Coherent perfect rotation

Abstract

Two classes of conservative, linear, optical rotary effects (optical activity and Faraday rotation) are distinguished by their behavior under time reversal. In analogy with coherent perfect absorption, where counterpropagating light fields are controllably converted into other degrees of freedom, we show that only time-odd (Faraday) rotation is capable of coherent perfect rotation in a linear and conservative medium, by which we mean the complete transfer of counterpropagating coherent light fields into their orthogonal polarization. This highlights the necessity of time reversal odd processes (not just absorption) and coherence in perfect mode conversion and may inform device design.PACS numbers: 42.25. Bs, 78.20.Ls, 42.25.Hz Coherent Perfect Absorption (CPA) [1,2] illuminates the role optical coherence plays in the perfect conversion of optical energy into other modes (typically incoherent fluorescence or heat). CPA is a non-conservative linear process, typically modeled using a non-Hermitian Hamiltonian. 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. By contrast T-even conservative processes cannot effect such a transformation. CPR denotes a conservative (thus fully Hermitian Hamiltonian) process that first appears at a particular "threshold" value of the parameter scaling the Todd process, and there are many phenomenological correspondences between CPA and CPR, illustrated schematically in Fig. 1. Beyond revealing a connection between T-odd processes, Hermiticity, and CPA, CPR may inform the design of novel magneto-optical sensors and devices.We adopt a 4 × 4 transfer matrix approach to describe linear optical transport of a monochromatic ray moving back and forth along theẑ-axis,where the M 's, B and C are 2 × 2 (in general complex) matrices; here we are working in the basis where the local field (complex) amplitudes are v = (E x , H y , E y , −H x ). Note that for birefringent materials M = M ′ , but since we are interested in systems that transform any input polarization into the orthogonal polarization, we will focritical coupling Λ, α 1. CPA and CPR are distinct from critical coupling and critical rotation [7][8][9]. For a fixed value of Λ, the system's length in terms of the vacuum wavelength, critical coupling and CPA occur at a particular value of the absorption α and index. Critical half-wave rotation and CPR first occur at "threshold" value...

Structure and symmetry in coherent perfect polarization rotation

“…Analytically for a slab dielectric Faraday rotator the M and C parts of the M in our field basis are [1,30] C ,+ C 2…”

“…In the original derivation of the CPR effect [1] in a simple slab dielectric, increasing the index of refraction of the material reduces the CPR threshold, as shown graphically in Fig. 8 using the formula in Ref.…”

“…C oherent perfect polarization rotation (CPR) [1] is a conservative, reversible exam ple o f a m ultiport, m axim ally efficient, optical m ode conversion process. As such, it shares phenom enological correspondences w ith the coherent perfect absorber (CPA, also called the antilaser) [2,3], w hich has been w ell studied [4][5][6][7].…”

“…The required field is significantly below that o f a single port rotator, however. For one example, the com plete conversion o f one polarization into its orthogonal polarization using an uncoated terbium gallium garnet slab requires only 60% o f the field-length product needed for the sam e rotation in ju st the transm itted light [1], A chieving com plete polarization conversion at a low er field-length product is technologically useful because it is precisely the seem ing "incom pressibility" o f this product and the m odest Verdet coefficients o f com m ercially available optical m aterials that pose a m ajor obstacle to the diffusion o f single-port designs into integrated optical assem blies and low -cost devices. The prim ary motivation for the w ork reported here is to quantify in typical one-dim ensional optical geom etries how C PR-based optical design significantly lowers the field-length product.…”

Dynamic Control of the Extraordinary Optical Scattering in Semicontinuous 2D Metamaterials

“…[ 5 ] Besides, the polarization states could also be coherently controlled as demonstrated in previous work, and the effi ciency could reach near 100% with frequency-independent property. [ 24,25 ] Very recently, spatial mode multiplexing by coherent control method is also reported. [ 26 ] Furthermore, the coherent control method provides a viable alternative for the signal processing based on nonlinear materials.…”