Clear[P, S1, S2, \[Rho]];
c = 3*10^5; neff = 1.467; n = 1.444; Lext = 5/10^5; gB =
2.4/10^18; Aeff = 8/10^17; k = 1.155/10^5; \[Lambda] =
1.55/10^9; Nu = N[c/\[Lambda], 20]; \[CapitalGamma]b = 10^8;
v = 2.9824/10^3; Lr = 8; L = 20; \[Alpha] = 0.05; \[Eta] =
1.08/10^4; kb = 1.38/10^23; T = 300; \[Rho]0 = 2.65*10^15; v0 = 2.38;
eqns = {(n/c)*D[P[Z, t], t] +
D[P[Z, t], Z] == (-(gB/Aeff))*S2[Z, t]*\[Rho][Z, t] - \[Alpha]*
P[Z, t], (n/c)*D[S2[Z, t], t] - D[S2[Z, t], Z] ==
(-\[Alpha])*S2[Z, t] + (gB/Aeff)*P[Z, t]*
Conjugate[\[Rho][Z, t]] + \[Eta]*S1[Z, t] - \[Eta]*
S2[Z, t], (n/c)*D[S1[Z, t], t] - D[S2[Z, t], Z] ==
(-\[Alpha])*S1[Z, t] + \[Eta]*S2[Z, t] - \[Eta]*S1[Z, t],
D[\[Rho][Z, t], t] ==
0.2*P[Z, t]*Conjugate[S2[Z, t]] - \[CapitalGamma]b*\[Rho][Z, t],
P[0, t] == 25, S1[0, t] == 0}
sols = NDSolve[{eqns, DirichletCondition[S2[Z, t] == 0, Z = 20],
PeriodicBoundaryCondition[
k*Exp[-4*Pi*Nu*I*((Lext + v*t*Cos[78*Degree])/c)]*S2[Z, t],
Z == 0, TranslationTransform[{20}]]}, {P[Z, t], S1[Z, t],
S2[Z, t], \[Rho][Z, t]}, {Z, 0, 20, 0.001}, {t, 0, 1, 10^(-7)}];
Plot[Evaluate[S2[20, t]], {t, 0, 1}]
Plot[Evaluate[P[0, t]], {t, 0, 1}]

DirichletCondition里有个低级错误。