The second harmonic generation (SHG) process is investigated theoretically using the quantum mechanics method of coherent control. Based on the extremum conditions for the SHG intensity at the center frequency, a Fresnel-inspired binary phase shaping scheme is proposed for tailoring the fundamental pulse. The SHG spectrum can be compressed into a narrowband signal with lower background by modulating the relative phases between the frequency components within the fundamental pulse, inducing constructive interference at the center frequency and destructive interference elsewhere. Multipeak second harmonic signals can also be obtained by properly modulating various interference pathways. These results have potential applications in high resolution nonlinear spectroscopy, microscopy, and information coding.
The second harmonic generation (SHG) process is investigated theoretically using the quantum mechanics method of coherent control. Based on the extremum conditions for the SHG intensity at the center frequency, a Fresnel-inspired binary phase shaping scheme is proposed for tailoring the fundamental pulse. The SHG spectrum can be compressed into a narrowband signal with lower background by modulating the relative phases between the frequency components within the fundamental pulse, inducing constructive interference at the center frequency and destructive interference elsewhere. Multipeak second harmonic signals can also be obtained by properly modulating various interference pathways. These results have potential applications in high resolution nonlinear spectroscopy, microscopy, and information coding.
Chirped biphotons generated via spontaneous parametric down-conversion in chirped quasi-phase-matched nonlinear crystals have ultrabroadband frequency spectra, while their correlation times are not ultranarrow, due to the nonlinear frequency dependence of the phase factor. Based on the idea of Fresnel zone lenses, we propose a Fresnel-inspired binary phase-shaping scheme for tailoring broadband biphoton spectra. By applying binary phase masks to the biphoton spectrum, a Fresnel zone lens was produced in the frequency domain, compressing the broadband temporal wave packets of the chirped biphotons to the Fourier-transform limit due to the effective removal of the quadratic phase. Furthermore, biphoton correlation trains can also be generated by properly shaping the biphoton spectrum with this scheme. This provides a method for biphoton compression and shaping, which avoids the length dependence and the impact of higher-order dispersion in a dispersive medium by using the phase compensation method. Our results could prove useful in quantum metrology, lithography, and coding of entangled photons.
We theoretically investigate the nonresonant two-photon absorption (TPA) process in a two-level atom induced by a weak chirped pulse in the frequency domain. According to the extremum condition of the two-photon transition probability (TPTP) at the transition center frequency, we propose a Fresnel-inspired pulse tailoring scheme for TPA that is significantly different from that of Broers et al. [Phys. Rev. A46, 2749 (1992)]. Using this scheme, the TPTP can be focused or eliminated completely by constructively or destructively modulating various pathways of the quantum interference. Our results are a significant improvement on those obtained by Broers et al. and will have potential applications in selective two-photon microscopy and spectroscopy.
We demonstrate a novel all-optical scheme for measuring the correlation of spectrally phase-coded ultrashort optical waveforms that uses second-harmonic generation (SHG) in long, periodically poled lithium niobate crystals. The SHG yield can be controlled over a range of ~30 dB, depending on the correlation of the applied phase codes. Such a spectral phase correlator has applications for ultrashort-pulse optical code-division multiple-access networking and could serve as a nonlinear optical but classical analog for certain schemes for coherent quantum control of multiphoton processes.
We calculate the spectrum of second-harmonic generation (SHG) for multimode input fields. We show that SHG cannot be described as the degenerate limit of sum-frequency generation (SFG) for multimode fields, because the dynamical equations describing SFG do not properly account for this degeneracy. We consider SHG for amplitude-modulated as well as frequency-modulated fundamental fields. The bandwidth of the second harmonic generated from an amplitude-modulated fundamental field depends on the fundamental input intensity and the conversion strength of the nonlinear medium. Additional frequencies that are not contained in the set of frequencies ${\mathrm{\ensuremath{\omega}}}_{1\mathit{i}}$+${\mathrm{\ensuremath{\omega}}}_{1\mathit{j}}$ will be created at intermediate conversion strengths. However, the growth of the spectral bandwidth is much less pronounced than in SFG. For very high conversion, the spectrum of the second harmonic narrows with increased conversion strength. For frequency-modulated input fields, the second-harmonic spectrum is independent of both the fundamental input intensity and the conversion strength.
