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From Classical to Quantum Devices By Nonlinear periodic structures: from classical to quantum devices by Peyman Sarrafi A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Electrical and Computer Engineering University of Toronto c Copyright 2014 by Peyman Sarrafi Abstract Nonlinear periodic structures: from classical to quantum devices Peyman Sarrafi Doctor of Philosophy Graduate Department of Electrical and Computer Engineering University of Toronto 2014 In this thesis, nonlinear periodic structures and their applications in both classical and quantum regime are investigated. New theoretical models are developed, and novel ap- plications of nonlinear periodic structures are proposed and demonstrated. The theoretical studies, both design and simulation, are based on but not limited to InGaAsP material. A new method, namely the time-domain transfer-matrix (TDTM), is presented to simulate optical pulse propagation in layered media with resonant non- linearity. As there were no satisfactory methods in the literature to model this problem, in order to validate and compare with the TDTM method, the standard FDTD method is generalized to include the rate equation in the analysis of semi-conductors. Also in this work, optical manipulation of absorption in periodic structures is studied for the first time. Thanks to the large accessible nonlinearity that results from the absorption saturation and frequency selectivity of periodic structures, a sensitive and compact opti- cal limiter is designed. The novel design and modeling work developed in this thesis has provided new insights and tools to the utilization of resonant nonlinearities in compact all-optical devices. The experimental studies are based on quasi-phase matched AlGaAs superlattice waveguides. These devices have been previously designed and used for classical opti- cal wavelength conversion such as second harmonic generation and difference frequency generation. In this work, these devices are exploited for spontaneous down conversion, ii which is a quantum effect, for the first time, through this process, entangled photon pairs are generated. Unprecedented performance, in terms of brightness and purity, of III-V semiconductor-based entangled photon sources has been demonstrated here. Moreover, the quantum properties of these entangled photons are characterized. The experimental studies presented in this thesis open up new application areas for III-V nonlinear optical devices as quantum sources and convincingly demonstrate the promising role of such devices will play in future quantum technologies. iii Contents Abstract ii Contents iv List of Tables vii List of Figures x 1 Introduction 1 1.1 Nonlinear periodic devices . 2 1.1.1 Periodicity and non-phase matched . 3 1.1.2 Quasi phase matching . 4 1.2 Scope of this thesis . 5 2 Modeling periodic nonlinear structures 7 2.1 Finite-difference time-domain method . 9 2.2 Generalized time domain transfer matrix method . 12 2.2.1 Formulation . 12 2.2.1.1 Pulse Decomposition . 13 2.2.1.2 Time-Domain Transfer-Matrix . 15 2.2.1.3 Updating process . 19 2.2.2 Numerical result and comparison . 21 2.2.2.1 Linear and Nonlinear Responses of a 200fs, 800fs, and 3.2ps Gaussian Pulses . 22 iv 2.2.2.2 Nonlinear Responses of 50fs Incident Pulses . 25 2.2.2.3 Comparison between the two methods of TDTM: FT- TDTM vs. TDOTM. 27 2.3 Conclusion . 28 3 Application of layered structure with resonant nonlinearity in optical limiting 29 3.1 Traditional optical limiting methods . 30 3.1.1 Reverse saturable absorber . 31 3.1.2 Two-photon absorption (TPA) . 31 3.1.3 Free-carrier absorption . 32 3.1.4 Nonlinear refraction . 32 3.1.5 Self-phase modulation (SPM) . 32 3.2 Resonant nonlinearity in InGaAsP . 33 3.3 Non-trivial phase shift in the interface of lossy material . 34 3.4 Compact optical limiter based on resonant optical nonlinearity in a layered semiconductor structure . 38 3.5 Conclusion . 44 4 Low noise on-chip source of correlated photons 45 4.1 Nonlinear optical methods for the generation of entangled photon pairs . 47 4.2 The importance of the low noise PPS . 50 4.3 Low noise entangled photon generation in AlGaAs superlattice Waveguides 51 4.4 Characterization of QPM AlGaAs superlattice waveguides . 53 4.5 Coincidence measurement . 56 4.6 Discussion and conclusion . 59 5 On-chip Time-Energy Entangled photon pair source 62 5.1 Franson Interferometry . 63 5.2 Franson interferometer: meeting constraints and overcoming challenges . 66 5.2.1 Matching the MZIs' imbalance using reference fiber-based MZI . 67 v 5.2.2 MZI characterization: phase-voltage relation . 68 5.2.3 High brightness and detector's dead time limitation . 