Spatial Characterization Of Two-Photon States - GAP-Optique

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4. OAM transfer in noncollinear configurations The different spatial shapes in figure 4.12 clearly show that the downconversion cone does not posses azimuthal symmetry. As was predicted by the theoretical calculations, the coincidence measurement for α = 90 ◦ , presents a nearly Gaussian shape, while the other cases are highly elliptical. The slight discrepancies between experimental data and theoretical predictions observed might be due to the small (but not negligible) bandwidth of the pump beam, and due to the fact that the resolution of our system is limited by the detection pinhole size. Conclusion The spdc parameters and the detection system determine the portion of the cone that is detected in a noncollinear configuration. This chapter explains how the pump beam waist and the Poynting vector walk-off affect the oam transfer. By tailoring both parameters it is possible to generate photons with specific spatial shapes. The walk-off affects especially those configurations where pairs of photons with different α are used. The next chapter extends the analysis of the spatial correlations to pairs of photons generated in Raman transitions. The chapter describes how the specific characteristics of that source are translated into the two-photon spatial state. 50
CHAPTER 5 <strong>Spatial</strong> correlations in Raman transitions <strong>Two</strong>-photon states can be generated in different nonlinear processes, and in every case the oam transfer will depend on the particular configuration. Raman transition is an alternative method for the generation of two-photon states. Several authors have proven the generation of correlated photons in polarization [59], frequency [60] and oam [23] via Raman transitions. Typical configurations involve the partial detection of the generated photons [61, 62, 63] in quasi-collinear configurations [64]. Just as in the case of spdc, the geometrical conditions determine the oam transfer. This chapter analyses the oam transfer in Raman transitions using the techniques of the previous chapters. This chapter is divided in three sections. Section 5.1 describes the generated two-photon state by introducing its mode function. Section 5.2 studies the oam content of one of the photons with the oam of the other photons fixed. Section 5.3 describes the effect of the geometry of the process on the spatial entanglement between the photons. Numerical calculations show the effect of the geometrical configuration on the oam transfer mechanism. The finite size of the nonlinear medium results in new effects that do not appear in spdc. 51
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DOCTORAL THESIS IN PHOTONICS ICFO B
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Spatial Characterization Of Two-Pho
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Contents Contents vii Acknowledgeme
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Acknowledgements This thesis compil
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Abstract In the same way that elect
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Resumen De la misma manera que la e
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Introduction The role of photons in
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This thesis is based on the followi
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1. General description of two-photo
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CHAPTER 2 Correlations and entangle
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2.1. The purity as a correlation in
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2.2. Correlations between space and
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2.2. Correlations between space and
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2.3. Correlations between signal an
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2.3. Correlations between signal an
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Signal purity 1 0 (a) 0.1 3 2.3. Co
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CHAPTER 3 Spatial correlations and
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3.2. OAM transfer in general SPDC c
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3.2. OAM transfer in general SPDC c
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Phase front 3.3. OAM transfer in co
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4. OAM transfer in noncollinear con
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5. Spatial correlations in Raman tr
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CHAPTER 6 Summary This thesis chara
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APPENDIX A The matrix form of the m
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v =γ 2 L 2 Np sin ϕi − γ 2 L 2
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The matrix C is given by C = 1 ⎛
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B. Integrals of the matrix mode fun
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C. Methods for OAM measurements Inp
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Bibliography [13] M. Barbieri, C. C
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Bibliography [41] C. I. Osorio, A.
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Bibliography [68] S. Chen, Y.-A. Ch
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Spatial Characterization Of Two-Pho
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A Luz Stella y Luis Alfonso, mis pa
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Contents B Integrals of the matrix
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When he [Kepler] found that his lon
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Abstract The matrix notation, intro
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Abstract La notación matricial int
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Introduction the transfer of oam fr
Page 121 and 122: CHAPTER 1 General description of Tw
Page 123 and 124: y y x z z pump s i (a) signal idle
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Page 129 and 130: x Wave fronts 1.3. Approximations a
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Page 142 and 143: 2. Correlations and entanglement Fi
Page 144 and 145: 2. Correlations and entanglement q
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Page 184 and 185: A. The matrix form of the mode func
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Page 189 and 190: APPENDIX B Integrals of the matrix
Page 191 and 192: APPENDIX C Methods for OAM measurem
Page 193 and 194: Bibliography [1] M. A. Nielsen and
Page 195 and 196: Bibliography [27] J. P. Torres, A.
Page 197 and 198: Bibliography [55] M. C. Booth, M. A
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Spatial Characterization Of Two-Photon States - GAP-Optique

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