAAB6nicdVDLSgMxFM34rPVVdekmWARXQ2Zsp3UhFN24rGgf0A4lk2ba0ExmSDJCHfoJblwo4tYvcuffmD4EFT1w4XDOvdx7T5BwpjRCH9bS8srq2npuI7+5tb2zW9jbb6o4lYQ2SMxj2Q6wopwJ2tBMc9pOJMVRwGkrGF1O/dYdlYrF4laPE+pHeCBYyAjWRrq5P0e9QhHZqFR2ywgi+7TqesgzxPPOnIoLHRvNUAQL1HuF924/JmlEhSYcK9VxUKL9DEvNCKeTfDdVNMFkhAe0Y6jAEVV+Njt1Ao+N0odhLE0JDWfq94kMR0qNo8B0RlgP1W9vKv7ldVIdVv2MiSTVVJD5ojDlUMdw+jfsM0mJ5mNDMJHM3ArJEEtMtEknb0L4+hT+T5qu7Rh+XSrWLhZx5MAhOAInwAEVUANXoA4agIABeABP4Nni1qP1Yr3OW5esxcwB+AHr7RNBTI3H</latexit><latexit sha1_base64="9NPZW731DiDGc9zsVU/sDXdDHE0=">AAAB6nicdVDLSgMxFM34rPVVdekmWARXQ2Zsp3UhFN24rGgf0A4lk2ba0ExmSDJCHfoJblwo4tYvcuffmD4EFT1w4XDOvdx7T5BwpjRCH9bS8srq2npuI7+5tb2zW9jbb6o4lYQ2SMxj2Q6wopwJ2tBMc9pOJMVRwGkrGF1O/dYdlYrF4laPE+pHeCBYyAjWRrq5P0e9QhHZqFR2ywgi+7TqesgzxPPOnIoLHRvNUAQL1HuF924/JmlEhSYcK9VxUKL9DEvNCKeTfDdVNMFkhAe0Y6jAEVV+Njt1Ao+N0odhLE0JDWfq94kMR0qNo8B0RlgP1W9vKv7ldVIdVv2MiSTVVJD5ojDlUMdw+jfsM0mJ5mNDMJHM3ArJEEtMtEknb0L4+hT+T5qu7Rh+XSrWLhZx5MAhOAInwAEVUANXoA4agIABeABP4Nni1qP1Yr3OW5esxcwB+AHr7RNBTI3H</latexit><latexit sha1_base64="9NPZW731DiDGc9zsVU/sDXdDHE0=">AAAB6nicdVDLSgMxFM34rPVVdekmWARXQ2Zsp3UhFN24rGgf0A4lk2ba0ExmSDJCHfoJblwo4tYvcuffmD4EFT1w4XDOvdx7T5BwpjRCH9bS8srq2npuI7+5tb2zW9jbb6o4lYQ2SMxj2Q6wopwJ2tBMc9pOJMVRwGkrGF1O/dYdlYrF4laPE+pHeCBYyAjWRrq5P0e9QhHZqFR2ywgi+7TqesgzxPPOnIoLHRvNUAQL1HuF924/JmlEhSYcK9VxUKL9DEvNCKeTfDdVNMFkhAe0Y6jAEVV+Njt1Ao+N0odhLE0JDWfq94kMR0qNo8B0RlgP1W9vKv7ldVIdVv2MiSTVVJD5ojDlUMdw+jfsM0mJ5mNDMJHM3ArJEEtMtEknb0L4+hT+T5qu7Rh+XSrWLhZx5MAhOAInwAEVUANXoA4agIABeABP4Nni1qP1Yr3OW5esxcwB+AHr7RNBTI3H</latexit>
z<latexit sha1_base64="QK3/7t/PbSHRgOuzMGM6FRBLofE=">AAAB6nicdVDLSgMxFM3UV62vqks3wSK4GjK1ndaFUHTjwkVF+4B2KJk004ZmMkOSEerQT3DjQhG3fpE7/8b0IajogQuHc+7l3nv8mDOlEfqwMkvLK6tr2fXcxubW9k5+d6+pokQS2iARj2Tbx4pyJmhDM81pO5YUhz6nLX90MfVbd1QqFolbPY6pF+KBYAEjWBvp5v7sqpcvIBuVysUygsg+qRZd5BriuqdOpQgdG81QAAvUe/n3bj8iSUiFJhwr1XFQrL0US80Ip5NcN1E0xmSEB7RjqMAhVV46O3UCj4zSh0EkTQkNZ+r3iRSHSo1D33SGWA/Vb28q/uV1Eh1UvZSJONFUkPmiIOFQR3D6N+wzSYnmY0MwkczcCskQS0y0SSdnQvj6FP5PmkXbMfy6VKidL+LIggNwCI6BAyqgBi5BHTQAAQPwAJ7As8WtR+vFep23ZqzFzD74AevtE2u8jeM=</latexit><latexit sha1_base64="QK3/7t/PbSHRgOuzMGM6FRBLofE=">AAAB6nicdVDLSgMxFM3UV62vqks3wSK4GjK1ndaFUHTjwkVF+4B2KJk004ZmMkOSEerQT3DjQhG3fpE7/8b0IajogQuHc+7l3nv8mDOlEfqwMkvLK6tr2fXcxubW9k5+d6+pokQS2iARj2Tbx4pyJmhDM81pO5YUhz6nLX90MfVbd1QqFolbPY6pF+KBYAEjWBvp5v7sqpcvIBuVysUygsg+qRZd5BriuqdOpQgdG81QAAvUe/n3bj8iSUiFJhwr1XFQrL0US80Ip5NcN1E0xmSEB7RjqMAhVV46O3UCj4zSh0EkTQkNZ+r3iRSHSo1D33SGWA/Vb28q/uV1Eh1UvZSJONFUkPmiIOFQR3D6N+wzSYnmY0MwkczcCskQS0y0SSdnQvj6FP5PmkXbMfy6VKidL+LIggNwCI6BAyqgBi5BHTQAAQPwAJ7As8WtR+vFep23ZqzFzD74AevtE2u8jeM=</latexit><latexit