在超快光學領域中，脈衝的脈衝寬度通常在幾個皮秒(ps)以下，現有的光偵測器無法在時域上直接解析超快脈衝。雙九十度相差光譜剪切干涉法(Dual-quadrature spectral shearing interferometry, DQ-SSI)是藉由三次測量待測脈衝與探測電場(probe electric field)，經非線性和頻轉換(sum-frequency generation)後所得的光譜，來解析脈衝、取得脈衝的頻譜相位(spectral phase)資訊。探測電場本身由一對單頻光源組成。在此論文中，建構探測電場存在相位雜訊(phase noise)時的數學模型，理論推導相位雜訊對和頻光譜所產生的影響。最後，探討當探測電場存在相位雜訊時，影響頻譜相位重建的相位雜訊參數，並討論這些參數對重建頻譜相位所造成的誤差。

The pulse width of a ultrafast optical pulse is usually less than a few picoseconds and the ultrafast optical pulse can not be directly resolved in the time domain by the existing photodetectors. The method of Dual-quadrature spectral shearing interferometry (DQ-SSI) takes the three sum-frequency generation spectra of the pulse train with the probe electric field to recover the spectral phase of the pulse. The probe electric field consists of a pair of single-frequency tones. In the thesis, the mathematical model of the probe electric field with random phase noise has been built up. The sum-frequency generation spectrum in the presence of random phase noise has been theoretically derived. And the key parameters of the random phase noise which affect the reconstruction of spectral phase have been found out. The dependence between the error of the reconstruction of spectral phase and these key parameters has been discussed.

[1]Claude Rullière, “Femtosecond laser pulses：principles and experiments,” chapter 3, Springer, Second Edition.

[2]C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792-794 (1998).

[3]Chris Iaconis and Ian A. Walmsley, “Self-Referencing Spectral Interferometry for Measuring Ultrashort Optical Pulses,” IEEE J. Quantum Electon. 35, 501-509 (1999).

[4]Houxun Miao, Daniel E. Leaird, Carsten Langrock, Martin M. Fejer, and Andrew M. Weiner, “Optical arbitrary waveform characterization via dual-quadrature spectral shearing interferometry,” Opt. Express 17, 3381-3389 (2009).

[5]Hitoshi Tomita and Hajime Nishioka, “Wide-time-range spectral-shearing interferometry,” Opt. Express 17, 14023-14028 (2009).

[6]Jonathan R. Birge, Richard Ell, and Franz X. Kärtner, “Two-dimensional spectral shearing interferometry for few-cycle pulse characterization,” Opt. Lett. 31, 2063-2065 (2006).

[7]Tobias Witting, Dane R. Austin, and Ian A. Walmsley, “Improved ancilla preparation in spectral shearing interferometry for accurate ultrafast pulse characterization,” Opt. Lett. 34, 881-883 (2009).

[8]Haus H A, ”Waves And Fields In Optoelectronics,” Sec. 1.5, Prentice-Hall (1984).

[9]Julius S. Bendat, “Principles and applications of random noise theory,” Wiley (1958).

[10]R. P. Scott, C. Langrock, and B. H. Kolner, “High dynamic range laser amplitude and phase noise measurement techniques,” IEEE J. Sel. Top. Quantum Electron. 7, 641–655 (2001).

[11]C.-B. Huang, Z. Jiang, D. E. Leaird, and A. M. Weiner, “High-rate femtosecond pulse generation via line-by-line processing of a phase-modulated CW laser frequency comb,” Electron. Lett. 42, 1114-1115 (2006).

[12]T. Kobayashi, H. Yao, K. Amano, Y. Fukushima, A. Morimoto, and T. Sueta, “Optical pulse compression using high-frequency electrooptic phase modulation,” IEEE J. Quantum Electron. 24, 382–387 (1988).