這本論文主要是研究垂直共振腔面射型雷射中的慢光效應，慢光效應可以應用在光通訊上，可以作為一個光學緩衝器，同時對於光資訊的儲存及處理也有很大的幫助。
慢光效應可以使用各種不同的物理機制，包括電磁波導致透明(Electromagnetically induced transparency) 同調居量振盪(Coherent population oscillations)，拉曼散射，布里淵散射等等，而在這本文中我們使用的是同調居量振盪這個物理機制，這個機制的優點是可以在室溫的條件下發產生慢光效應，而且也可以使用半導體的材料，所以在本論文中我們是在一種面射型的半導體雷射中觀察慢光效應。
同調居量振盪是在一個2能階的系統中有兩道輸入的光束，一個是能量較強的驅動光束(pump beam)，另一個是頻率有些微不同的探測光束(probe beam)，當兩個光源都處在系統共振頻率的時候，會有隨時間改變的干涉現象產生，此時折射率頻譜會同時產生一個正常色散，因此我們就可以觀察到慢光效應在這裡出現。
我們所使用的理論模型，是根據載子的速率方程式，去尋找物質中由載子所引起極化率變化所對應到折射率的改變，以及同時考慮到面射型雷射的特性，加入共振腔效應在我們的分析模型中。用適當而且合理的物理參數，我們可以模擬出接近實驗的數據。

In this thesis, we study slow light in vertical cavity surface emitting laser. The slow light can apply in the optical communication, optical memories and signal processing.
Various mechanisms have been used to achieve slow light. These include electromagnetically induced transparency, coherent population oscillations, Raman scattering, Brillouin scattering. In this thesis, we focus on coherent population oscillations. The process of coherent population oscillations leads to very slow propagation of light pulses and this can occur in room temperature solids.
When a strong pump beam and a probe beam of slightly different frequencies interact in a material, the population of excited state will oscillate in time at beat frequency. Significant population beating occurs due to the time dependent interference between the optical fields of the pump and probe beams. It leads to a reduction of the absorption, which shows a coherent spectra hole in absorption spectrum. According to Kramers-Kronig relation, an absorption dip leads to a variation of refractive index spectrum with a positive slope in the same frequency range. Slow light occur here.
Based on the two-wave model and carrier rate equation, we analyze the slow light effect in semiconductor optical amplifiers. The dependences of pumping power, injection current and wavelength detuning for group delays are evaluated. At the same time, we also considered the feature of surface emitting laser to join cavity effect in the theory. We can fit experimental data with reasonable parameters by this model.

Chapter 1
[1]R. W. Boyd and D. J. Gauthier, "Slow" and "Fast" Light," in Progress in Optics, 43, E. E. Wolf, ed., (Amsterdam: Elsevier, 2002), pp. 497-530.
[2]C. J. Chang-Hasnain and S. L. Chuang, " Slow and Fast Light in Semiconductor Quantum-Well and Quantum-Dot Devices," J. Lightwave Technol. 24, 4642-4654 (2006)
[3]M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, "Superluminal and Slow-light propagation in a room temperature solid," Science 301, 200-202 (2003).
[4]陳泳帆, 博士論文 “應用慢光效應對光資訊的儲存和操控” 清華大學物理系 (2005)
[5]管培辰 , 碩士論文 “塞曼簡併態對慢光及光儲存之影響” 清華大學物理系 (2006)
[6]蔡文凱 , 碩士論文 “量子點面射型雷射高頻特性之研究” 交大顯示科技所(2005)

Chapter 2
[1]B.Saleh “fundamentals of photonics” ch5 (1992)
[2]G. P. Agrawal, “Population pulsations and nondegenerate four-ware mixing in semiconductor lasers and amplifiers,” J. Opt. Soc. Am. B 5, 147 (1988).
[3]S. W. Chang and S. L. Chuang, "Slow light based on population oscillation in quantum dots with inhomogeneous broadening," Phys. Rev. B 72, art. 235330 (2005).
[4]N.Laurand, S.Calvez and M.Dawson “Slow-light in a vertical-cavity semiconductor optical amplifier” 24 July 2006 / Vol. 14, No. 15 / OPTICS EXPRESS 6858
[5]H. Su, and S. L. Chuang, "Room temperature slow and fast light in quantum-dot semiconductor optical amplifiers," Applied Physics Letters 88, Art. No. 061102 (2006).
[6]M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, "Superluminal and Slow-light propagation in a roomtemperature solid," Science 301, 200-202 (2003).
[7]X. Zhao, P. Palinginis, B. Pesala, C. J. Chang-Hasnain, and P. Hemmer, "Tunable ultraslow light in vertical-cavity surface-emitting laser amplifier," Opt. Express 13, 7899-7904 (2005).
[8]T.E. Sale “Vertical Cavity Surface Emitting Lasers” (1995)
[9]T.Suhara “Semiconductor laser fundamentals” (2004)
[10]P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S. W. Chang and S. L. Chuang, “Slow light in semiconductor quantum wells,” Optics Lett. 29, 2291-2293 (2004).
[11]H. Su, P. Kondratko, and S. L. Chuang, "Variable optical delay using population oscillation and four-wave mixing in semiconductor optical amplifiers," Opt. Express 14, 4800-4807 (2006).
[12]E. S. Björlin, B. Riou, P. Abraham, J. Piprek, Y.-J. Chiu, K. A. Black,A. Keating, and J. E. Bowers, “Long wavelength vertical-cavity semiconductor optical amplifiers,” IEEE J. Quantum Electron., vol. 37, no.2, pp. 274–281, Feb. 2001.
[13]R. Lewen, K. Streubel, A. Karlsson, and S. Rapp, “Experimental demonstration of a multifunctional long-wavelength vertical-cavity laser amplifier-detector,” IEEE Photon. Technol. Lett., vol. 10, no. 8,pp. 1067–1069, Aug. 1998.
[14]P. Royo, R. Koda, and L. A. Coldren, “Vertical cavity semiconductor optical amplifiers: Comparison of Fabry-Perot and rate equation approaches,”IEEE J. Quantum Electron., vol. 38, no. 3, pp. 279–284,Mar. 2002.

Chapter 3
[1]G. P. Agrawal, “Population pulsations and nondegenerate four-ware mixing in semiconductor lasers and amplifiers,” J. Opt. Soc. Am. B 5, 147 (1988).
[2]Takahashi, T.; Arakawa, Y “Theoretical analysis of nonlinear gain effects in InGaAsP/InP quantum well lasers” Semiconductor Laser Conference, 1990

Chapter 4
[1]P. C. Peng et al., “Tunable slow light device using quantum dot semiconductor laser,” 42,33 Electron. Lett. (2006).

[2]Y. H. Chang, P. C. Peng, W. K. Tsai, G. Lin, F. I. Lai, R. S. Hsiao, H. P. Yang, H. C. Yu, K. F. Lin, J. Y. Chi, S. C. Wang, and H. C. Kuo, "Singlemode monolithic quantum-dot VCSEL in 1.3 μm with side-mode suppression ratio over 30dB," IEEE Photonics Technology Letters 18, 847-849 (2006).