Theory And Applications Of All-optical Temporal Linear Canonical Transformers

Optical analog signal processing based on all-optical temporal linear canonicaltransformers(TLCT)has the advantages of dynamic adjustment,multiple functions,and high speed.Compared with resonant,multi-waveguide coupling and spatial Fourier transform based optical signal processing,TLCT based optical signal processing can avoid problems such as wavelength misalignment,light splitting or coupling error,and space-time coupling error.From the perspective of novel structures,novel functionalities and improvement of cost performance,this thesis addresses the challenges faced by the research of TLCTs and their application systems,and carries out theoretical and simulation research work,in application areas including physical layer encryption for optical communications,repetition rate multiplication of optical pulse sequence,and optical differentiation for optical computing.This thesis is funded by the National Natural Science Foundation of China.The main innovations of the thesis are as follows:(1)The time-frequency matrix,that is,the transform matrix for time-frequency plane of optical analog signal,is proposed as the time domain counterparts of the ray matrix,ABCD matrix or transmission matrix in geometric optics.The time-frequency matrix is employed to simplify the analysis of complexly-cascaded time domain optical systems,including the determination of the macroscopic integral expression of linear systems,and the analysis of the microscopic time-frequency component transformation behavior induced by nonlinear systems.The time-frequency matrices of the narrow-band dispersion element and the parabolic time lens are definded.Thougth matrix multiplications,these two kinds of matrices are used to simplify the derivation process of the integral expression of the ideal TLCT formed by the cascade of multiple narrow-band dispersion elements and the parabolic time lens.Conditions of ideal TLCTs system to be specified as the commonly-used time-domain Fraunhofer transformer(TFh T),time-domain Fresnel transformer(TFr T),frequency to time mapper,time to frequency mapper,time domain imager,time domain fractional Fourier transformer,and time-domain Fourier transformer(TFT),are determined.In addition to element-constant determinant-unit(or canonical)time-frequency matrices,the element-varying and non-canonical time-frequency matrices of time prisms,temporal gratings.time mirrors,and non-ideal or anamorphic TLCTs are also definded,whose transformations on time-frequency components of optical analog signals are analyzed.This achievement provides a solid theoretical foundation for proposing new structures of TLCT,exhausting the functionalities of TLCT,and improving the cost performance of TLCT.(2)According to the similarity between the partially overlapped time-domain intervals with different center positions and the parallel line clusters with overlapped spatial ranges and different directions,the time-domain counterpart of the spatial cylindrical lens,namely the anamorphic time lens(ATL),is proposed.By embedding ATL between two identical dispersive elements,a new type of TLCT system,namely the anamorphic TLCT(ATLCT)system,is proposed,which has high adjustability and scrambling capability,and is suitable for application scenarios of all-optical encryption for optical analog signal.By replacing the TFT in the convectional optical time-domain double random phase encoding(DRPE)and phase truncated DRPE(PT-DRPE)systems with ATLCT,two time-domain optical encryption systems,namely ATLCT-DRPE and ATLCT-PTDRPE are proposed.Compared with TFT,ATLCT does not have analytical and fixed characteristic signals,so that ATLCT-DRPE and ATLCT-PTDRPE systems can effectively resist against chosen plaintext attacks and phase retrieval attacks.The ATL in ATLCT can only be cracked by brute force attacks,and the key space of ATL makes brute force attacks extremely expensive.By simulating the brute-force attacks of illegal users on the ATLCT-DRPE and ATLCT-PTDRPE systems,it is measured that the key space provided by ATL for the two types of optical cryptosystem is at least 2⁹¹⁴and 2¹²⁷⁷ respectively,which is much larger than the lower bound of the key space2¹²⁸ required to resist against brute-force attacks.(3)Combining TLCT with comb-shaped time-domain modulation,a TFT based repetition rate multiplier for phase code sequences and a TFr T based repetition rate multiplier for frequency-swept pulse sequences are respectively proposed to overcome the difficulties faced by conventional all-optical repetition rate multipliers in mantaining local detailed phase features and global chirp features of input optical signals.A phase code sequence has a continuous wave in amplitude and a periodic repetitive phase code(such as Barker code)in phase,which possesses large bandwidth and anti-interception characteristics.If combined with optical heterodyne technology,the proposed repetition rate multiplier for phase code sequences has great application potential in improving the agility and adaptability of continuous wave radars.The proposed repetition rate multiplier for frequency-swept pulse sequences can adjust the time interval and frequency interval of adjacent frequency-swept optical pulses,and has unique application value in the optical-assisted phased array antenna and the 5G wireless communication field.The research result is an in-depth exploration of the potential of TLCT to process phase-coded optical signals.(4)A TLCT based optical differentiator is proposed to extend the narrow adjustment range of conventional all-optical differentiators.The optical differentiator adopts an architecture in which a time-domain power-function modulation mask is embedded between two reciprocal TLCTs,thus has the advantage of real-time adjustable differentiation order.The time-domain power-function modulation mask is implemented by cascading of amplitude modulation and phase modulation,enabling arbitrary integer and fractional differentiation orders.The arbitrarily adjustable all-optical differentiator has unique application value in relay communication,which can improve the flexibility of communication symbol switching,thereby enhancing the adaptability of the communication system to channel quality.The TLCT is embodied as TFh T,which allows the reuse of a unified root linear chirped fiber Bragg grating to realize a reciprocal TLCT,improving the compactness of the optical differentiator.The time-frequency mapping resolution of TFh T is enhanced by cosine instead of parabolic time lens,improving the cost-effectiveness of the optical differentiator.The common problem of optical differentiators,that is,performance degradation of high-order differentiation,is alleviated by the feedback cascade scheme that reuses a low-order optical differentiator.The research result is also an example of strategies to improve the cost-effectiveness of TLCT for time-frequency mapping.