506
A. Karabchevsky et al.
18.3.4 Microresonators
PT symmetry can be realised on a resonator platform promising for interesting applications on a chip. In Fig. 18.5d we show a typical system comprising two coupled
gain and loss cavities. It is shown in [45] that a non-Hermitian optical microring
resonator coupled to a waveguide can be used as an asymmetric absorber, if a mirror
is placed on one side of the waveguide. Robustness of the asymmetric absorption
is explained by the emergence of the chiral exceptional surface, which can be also
exploited for directional absorption control. Unidirectional lasing and coherent perfect absorption can be achieved using unidirectional destructive interferences being
realised with an asymmetrically coupled passive resonator chain [46]. Asymmetry
in coupling breaks the reciprocity in transmission due to the destructive interference. A PT-symmetric side-coupled resonator can be realised using unidirectional
lasing together with perfectly absorbing resonators and can result in simultaneous
unidirectional lasing and perfect absorption effects. In a similar fashion, the spectral singularities of scattering matrix can be investigated in a PT-symmetric two-arm
Aharonov-Bohm interferometer [46]. Such spectral singularities can be tailored to
realise symmetric, asymmetric and unidirectional lasing onsets.
Non-Hermitian resonators are widely used as extremely sensible sensors at exceptional points. The sensitivity can be even more increased for higher-order exceptional
points, at which more than two eigenvalues of a non-Hermitian Hamiltonian coincide. In this case, the frequency splitting stems from a perturbation ε 1 follows the
law ε
1/N , where N is the order of the exceptional point [47]. Since the susceptibility
d(ε
1/N
)/dε diverges at ε = 0, the sensitivity can be arbitrarily high. This idea was
experimentally validated in a PT-symmetric ternary (loss-neutral-gain) micro-ring
system [48] and micro-toroid cavity [49], the non-Hermiticity of the latter being
introduced by a scatterer resulting in coupling eigenmodes of the cavity. Sensitivity of parameter estimation can be analysed using the formalism of quantum Fisher
information without referring to a specific measurement scheme. The average of all
merging eigenstates cancels out the divergence at the singularity resulting to a finite
value at the exceptional point [38].
PT-symmetric [50] and anti-PT-symmetric [51] optical gyroscopes were proposed
on the basis of ring resonators coupled to a waveguide. Frequency splitting and,
hence, sensitivity in gyroscopes are normally limited by the ring dimensions. In PTsymmetric gyroscopes, the frequency splitting is independent of the ring radius and,
therefore, the phase shift of interference fringes is enhanced in vicinity of exceptional
points. A unique “superluminal” lasing may be used as a sensor and can be obtained
in a broken PT-symmetry phase of the white-light cavity that consists of gain and
lossy coupled micro-resonators [52].
Finally, PT-symmetric microcavities possess indispensable nanophotonic properties for suppression of spontaneous relaxation rate [53]. In the next section we will
discuss this subject in detail.
A. Karabchevsky et al.
18.3.4 Microresonators
PT symmetry can be realised on a resonator platform promising for interesting applications on a chip. In Fig. 18.5d we show a typical system comprising two coupled
gain and loss cavities. It is shown in [45] that a non-Hermitian optical microring
resonator coupled to a waveguide can be used as an asymmetric absorber, if a mirror
is placed on one side of the waveguide. Robustness of the asymmetric absorption
is explained by the emergence of the chiral exceptional surface, which can be also
exploited for directional absorption control. Unidirectional lasing and coherent perfect absorption can be achieved using unidirectional destructive interferences being
realised with an asymmetrically coupled passive resonator chain [46]. Asymmetry
in coupling breaks the reciprocity in transmission due to the destructive interference. A PT-symmetric side-coupled resonator can be realised using unidirectional
lasing together with perfectly absorbing resonators and can result in simultaneous
unidirectional lasing and perfect absorption effects. In a similar fashion, the spectral singularities of scattering matrix can be investigated in a PT-symmetric two-arm
Aharonov-Bohm interferometer [46]. Such spectral singularities can be tailored to
realise symmetric, asymmetric and unidirectional lasing onsets.
Non-Hermitian resonators are widely used as extremely sensible sensors at exceptional points. The sensitivity can be even more increased for higher-order exceptional
points, at which more than two eigenvalues of a non-Hermitian Hamiltonian coincide. In this case, the frequency splitting stems from a perturbation ε 1 follows the
law ε
1/N , where N is the order of the exceptional point [47]. Since the susceptibility
d(ε
1/N
)/dε diverges at ε = 0, the sensitivity can be arbitrarily high. This idea was
experimentally validated in a PT-symmetric ternary (loss-neutral-gain) micro-ring
system [48] and micro-toroid cavity [49], the non-Hermiticity of the latter being
introduced by a scatterer resulting in coupling eigenmodes of the cavity. Sensitivity of parameter estimation can be analysed using the formalism of quantum Fisher
information without referring to a specific measurement scheme. The average of all
merging eigenstates cancels out the divergence at the singularity resulting to a finite
value at the exceptional point [38].
PT-symmetric [50] and anti-PT-symmetric [51] optical gyroscopes were proposed
on the basis of ring resonators coupled to a waveguide. Frequency splitting and,
hence, sensitivity in gyroscopes are normally limited by the ring dimensions. In PTsymmetric gyroscopes, the frequency splitting is independent of the ring radius and,
therefore, the phase shift of interference fringes is enhanced in vicinity of exceptional
points. A unique “superluminal” lasing may be used as a sensor and can be obtained
in a broken PT-symmetry phase of the white-light cavity that consists of gain and
lossy coupled micro-resonators [52].
Finally, PT-symmetric microcavities possess indispensable nanophotonic properties for suppression of spontaneous relaxation rate [53]. In the next section we will
discuss this subject in detail.