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For standard Fibonacci sequence, the ratio is τ = (1 + √5)/2. The ratios other than τ can be derived from other 1D quasi-periodic subclasses. All possible subclasses have been classified [D. Levine and P. J. Steinhardt, Phys. Rev. B 34, 596 (1986)].
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Some essential simplifications of the theoretical treatment were considered, including the approximation of slowly varying envelope for fundamental, second-, and third-harmonic fields and ignoring depletion of the fundamental and harmonic field.
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3 has short-wavelength transparency from 280 nm [K. Mizuuchi, K. Yamamoto, T. Taniuchi, ibid. 58, 2732 (1991)]. Thus, by a suitable choice of a QPOS, harmonic generation in the UV region is possible.
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1842370694
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note
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We thank D. Feng for stimulating discussions. Supported by a grant for the Key Research Project in Climbing Program from the National Science and Technology Commission of China.
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