本論文研究目標是在控制電場的相位和振幅合成亞週期或任意電場波型。本實驗中基頻及其四個諧波是由窄頻的Nd:YAG雷射為基頻，共線串接的方式且同調產生雷射基頻的二、三、四、五次諧波。根據傅立葉分析，任意的電場波形皆可以分解成不同的諧波，且諧波對應不同頻率具有特定的相位和振幅。 藉由調制諧波的相位及振幅，可以合成任意電場波形．我們使用類似差頻的方式，去量測諧波之間的相位關係，計算基頻與二倍、三倍、四倍及五倍頻之間的相位並加以控制。在六十秒內相位穩定度介於 ±0.0407π，且使用線性交互相關的方式，量測合成的波形。目前我們合成了方波以及鋸齒波,且量測到的實驗結果與理論計算的結果吻合.

ABSTRACT
The objective of the research was to control the electric field of multiple optical waves to synthesize sub-single cycle or arbitrary electric waveforms. In our experiment, harmonics up to the fifth order harmonic are generated in csacade by a narrow-band Nd:YAG laser. Based on principles of the Fourier synthesis, arbitrary light waveforms can be synthesized by multiple harmonics with particular relationship of phase and amplitude. We used a method which is similar to 1f-2f interferometry to measure the relative phase of each harmonic. We successfully measure the relative phase of the fundamental with respect to the second or third or fourth or fifth harmonic and control the phase of the each harmonic to synthesize the desire waveform. The phase stability can reach to ± 0.0407π in sixty seconds. Waveforms of electric field are synthesized and measured by the technique of linear cross-correlation. We have synthesized and measure the Fourier-synthesized square and sawtooth waveforms. The experimental results are in good agreements with the theoretical results.

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