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上转换成像是基于非线性晶体中的和频过程(Sum-Frequency Generation, SFG)的一种技术,其中频率为$ {\omega _s} $的中红外信号光通过频率为$ {\omega _p} $的泵浦光上转换为$ {\omega _{S F}} $的和频光。该过程满足能量守恒定律,即$ \hbar {\omega _s} + \hbar {\omega _p} = \hbar {\omega _{S F}} $,其中$ \hbar $是普朗克常数。为了利用最高的晶体非线性系数,准相位匹配(Quasi-Phase Match, QPM)技术被提出并广泛应用于补偿三束光在晶体内的相位失配,并且晶体的极化周期引入的空间矢量$ {\stackrel{\rightharpoonup }{k}}_{\varLambda } $被设计为$ \Delta \stackrel{\rightharpoonup }{k}={\stackrel{\rightharpoonup }{k}}_{s}+{\stackrel{\rightharpoonup }{k}}_{p}+{\stackrel{\rightharpoonup }{k}}_{\varLambda }-{\stackrel{\rightharpoonup }{k}}_{S F}=0 $,满足动量守恒条件。在大多数非线性过程的应用场景中,一般利用共线匹配以实现更大长度的光束交叠区域,从而获得更高的转换效率。然而,对于图像上转换场景,图像不同部分在晶体内的传播角度不同,因此非共线相位匹配将直接影响上转换成像的视场、效率、带宽等重要参数。在传播方向与垂直传播方向上分解空间矢量,如图1所示,可以将相位匹配条件用公式(1)描述:
$$ \left\{ \begin{array}{l} {k_{S F}}\cos \varphi = {k_s}\cos \theta + {k_p} + {k_{\rm{\varLambda}} } \\ {k_{S F}}\sin \varphi = {k_s}\sin \theta \end{array} \right. $$ (1) 式中:$ {k_s},{k_p},{k_{S F}},{k_\varLambda } $分别代表中红外信号光、泵浦光、和频光和晶体极化引入的空间矢量大小,可以表示为$ {k_i} = 2\pi {n_i}/{\varLambda _i}(i = s,p,S F) $,$ {n_i} $和$ {\varLambda _i} $分别为三束光在晶体中的折射率(一般与波长、晶体温度相干,可利用smellier公式求解)和在真空中的波长,$ {k_\varLambda } = 2\pi m/\varLambda $,$ m $为相位匹配阶数,$ \varLambda $为晶体的极化周期长度;$ \theta $和$ \varphi $分别表示信号光、和频光与传播方向的夹角。
在实际转换过程中,泵浦光的波长和传输方向通常是确定的,结合能量守恒方程,利用公式(1)可以建立起晶体极化引入的格矢量大小$ {k_\varLambda } $与信号光波长$ {\varLambda _s} $、入射角度$ \theta $的二元函数关系。因此在上转换成像过程中,转换带宽和视场大小是相互关联的两个参量,即一般较大的转换带宽对应着较大的转换视场。对于确定的信号光波长,如图2所示,一般而言随着入射角度$ \theta $增大,满足相位匹配条件的格矢量大小$ {k_\varLambda } $越大,即需要更小的极化周期。
单周期极化铌酸锂(PPLN)晶体常用于红外上转换技术中,由于具有确定且唯一的极化周期(即唯一确定的极化空间格矢),其转换带宽和视场角度都相应较小,这在一定程度上限制了大带宽、大视场角的上转换成像技术发展。解决这些问题的可行解决方案有:在晶体中制造温度梯度,或者利用具有宽谱泵浦光进行泵浦[19-20],即在公式(1)中增加一个可调谐的自变量,从而扩大满足相位匹配条件的波长和角度范围。然而,这类方案不仅增加了系统的复杂程度,对泵浦光源也提出了更高的要求,使其难以满足各种应用场景。另一种方案是采用在极化过程中引入不同极化周期的啁啾极化晶体,相当于$ {k_\varLambda } $具有一系列不同的取值,从而极大地增加了晶体的转换接受带宽和成像视场。 如图2所示,红色阴影区域表示单周期极化晶体的匹配范围,蓝色阴影区域代表啁啾极化晶体的匹配范围。 因此,啁啾极化晶体在接受带宽和视场角度的表现上优于单周期极化晶体。
图 2 铌酸锂晶体处于30 ℃,在1080 nm泵浦光作用下,不同极化周期对应的相位匹配波长和角度的关系图
Figure 2. The relationship between phase matching wavelength and half-angle of the field of view with different polarization periods of lithium niobite (LN) crystal at 30 ℃ under the action of 1080 nm pump beam
在成像应用中,特别是当探测目标为物体热辐射发出的完全非相干光时,信号光中包含了不同的波长和空间角度分量。这种应用场景需要不同的极化周期来满足相位匹配条件,以实现大视场和大带宽的图像转换,因此啁啾极化晶体在中红外上转换成像领域具有显著优势。
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耦合波方程描述了三束光的电矢量在晶体内传播过程中的相互作用,可以写为[21-22]:
$$ {\nabla }^{2}\stackrel{\rightharpoonup }{E}\left({\omega }_{n},z\right)+{\mu }_{0}{\omega }_{n}^{2}\stackrel{\rightharpoonup }{\varepsilon }\left({\omega }_{n},z\right)\cdot\stackrel{\rightharpoonup }{E}\left({\omega }_{n},z\right)=-{\mu }_{0}{\omega }_{n}^{2}\stackrel{\rightharpoonup }{{P}_{NL}}\left({\omega }_{n},z\right) $$ (2) 对于二阶非线性和频过程,在慢变振幅近似的条件下,和频光束的电场复振幅沿传播方向(假设为z轴)变化的标量方程可以表达为:
$$ i2{k_{S F}}\frac{{\partial {E_{S F}}}}{{\partial z}} + \nabla _ \bot ^2{E_{S F}} = - \frac{{\omega _{S F}^2{d_{eff}}}}{{{\varepsilon _0}{c^2}}}{E_s}{E_p}{{\rm{e}}^{i\Delta kz}} $$ (3) 式中:$ \Delta k = {k_{S F}} - {k_{sz}} - {k_{pz}} + 2\pi /\varLambda $为和频过程中传播方向上的相位失配;$ {k_{sz}},{k_{pz}} $分别代表信号光和泵浦光波矢在z方向上的投影大小;$ {\varepsilon _0} $和$ c $分别代表真空中的介电常数和光速;$ {d_{eff}} $为有效非线性系数;$ {E_i}\left( i = s,p,SF \right) $分别代表信号光、泵浦光和和频光的标量复振幅;$ \nabla _ \bot ^2{\text{ = }}\dfrac{{{\partial ^2}}}{{\partial {x^2}}}{\text{ + }}\dfrac{{{\partial ^2}}}{{\partial {y^2}}} $代表垂直传播方向的拉普拉斯算子。
信号光、泵浦光以及和频光在入射晶体前的复振幅分布信息是容易确定的,即z=0位置$ {E_i}\left( {i = s,p,S F} \right) $分布确定。根据此条件,可以利用向前差分方法离散和频光的耦合波方程:
