2677.1.KERR-LENSMODELOCKING(KLM)By symmetry, we find the spot size on mirror 3 via switching index 1 and 2:12入L91ws(7.29)92 1- 9192Ri-入R2LL(7.30)R2- LRi+R2-The intracavity focus can be found by transforming the focused Gaussianbeam with the propagation matrixM-1n1. -录21(7.31)示1to its new focus byproperly choosing z1,seeFigure7.9W-Z1R2R1Figure 7.9: Two-mirror resonatorFigurebyMIT OcW.A short calculation results in92 (g1 - 1)(7.32)Z212g192 — 91 - 92L(L - R2)(7.33)2L- R1- R2and,again,by symmetry91 (92 - 1)(7.34)22一29192-91-92L(L - Ri)(7.35)L-212L-R1-R2
7.1. KERR-LENS MODE LOCKING (KLM) 267 By symmetry, we find the spot size on mirror 3 via switching index 1 and 2: w4 2 = µ2λL π ¶2 g1 g2 1 1 − g1g2 (7.29) = µλR2 π ¶2 R1 − L R2 − L µ L R1 + R2 − L ¶ . (7.30) The intracavity focus can be found by transforming the focused Gaussian beam with the propagation matrix M = µ 1 z1 0 1 ¶ µ 1 0 −1 2f1 1 ¶ = µ 1 − z1 2f1 z1 −1 2f1 1 ¶ , (7.31) to its new focus by properly choosing z1, see Figure 7.9. Figure 7.9: Two-mirror resonator A short calculation results in z1 = L g2 (g1 − 1) 2g1g2 − g1 − g2 (7.32) = L(L − R2) 2L − R1 − R2 , (7.33) and, again, by symmetry z2 = L g1 (g2 − 1) 2g1g2 − g1 − g2 (7.34) = L(L − R1) 2L − R1 − R2 = L − z1. (7.35) R1 R2 0 Wo z2 z -z1 L Figure by MIT OCW
268CHAPTER7.KERR-LENSANDADDITIVEPULSEMODELOCKINGThe spot size in the intracavity focus is9192 (1 - 9192)A1we(7.36)(29192 - 91 - 92)2L(R1 - L)(R2 - L)(Ri + R2 - L)(7.37)(R1 + R2 - 2L)2All these quantities for the two-mirror resonator are shown in Figure 7.11.Note, that all resonators and the Gaussian beam are related to the confocalresonator as shown in Figure 7.10ConfocalResonatorR2RGeneralResonatorRFigure 7.10: Two-mirror resonator and its relationship with the confocalresonator.FigurebyMITOCW
268CHAPTER 7. KERR-LENS AND ADDITIVE PULSE MODE LOCKING The spot size in the intracavity focus is w4 o = µλL π ¶2 g1g2 (1 − g1g2) (2g1g2 − g1 − g2)2 (7.36) = µλ π ¶2 L(R1 − L)(R2 − L)(R1 + R2 − L) (R1 + R2 − 2L)2 . (7.37) All these quantities for the two-mirror resonator are shown in Figure 7.11. Note, that all resonators and the Gaussian beam are related to the confocal resonator as shown in Figure 7.10. Figure 7.10: Two-mirror resonator and its relationship with the confocal resonator. R1 R2 R L General Resonator Confocal Resonator Figure by MIT OCW