Chirped biphotons generated via spontaneous parametric down-conversion in chirped quasi-phase-matched nonlinear crystals have ultrabroadband frequency spectra. However, the presence of quadratic frequency phase factor restricts their applications in quantum metrology and quantum lithography due to simultaneously lengthening the correlation times of biphotons. The key point to improve the temporal correlation of chirped biphotons is how to compensate for or remove the quadratic frequency phase factor. Phase compensation methods have been demonstrated to solve this problem in earlier reports. But the compressed efficiencies of these methods are strongly dependent on the length of the utilized dispersive medium and decreased by the higher-order dispersion of the dispersive medium. In this paper, based on the phase transform of a lens for a light field in spatial domain, we theoretically propose a method of the equivalent removal of the quadratic phase by realizing a Fresnel-zone lens-like modulation on the biphotons spectrum in frequency domain, thereby compressing the correlation time of chirped biphotons to the Fourier-transform limited width. By analogy to the idea of Fresnel wave zone plate, this lens-like modulation can be realized by dividing the biphoton spectrum into Fresnel frequency zones and applying only binary spectral phase (0, ) sequentially to these zones. The theoretical results show that the correlation time width of chirped biphotons can be reduced, and the correlation signal intensity can be increased compared with the original one, by a factor about 100 and 30, respectively. The physical reason is that these Fresnel frequency zones under binary spectral phase modulation will lead to constructive interference at zero delay and destructive interference elsewhere. This method can significantly enhance biphoton time correlation without biphoton signal loss and avoids the limitations of phase compensation methods. Therefore, we can obtain biphotons with both ultra-broad bandwidth and ultra-short correlation times by using our proposed method. The attainable compression efficiency is constrained by the division resolution of the Fresnel frequency zones and the precision of applied binary phase modulations. It should be noted that a constraint condition about crystal length, chirp parameter and the number of frequency zones is summarized in designing the experimental parameters for the desired compression goal. Since binary spectral phase and 0 are easy to obtain and calibrate in practice, we thus believe that our proposed method is feasible to implement experimentally. Moreover, the proposed method can also be generalized to other fields relating to the quadratic phase factor, such as two-photon absorption, second-harmonic generation and chirped pulse compression.
This thesis is about coherent control on disordered samples. Coherent control is the steering of processes with light of different frequencies. The relative phases between the frequencies determines in which di- rection the process is steered. When many frequencies are used, the light composes a short pulse. Changing the relative phases of the fre- quencies changes the shape of this pulse. We used such shaped pulses to guide processes on our samples. Pulse shaping and the different disordered samples are introduced in chapter 1, after which chapter 2 proceeds with the experimental details behind our studies. To perform a measurement with a shaped pulse, a nonlinear pro- cess is required. Second-harmonic generation (SHG) is one of the most straightforward nonlinear processes and plays an important role in this thesis. In chapter 3 theory of SHG is developed. Specifically, we deter- mine how to calculate the SHG intensity from shaped pulses on sam- ples with a resonance near the frequency of the illuminating light. We show that two mechanisms that broaden the line width of a resonance can not be distinguished by measuring the SHG signal. In the absence of resonances the maximum SHG intensity is produced by a transform- limited pulse. This pulse shape is required for many nonlinear optical spectroscopies and maximizing the SHG intensity is a useful method to obtain it. For such optimizations, algorithms are used that tune the coefficients for basis functions of the spectral phase. We looked at the fitness landscape of the SHG when a common basis set is used and by inspecting projections of the landscapewe constructed a more efficient basis set, that will make optimizations of SHG more efficient. In chapter 4 we describe simulations of the electric field in a ran- dom electrical network. The electrical network serves as a model for a film of randomly positioned gold islands, which we studied as re- ported in chapter 5. The simulations show that a metal density close to the percolation threshold results in a structure that has favourable properties for selective local excitation of the surface. In chapter 5 we proceed with this experiment on a random gold structure. The structure was coated with a layer of quantum dots. We imaged the fluorescence from this layer with a microscope and in this way were able to detect the local field intensities on the surface. We found that some control on the field intensity is possible, but the effect is minimal compared to the results of the simulations. The reason for this discrepancy is in the radiative damping of the oscillations, which was not included in the simulation. The radiative damping of plas- mons causes dephasing within �20 fs, making control with shaped pulses difficult. We further studied SHG from arrays of sub-wavelength holes in a gold film. The results of this study are presented in chapter 6. The amount of disorder in the positions of the holes in the arrays was var- ied. We found that the the SHG is produced in a resonance with a long lifetime of 55 fs. This lifetime is longer than most plasmonic resonances and shows that the effect of radiative damping is decreased on this structure. Furthermore, the SHG from all the structures has the same features. The disorder does not influence the SHG and the same reso- nance was found on all structures. Thus, it is likely that the resonance is a property of a single hole. Finally, we studied the coherent control of a dye in solution. Here the disorder is not in the structure, but in the transition frequency of the dye. Due to the interaction of the dye with the solvent, this fre- quency is constantly changing. These changes cause coherence to be lost in the system in a short time. We ran a closed-loop optimization to maximize the stimulated emission from the dye. All the pulse shapes tried in the optimization were saved and subsequently tried with the dye dissolved in other solvents. We found that the yield of the opti- mization varied greatly with the used solvent. These results formed a trend with the viscosity of the particular solvents. The viscosity can be related directly to the dephasing time, the time in which coherence is lost in the system. The trend of the optimization yield versus the vis- cosity shows directly that the fluctuations of the solvent are limiting the coherent control of the dye.