實驗方面：
以 Nd:YVO4為增益介質的實驗架構中，我們由實驗結果，分析 914 nm 不出光，而是 1064 nm 出光的原因，並且歸納兩個解決方法：
解決散熱問題及增加對 1064 nm 的抑制。
以 Nd:YAG 為增益介質的實驗架構中，使用β-BBO 為倍頻晶 體，結合 80 %初始穿透率的 Cr4+:YAG，在 3 W 幫浦下，可產生峰值 功率達 114 W，脈衝寬度為 10.6 ns，波長為 473 nm 的藍光脈衝雷射。
理論方面：
首次建立被動式 Q 開關準三能階藍光雷射模型，其程式模擬結 果與實驗數據間有不錯的吻合，此外，我們也從理論模擬方面計算重 複吸收損耗對增益介質的影響、晶體溫度對重複吸收損耗的關係及不 同初始穿透率的飽和吸收體對雷射輸出關係，使的我們對影響雷射性 能有更深入的瞭解。
未來工作
若要進一步提高藍光的輸出功率，在幫浦方面可以使用雷射二極 體陣列(LD array)來提高輸入功率，此外，改用複合式晶體或晶體光 纖，配以致冷器，使晶體的散熱問題能獲得改善，減少重複吸收損 耗 ，並且採用較低初始穿透率的飽和吸收體，以產生高峰值功率的 藍光脈衝雷射。
而共振腔形式也改用成圖 5.1 的折疊式共振腔(folded cavity)，此 架構可同時控制腔內光束在增益介質上的光點大小與入射倍頻晶體
的發散角，以得到最佳的紅外光量子效率及倍頻轉換效率。
圖 5.1 折疊式共振腔之藍光雷射
藍光雷射輸出
聚焦透鏡
飽和吸收體 倍頻晶體 輸出耦合透鏡
雷射陣列 複合式
晶體 偏振片
參考文獻
[1] 吳文朗，“對半導體雷射激發之摻釹釩酸釔/磷酸鈦化鉀高功率固態綠光雷
射之熱性質研究，”國立中山大學光電工程研究所碩士論文，1998.
[2] D. Hargis and A. Earman, “Diode-pumped microlasers promise portable projectors,” Laser Focus World, May, 1998.
[3] D. Hargis and A. Earman, “Lasers replace conventional technology in display designs,” Laser Focus World, July, 1998.
[4] H. Jones-Bey, “Expiring license opens field for solid-state blue lasers,” Laser Focus World, pp. 133-137, Jan., 2000.
[5] S. Guy, DP. Shepherd, MF. Joubert, B. Jacquier, “Blue Avalanche Up-Conversion in TM:Zblan Fiber,” Journal of The Optical Society of America B-Optical Physics, pp 926-934, vol. 14, Iss. 4, 1997.
[6] R. G. Batchko, M. M. Fejer, R. L. Byer, D. Woll, R. Wallenstein, V. Y. Shur, and L. Erman, “Continuous-wave quasi-phase- matched generation of 60 mW at 465 nm by single-pass frequency-doubling of a laser-diode in backswitch-poled lithium- niobate,” Optics Letters, vol. 24, No. 18, pp.
1293-1295, 1999.
[7] M. Pierrou, F. Laurell, H. Karlsson, T. Kellner, C. Czeranowsky, and G. Huber,
“Generation of 740 mW of blue-light by intracavity frequency-doubling with a first-order quasi-phase- matched KTiOPO4 crystal,” Optics Letters, vol. 24, No.
4, pp. 205-207, 1999.
[8] P. Zeller and P. Peuser, “Efficient, multiwatt, continuous-wave laser operation on the 4F3/2-4I9/2 transition of Nd:YVO4 and Nd:YAG” Optics Letters, vol. 25, No. 1, pp. 34-36, 2000.
[9] A. Suda, A. Kadoi, K. Nagasaka, H. Tashiro, and K. Midorikawa, “Absorption and oscillation characteristics of a pulsed Cr4+:YAG laser investigated by a doub le-pulse pumping technique,” IEEE J. Quantum Electron., vol. QE-35, No.
10, pp. 1548-1553, 1999.
[10] G. Xiao and M. Bass, “A generalized model for passively Q-switched lasers including excited state absorption in the saturable absorber,” IEEE J.
Quantum Electron., vol. QE-33, No. 1, pp. 41-44, 1997.
