Shortcuts to adiabaticity in optical waveguides

Abstract

In recent years, the concept of shortcuts to adiabaticity (STA), originally developed for speeding up slow adiabatic state evolution in quantum systems, has found numerous applications in guided-wave optics. Optical waveguides, enabled by the advanced fabrication technologies, provide an ideal platform to implement the STA protocols in terms of geometry variations; moreoever, STA has enabled the development of short and robust waveguide components, with applications in beam couplers, beam splitters, mode converters, mode (de)multiplexers, and polarization manipulation devices. Concepts such as counterdiabatic driving, invariant-based inverse engineering, fast-forward approach, or fast quasiadiabatic dynamics, have been shown to provide shortcuts to adiabatic mode evolution in optical waveguides, resulting in compact functional devices with large bandwidth and fabrication tolerance. Novel devices have recently been fabricated following years of theoretical efforts, showing that STA have emerged as a new paradigm in optical waveguides. In this work, we discuss the major STA protocols for applications in optical waveguides and illustrate the shortcuts with device examples.

Shortcuts to adiabaticity in waveguide couplers–theory and implementation

“…Adiabatic processes, first considered by Fock and Born [1], arise in areas of physics and engineering such as atomic physics, quantum mechanics and photonics. Adiabatic processes occur slowly enough that the wave function or field remains in the same Eigenstate or mode throughout the evolution, even when the physical nature of this Eigenstate changes strongly [2][3][4][5][6]. The process may evolve as a function of time, as usually applies in quantum mechanics, or of propagation length, as typically applies in photonics.…”

“…In contrast to these two devices, adiabatic couplers, introduced into photonics by Cook [11], are relatively robust devices that can have a large bandwidth [6,9,[12][13][14][15][16][17][18]. The type of adiabatic coupling device we are considering here is illustrated in Fig 1(c).…”

“…It is therefore not surprising that a number of techniques have been developed that promise to minimize this length, while maintaining performance. Most of these techniques are referred to generically as Shortcuts to Adiabaticity (STA) [3][4][5][6]-developed initially in the context of quantum mechanics, these have been considered for applications in optics since 2009 [19]. In Section 3, we discuss these techniques and clarify their mutual relationships.…”

Connection between Inverse Engineering and Optimal Control in Shortcuts to Adiabaticity

“…The concept of STA was originally proposed to speed up the adiabatic processes in quantum control. Nowadays, STA become versatile toolboxes for controlling the dynamics and transformation in quantum physics [ 1 , 2 ], statistical physics [ 3 , 4 ], integrated optics [ 5 ], and classical physics [ 6 , 7 , 8 , 9 ]. In this context, the most popular STA techniques are the fast-forward scaling [ 10 , 11 ], the counterdiabatic driving [ 12 , 13 ] (or transitionless quantum algorithm [ 14 , 15 , 16 , 17 ]), and the invariant-based inverse engineering [ 18 ], and their variants.…”

Shortcuts to Adiabaticity for Optical Beam Propagation in Nonlinear Gradient Refractive-Index Media

“…More interestingly, there exists freedom left in the method of inverse engineering by only fixing the boundary condition, thus the optimal control theory can be supplemented with perturbation theory to maximize the stability of shortcuts-to-adiabaticity protocols with respect to noise and systematic errors [ 32 , 33 , 34 ]. In this context, the compatible coupled optical waveguides have been designed from STA, and the better tolerances with respect to input wavelength and spacing errors are achieved as well [ 35 , 36 , 37 , 38 , 39 ]. Similar ideas can be applicable to mode converters [ 40 ], polarization rotators [ 41 ] and waveguide junctions [ 42 ] in the applications of optical waveguides.…”