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LD的相干长度
$ \Delta x $ 可用激光器中心波长$ \lambda $ ,谱线宽度$ \Delta \lambda $ 表示为:$$ \Delta x = \frac{{\mathop \lambda \nolimits^2 }}{{\Delta \lambda }} $$ (1) 可见,要降低LD的相干长度,需要将激光器的线宽展宽。基于射频调制的LD线宽展宽方案如图1所示。高速大正弦信号加载在恒流驱动上,带有偏置的射频信号对FP激光器进行直接调制,输出为多纵模,进而可以实现激光器的线宽展宽。
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LD有源区内电子和光子之间相互的能量交换是由其自发辐射和受激辐射过程所支配的,光子和电子之间能量交换的速率可以用速率方程来描述。基于FP腔的LD工作在阈值附近时输出的激光光谱一般是多纵模的[16],其速率方程有如下形式[17]:
$$ \frac{{{\text{d}}N}}{{{\text{d}}t}} = \frac{J}{{eV}} - \frac{N}{{{\tau _e}}} - \frac{C}{n}{g_m}{S _ m} $$ (2) $$ \frac{{{\text{d}}{S _m}}}{{{\text{d}}t}} = \frac{{\varGamma \gamma N}}{{{\tau _e}}} + \frac{C}{n}{g_m}{S _ m} - \frac{{{S _m}}}{{{\tau _p}}} $$ (3) 其中:
$$ {g_m}{\text{ = }}g\left( {N{{ - }}{N'}} \right)\left[ {1 - {{\left( {\frac{m}{M}} \right)}^2}} \right]\quad m = 0, \pm 1, \pm 2, \cdots , \pm M $$ (4) 式中:
$ N $ 为注入电子浓度;$ J $ 为注入电流密度;$ e $ 为电子电荷;$ V $ 为有源区体积;$ {\tau _e} $ 为载流子寿命;$ C $ 为光速;$ n $ 为有源区折射率;$ {g_m} $ 为$ m $ 阶模的增益;$ {S _m} $ 为$ m $ 阶模的光子密度;$ \varGamma $ 为限制因子;$ \gamma $ 为自发辐射因子;$ {\tau _p} $ 为光子寿命;$ g $ 为微分增益系数;${N'}$ 为透明载流子浓度;$ M $ 为边模数。令
$ \dfrac{{{\text{d}}N}}{{{\text{d}}t}} = 0 $ 和$ \dfrac{{{\text{d}}{S _ m}}}{{{\text{d}}t}} = 0 $ ,得到$ m $ 阶模的光子密度$ {S_ m} $ 的表达式为:$$ {S _m} = \dfrac{{\dfrac{{N\gamma }}{\varGamma }}}{{\dfrac{C}{n}g{\tau _e}\left( {{N_{{\text{th}}}} - N} \right)\left[1 + \dfrac{{N - {N'}}}{{{N_{{\text{th}}}} - N}}{{\left( {\dfrac{m}{M}} \right)}^2}\right]}} $$ (5) 式中:
$ {N_{{\text{th}}}} $ 为阈值载流子浓度,其表达式为:$$ {N_{{\text{th}}}} = {N'} + \frac{C}{{n{\tau _p}\varGamma g}} $$ (6) 通常半高宽为
$ \Delta \lambda $ 的光谱高斯增益曲线$ G(\lambda ,\Delta \lambda ) $ 可以表示为:$$ G\left( {\lambda ,\Delta \lambda } \right) = \sqrt {\frac{{\ln 2}}{{\text{π }}}} \frac{1}{{\Delta \lambda }}\exp \left( { - \frac{{4{{(\lambda - {\lambda _0})}^2}\ln 2}}{{{{(\Delta \lambda )}^2}}}} \right) $$ (7) 式中:
$ {\lambda _0} $ 为中心波长,若主模光强下降一半处对应的$ q $ 阶模波长为$ \lambda q $ ,则有$$ G\left( {\lambda q,\Delta \lambda } \right){\text{ = }}{S _ q} $$ (8) FP激光器线宽
$ \Delta \lambda $ 可以表示为:$$ \Delta \lambda = \frac{1}{2}\sqrt {\frac{{\ln 2}}{{\text{π }}}} \left( {\frac{{C{\tau _{\text{e}}}\varGamma G}}{{nN\gamma }}M + \frac{{n - C{\tau _{\text{e}}}{\tau _p}\varGamma G}}{{nN\gamma {\tau _p}}}} \right) $$ (9) 式中:
$ G $ 为受激辐射净增益。从上式可以得LD的谱线宽度正比于模式数量,即$ \Delta \lambda \propto M $ 。物理原理为:LD在高频大信号调制作用下,注入电流的变化使得载流子浓度$ N $ 发生变化,载流子浓度的变化又必然引起折射率的变化,光模的频率发生漂移,从而使更多的模式达到阈值增益,激光器主模的强度下降,而次模的强度相对增加,除主模外的其他边模的光子浓度$ {S_ m} $ 同时出现振荡,因此,FP激光器输出光谱纵模数增多,导致其谱线越宽。 -