[11] G. Xiao, J. H. Lim, S. Yang, E. Van Stryland, M. Bass, and L. Weichman,
“Z-scan measurement of the ground and excited state absorption cross sections of Cr4+ in yttrium aluminum garnet,” IEEE J. Quantum Electron., vol. QE-35, No. 7, pp. 1086-1091, 1999.
[12] A. Szabo and R. A. Stein, “Theory of laser giant pulsing by a saturable absorber,” J. Appl. Phys., vol. 36, pp. 1562-1566, 1965.
[13] J. J. Degnan, “Optimization of passively Q-switched lasers,” IEEE J. Quantum Electron., vol. QE-31, No. 11, pp. 1890-1901, 1995.
[14] S. M. Shahruz and T. A. Mahavaraha, “A system-theoretic approach to the stability of passively Q-switched lasers,” IEEE Trans. on Circuits and Systems- I: Fundamental Theory and Applications, vol. 46, No. 4, pp. 512-517, 1999.
[15] T. Y. Fan, and R. L. Byer, “Modeling and CW operation of a quasi-three- level 946 nm Nd:YAG laser,” IEEE J. Quantum Electron., Vol. QE-23, No. 5, pp.
605-612, 1987.
[16] T. Y. Fan, “Optimizing the efficiency and stored energy in quasi-three- level lasers,” IEEE J. Quantum Electron, vol. QE-28, No. 12, pp. 2692-2697, 1992.
lasers,” IEEE J. Quantum Electron, vol. QE-28, No. 12, pp. 2692-2697, 1992.
[17] CASIX Crystal Guide, 1999
[18] A. A. Kaminskii, Crystalline Lasers: Physical processes and operating schemes, CRC Press, Inc., 1996.
[19] F. Hanson, “Improved laser performance at 946 and 473 nm from a composite Nd:Y3Al5O12,” Appl. Phys. Lett, vol. 66, pp. 3549-3551, 1995.
[20] 霍 玉 晶，黃 哲 林，段 玉 生，周炳琨，“ LD 泵 浦 的 整 體 式 CW Nd:YAG 單 晶 光 纖 激 光 器 ”， 中 國 激 光 ， 第 十 七 卷 ， 第 12 期 ， 1990 年 。 [21] M. M. Fejer, J. L. Nightingale, G. A. Magel and R. L. Byer, “Laser-Heated
Miniature Pedestal Growth Apparatus for Single-Crystal Fibers,” Rev. Sci.
Instrum., vol. 55, no. 11, pp. 1791-1796, Nov. 1984.
[22] P. A. Franken, A. E. Hill, C. W. Peter, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett., vol. 7, pp. 118, 1961.
[23] W. Koecner, “Solid-state laser engineering,” 4nd ed, ch10 1996
[24] V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, “Handbook of nonlinear optical crystal,” 3nd ed. 1999. Springer.
[25] X. Zhang, S. Zhao, O. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+-doped saturable-absorber Q-switched lasers,” IEEE Journal of Quantum Electronics, vol. 33, No. 12, pp. 2286-2294, 1997.
[26] J. Liu and D. Kim, “Optimization of intracavity doubled passively Q-switched solid-state lasers,” IEEE J. Quantum Electron., vol. QE-35, No. 12, pp.
1724-1730, 1999.
[27] M. Tsunekane, N. Taguchi, and H. Inaba, “Efficient 946- nm laser operation of a composite Nd:YAG rod with undoped ends,” Applied Opptics, vol.37, No. 24, pp.5713, 1998.
[28] W. P. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B, vol. 5, No. 7, pp. 1412-1423, 1988.
[29] C. F. Gerald, “Applied numerical analysis,” 2nd ed. Wesley, ch. 8, 1992.
[30] 崔宗元，“被動式 Q 開關 Nd:YAG/Cr4+:YAG 雷射研究，”國立中山大學光 電工程研究所碩士論文，1998.
[31] 翁義龍，“腔內倍頻之被動式 Q 開關藍光雷射，”國立中山大學光電工程研
究所碩士論文，2000.
[32] T. Kellner, F. Heine, V. Ostroumov, and G. Huber, “High power diode-pumped intracavity frequency doubled cw Nd:YAG laser at 473 nm,” advanced Solid State Laser, vol. 10, 1997.
