Research On Synthesizing Bessel Beams On Integrated Photonic Chips And Their Applications

Vortex beam is a novel optical mode with spiral phase around the optical axis,which has a wide range of applications in ultra large capacity optical communication,optical micro manipulation,optical holographic encryption,and quantum information processing.High order Bessel Gaussian beam（BGb）is one of the most commonly used vortex beams,which is very important in super-resolution imaging and three-dimensional imaging.The traditional method of generating BGb has a huge structure and complex system,which seriously limits its application.We use integrated photonics as a platform to design,optimize,and manufacture silicon photonic chips capable of emitting BGb.We have conducted systematic and comprehensive research on the emission of vortex beams on integrated photonic chips,including theoretical models,chip design,experimental testing,and cutting-edge applications.The research content includes:（1）We have established and validated a Conical Wave Model（CWM）suitable for integrated vortex beam emitters.The mathematical description of this model is clear and concise,and it can accurately calculate the vortex light field distribution of high-order and fractional order topological charges,as well as vortex light in various initial polarization states.In the process of establishing the theoretical model of long-distance BGb,Gaussian beams were used instead of the plane waves mentioned above.After one translation transformation and two rotation transformations,the generation model of BGb was established and the conditions for generating long-distance BGb were obtained,namelyθ_G2≥|θ_G1|（The former is the divergent half angle of a Gaussian beam,while the latter is the conical half angle in CWM or the emission angle of a grating in silicon photonics）,this conclusion provides clear theoretical support for the study of BGb propagation length.（2）We developed a silicon photonic chip with a diameter of 870μm for generating long-distance BGb,the area is less than 1 mm².The chip is composed of 64 grating antennas arranged in a circular pattern,and the size of each antenna area is only 30.38μm×40μm.There are 16 parallel waveguides in this area（width×thickness:380 nm×220 nm）,with an interval of 1.62μm between adjacent waveguides.The grating period is 800 nm,the duty cycle is 0.5,and the etching depth is 70 nm.In the working wavelength range of 1500-1630 nm,we measured the intensity of the BGb optical field beyond 10.24 m,which conforms to the contour of the Bessel function distribution.This is the first time in the world that long-distance BGb has been generated on silicon photonic chips.It provides an integrated solution for BGb’s long-distance communication and sensing applications.（3）The velocity of a rotating object was measured using the on-chip generated BGb and based on the rotational Doppler effect.The maximum error is only 0.1 Hz,which is currently the smallest reported absolute error（0.05%）;The high robustness of BGb speed measurement was verified by using cylindrical copper wires with diameters of 1.18 mm and 2 mm to block the experimental spot.This excellent anti-interference ability is expected to be applied in optical communication in complex environments.Based on the principle of laser phase ranging,the distance information of the object was measured,and the maximum error between the measured value and the actual value was 19 mm,with a minimum error of 3 mm.（4）We incorporate the concept of Decentered Gaussian beams into the BGb theoretical model and provide the exact equation for BGb and the optical field expression for fractional order BGb.This equation exhibits simple and fast computational power,which is over a hundred times faster than the rotation matrix method.（5）We designed and fabricated an integrated photonic chip with tunable BGb length.Theoretical calculations show that when the incident wavelengths of the photonic chip are 1500 nm and 1528 nm,the emission angles of the grating antennas are-6°and-11°,respectively.Based on different measurement systems,we measured lengths of only 900μm and 9.56 m for BGb separately.By changing the incident wavelength,the tunable range of BGb can span four orders of magnitude.This type of BGb integrated on the platform of silicon photonics with an ultra-long tunable range is the first reported in the world.In summary,using integrated silicon photonics as a platform,we have conducted systematic research on the theoretical description,on-chip generation,and cutting-edge applications of BGb.In terms of theoretical description,we use plane waves,Gaussian beams,and Decentered Gaussian beams as wavelet coherent superposition to form BGb,and provide corresponding theoretical expressions.In terms of on-chip generation,we carefully designed the size of grating arrays or optical phased arrays,and used the structure of circular chips to generate long-distance BGb and four orders of magnitude of length tunable BGb.In terms of application,we used on-chip generated BGb and measured the velocity and distance information of rotating objects based on the principles of rotational Doppler effect and phase ranging.The above results provide significant reference value for the large-scale and integrated application of BGb.