LD输出功率与注入电流的大小直接相关。为了获得更高的调制效率,使输出信号不失真,需要在加调制信号电流的同时加上一个偏置电流
$ {I_b} $ ,且通常选择在阈值电流$ {I_{th}} $ 附近[18]。注入电流包括直流分量和交流分量,可以表示为:$$ I = {I_b} + {I_m}\cos {\omega _m}t $$ (10) 式中:
$ {I_b} $ 为偏置电流;$ {I_m} $ 为调制信号的幅度;$ {\omega _m} $ 为调制信号的角频率。注入电流对模式功率的直接调制,必然伴随着模式相位和频率的调制[18],此时,输出激光光波的强度可以表示为:$$ E\left( t \right) = {E_0}\left( {1 + \frac{{{I_m}}}{{{E_0}}}\cos {\omega _m}t} \right)\cos \left( {{\omega _{\text{c}}}t + \alpha \sin {\omega _m}t + {\varphi _c}} \right) $$ (11) 式中:
$ {E_0} $ 为激光信号幅度;$ {\omega _{\text{c}}} $ 为激光信号角频率;$ {\varphi _c} $ 为激光信号相位角;$ \alpha $ 为调制系数。其表达式为:$$ \alpha = \frac{{\Delta \omega }}{{{\omega _m}}} $$ (12) 式中:
$ \Delta \omega $ 为最大角频率调制量,其值与调制信号幅值成正比。利用三角函数公式和贝塞尔函数公式将公式(11)展开为:$$ \begin{split} E\left( t \right) =& {E_0}{{{J}}_0}\left( \alpha \right)\cos \left( {{\omega _{\text{c}}}t + {\varphi _c}} \right){\text{ + }} \\& \frac{{{I_m}}}{2}{{{J}}_0}\left( \alpha \right)\cos \left( {\left( {{\omega _{\text{c}}} + {\omega _m}} \right)t + {\varphi _c}} \right) +\\& \frac{{{I_m}}}{2}{{{J}}_0}\left( \alpha \right)\cos \left( {\left( {{\omega _{\text{c}}} - {\omega _m}} \right)t + {\varphi _c}} \right) + \\& \left( {{E_0} + \frac{{{I_m}}}{2}} \right)\sum\limits_{{{n}} = 1}^\infty {{{{J}}_{{n}}}\left( \alpha \right)} \{ \cos \left[ {\left( {{\omega _{\text{c}}} + n{\omega _m}} \right)t + {\varphi _c}} \right] + \\& {{\left( { - 1} \right)}^n}\cos \left[ {\left( {{\omega _{\text{c}}} - n{\omega _m}} \right)t + {\varphi _c}} \right] \} \end{split} $$ (13) 从上式可知电流调制的结果是在基频
$ {\omega _{\text{c}}} $ 两侧间隔$ {\omega _m} $ 处产生无穷多对新的频率成分,在光谱中称为边模,边模强度与调制信号频率和幅度有关。激光器的谱线宽度即半高全宽(Full Width at Half Maxima, FWHM)是边模光强为主模光强一半处两个边模波长之差[19]。新产生的边模越多、距离主模越远、强度越大谱线展的就会越宽。 -
实验搭建了短相干光源系统,使用光谱仪测量激光器输出光谱线宽,研究了两台不同斜率效率FP激光器的短相干特性,并将获得的短相干光源应用于斐索干涉仪,实现对平行平板玻璃面形的检测。基于短相干光源的实验装置如图2所示。中心波长为635 nm和637 nm的LD安装在LDM9LP激光器底座上,激光器驱动器的最大驱动电流为1 A,最大温度控制电流为4.5 A,最大温度控制电压为3 V,TEC加热/冷却能力可达7 W,最大射频输入功率为500 mW,调制频率可从200 kHz到1 GHz。自制恒流源电路输出电流范围可以任意调节,且加入了延时启动电路和功率保护电路,能够有效保护激光器。WTC3243温度控制芯片最大驱动电流可达±2.2 A,温度稳定度可达到0.0009 ℃,通过调整控制回路的P、I值可以精确控制温度。射频模块采用HMC830芯片,该芯片输出频率25~3000 MHz,输出幅度经放大器放大后可达19 dBm,相位噪声低至−110 dBc/Hz。AQ6370D型光谱仪用来测量600~1 700 nm波段的光谱,测量精度可达0.01 nm。
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LD的P-I曲线在阈值以上具有非常好的线性关系,定义激光器斜率效率
$ \eta $ 表达式为:$$ \eta = \frac{{\Delta P}}{{\Delta I}} $$ (14) 在相同的调制信号作用下,斜率效率大的LD拥有更大的输出功率变化,有助于实现好的调制效果。图3为实验所测FP激光器的P-I特性曲线。两台激光器的中心波长分别为635 nm和637 nm,P-I特性曲线斜率分别为2.72 W/A 和5.40 W/A,阈值电流均为
${I_{th}} = 45\;{\text{ mA}}$ ,其工作温度通过温控系统控制在25 ℃。在实验中,改变偏置电流大小、射频信号频率和幅值,记录光谱的半高全宽来描述LD的相干性。 -