中英對照表
absorption coefficient 吸收係數
absorption depth 吸收深度
acceptance angle 可接收角
active 主動式
active ion 活性離子
beam divergence angle 光束發散角
beam quality 光束品質
beam waist 光腰
birefringence 雙折射性
Boltzmann distribution law 玻茲曼分佈原理
cavity 共振腔
coercive field 矯頑電場
coherence length 同調長度
composite gain medium 複合式增益介質 conversion efficiency 轉換效率
crystal fiber 晶體光纖
crystal field 晶格場
cubic 立方晶格
dielectric coating 介電質鍍膜
dielectric material 介電質材料
dipole moment 偶極矩
dispersion 色散
doping 摻雜
double refraction 雙折射效應
effective emission cross section 有效輻射截面
end pumping 縱向幫浦
excited state absorption 激發態吸收
fall time 下降時間
far infrared 遠紅外光
fiber-lens collimated 光纖耦合透鏡
folded cavity 折疊式共振腔
four-level laser 四能階雷射
frequency doubling 倍頻
gain medium 增益介質
GRIN lens 自聚焦透鏡
ground state 基態能階 ground state absorption 基態能階吸收 half symmetric cavity 半對稱式共振腔
harmonic generation 諧波產生
high brightness 高亮度
high density optical storage 高密度的光學儲存 high resolution laser printing 高解析度的雷射列印技術
holography 全像術
initial transmission 初始穿透率 laser based display devices 雷射顯示元件
LIDAR 雷射雷達
Lifetime 生命期
linear susceptibility 線性電化率
LHPG 雷射加熱提拉長晶法
low power transmission 低功率透射率
lower laser level 雷射下能階
manifold 能階
Maxwell’s equations 馬克士威爾方程式 mechanical Q-switch 機械式 Q 開關
metastable state 亞穩態能階
micromachining 微機械加工
mode matching 模態匹配
mode spacing 模態間距
Mohs hardness 莫氏硬度
nonlinear optical coefficient 光學非線性係數 optical damage threshold 光損壞閥值
output coupler 輸出耦合鏡
polarization 極化
polarizer 偏振片
population inversion 居量反轉
pumping power threshold 幫浦功率閥值
quality factor 品質因子
quantum efficiency 量子轉換效率
quartz crystal 石英晶體 quasi-phase-matching 準相位匹配
quasi-three-level 準三能階
random 隨機
reabsorption loss 重複吸收損耗
ruby laser 紅寶石雷射
saturable absorber 飽和吸收體
second harmonic generation 二次諧波產生
side pumping 橫向幫浦
single frequency 單頻
spectroscopy 光譜學研究
spontaneous lifetime 自發輻射生命期
stimulated emission 激發輻射
TE cooler 致冷器
temperature bandwidth 溫度頻寬
tetragonal 四方晶系
thermal birefringence 熱致雙折射
thermal conductivity 熱傳導性
thermal-lens effect 熱透鏡效應
three-level laser 三能階雷射
type I phase matching 第一型相位匹配 type II phase matching 第二型相位匹配
ultraviolet 紫外光
underwater ranging 水下探測
uniaxial 單光軸
unpolarized 非極化
upper laser level 雷射上能階
vacuum permittivity 真空介電係數
valence electrons 價電子
walk-off angle 分離角
附 錄
準三能階被動式 Q 開關雷射模擬程式(for Fortran) 主程式
Program Main
implicit none !使不經宣告的變數無法使用
!變數宣告
integer I,peak1_location,peak2_location,tw_points
real*8 time,dt,points,c,pi,n,tc,R1,R2,L,Le,Rp,h,v1,v2,Pump,Roundtrip_t,Initial_T &
,Absorp_pump,K_GRIN,K_NdYAG,mn,T,tw,Peak_Power,Average_Power,u
&
,k,Temperature,a,Repetition_Rate,f0,f1,f2,N0i,N0,N10 &
