Time-Reversed Optical Parametric Oscillation

Abstract

In recent works, the idea of time-reversed laser oscillation has been proposed and demonstrated to realize a two-channel coherent perfect absorber [Y.D. Chong et al., Phys. Rev. Lett. 105, 053901 (2010); W. Wan et al., Science 331, 889 (2011)]. Here the time reversal of optical parametric oscillation in a nonlinear χ (2) medium is considered and shown to realize a coherent perfect absorber for colored incident signal and idler fields. A detailed analysis is presented for the time-reversed process of mirrorless optical parametric oscillation in the full nonlinear regime.PACS numbers: 42.65. Yj, 42.65.Ky, 42.65.Sf Introduction. Time-reversal symmetry plays an important role in classical electromagnetic theory and nonrelativistic quantum mechanics [1]. Such a symmetry implies that, if a particular physical process is allowed, then there also exists a time-reversed process, which is obtained by changing the sign of the time variable in the dynamical equations. In recent works, the time-reversed process of laser oscillation has been explored, both theoretically [2] and experimentally [3], and shown to realize a coherent perfect absorber (CPA). Under additional symmetry constraints, the processes of lasing and CPA can even occur simultaneously, and a CPA-laser device can be in principle realized [4,5]. Since in a steady-state process time reversal corresponds to interchanging incoming and outgoing fields, the time-reversed process of a laser instability corresponds to perfect absorption of incoming light fields. Such a phenomenon is rather general and expected to occur for the time reversal of other optical instabilities. Among these, optical parametric oscillation (OPO) provides an important example of instability in nonlinear optics, which is at the core of the operation of such important devices as optical parametric oscillators [6][7][8][9]. In a parametric oscillator at the onset of instability, a pump field at frequency ω 3 propagating in a nonlinear χ (2) crystal generates down-converted fields at frequencies ω 1 (the signal field) and ω 2 = ω 3 −ω 1 (the idler field), provided that the phase matching (momentum conservation) condition is satisfied. Generally, at least one of the signal or idler waves resonates in an optical cavity. In the time-reversed process, exactly the opposite occurs: two coherent signal and idler fields, with appropriate amplitude and phase relationship incident onto the pumped nonlinear crystal, are completely annihilated, thus realizing a kind of "colored" CPA device. While a CPA based on time reversal of a laser usually converts the absorbed light into heat [2,3], in the time reversal of OPO the annihilated photons are converted into light of different frequency (the sum-frequency field). Moreover, since the OPO instability and its time-reversal process are allowed in the same medium, an ordinary OPO device can behave at the instability like a CPA-laser device [4,5], i.e. it can simultaneously emit outgoing colored fields and absorb incoming colored fields with appropriate phase re...

Conservation relations and anisotropic transmission resonances in one-dimensionalPT-symmetric photonic heterostructures

“…Interestingly, the S-matrix describing three-wave mixing in the undepleted pump approximation corresponds to the the special case where R L = R R [22,23]. The case T + R = 1 describes frequency conversion by absorption or emission of a pump photon, and T − R = 1 describes parametric amplification of both signal and idler by down conversion of pump photons.…”

Coherent perfect absorbers: linear control of light with light

“…It is unclear whether there can be any useful CPA analog of laser self-organization -it could be perhaps found in the presence of nonlinear absorptive media, as suggested by several theoretical studies [42,43,139,140,152]. Furthermore, interesting variants of the time-reversal concept have been formulated for nonlinear processes such as wave mixing and parametric oscillations [153][154][155]. For instance, the idea of a coherent perfect absorber for waves of different frequencies, acting as the time-reverse of an optical parametric oscillator, was put forward [153].…”

“…Furthermore, interesting variants of the time-reversal concept have been formulated for nonlinear processes such as wave mixing and parametric oscillations [153][154][155]. For instance, the idea of a coherent perfect absorber for waves of different frequencies, acting as the time-reverse of an optical parametric oscillator, was put forward [153].…”

Coherent perfect rotation

“…In its original formulation, this non-Hermitian Hamiltonian included absorption/gain to explicitly break the time reversal invariance of the underlying fundamental processes. This is also the case with the formulation of CPA in PT-invariant theories [3,4], which has led to a fertile way to explore many subtleties in optical processes [5,6].…”

“…In its original formulation, this non-Hermitian Hamiltonian included absorption/gain to explicitly break the time reversal invariance of the underlying fundamental processes. This is also the case with the formulation of CPA in PT-invariant theories [3,4], which has led to a fertile way to explore many subtleties in optical processes [5,6].In this paper we develop theory for Coherent Perfect Rotation (CPR), the conservative transfer of any fixed input polarization state of coherent counterpropagating light fields completely into its orthogonal polarization. CPR highlights the necessity of combining T-odd processes (in, for example, magneto-optics) with optical coherence to achieve this perfect conversion.…”