根据LD直接调制特性理论分析,在实验中,设置射频信号频率
$ {f_m} = {{950 \; {\rm{MHz}}}} $ ,幅值$ {A_m} = {{19\; {\rm{dBm}}}} $ ,研究偏置电流变化对LD相干长度的影响。实验结果如图4所示,在偏置电流较小时,激光器的线宽较窄,这是由于部分射频信号工作在激光器的阈值电流以下,导致激光器的输出功率异常低,影响激光器的射频调制性能;随着偏置电流的增大,两台激光器的谱线宽度随之增大,相干长度随之降低,均在偏置电流$ {I_b} = 1.3{I_{th}} $ 时达到最小,且637 nm激光器的相干长度比635 nm激光器更短,相干长度可降低至89.4$ {\text{μm}} $ ;随着偏置电流的进一步增大,光源相干性增强,此时在其他条件不变的情况下,激光器的线宽主要受偏置电流的影响,增大的注入电流加剧了模式竞争,使LD输出纵模数量减少,谱线宽度变窄。 -
为减小偏置电流的影响,设置偏置电流
$ {I_b} = 1.3{I_{th}} $ ,射频信号幅值$ {A_m} = {{19\; {\rm{dBm}}}} $ ,改变调制信号频率100~950 MHz,研究射频调制信号频率对LD相干长度的影响。实验结果如图5所示,电流调制使LD谐振腔折射率发生变化,引起更多的模式产生振荡,在调制信号频率较低时,由于振荡模式可以响应电流的变化,射频调制的作用不明显,激光器的线宽较窄;随着调制信号频率的增大,此时模式数目不能响应于高频调制电流的快速变化,LD发射光谱呈现多纵模输出,因此两台激光器的线宽逐渐展宽,相干长度随之减小,且637 nm激光器的相干长度比635 nm激光器更短,当调制频率为950 MHz时,相干长度可降低至88.6$ {\text{μm}} $ 。 -
设置偏置电流
$ {I_b} = 1.3{I_{th}} $ ,射频信号频率${f_m} = {{950\; {\rm{MHz}}}}$ ,改变调制信号幅值0~19 dBm,研究射频信号幅值对LD相干长度的影响。实验结果如图6所示,随着调制信号幅值的增大,由于LD内振荡模式的增益发生变化,主模强度下降,边模强度相对增加,调制深度的增大使两台激光器的线宽逐渐展宽,相干长度随之减小,且637 nm激光器的相干长度比635 nm激光器更短,在调制幅值为19 dBm时,相干长度可降低至89.9$ {\text{μm}} $ 。综上所述,在偏置电流
$ {I_b} = 1.3{I_{th}} $ 、射频信号频率$ {f_m} = {{950\; {\rm{MHz}}}} $ 、射频信号幅值$ {A_m} = {{19\; {\rm{dBm}}}} $ 时,光源相干长度最短。因此,使激光器工作在略大于阈值电流的状态,提高射频调制信号频率和幅值,选择斜率效率更大的FP激光器,更有利于短相干特性的实现。 -
通过对两台激光器的短相干特性研究,选用斜率效率更大的637 nmFP激光器作为短相干激光器系统光源,图7为光谱仪采集的射频调制前后的光谱图。不加调制时,工作在阈值附近的FP激光器输出光谱线宽较窄为1.588 nm,相干长度为256
$ {\text{μm}} $ ;在偏置电流为$ {I_b} = 1.3{I_{th}} $ 和频率${f_m} = {950} \;{\rm{MHz}}$ 、幅值$ {A_m} = {{{{19}} \;{\rm{dBm}}}} $ 的高速大正弦信号调制下,模式增益发生改变,激光器主模的强度下降,而次模的强度相对增加,更多模式发生振荡,形成类高斯的光谱,这与前述的理论一致,展宽后的光谱线宽可以达到4.456 nm,此时激光器的相干长度降至90$ {\text{μm}} $ 。将该短相干光源应用于斐索干涉仪上,对厚度为0.15 mm的透明平行平板玻璃面形进行测量,见图8。
图 8 基于短相干光源的平行平板玻璃干涉测量实验装置图
Figure 8. Experimental setup of parallel plate glass interferometry based on short coherent light source
测量原理为:FP激光器输出的短相干光源发出一束平行细光束,经分光棱镜BS1被分为光束P1和P2。P1和P2分别经平面镜M1和平面镜M2反射后再次经过BS1相遇,其中平面镜M1固定,平面镜M2可移动,从而会在P1和P2之间引入2
$ \Delta $ 的光程差。P1和P2重合后进入光纤,经扩束镜L1和准直物镜L2后扩束准直,分别在参考镜R和被测样品T上反射,通过调整R和T之间的距离为$ \Delta $ ,匹配P1和P2之间的光程差,由于光源相干长度小于被测样品厚度,仅有参考镜R下表面和被测样品T上表面反射的光小于相干长度,满足干涉条件,反射的光束经过分光棱镜BS2和成像镜头L3后通过CCD采集、软件处理后输出干涉条纹,通过干涉条纹的凹凸判断平行平板玻璃面形平整度。该短相干光源可以有效避免平板玻璃上下表面反射光干涉混叠所引起的背景噪声,如图9所示。未调制时的激光光源由于相干性好,线宽窄,相干长度较长,平板玻璃上下表面的反射光也会形成干涉,与平板玻璃表面的干涉条纹相互叠加,对面形信息形成了严重干扰,如图9(a)所示;经过射频调制的光源相干长度降低,小于平板玻璃的厚度,平板玻璃上下表面的反射光不会产生干涉,因此,CCD采集到仅有携带平板玻璃面形信息的两束光干涉形成的条纹图,避免了干扰条纹的产生,如图9(b)所示。
通常干涉图像的质量用干涉条纹的对比度
$ K $ 来衡量,它的定义为:$$ K = \frac{{{I_{\max }} - {I_{\min }}}}{{{I_{\max }} + {I_{\min }}}} $$ (15) 式中:
$ {I_{\max }} $ 为干涉场中某点附近光强的极大值;$ {I_{\min }} $ 为该点附近光强的极小值。使用文中的参数获得的短相干光源使得干涉图像拥有更高的图像质量,如图9(b)所示,相比现有的短相干光源[13],对比度可达0.9318,提升了约51.1%,在避免背景噪声的同时,携带面型信息的干涉条纹显示更加清晰。
Radio frequency modulation characteristics and application of short coherent semiconductor laser
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摘要: 短相干激光光源在进行高精度的干涉测量时,可以消除被测光学元件前后表面反射形成的杂散光,是低相干干涉仪的理想光源。针对低相干干涉应用对光源的需求,依据速率方程和激光调制特性对射频调制下的短相干半导体激光器光谱特性进行了理论研究。搭建了短相干光源系统,研究了半导体激光器斜率效率
$ \eta $ 、偏置电流$ {I_b} $ 、射频信号频率$ {f_m} $ 和幅度$ {A_m} $ 对其相干长度的影响。实验结果表明,斜率效率大的半导体激光器更有助于短相干特性的实现,随着调制信号频率和幅值增加,工作在阈值附近的激光器相干长度随之降低,该系统在$ {I_b} = 1.3{I_{th}} $ 、$ {f_m} = {\text{950\;MHz}} $ 、$ {A_m} = {\text{19\;dBm}} $ 的条件下获得了相干长度为90$ {\text{μm}} $ 的短相干光源。并成功应用于斐索干涉仪上,获得了对比度$ K = 0.931\;8 $ 的清晰干涉图像,与现有短相干光源相比,对比度提高了约51.1%,实现了对平行平板玻璃面形的测量。Abstract:Objective Short coherent laser light source can eliminate the stray light formed by the reflection of the front and rear surfaces of the optical element to be measured in high-precision interferometry, which is an ideal light source for low-coherence interferometers. There are important applications in optical coherence tomography, refractive index and thickness measurement of organic materials, surface profile detection of optical elements, etc. The imaging quality of the interferometer will be affected by the light source, and the appropriate parameters are very important for the semiconductor laser to obtain high-quality short coherent light source through RF modulation. However, the spectral linewidth of semiconductor lasers is narrow. It is of great significance to reduce coherence length through the coherence control technology. Methods A short coherent light source was obtained by radio frequency modulation using a Fabry-Perot laser diode with central wavelength of 637 nm. The spectral properties of short coherent semiconductor lasers under RF modulation are theoretically studied based on laser rate equations and modulation characteristics. A short coherent light source system (Fig.2) was built to study the effects of laser slope efficiency, bias current, RF signal frequency and amplitude on the coherence length of semiconductor lasers. Compared with the existing short coherent light source with RF modulation under the same conditions, its improvement effect on the interference image quality was verified. Results and Discussions The spectral linewidth of laser was measured by spectrometer. The short coherence characteristics of two Fabry-Perot lasers with different slope efficiency were studied and the results show