1. Modeling and Simulation of Broad-Area Semiconductor Lasers using FFT-BPM 研究單位 : 國立成功大學微電子工程研究所 計畫主持人 : 蔡宗祐 研究生 : 陳騰麒，賴俊翔，黃商殷 工研院南分院 FY96 分包學界研究案 二極體雷射陣列光源傳播特性之研究 B200-96ED4

2. Modeling and Simulation of Broad-Area Semiconductor Lasers using FFT-BPM 2.Naoyuki Morimoto,* Tomoaki Toda, and Tadashi Takano, “Radiation Characteristics Analysis of Broad Area Laser Diodes and the Proposal of Improvement Methods,” Electronics and Communications in Japan, Vol. 85, No. 3, pp 40-49, 2002. 3.John R. Marciante and Govind P. Agrawal, “Nonlinear Mechanisms of Filamentation in Broad- Area Semiconductor Lasers,” IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL 32, NO 4, pp. 590-596, APRIL 1996. 1.“Introduction to optical waveguide analysis”, Authors: Kenji Kawano and Tsutomu Kitoh References: 1.Pump intensity, pump stripe shape 2.Cavity length, width, mirror reflectivity, cavity internal loss. 3.Kerr effect coefficient, confinement factor, linewidth enhancement factor Modeling Variables:

3. Simulation of Semiconductor Laser using FFT-BPM Naoyuki Morimoto,* Tomoaki Toda, and Tadashi Takano, “Radiation Characteristics Analysis of Broad Area Laser Diodes and the Proposal of Improvement Methods,” Electronics and Communications in Japan, Vol. 85, No. 3, pp 40-49, 2002. John R. Marciante and Govind P. Agrawal, “Nonlinear Mechanisms of Filamentation in Broad-Area Semiconductor Lasers,” IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL 32, NO 4, pp. 590-596, APRIL 1996. 1. 2. 1. 2. Considerrations of the gain g, internal cavity loss  int, Kerr effect n 2, confinement factor , and linewidth enhancement factor  are all included in  n(x,z)

4. Derivation of  n Assume the wave propagating toward After pumping Gain and loss

5. Correction of Equations Naoyuki Morimoto,* Tomoaki Toda, and Tadashi Takano, “Radiation Characteristics Analysis of Broad Area Laser Diodes and the Proposal of Improvement Methods,” Electronics and Communications in Japan, Vol. 85, No. 3, pp 40-49, 2002. John R. Marciante and Govind P. Agrawal, “Nonlinear Mechanisms of Filamentation in Broad-Area Semiconductor Lasers,” IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL 32, NO 4, pp. 590-596, APRIL 1996. 1. 2. 1. 2.

6. Theory of FFT-BPM Reference: 1.“Introduction to optical waveguide analysis”,Authors: Kenji Kawano and Tsutomu Kitoh c If refractive index is uniform,  n=0, thus it can be simplified as Ex. Far-Field Profile (FFP) Near-Field Profile (NFP) in free space

7. x z

8. Matlab Programs 1.Fast-Fourier-Transform Beam-Propagation Method (FFT-BPM) Matlab program: FFTBPM_MMI.m

9. 2. Matlab program: FFTBPM_Laser.m PumpStripeWidth=10  m The first 10 roundtrip The 200th roundtrip

10. The first 10 roundtrip The 300th roundtrip 2. Matlab program: FFTBPM_Laser.m PumpStripeWidth=100  m

11. 3. Matlab program: BPM_FarFieldProfile.m For the case of ‘PumpStripeWidth=10  m’

12. 3. Matlab program: BPM_FarFieldProfile.m, 4. Matlab program: BPM_NearFieldProfile.m, For the case of ‘PumpStripeWidth=100  m’

13. 5. Matlab program: FFTBPM_Laser_c.m, For the case of ‘PumpStripeWidth=100  m’ with phase correction at the output end of the laser