,level(6),delta_E(6),f(6) &
,Kc,Wp,Pump_thermal,alfa,dndT,focus,R_YAG,R_Coupler,g1,g2,g &
,z1,z0,L3,W0,lamda,Z_left,Z_right,V,Vt &
,Kg,tg,Vg,Sg,Lg &
,Ks,ts,Vs,Ss,Ls,Ns0 &
,Ld,nd &
,eff,Ad,keff,Peak_Blue,Average_Blue &
,S13,S24,Ks1,Ks2
real*8 , allocatable :: phi(:),Ng(:),Ns(:),N1(:) !宣告為可變大小的矩陣
!開啟檔案
open( unit=40, file='Repetition_Rate.txt' ) open( unit=50, file='Pulse_Width.txt' ) open( unit=80, file='Average_Power.txt' ) open( unit=90, file='Peak_Power.txt' ) open( unit=100, file='Pump.txt' ) open( unit=110, file='Peak_Blue.txt' ) open( unit=120, file='Average_Blue.txt' )
!設定計算的時間
time = 1000.0E-6 !second !欲計算的時間長度 dt = 1.0E-10 !second !兩點間的時間間隔
points = time/dt !計算的點數
!設定陣列的大小
allocate( phi(0:int(points)) ) allocate( Ng(0:int(points)) ) allocate( Ns(0:int(points)) ) allocate( N1(0:int(points)-1) )
!常數設定
c = 3.0E8 !m/s !光速
h = 6.626E-34 !J-s !普朗克常數 k = 1.38062E-23 !J/K !玻茲曼常數 pi = 3.1415926
!晶體參數設定
Lg = 1.5E-3 !m !Length of Nd:YAG
Vg = 6E-12 !m^3 !Mode Volume of Nd:YAG tg = 230.0E-6 !second !Spontaneous Lifetime of Nd:YAG N0i = 1.32E26 !1/m^3 !Nd doped 的濃度
alfa = 10.0E2 !1/m !Nd:YAG 的吸收係數
Sg = 2.8E-24 !m^2 !Capture Cross Section of Nd:YAG
n = 1.82 !Nd:YAG 的折射率
dndT = 7.3E-6 !1/K !Nd:YAG 之熱光係數 Kc = 10.5 !W/m-K !熱傳導率@25 度 Ls = 0.75E-3 !m !Length of Cr:YAG Vs = 6E-12 !m^3 !Mode Volume of Cr:YAG ts = 3.2E-6 !second !Spontaneous Lifetime of Cr:YAG Initial_T = 0.9 !Cr:YAG 之初始穿透率
S13 = 1.4E-22 !m^2 !Ground State Cross Section of Cr:YAG S24 = 1.2E-23 !m^2 !Excited State Cross Section of Cr:YAG Ld = 7E-3 !m !BBO 的長度
nd = 1.66 !BBO 的折射率
!系統參數設定
v1 = c/808.0E-9 !Hz !幫浦光之頻率 v2 = c/946.0E-9 !Hz !雷射的頻率 lamda = 946E-9 !m !雷射波長
L = 52.3E-3 !m !實際的共振腔長度
Absorp_pump = Pump*K_GRIN*K_NdYAG !W !Nd:YAG 吸收的功率 Pump_thermal = Absorp_pump*(946.0-808.0)/946.0 !W !Pump 轉換成熱的功率 Temperature = a*Absorp_pump + 300.0 !K !Nd:YAG 的溫度 Rp = Absorp_pump/(h*v1*Vg) !光子/second-m^3 !Pumping Rate Roundtrip_t = 2.0*( n*(Lg+Ls)/c + (L-Lg-Ls)/c ) !s !Round Trip Time tc = Roundtrip_t/(1.0-R1*R2) !second !Photon Lifetime Ns0 = -log(Initial_T)/(Ss*Ls) !1/m^3 !Cr:YAG 活性離子數 Kg = (c/n)*(Sg/Vg)*(Lg/L) !1/second !Nd:YAG 的耦合常數
Data level /134,197,311,848,11414,11502/
delta_E = level*c*1.0E2*h !J f = exp(-delta_E/(k*Temperature)) f0 = 1.0/( 1.0+f(1)+f(2)+f(3)+f(4) ) f1 = f(4)/( 1.0+f(1)+f(2)+f(3)+f(4) ) f2 = 1.0/(1.0+f(6)/f(5))
!phi,Ng,Ns 的初始值設定
phi(0) = 1.0E-30 !腔內的光子數
Ng(0) = 1.0E14 !1/m^3 !Nd:YAG 居量反轉
N10 = N0i*f(4) !熱致居量分佈
Ns(0) = Ns0 !1/m^3 !Cr:YAG 居量差
!重新計算初始值 Do I=0,1E8
phi(1) = phi(0)+dt*phi(0)*(Kg*Ng(0)*Vg-Ks*Ns(0)*Vs-1.0/tc) If ( phi(1) < mn ) Then