that the semiconductor laser with high slope efficiency has greater output power variation under the same modulation signal, which is helpful to achieve good modulation effect. The coherence length of a semiconductor laser is the smallest when the bias current is slightly larger than the threshold current (Fig.4). When the bias current is small, the linewidth of the laser is narrow. This is because some RF signals work below the threshold current, which leads to the abnormally low output power of the laser and affects the RF modulation performance. When the bias current is too large, the coherence of the light source is enhanced, and the increased injection current intensifies the mode competition, the number of longitudinal modes output by the semiconductor laser is reduced and the spectral line width is narrowed. The coherence length of the semiconductor laser is negatively correlated with the frequency (Fig.5) and amplitude (Fig.6) of the RF modulation signal. With the increase of the frequency and amplitude of the modulation signal, the emission spectrum of the semiconductor laser shows multi-longitudinal mode output, the spectral line width is broadened, and the coherence length decreases. An experimental setup for measuring the surface profile of transparent parallel plate glass was built (Fig.8). The short coherent light source obtained by using the parameters in this paper makes the interference image have higher image quality. Compared with the existing short coherent light source, the contrast can reach 0.9318, which is increased by about 51.1%. While avoiding background noise, the interference fringes with surface information are displayed more clearly (Fig.9). Conclusions Under the condition of bias current ${I_{\rm{b}}} = 1.3{I_{{\rm{th}}}}$ , a semiconductor laser with higher slope efficiency is selected. With the increase of modulation signal frequency and amplitude, the coherence length of the laser decreases, and the shortest coherence length can reach 90$ {\text{μm}} $ at RF signal frequency$ {f_m} = {\text{950 MHz}} $ and amplitude$ {A_m} = {\text{19 dBm}} $ . It can be used to measure transparent parallel plate optical elements as thin as 0.09 mm, and the interference image contrast is 0.9318, which is higher than the existing short coherent light source. The research improves the performance of short coherent light source and has broad application prospects in the field of low coherent interferometry. -
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