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测得传统液晶盒器件激光辐射谱如图3(a)所示。激光辐射谱波长范围在575~600 nm,辐射峰呈现多个离散的随机激光峰,随机激光峰分布在荧光辐射谱的鼓包上面,最强峰位波长已在图中标出,阈值泵浦能量为10.33 μJ/pulse。传统液晶盒中,液晶分子充当无序或部分有序的散射颗粒,激光染料作为增益介质,光波在液晶分子间的散射作用较强,经过多次散射,形成闭合回路,获得反馈放大,当增益超过损耗时获得激光辐射。在前期研究中发现影响随机激光辐射阈值的主要因素之一为液晶层厚度和温度[12]。文中实验在器件侧面测得随机激光辐射输出,充分说明传统液晶盒结构具有光波导作用。光波在液晶层中传输时折射率分别为no=1.522和ne=1.692 (室温),而PI的折射率nPI=1.516。 no和ne值均大于nPI
,满足光波导条件,并且是结构对称光波导。在光波导中传输的光波,可以有辐射模式、衬底模式、导波模式等三种形式。辐射模式和衬底模式分别从液晶盒的正面方向辐射输出,而导波模式则从器件侧面方向辐射输出[13]。因此,不难分析得出,传统液晶盒中形成的随机激光即可以从器件正面方向辐射输出,也可以从器件侧面辐射输出。 图 3 器件侧面方向的激光辐射谱。 (a) 传统液晶盒器件;(b)、(c) 周期100 μm和8 μm光栅结构器件,插图为辐射强度与泵浦能量的依赖关系
Figure 3. Laser emission spectrum at the side of the cell. (a) Standard NLC cell; (b), (c) NLC cell with a period of 100 μm and 8 μm grating, the inset shows the dependence of the emission intensity on the pumping energy
图3(b)、(c)为引入周期100 μm 和 8 μm SU-8光栅器件在室温下的激光辐射谱。周期100 μm器件激光辐射谱波长范围约575~600 nm,半高全宽(Full width at half maximum, FWHM)约0.3 nm,阈值泵浦能量为 2.81 μJ/pulse。周期 8 μm 器件,激光辐射谱波长范围约580~610 nm,FWHM约0.3 nm,阈值泵浦能量为 4.62 μJ/pulse。与随机激光辐射谱比较,荧光辐射谱的鼓包上面出现了相对强度较强的一个或多个辐射峰。最强峰位波长已在图中标出。这说明引入SU-8光栅,增强了液晶器件的光波导效应。
以上三种器件阈值泵浦能量大小关系为周期100 μm 光栅液晶器件 < 周期 8 μm 光栅液晶器件 < 传统液晶盒器件。SU-8光栅器件,周期100 μm的阈值略低于周期8 μm的。分析认为,光栅周期小,使得激光染料分布较分散,相同泵浦能量下,可获得增益较小,导致泵浦阈值能量较大。另外,可以看出周期8 μm器件的最强峰位波长较周期100 μm器件有所红移。由下面的理论分析将会得出,光栅周期不同,光波导层的有效折射率值
${n}_{e f f}$ 不同,从而引起器件输出激光波长不同。将液晶器件视为光波导,上下PI取向层为覆盖层和衬底层,液晶层为导光薄膜层。在液晶层和PI层界面,满足全反射条件的光波,不断干涉加强,在波导中传输,图中用绿色光线画出,如图4所示。当然,液晶层中传输的光波路径不仅仅是图中所示。光波在液晶分子间不断散射,同时在SU-8光栅中反复透射和反射。
由光波导理论公式[13]可推演出器件中可传输光波长计算公式如下:
$$ \frac{\pi d \cos{\theta }_{i}}{\lambda }=\frac{m\pi }{2}+{\rm {arctan}}\left(\frac{\sqrt{{n}_{eff}^{2}{\sin}^{2}{\theta }_{i}-{n}_{{\rm{PI}}}^{2}}}{{n}_{eff}\cos{\theta }_{i}}\right) $$ (1) 式中:
$ d $ 为液晶盒厚度10 μm;$ {\theta }_{i} $ 如图4所示;$ m $ 为模阶数,取有限正整数;${n}_{\rm{{PI}}}$ =1.516。有效折射率$ {n}_{eff} $ 由下式给出:$$ {n}_{eff}=\frac{a}{\varLambda }{n}_{\rm{{NLC}}}+\frac{\varLambda -a}{\varLambda }{n}_{\rm{{SU-8}}} $$ (2) 式中:
$ a $ 为光栅槽宽;$ \varLambda $ 为光栅周期;${{n}}_{\mathrm{S}\mathrm{U}-8}$ 为SU-8光栅折射率1.5742 (厂家提供参数,由柯西公式计算得出);$ {n}_{{\rm{NLC}}}={n}_{o}\mathrm{或}{{n}}_{{e}}\left({\theta }_{i}\right) $ ,即在液晶层中可传输的线偏振光的折射率;o光的振动方向垂直xoz平面,折射率$ {n}_{o} $ ;e光的振动方向在xoz平面内,折射率$ {n}_{e}\left({\theta }_{i}\right) $ 由下式给出:$$ {n}_{e}\left({\theta }_{i}\right)=\sqrt{\frac{{n}_{o}^{2}{n}_{e}^{2}}{{n}_{o}^{2}{\sin}^{2}{\theta }_{i}+{n}_{e}^{2}{\cos}^{2}{\theta }_{i}}} $$ (3) 式中:
$ {n}_{e} $ =1.692;$ {n}_{o} $ =1.522。由全反射公式,在PI取向层和液晶层界面处,e光入射角度大于66°会在界面发生全反射,小于66°则有透射有反射;o光入射角度大于85°发生全反射,小于85°则有透射有反射。光波通过在上下界面处反射,获得干涉加强,当增益大于损耗时,由器件侧面辐射输出。由公式(1)~(3),可分别计算出光波导中传输波长,即器件输出激光波长值,如表1所示。可以看出理论值与图3(c)、(d)中实验测得波长值基本符合。
表 1 输出波长理论值
Table 1. Theoretical values of output wavelength
