石明豐臺灣大學：物理研究所涂銘峰Tu, Ming-FengMing-FengTu2007-11-262018-06-282007-11-262018-06-282005http://ntur.lib.ntu.edu.tw//handle/246246/54507We hope to verify the conservation of orbital angular momentum (OAM) of light under the spontaneous parametric down-conversion (SPDC) process. We use laser(with 355nm-wavelength) to pump a β − BaB2O4 (BBO) crystal. Because of the nonlinear property of the BBO crystal, the degenerate SPDC could happen in the crystal. Therefore, one 355nm photon would converted to two 710nm photons. We make use of the birefringence property of the BBO crystal to achieve beamlike Type II phase-matching. Under this phase-matching, it is efficient to collect the down-converted 710nm light. We plan to make the pump light carry the OAM with l = 0 or l = 1 by means of the hologram. On the other way, we use a new-reported method to measure the OAM of the down-converted 710nm light. And, making use of the coincidence-counting tool, we could verify the conservation of OAM of light. Under the SPDC process, the down-converted 710nm photon pairs are in the entangled state. Therefore, this experiment is related to the OAM of light and the entangled state which the quantum theory predicts. These two subjects are worthy of studying.1 Introduction 1 1.1 measuring OAMof entangled photons . . . . .1 1.2 newmethod for measuring OAMof light . . . 2 1.3 objective of our experiment . . . . . . . .3 2 EPRParadox . . . . . . . . . . . . . . . . . 4 2.1 Einstein’s Locality Principle . . . . . . 4 2.2 Bell’s inequality . . . . . . . . . .. . .5 2.3 QuantumOptics . . . . . . . . . . . . . . .6 3 Spontaneous Parametric Down Conversion . . .7 3.1 Maxwell’s equation . . . . . . . . . . . .8 4 Anisotropic crystal . . . . . . . . . . . . .14 4.1 dielectric tensor . . . . . . . . . . . . .14 4.2 Birefringence . . . . . . . . . . . . . . .15 4.3 Normal surface . . . . . . . . . . . . . . 16 4.4 Index Ellipsoid . . . . . . . . . . . . . .18 4.5 classification . . . . . . . . . . . . . . 18 4.6 light propagation in uniaxial crystals . . 20 4.7 BBO crystal . . . . . . . . . . . . . . . .21 5 Phase Match . . . . . . . . . . . . . . . . .22 5.1 Type I & Type II . . . . . . . . . . . . . 23 5.2 Collinear & Noncollinear . . . . . . . . . 23 5.3 Beamlike Type II . . . . . . . . . . . . . 25 5.4 cutting crystal at appropriate angle . . .27 6 Experiment . . . . . . . . . . . . . . . . . 30 7 Orbital Angular Momentum of Photons . . . . 38 7.1 introduction . . . . . . . . . . . . . . . 38 7.2 Measuring the OAMof a Single Photon . . . 41 7.3 accomplish the device with α = π . . . . . 42 8 Conclusion . . . . . . . . . . . . . . . . .471050723 bytesapplication/pdfen-US軌道角動量光相位匹配參數振動orbital angular momentumlightphase matchingdown conversionthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/54507/1/ntu-94-R92222034-1.pdf