Abstract
The structure of the sunflower head can be used to realize broadband applications in optics. However, this 2D structure, with a ring-shaped reciprocal space, only has a normalized Fourier coefficient peak around 0.033, which leads to a relatively low conversion efficiency and may restrict its applications. We tried to maintain its broadband features while with larger Fourier coefficients by structure dimension reduction. We obtained an aperiodic 1D structure from a 2D Vogel sunflower spiral array by a cut-and-projection method. Workable reciprocal vector bands were found with this 1D structure in the vicinity of a pre-set central wavelength λ0 = 1.4 µm, and its peak Fourier coefficients can be 5–7 times as large as the original 2D structure. With this, we investigated broadband quasi-phase matching (QPM) second harmonic generation (SHG) in samples with different reversed ratios D. To illustrate in more detail, three samples were closely examined with D = 0.4, 0.5, and 0.6. Bandwidths of these three samples for first-order QPM SHG are 90, 70, and 30 nm, respectively, with a fundamental wave in the vicinity of λ0 = 1.4 µm. The exact SHG solution of coupled-wave equations was used in the evaluation of conversion efficiencies. Calculations showed broadband high conversion efficiency.
Highlights
The sunflower head, a natural beauty, amazes its appreciators and scientists
We numerically analyzed the Fourier space of this structure, and the results show that this projection structure can achieve effective second harmonic generation (SHG) in the band of 1.32–1.42 μm with parameter adjustments
Former studies25–27 of similar projections have linked 2D structures to once-pioneering Fibonacci and some other general aperiodic quasi-phase matching (QPM) structures,28,29 the studied 2D prototypes are generally periodic and provide their 1D projected substructure a rather discrete distribution of reciprocal lattice vectors (RLVs), and the peak Fourier coefficient hardly doubled after the projection procedure
Summary
The sunflower head, a natural beauty, amazes its appreciators and scientists. The spiral geometry it holds is a common mathematical model in physical systems and plays an important role in morphological studies of plants and animals. Similar spiral geometry structures have found favor among academics, such as the phyllotaxis of spiral aloe and nautilus shell’s logarithmic growth spiral. These spiral structures are usually aperiodic with a potential of multi-wavelength or broadband applications. The sunflower head, a natural beauty, amazes its appreciators and scientists The spiral geometry it holds is a common mathematical model in physical systems and plays an important role in morphological studies of plants and animals.. Similar spiral geometry structures have found favor among academics, such as the phyllotaxis of spiral aloe and nautilus shell’s logarithmic growth spiral.2,3 These spiral structures are usually aperiodic with a potential of multi-wavelength or broadband applications. Structures and random QPM structures can be of potential broadband frequency conversion with either singular continuous RLVs or smaller Fourier coefficients. We use a projection method to produce 1D structures from VSSA with continuous RLVs, which may serve as an alternative for 1D broadband structures, such as random or chirped domains. The projected 1D structure fully utilizes the broadband characteristic of the 2D VSSA structure, but successfully lessens diffraction and deflection of SHG from its 2D progenitor as the fundamental wave (FW) propagates along its 1D RLVs, such as the nonlinear Raman–Nath diffraction or the QPM conical SHG. We numerically analyzed the Fourier space of this structure, and the results show that this projection structure can achieve effective SHG in the band of 1.32–1.42 μm with parameter adjustments
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