Quantum Gravity Simulations And Photon Tunneling Effect In Transformation Optical Waveguides

In recent years,two shocking events have occurred in the research field of astronomy and physics: In 2015,“LIGO” gravitational wave detector successfully detected gravitational waves for the first time,and Rainer Weiss,Barry C.Barish and Kip S.Thorne won the 2017 Nobel Prize in physics for their pioneering work in gravitational wave detection.In 2019,horizon telescope successfully took the first picture of a black hole.The achievement of these two milestones marks the great success of Einstein's theory of general relativity,as well as the great breakthrough in the study of gravity and general relativity in recent years.At present,however,astronomical observation and experiments are limited to the classical effects of gravity,and the research on the quantum effects of gravity still lacks effective experimental techniques and measurement methods.Transformation optics has become an important method and means to study and simulate the effects of general relativity by establishing the effective correspondence between curved spacetime and the electromagnetic parameters of materials.In the past decade,the method of transformation optics has developed rapidly in the simulation of gravity and achieved a series of gratifying results,such as: simulation of black holes,wormholes,Einstein rings,the big bang and so on.However,these studies are basically limited to the consideration and simulation of the classical properties of gravity and do not involve the quantum effects of gravity.Though there is no self-consistent,fullfledged quantum gravity theory to reveal the nature of gravity and solve the problem of quantization of gravity so far,but the curved spacetime quantum field theory under semiclassical approximation has been successfully revealed to us a lot of novel and interesting quantum gravity effects,such as: Unruh effect,particles production in expanding universe,gravity Schwinger effect,etc.,and the most notably is Hawking radiation effect of black holes.Theoretical physicists have long predicted that there would be a wealth of quantum gravity effects near the event horizon of a black hole with a strong gravity.This is something that has rarely covered by many previous researches of analogue black holes.Therefore,the innovation point of this paper is to study the gravitational quantum effect of black holes by using precise and controllable experimental platform of transformation optical system.The specific research idea is as follows: using transformation optical structures such as spacetime embedding diagram curved waveguide and Silicon nanobeam photonic crystal with gradient period to study and mimic the formation and the photon tunneling effect(Hawking radiation)of the event horizon of the black hole in optical simulation and experiment.The main contents of this thesis include the following aspects:1.We use spacetime embedding diagram and the corresponding projected index to simulate the whole process of gravitational collapse of the star and the formation of the horizon from geometrical optics and wave optics aspects respectively.Then we observed photons tunneling effect near the horizon from the simulation calculation.Further theoretical analysis shows that the effect is essentially related to the Hawking radiation of the black hole.The advantage of this system lies in that it can use the infinite curvature on the surface to construct the infinite equivalent refractive index which cannot be realized in the traditional metamaterial system.Besides,the current mature 3D printing technology makes the embedding diagram curved waveguide have the advantages of high precision and short period in fabrication.It is highly feasible in the simulation of complex cosmological effects.2.Based on the tunneling probability interpretation of Hawking radiation,we believe that the core of the simulation of Hawking radiation is to construct the group velocity distribution increasing linearly from 0 in the system.Then we adjust the dispersion by changing the periodic parameters of the silicon-based nanobeam photonic crystal,and obtain the needed gradient periodic nanobeam waveguide.By further simulation,we obtained the Hawking radiation spectrum which satisfying the blackbody radiation law for the first time and we obtain the effective Hawking temperature that strictly conforms to the Hawking temperature formula for the first time.3.We construct defect microcavity by introducing point defect into the siliconbased nanobeam structure and analyze the coupling properties of the microcavity based on the photon tunneling effect of the microcavity and the coupled mode theory(CMT).Then we extend to a one-dimensional SSH defect microcavity array and analyze the topological properties of the band with COMSOL and CMT respectively.The topological boundary states were verified in simulation and experiment by using the structure's reflection property.Finally,we propose a model to simulate the onedimensional gravity field by micro-cavity array with gradual coupling coefficient and carry out the preliminary simulation analysis.