sha1_base64="QK3/7t/PbSHRgOuzMGM6FRBLofE=">AAAB6nicdVDLSgMxFM3UV62vqks3wSK4GjK1ndaFUHTjwkVF+4B2KJk004ZmMkOSEerQT3DjQhG3fpE7/8b0IajogQuHc+7l3nv8mDOlEfqwMkvLK6tr2fXcxubW9k5+d6+pokQS2iARj2Tbx4pyJmhDM81pO5YUhz6nLX90MfVbd1QqFolbPY6pF+KBYAEjWBvp5v7sqpcvIBuVysUygsg+qRZd5BriuqdOpQgdG81QAAvUe/n3bj8iSUiFJhwr1XFQrL0US80Ip5NcN1E0xmSEB7RjqMAhVV46O3UCj4zSh0EkTQkNZ+r3iRSHSo1D33SGWA/Vb28q/uV1Eh1UvZSJONFUkPmiIOFQR3D6N+wzSYnmY0MwkczcCskQS0y0SSdnQvj6FP5PmkXbMfy6VKidL+LIggNwCI6BAyqgBi5BHTQAAQPwAJ7As8WtR+vFep23ZqzFzD74AevtE2u8jeM=</latexit><latexit sha1_base64="QK3/7t/PbSHRgOuzMGM6FRBLofE=">AAAB6nicdVDLSgMxFM3UV62vqks3wSK4GjK1ndaFUHTjwkVF+4B2KJk004ZmMkOSEerQT3DjQhG3fpE7/8b0IajogQuHc+7l3nv8mDOlEfqwMkvLK6tr2fXcxubW9k5+d6+pokQS2iARj2Tbx4pyJmhDM81pO5YUhz6nLX90MfVbd1QqFolbPY6pF+KBYAEjWBvp5v7sqpcvIBuVysUygsg+qRZd5BriuqdOpQgdG81QAAvUe/n3bj8iSUiFJhwr1XFQrL0US80Ip5NcN1E0xmSEB7RjqMAhVV46O3UCj4zSh0EkTQkNZ+r3iRSHSo1D33SGWA/Vb28q/uV1Eh1UvZSJONFUkPmiIOFQR3D6N+wzSYnmY0MwkczcCskQS0y0SSdnQvj6FP5PmkXbMfy6VKidL+LIggNwCI6BAyqgBi5BHTQAAQPwAJ7As8WtR+vFep23ZqzFzD74AevtE2u8jeM=</latexit> =L
Figure 2.6: Ring cavity configuration and field labeling. Here 𝑀0is the front mir- ror with amplitude reflectivity 𝑟0 and transmittance 𝑡0, 𝑀1,2 are two fixed totally reflective end mirror,𝑀 is the movable membrane with amplitude reflectivity𝑟and transmittance𝑖𝑡. 𝐿is the total cavity length, 𝐿1= 𝐿2= 𝐿/2 are the distances from the 𝑀0to the equilibrium position of 𝑀 in clockwise and counterclockwise direc- tions,𝑥 is the microscopic displacement of𝑀 from its equilibrium. For fields, ˆ𝑐1,2 are the counterclockwise, clockwise propagating field directly coupled from outside continuum ˆ𝑎1,2. Defined at the instantaneous position of the membrane, ˆ𝑒2,1( ˆ𝑓1,2) are the propagating fields towards (away from) the membrane in counterclockwise, clockwise direction separately.
couples the two circulating waves and opens the mode degeneracy, as shown in Fig. 2.7. We first consider resonant cavity modes assuming a perfectly reflective front mirror𝑀0. In this case no outside field can couple into the cavity and the field operator vector ˆe(𝑘)= (𝑒ˆ1(𝑘),𝑒ˆ2(𝑘))Tobeys the following matrix formula:
T𝑐(𝑘)e(ˆ 𝑘)= ˆ0, (2.23) whereT𝑐(𝑘)is the closed form transfer matrix:
T𝑐(𝑘) = 1−𝑖𝑡 𝑒𝑖 𝑘 𝐿 −𝑟 𝑒𝑖 𝑘 𝐿
−𝑟 𝑒𝑖 𝑘 𝐿 1−𝑖𝑡 𝑒𝑖 𝑘 𝐿
!
. (2.24)
Solving this equation allows us to find wave numbers𝑘± of the resonant fields:
𝑘± = 1
𝑖 𝐿 log(±𝑟−𝑖𝑡). (2.25)
The two corresponding resonant frequencies 𝜔± = 𝑐 𝑘± within one free spectral range (FSR)Δ𝜔FSR =2𝜋 𝑐/𝐿 are separated by:
𝜔𝑠 = 𝑐arcsin𝑟 𝐿
. (2.26)