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1、光电子学作业参考答案,作业1,Fundamentals of Photonics （括号内为中文教材上题目的位置）： 1.4-1 1.4-4 3.1-2 (P41-2) 3.1-3 (P41-3) 3.2-1 (P41-4),作业1,1.4-1 Ray-Transfer Matrix of a Lens System. Determine the ray-transfer matrix for an optical system made of a thin convex lens of focal length f and a thin concave lens of focal lengt
2、h -f separated by a distance f. Discuss the imaging properties of this composite lens.,f,-f,f,作业1,注意矩阵相乘的顺序,作业1,1.4-4 4X4 Ray-Transfer Matrix for Skewed Rays. Matrix methods may be generalized to describe skewed paraxial rays in circularly symmetric systems, and to astigmatic (non-circularly symmetr
3、ic) systems. A ray crossing the plane z=0 is generally characterized by four variables-the coordinates (x, y) of its position in the plane, and the angles ( ) that its projections in the x-z and y-z planes make with the z axis. The emerging ray is also characterized by four variables linearly relate
4、d to the initial four variables. The optical system may then be characterized completely, within the paraxial approximation, by a 4X4 matrix. (a)Determine the 4X4 ray-transfer matrix of a distance d in free space. (b)Determine the 4X4 ray-transfer matrix of a thin cylindrical lens with focal length
5、f oriented in the y direction (Fig. P1.4-4). The cylindrical lens has focal length f for rays in the y-z plane, and no focusing power for rays in the x-z plane. 可列式求解：,作业1,(a)过长度为d的自由空间，光线角度不变，位置改变 (近轴光线 ),作业1,(b)薄透镜厚度d 0, y-z面上为焦距为f的薄透镜,作业1,3.1-2 Beam Identification by Two Widths. A Gaussian beam o
6、f wavelength =10.6 pm (emitted by a CO2 laser) has widths W1=1.699mm and W2=3.38mm at two points separated by a distance d=10 cm. Determine the location of the waist and the waist radius. 借助公式： 可求解，计算较麻烦,作业1,由方程组可得 （舍去） 由(2)得: 解得： 所以 或者,作业1,3.1-3 The Elliptic Gaussian Beam. The paraxial Helmholtz eq
7、uation admits a Gaussian beam with intensity in the z=0 plane, with beam waist radii W0x and W0y in the x and y-directions respectively. The contours of constant intensity are therefore ellipses instead of circles. Write expressions for the beam depth of focus, angular divergence, and radii of curva
8、ture in the x and y directions, as functions of W0x W0y, and the wavelength . If W0x=2W0y sketch the shape of the beam spot in the z=0 plane and in the far field (z much greater than the depths of focus in both transverse directions). X和Y两方向独立求解,作业1,(a) (1)扩散角： (2)焦深： (3)曲率半径：,作业1,(b)当W0x=2W0y时: (1)
9、z=0 (2)z=Mz0,作业1,3.2-1 Beam Focusing. An argon-ion laser produces a Gaussian beam of wavelength =488 nm and waist radius W0=0.5 mm. Design a single-lens optical system for focusing the light to a spot of diameter 100 um. What is the shortest focal-length lens that may be used?,作业1,由(3.2-5)及(3.2-9)得：
10、 求导得：,作业1,故z=0.1z0 即f=161.75mm时候，f取得最小值,作业2,Fundamentals of Photonics （括号内为中文教材上题目的位置）： 1. 3.1-1 (P41-1) 2. 3.2-2 (P41-5) 3. 3.2-3 (P41-6) 4. 9.1-1 (P42-10) 5. 9.1-2 (P43-11),作业2,3.1-1 Beam Parameters. The light from a Nd:YAG laser at wavelength 1.06 um is a Gaussian beam of 1-W optical power and be
11、am divergence 2 =1mrad. Determine the beam waist radius, the depth of focus, the maximum intensity, and the intensity on the beam axis at a distance z=100cm from the beam waist. 本题求解激光（高斯）光束的束腰半径，焦深，最大光强和在光轴上z=100cm处的光强,作业2,由发散角公式 得 由 得：,作业2,由光功率公式： 得： 由光轴上的光强分布公式 得：,作业2,3.2-2 Spot Size. A Gaussian
12、beam of Rayleigh range z0 =50cm and wavelength =488nm is converted into a Gaussian beam of waist radius using a lens of focal length f=5cm at a distance z from its waist, as illustrated in Fig. 3.2-2. Write a computer program to plot Wd as a function of z. Verify that in the limit z-fz0(3.2-10) and
13、(3.2-12) hold; and in the limit zz0 (3.2-13) holds. 本题是证明题，涉及高斯光束聚焦，需要简单编程,作业2,涉及公式：,作业2,原函数： z0=50;r=0.0000488;f=5; for z=0:0.1:1000; w0=abs(f/(z-f)/sqrt(1+(z0/(z-f)2)*sqrt(r*z0/pi); plot(z,w0,r); hold on; end,作业2,（1）当z-fz0时 该近似在z400后与原图像差别不大,作业2,(2)当zz0时 该近似在zz0时可使用,作业2,3.2-3 Beam Refraction. A Ga
14、ussian beam is incident from air (n=1) into a medium with a planar boundary and refractive index n=1.5. The beam axis is normal to the boundary and the beam waist lies at the boundary. Sketch the transmitted beam. If the angular divergence of the beam in air is 1 mrad, what is the angular divergence
15、 in the medium? 求解高斯光束经过光学系统后的变化，一般用ABCD法则来求解,作业2,复参数q表达形式： 界面传输矩阵为: q参数满足ABCD法则： 则： 又 故： 发散角 为：,作业2,9.1-1 Resonance Frequencies of a Resonator with an Etalon. (a) Determine the spacing between adjacent resonance frequencies in a resonator constructed of two parallel planar mirrors separated by a di
16、stance d=15 cm in air (n=1). (b) A transparent plate of thickness d1=2.5 cm and refractive index n=1.5 is placed inside the resonator and is tilted slightly to prevent light reflected from the plate from reaching the mirrors. Determine the spacing between the resonance frequencies of the resonator. 求纵模间隔，直接带入公式,作业2,(a) (b),作业2,9.1-2 Mirrorless Resonators. Semiconductor lasers are often fabric
