# Retrospective Spectrum-Conversion Method Based on Time-Modulated Van Atta Array
## 1 Introduction  
Spectrum conversion is usually observed in natural materials interacting with electromagnetic (EM) waves from microwave to optical frequencies as a typical electromagnetic non-linear phenomenon. Such phenomena are generally associated with dielectric polarization responding in a non-linear way to the incident field intensity, causing the radiated field to oscillate at a new frequency. These spectrum-conversion phenomena has offered a diverse range of applications from communication to sensing [1, 2, 3, 4, 5, 6, 7, 8, 9]. In recent years, many experts have gradually begun to conduct in-depth and systematic research on the spectrum-conversion phenomenon. As a reported method, phase-switched surface (PSS) [10, 11] imposes phase modulation onto the radar reflected-signal through intermittent on-off control of the active impedance layer. As a result, EM wave energy is redistributed into the generated harmonics with none remaining at the original incident carrier frequency. These harmonics are located outside the passband of the radar receiver, which is widely applied in the radar stealth [12, 13]. [PERSON] [14] proposed a self-adaptive retro-reflective planar Doppler cloak composed of a pair of space-time-modulated metasurfaces, which can perform frequency conversion. The first metasurfacefocuses the incident field in a specific location on the second metasurface, which is designed for enabling retro-reflection and Doppler frequency shift compensation. Adaptive Doppler stealth can improve the undetectability of invisible moving objects. [PERSON] places the generated harmonics in the receiver passband and studies its radar matched filtering characteristics [15]. In addition, a time-modulated method based active frequency selective surface (AFSS) absorber/reflector [16; 17; 18] is proposed to modulate the radar signal [19; 20; 21; 22; 23]. The digital-coding control network is utilized to realize the predefined modulating function for spectrum conversion. On this basis, the imaging properties of the generated harmonic based on time-modulated AFSS are further investigated. The phenomenon of distance transformation and image defocusing are successively discovered [24; 25]. However, the above method can only achieve EM wave modulation in the vertical direction due to the limitation of the mirror reflection mechanism. When the incident EM wave is at oblique incidence directions, the spectrum-conversion modulation effect will be significantly reduced. In terms of harmonic modulation in wide-angle domain, researchers have proposed many feasible solutions. [PERSON] introduces a time-modulated reflector array (TMRA) to realize spectrum conversion in different angles. The structure can control the radiation pattern at both central and harmonic frequencies through multiple PIN diodes integrated into the array elements [26]. [PERSON] [27] reports an acoustic planar retroreflector capable of effectively reflecting sound along its incident direction for a wide operating angle range (0\(-\)70\({}^{\circ}\)). Both the simulated and measured results provide evidence of the sound retroreflection effect. [PERSON] [28] proposes a wide-angle flat corner reflector based on the multiple phase gradient modulated metasurface. Through designing the related gradient phase, the propagation direction of the reflected electromagnetic wave is just opposite to the propagation of the incidence wave based on the generalized version of the reflection law. This guaranteed a radar cross section (RCS) enhancement in the vicinity of this incidence direction. [PERSON] has performed extensive research on information metamaterials and metasurfaces [29]. A general space-time-modulated digital coding metasurface theory is proposed to achieve EM wave modulation in both frequency and space domains [30]. Each unit or column of units in the structure shares a bias voltage to obtain more precise control for propagation direction and harmonic energy distribution simultaneously.