phi(1) = mn end If
N0 = f0*(N0i-Ng(0)/f2)/(1+f1/f2) !基態能階電子分佈量 N10 = N0*f(4)
Ng(1) = Ng(0)+dt*((f1+f2)*Rp-(Ng(0)+N10)/tg-(f1+f2)*Kg*Ng(0)*phi(0)) Ns(1) = Ns(0)+dt*((Ns0-Ns(0))/ts-Ks*Ns(0)*phi(0))
phi(0) = phi(1) Ng(0) = Ng(1) Ns(0) = Ns(1) end Do
!FDTD 計算 phi,Ng,Ns Do I=0,int(points)-1
phi(I+1) = phi(I)+dt*phi(I)*(Kg*Ng(I)*Vg-Ks*Ns(I)*Vs-1.0/tc) If ( phi(I+1) < mn ) Then
phi(I+1) = mn end If
N0 = f0*(N0i-Ng(I)/f2)/(1+f1/f2) N10 = N0*f(4)
Ng(I+1) = Ng(I)+dt*((f1+f2)*Rp-(Ng(I)+N10)/tg-(f1+f2)*Kg*Ng(I)*phi(I)) Ns(I+1) = Ns(I)+dt*((Ns0-Ns(I))/ts-Ks*Ns(I)*phi(I))
end Do
!找重複頻率
call Frequency(phi,points,dt,peak1_location,peak2_location,T,Repetition_Rate) write(40,*) Repetition_Rate !將計算結果寫入檔案
!找脈衝寬度
call Pulse(phi,points,dt,peak2_location,tw,tr,tf) write(50,*) tw
!求 Peak Power
Peak_Power = phi(peak2_location)*h*v2*(1-R2)/(2.0*tw*1.0E-9) write(90,*) Peak_Power
!求 Average Power
Average_Power = phi(peak2_location)*h*v2*(1-R2)/(2.0*T)*1.0E3
!求 Blue Average Power
Average_Blue = (keff*Average_Power**2)/Ad write(120,*) Average_Blue
write(80,*) Average_Power
!求 Blue Peak Power
Peak_Blue = Average_Blue*T*1E6/tw write(110,*)Peak_Blue
End Program Main
副程式—求重複頻率
Subroutine Frequency(phi,points,dt,peak1_location,peak2_location,T,Repetition_Rate) Implicit none
integer I,peak1_location,peak2_location real*8 points,dt,Repetition_Rate,T real*8 phi(0:int(points))
!找第一個脈衝峰值的位置 peak1_location = 0
Do I = 1,int(points)
If ( ( phi(I-1)<phi(I) ) .and. ( phi(I)>phi(I+1) ) ) then peak1_location = I !記錄位址
exit !跳出迴圈
end if end Do
if ( peak1_location == 0 ) then !判別是否有找到 peak1 write(*,*) 'Error!! 無法找到第一個 Peak'
Pause !程式暫停
end if
!找第二個脈衝峰值的位置 peak2_location = 0
Do I = peak1_location+1,int(points)
If ( ( phi(I-1)<phi(I) ) .and. ( phi(I)>phi(I+1) ) ) then peak2_location = I
exit end if end Do
if ( peak2_location == 0 ) then
write(*,*) 'Error!! 無法找到第二個 Peak' Pause
end if
!求重複頻率
T = real(peak2_location-peak1_location)*dt !s !脈衝週期 Repetition_Rate = ( 1.0/T )*1.0E-3 !KHz !重複頻率
Return !計算結果回傳
End
副程式—求脈衝寬度
Subroutine Pulse(phi,points,dt,peak2_location,tw,tr,tf) Implicit none
integer peak2_location,t1,t2,r1,r2,f1,f2 real*8 points,dt,tw,tr,tf
real*8 phi(0:int(points))
!找脈衝 FWHM 的左端點 t1 = peak2_location
Do while ( phi(t1) > phi(peak2_location)/2.0 ) !從 peak2 往左找 t1 = t1-1
end Do
! 找脈衝 FWHM 的右端點
t2 = peak2_location !從 peak2 往右找
Do while ( phi(t2) > phi(peak2_location)/2.0 ) t2 = t2+1
if ( t2 == points ) then
write(*,*) 'Error!! 無法找到脈衝 FWHM 的右端點' Pause
end if End Do
tw = ( real(t2-t1)*dt )*1.0E9 !ns !計算脈衝寬度 return
End