${n}_{{\rm{PI}}}$ $ m $ ${n}_{{\rm{NLC}}}$ $ {n}_{eff} $ $ {\theta }_{i} $ $\lambda /{\rm{nm}}$ $\varLambda /{\text{μ} }\mathrm{m}$ 100&8 100&8 100&8 100 8 100 8 100 8 e optical 1.516 12 1.667 1.646 1.632 69° 69° 585.722 590.435 1.516 10 1.674 1.652 1.636 72.3° 72.2° 583.406 589.346 1.516 8 1.680 1.656 1.640 75.5° 75.5° 585.690 587.681 1.516 6 1.684 1.660 1.643 78.8° 78.8° 583.333 585.083 1.516 4 1.688 1.663 1.645 82° 82° 585.402 587.045 1.516 2 1.690 1.665 1.647 85.2° 85.2° 588.457 590.051 o optical 1.516 2 1.522 1.533 1.542 85.55° 85.37° 591.038 602.760 1.516 2 1.522 1.533 1.542 85.56° 85.39° 589.534 599.883 1.516 2 1.522 1.533 1.542 85.57° 85.40° 588.031 598.447 1.516 2 1.522 1.533 1.542 85.58° 85.42° 586.529 595.575 1.516 2 1.522 1.533 1.542 85.59° 85.44° 585.028 592.707
Emission spectrum of lateral laser in nematic liquid crystal device
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摘要: 研究了向列相液晶激光器件侧面激光辐射谱,并深入分析了激光辐射机制。分别制备了传统液晶盒和引入SU-8光栅结构的两种器件,并注入向列相液晶TEB30A和激光染料PM597的混合物。利用Nd:YAG固体脉冲激光器倍频出的532 nm激光作为泵浦源正面入射器件,侧面探测激光辐射谱。在传统液晶盒器件侧面,测得 575~600 nm范围的随机激光辐射谱。而具有周期100 μm和8 μm 的SU-8光栅结构器件侧面,获得了多波长激光辐射谱。随着泵浦能量增大,最高强度激光辐射峰波长位置出现在583~585 nm和588~592 nm附近,FWHM约0.3 nm。基于光波导理论结合器件结构分析得出,在传统液晶盒中引入SU-8光栅结构增强了液晶器件的光波导效应,是获得多波长激光辐射谱的主要原因。Abstract: The spectra of the lateral laser radiation in nematic liquid crystal (NLC) laser devices are studied, and the characteristics of the laser radiation are deeply analyzed. Two types of NLC cells of standard NLC cell and SU-8 grating based NLC cell are fabricated and injected with a mixture of NLC TEB30A and laser dye PM597, respectively. A frequency-doubled Nd: YAG solid-state pulsed laser with a wavelength of 532 nm is used as the pump source. Random lateral laser radiation in the wavelength of 575-600 nm is observed in the standard NLC cell. Whereas, in the SU-8 grating based NLC cells with periods of 100 μm and 8 μm, the spectrum of the multi-wavelength lateral laser radiation is obtained. With the increase of the pump energy, the strongest lateral laser radiation peaks appear at 583-585 nm and 588-592 nm, and the FWHM is about 0.3 nm. According to the theory of the optical waveguide and analysis of the device structure, the introduction of the SU-8 grating into the standard NLC cell enhances the optical waveguide effect of the LC device and induces multi-wavelength laser radiation.
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Key words:
- nematic liquid crystal /
- SU-8 grating /
- multi-wavelength laser /
- random laser
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表 1 输出波长理论值
Table 1. Theoretical values of output wavelength
${n}_{{\rm{PI}}}$ $ m $ ${n}_{{\rm{NLC}}}$ $ {n}_{eff} $ $ {\theta }_{i} $ $\lambda /{\rm{nm}}$ $\varLambda /{\text{μ} }\mathrm{m}$ 100&8 100&8 100&8 100 8 100 8 100 8 e optical 1.516 12 1.667 1.646 1.632 69° 69° 585.722 590.435 1.516 10 1.674 1.652 1.636 72.3° 72.2° 583.406 589.346 1.516 8 1.680 1.656 1.640 75.5° 75.5° 585.690 587.681 1.516 6 1.684 1.660 1.643 78.8° 78.8° 583.333 585.083 1.516 4 1.688 1.663 1.645 82° 82° 585.402 587.045 1.516 2 1.690 1.665 1.647 85.2° 85.2° 588.457 590.051 o optical 1.516 2 1.522 1.533 1.542 85.55° 85.37° 591.038 602.760 1.516 2 1.522 1.533 1.542 85.56° 85.39° 589.534 599.883 1.516 2 1.522 1.533 1.542 85.57° 85.40° 588.031 598.447 1.516 2 1.522 1.533 1.542 85.58° 85.42° 586.529 595.575 1.516 2 1.522 1.533 1.542 85.59° 85.44° 585.028 592.707 -
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