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32 Ωi�PHz� 1.26 1.23 1.2 Φ�Ωs,Ωi� 1.17 1.17 1.2 1.23 1.26 Ωs�PHz� Figure 3.41: Different phasematching functions due to spatial modes in the proposed waveguides
3.3.3 Counterpropagating signal and idler fields Until now we only considered generating decorrelated two-photon-states with strictly copropagating signal and idler fields. In bulk crystal on the other hand, the use of angular phasematching is a common and widespread method. Counterpropagating photon pairs in waveguides have already been proposed in 2002 [23]. In this scenario, the created photon pairs are separated inside the crystal and leave the waveguide at opposing ends (see Figure 3.42). Figure 3.42: Counterpropagation in waveguided parametric downconversion, energy conservation and momentum conservation Describing the impact on the spectral correlations is straightforward. The pump envelope α(ωs, ωi) remains unaltered, whereas in the phasematching function the momentum mismatch is altered (Equation 3.31) as follows: ∆k(ωs, ωi) = kp(ωs + ωi) − ks(ωs)+ki(ωi) − 2πm . (3.57) Λ The momentum vectors of signal and idler are opposite to each other. Thus the crystal has to take a large amount of the pump momentum, hence very small grating periods are needed. Accordingly, the counterpropagation directly affects the decorrelation condition 3.49 which is changed to 2 σ 2 + γL2 (k ′ p − k ′ s)(k ′ p+k ′ i) = 0. (3.58) This simple sign change has an immense effect on the photon creation. Its impact can be understood by considering the impacts on the formula for the phasematching angle, which is now given by: Θ = − arctan � k ′ p − k ′ s k ′ p+k ′ i � . (3.59) In most materials, the denominator will be much larger than the numerator. This results in a phasematching contour oriented along the ωs-coordinate axis, independently from the applied material. In addition, the sign change leads to a narrow shaped contour. 33
Page 1 and 2: Towards a pure heralded single phot
Page 3: ii A.2 id201 programming . . . . .
Page 6 and 7: Chapter 1. Overview 2
Page 8 and 9: experimental data. This thesis is d
Page 10 and 11: a nonlinear, nonmagnetic material,
Page 12 and 13: Figure 3.3: Parametric down convers
Page 14 and 15: For the volume integration, we rest
Page 16 and 17: Figure 3.5: 1D square-wave periodic
Page 18 and 19: and 3.10). Figure 3.9: 0-0 waveguid
Page 20 and 21: By inserting the corresponding term
Page 22 and 23: Λi phasematching Λs Figure 3.18:
Page 24 and 25: pump mode → signal mode + idler m
Page 26 and 27: Hence, we have to ensure a separabl
Page 28 and 29: 3.2.2 Frequency entanglement of two
Page 30 and 31: 3.3 Generating pure heralded single
Page 32 and 33: Material: KTP Polarizations: y →
Page 34 and 35: Material: KTP Polarizations: y →
Page 38 and 39: The first appealing feature of coun
Page 40 and 41: Ωi�PHz� 0.10 0.05 1.22 1.215
Page 42 and 43: 38 Figure 3.53: Different pump freq
Page 45 and 46: 4 Experiment 4.1 Avalanche photodio
Page 47 and 48: kcounts / second 0.14 0.12 0.1 0.08
Page 49 and 50: kcounts per second 180 160 140 120
Page 51 and 52: or z-polarization, and we are left
Page 53 and 54: Gaussian functions. The result is a
Page 55 and 56: that the phasematching point was sh
Page 57 and 58: this two dimension plane on the bla
Page 59 and 60: plotted in Appendix A.4.3. Shg powe
Page 61 and 62: kSHG(762.5nm) 14.5506/ µm kp1(1525
Page 63 and 64: kSHG(762.5nm) 14.2703/ µm kp1(1525
Page 65 and 66: Outlook measurement signal counts/s
Page 67: This is the silliest stuff that eve
Page 70 and 71: �� pdc package Ver: 1.0 Main pa
Page 72 and 73: �� this is a list of all variab
Page 74 and 75: ��refracrtive index of the o�
Page 76 and 77: ��Begin: Sellmeier Equations fo
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4 enhancedSellmeier.m iassert�opt
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6 enhancedSellmeier.m ��extract
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8 enhancedSellmeier.m opte � ToEx
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10 enhancedSellmeier.m ��refrac
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A.2 id201 programming The data acqu
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(EXIM LSQI EGLVMWX 0EFSV MH MH ûMH
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(EXIM LSQI EGLVMWX 0EFSV MH MH û T
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kcounts / second kcounts / second k
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kcounts / second 80 70 60 50 40 30
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kcounts per second kcounts per seco
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E y E y -> E y E y E y -> E z E y E
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BCT0703-B12 second measurement The
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Shg power Pump power [a.u.] Shg pow
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Shg power Pump power [a.u.] 90 80 7
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ITI0706-B124 power measurement The
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Bibliography [1] H. J. Kimble, M. D
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[25] Carlot Canalias and Valdas Pas
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Thanks ❏ To Dr. Christine Silberh
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Erklärung Gemäß §31(2) der Dipl
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Diploma thesis

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