18 Purcell Effect in PT-Symmetric Waveguides
501
In the PT-broken regime, eigenvalues can be written as
β 1,2 = Re (β + δ) ± iκ sinh θ,
(18.32)
where cosh θ = α/2κ. Supermodes then read as
|1, 2 = |g + ie
∓θ
|l
(18.33)
The eigenmodes in PT-broken regime are not longer the eigenstates of the ˆ
P ˆ
T
operator. Instead, in this regime ˆ
P ˆ
T operator relates |1 and |2 as follows
Fig. 18.3 Mode profiles in
PT-symmetric regime: a
mode |1 and b mode |2
Fig. 18.4 Mode profiles in
PT-symmetry-broken
regime: a mode |1 and b
mode |2
Fig. 18.5 Schematics of state-of-art PT-symmetric structures: a coupled waveguides, b twodimensional photonic lattices, c multilayer systems and d microresonators
501
In the PT-broken regime, eigenvalues can be written as
β 1,2 = Re (β + δ) ± iκ sinh θ,
(18.32)
where cosh θ = α/2κ. Supermodes then read as
|1, 2 = |g + ie
∓θ
|l
(18.33)
The eigenmodes in PT-broken regime are not longer the eigenstates of the ˆ
P ˆ
T
operator. Instead, in this regime ˆ
P ˆ
T operator relates |1 and |2 as follows
Fig. 18.3 Mode profiles in
PT-symmetric regime: a
mode |1 and b mode |2
Fig. 18.4 Mode profiles in
PT-symmetry-broken
regime: a mode |1 and b
mode |2
Fig. 18.5 Schematics of state-of-art PT-symmetric structures: a coupled waveguides, b twodimensional photonic lattices, c multilayer systems and d microresonators