70 5.3 Time-Energy Entanglement and a measurement of visibility . 73 5.4 Discussion and conclusion . 78 6 Conclusion, contributions and future works 79 6.1 Conclusion and original contributions . 79 6.2 Future work . 81 References 83 vi List of Tables 4.1 Comparison with other AlGaAs based entangled photons sources . 61 vii List of Figures 2.1 A summary of the TDTM and updating process . 14 2.2 decomposition of the incident pulse to small subpulses . 15 2.3 Schematic plot of a spatial section in transfer matrix . 17 2.4 In a layered structure with resonant nonlinear material, each layer corre- sponds to the section illustrated in Fig. 2.3. d represents thickness, N the carrier density, n the refractive index, and α the absorption coefficient. 22 2.5 (a) Intensity linear response and (b) Intensity nonlinear response (Ipeak = 0:21GW=cm2) to a 200fs pulse. Intensities are normalized to the peak incident intensity. 23 2.6 Normalized reflection and transmission intensity of a 800 fs pulse. (a) 2 linear response (b) Nonlinear response, (Ipeak = 0:21GW=cm ) . 24 2.7 Normalized reflection and transmission intensity of a 3:2ps pulse. (Ipeak = 0:21GW=cm2)................................. 25 2.8 Normalized reflection and transmission intensity of a 50fspulse. (a) medium 2 intensity incident pulses (Ipeak = 0:21GW=cm ) (b) High intensity incident 2 pulse (Ipeak = 0:85GW=cm )......................... 26 2.9 Nonlinear response to a 6:4ps pulse. (a) FT-TDTM is compared with TDOTM with 12 order polynomial (b) FT-TDTM is compared with TDOTM with 8 and 6 order polynomials . 27 3.1 A schematic of optical limiter effect . 30 3.2 Absorption as a function of carrier density for In1−xGaxAs1−yPy semicon- ductor . 35 viii 3.3 Refractive index as a function of carrier density for In1−xGaxAs1−yPy semiconductor . 36 3.4 Schematic of incident light from medium 1 reflected from an interface with medium 2 . 36 3.5 The phase of reflection from a lossy medium for different refractive indexes in Fig. 3.4 . 37 3.6 Schematic of the proposed optical limiter consisting of a multilayered In- GaAsP structure (Type I and II alternating) sandwiched between two AR coatings. The periodicity of the InGaAsP is broken at the center, where two layers of Type II are next to each other. The bandgap energies of the Type I and II are designed to be lower and higher than the energy of the incident photons, respectively. 40 3.7 In case of complete absorption saturation a dip appears in the reflection spectrum. The 20dB-bandwidth of this dip is approximately 4nm. 41 3.8 Exponential saturation of the reflected pulse versus incident peak intensity. 43 3.9 Reflected pulse normalized to incident pulse intensity for different incident pulse intensities. 43 4.1 Energy level for SPDC and SFWM process . 49 4.2 The calculated band gaps of AlxGa1−xAs versus x . 52 4.3 A schematic of Quasi-Phase-Matched AlGaAs superlattice waveguides. Blue and pink beams have a wavelength around 775 nm and 1550 nm, respectively. 55 4.4 (a) Simulated TE mode profile at 1550 nm (b) Simulated TM mode profile at 775 nm . 55 4.5 SHG power as a function of fundamental wavelength for a QPM waveguide with width of 2 µm and a QPM periodicity of 3.5 µm. 56 4.6 Schematic of the setup for coincidence measurement in QPM AlGaAs su- perlattice waveguides. Blue lines are light propagating in free space, pink represents fibers . 57 ix 4.7 (a) The typical time-bin histogram for coincidence measurements (b) CAR as a function of coupled pump power. 59 4.8 CAR versus pump detuning. Figure inset: shows the spectral location of the collected pair photons (hatch pattern) . 60 5.1 Model of a Franson interferometric measurement, D1 and D2 are single photon detectors. 64 5.2 Schematic setup for comparing the path difference . 68 5.3 Interference pattern for (a) first MZI and (b) second MZI as a function of delay in reference MZI. 68 5.4 Schematic setup for MZI characterization . 69 5.5 Phase change in interference pattern as a function of voltage V=(0, 1.8, 3, 5, 6, 6.4, 6.5, 7, 7.5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 18.6). Pink solid line shows the pattern for V=0 and as voltage increases, it shifts toward the right. 70 5.6 Phase change as a function of voltage applied to the heater . 71 5.7 A time-bin histogram for a 2µm wavguide with 8 mW pum power. 72 5.8 The time-bin histogram for a 2µm wavguide with 16 mW pum power. 73 5.9 Schematic of the setup for Franson interferometry used to characterize the AlGaAs-waveguide-based photon pair source. 75 o o 5.10 The result of coincidence measurements at (a) φ1 = 270 , φ2 = 180 , and o o (b) φ1 = 90 ,φ2 = 180 . The red bins are used to calculate the coincidences for Fig.
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