$$ {E_{S F}}\left( {x,y,z + {\mathrm{d}}z} \right) = {E_{S F}}\left( {x,y,z} \right) + \frac{i}{{2{k_{S F}}}}\left[ {\nabla _ \bot ^2{E_{S F}}\left( {x,y,z} \right) + \frac{{\omega _{S F}^2{d_{eff}}}}{{{\varepsilon _0}{c^2}}}{E_s}\left( {x,y,z} \right){E_p}\left( {x,y,z} \right){{\mathrm{e}}^{i\Delta kz}}} \right]{\mathrm{d}}z $$ (4) 通过这种离散方法,在初始条件已知的情况下,可以对晶体内任意位置处的三束光的复振幅和强度分布进行求解。相比于传统的分步傅里叶方法,由于同时考虑了传播和非线性演化,这种计算方法将带来更高的计算精度。
对于非相干照明情况,可以对在z=0位置处的$ {E_s} $添加随机相位并多次求解取平均值、改变传播方向(即改变$ \Delta k $),从而消除了信号光的空间相干性和时间相干性。以此为基础模拟非相干照明光场,可以对图像转换进行较为准确的数值计算。
Mid-infrared up-conversion imaging based on chirp polarization crystals
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摘要: 将物体辐射或反射的中红外波段光转换到可见光区域、再利用高性能的硅基器件探测是一种有效的目标识别手段,规避了传统半导体中红外探测器在灵敏度、深制冷和噪声等性能方面的不足。文中利用啁啾极化的非线性晶体,在强连续泵浦光作用下,将中红外波段的光场信息高效、高保真地迁移到可见光域进行探测。通过建立简单的物理模型,理论上讨论了啁啾极化晶体参数对上转换成像性能的影响,并进行了数值仿真;通过实验进一步研究了啁啾晶体上转换方法在转换带宽、成像视场等成像关键参数上的优势,实验结果与理论计算值吻合较好。通过上转换方法,演示了相干光与非相干光照明条件下目标探测,实现了相干光照明下的光学边缘增强成像和非相干照明下的热辐射目标识别。这一工作对基于啁啾晶体的上转换成像系统的理解、设计和实际应用具有重要参考价值。Abstract:
Objective The mid-infrared band (2.5-25 μm) has important applications in the field of spectroscopy and imaging. Spectral migration technique up-converts mid-infrared signal light to visible/near-infrared light through a non-linear frequency process, which is then detected using high-performance detectors based on wide-band gap materials such as silicon. Compared to schemes directly using traditional semiconductor detectors, this technique has the advantages of fast response and room temperature operation. Bulk crystals have large aperture to realize array detection. In particular, chirped polarized crystals have obvious advantages in imaging acceptance bandwidth and field of view due to their large phase-matching bandwidth. Previous up-conversion imaging theory, however, didn't consider the nonlinear process of signal light in the crystal to affect the propagation. Therefore, there is some deviation between the theoretical analysis and the up-conversion imaging results under the weak signal light condition. Based on the basic imaging principle, a simple physical model of the up-conversion imaging process is presented by solving the coupled wave equation using finite difference method and considering the effect of nonlinear process on the optical propagation. On this basis, a theoretical derivation for up-conversion imaging under coherent/incoherent radiation illumination conditions based on chirped polarized crystals is provided. Methods A mid-infrared up-conversion detection imaging system based on a chirped polarized crystal is built (Fig.3). The target object is illuminated by the thermal radiation of an electric soldering iron, then the visible light in the signal is filtered out by a band pass filter (BP1). A strong 1 080 nm pump light is directed into the crystal through a dichroic mirror (DM) along with the signal beam. Through a 4f system, the up-conversion results of the target are imaged on the EMC CD. A chirped polarized lithium niobate (CPLN) crystal with a period interval of 0.01 μm and a period range of 21.6-23.4 μm is used in the experiment. The length of the crystals is 40 mm and the cross section size is 2 mm×3 mm. The temperature of CPLN crystal is controlled by a home-made temperature controller, whose fluctuation is ±0.002 ℃. Results and Discussions By using a mature spectrometer to measure the spectrum after up-conversion and combining with the law of conservation of energy, the accepted spectrum of the up-conversion process in the corresponding mid-infrared band can be obtained (Fig.4). The corresponding mid-infrared acceptance range is 2 915-3 512 nm, and its full-width of half-max (FWHM) is 597 nm. Due to the low transmittance of the DM at wavelengths greater than 3 400 nm, the actual conversion bandwidth is larger than the direct measurement results, which is in agreement with the numerical calculation results (Fig.2). In contrast, the wavelength acceptance bandwidth of single-period polarized crystals is only on the order of nanometers. In the up-conversion imaging results (Fig.5), the largest one-dimensional size of the target is 3.62 cm, corresponding to 125 mm propagation distance, thus the full angle of the field of view is 16.59°, which is slightly smaller than the numerical calculation result in Fig.2. Under the condition of weak signal light, the background of pattern directly imaged by mid-infrared light through the mercury cadmium telluride thermal imager is full of white noise, making it difficult to identify the target contour information, while the pattern obtained by the up-conversion method with the same power of light has clean background and high signal-to-noise ratio (SNR), which also can realize high SNR of the single photon level imaging (Fig.6-7). In addition, applications of up-conversion imaging under coherent/incoherent radiation illumination conditions are reported. The optical edge enhancement imaging is realized for the objects illuminated by mid-infrared coherent light (Fig.8). Real-time video frame rate imaging of incoherent illuminated objects is realized, and its temperature characteristics can be analyzed (Fig.9). Conclusions In the experiment, chirped polarized crystal is used to realize the up-conversion imaging detection of the mid-infrared receiving bandwidth of 597 nm and the field angle of view of 16.59°. By comparing with traditional mercury cadmium telluride mid-infrared detector, the up-conversion imaging technique has obvious advantages in improving the signal-to-noise ratio and sensitivity of imaging, and the low-light imaging of mid-infrared is realized by using the photon flux of 1.05×105 Hz. The paper further shows the application of the up-conversion imaging system to the objects illuminated by correlation light and incoherent light. This work has conducted a comprehensive study on the up-conversion based infrared imaging system, which will provide a basis for the design of various application scenarios and improve the system design. -
Key words:
- mid-infrared imaging /
- up-conversion /
- chirped polarization crystal /
- bandwidth /
- efficiency
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图 8 泵浦光具有不同空间模式时的成像结果。(a1)~(a4)泵浦光为高斯模式,实现了对光透过物体部分的成像;(b1)~(b4)泵浦光为拉盖尔-高斯模式,实现了对中红外信号光的边缘增强成像
Figure 8. Imaging results of pump with different spatial modes. (a1)-(a4) Pump is in Gaussian mode, achieving imaging of the signal passing through the object; (b1)-(b4) Pump is in Laguerre-Gaussian mode, achieving edge enhanced imaging of mid-infrared signal
图 10 不同温度电烙铁在热背景中的成像结果。(a)电烙铁温度高于背景;(b)电烙铁温度近似等于背景温度;(c)电烙铁温度低于背景温度;(d)~(f)烙铁在室温背景下成像结果,对应温度分别为333 、453、763 K
Figure 10. Imaging results of soldering irons at different temperatures in a thermal background. (a) The temperature of the soldering iron is higher than the background; (b) The temperature of the soldering iron is approximately equal to the background temperature; (c) The temperature of the soldering iron is lower than the background temperature; (d)-(f) Imaging results of soldering iron under room temperature background, corresponding to temperatures of 333, 453, and 763 K, respectively
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