ABSTRACT 1. INTRODUCTION

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1 Laser Speckle Suppression by the Phase Modulation of Input Beam in a Multimode Fiber Cong Yang* 1,2,3, Jian Han 1,2, Yuanjie Wu 1,2,3, Huiqi Ye 1,2, Dong Xiao 1,2 1.National Astronomical Observatories / Nanjing Institute of Astronomical Optics & Technology, Chinese Academy of Sciences, Nanjing, P.R.China 2.Key Laboratory of Astronomical Optics &Technology, Nanjing Institute of Astronomical Optics & Technology, Chinese Academy of Sciences, Nanjing, P.R.China 3. University of Chinese Academy of Sciences, Beijing, P.R.China ABSTRACT When a multimode fiber transmits a laser beam, the speckle will form in its output field. A dynamic fiber scrambler could be used to suppress the speckle. No matter what actual way of suppressing speckle is, such as fiber scrambling or using a rotating phase plate, the suppression is the result of exerting disturbance in the process of the speckle forming. We could disturb the phase of the input beam with specific method to weaken the speckle effect. To get a speckle image formed by a multimode fiber, we simulate different diffraction patterns under different phase conditions using diffraction model, in which the phase of the input beam is modulated by a rough surface, and then sum them to form the instantaneous speckle. To study the speckle suppression, we superpose instantaneous speckles, and as a consequence the final speckle is suppressed. The simulation would help us understand the speckle suppression experiment with the input beam phase modulation conducted in our lab. Keywords: multimode fiber, speckle suppression, phase modulation, simulation 1. INTRODUCTION When a laser beam was reflected from a rough surface, a high-contrast, fine-scale granular pattern would be seen by an observer looking at the scattering spot. This fine spotted structure is known as speckle, it could be found in many occasions, such as a laser beam passing through a frosted glass, reflecting from a paper, propagating through a multimode fiber and so on. With more and more in-depth research, two main aspects, speckle suppression and taking advantage of it have been studied extensively. In a multimode fiber, multitudes of propagating modes exist. From a geometrical-optics point-of-view, these rays of different modes propagate in various paths at different angles to the axis of the fiber. The rays travel varying distances for the reason of their different angles of propagation to the axis, and lead to different phase delays as they propagate from the input to the output of the fiber. A more complex electromagnetic theory of transmitting light in a multimode fiber shows more propagate modes existing with a number of different phase velocities in a multimode fiber. According to the theory of diffraction, the light at any point on the output field of the fiber is a sum of multitudes of individual field contributions. If the phase delays of modes in the multimode fiber vary by more than 2π radians, the output field of the fiber appears speckle phenomenon [1]. In addition to the reason above, the diffraction effect from the interface between the fiber core and cladding contribute the speckle formation from a multimode fiber.. In astronomy, fibers are widely used to transmit light beams. However the output beam from a multimode fiber has speckle phenomenon. In a high resolution spectrograph, such as the HARPS at ESO [2], a multimode fiber is used to transmit the star light and reference light into the spectrograph. When transmitting the coherent light, the speckle is formed at the output beam, reducing the precision of spectra measurement. cyang@niaot.ac.cn; phone ; fax ; Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation, edited by Ramón Navarro, Colin R. Cunningham, Allison A. Barto, Proc. of SPIE Vol. 9151, 91514U 214 SPIE CCC code: X/14/$18 doi: / Proc. of SPIE Vol U-1

2 In a high-precision spectral calibration system based on Astronomical Frequency Comb, a multimode fiber is used to transmit the coherent light. A great effort should be paid to eliminate the error introduced by the speckle. To restrain speckle, exerting disturbance in the process of speckle forming is an effective way to get suppressed speckle. Researchers exert mechanical disturbance on the fiber in the process of speckle forming to superpose speckle [3], [4]. 2. SIMULATION OF SPECKLE FORMATION BY A MULTIMODE FIBER To simulate the speckle from a multimode fiber (a step-index fiber), which is determined by both the modular interference and the interface between the fiber core and cladding, here we consider only the interface as a simplification. As Figure 1 shows, a ray of the laser beam would reflect from the interface in the fiber, we could get its diffraction pattern. The rays propagate through the multipath, so we sum all of the diffraction patterns to get the speckle in the output field. fiber cladding fiber core rays Figure 1.The optical multipath of laser beam in a fiber As the interface of fiber core and cladding is rough, we use the following diffraction model to simulate the all reflections of a ray in a multimode fiber. laser beam rough surface lens image plane Figure 2. The diffraction model. The final optical field at the image plane is [5] : 1 π z i4 h( x, y ) i2 π ( xx + yy ) U( x, y) = exp[ i (1 )( x + y )] P( x, y )exp[ ]exp[ ] dx dy iλ f λ f f λ λ f Px (, y ) is the complex amplitude distribution of laser beam at the object plane. rough surface [6]. 2 2 ( x u ) + ( y u ) hx (, y) ( u, u)exp[ 2 ] d d v π v w + x y = η x y 2 ux u y (1) hx (, y ) is the height of the (2) Proc. of SPIE Vol U-2

3 λ =.532µm, z =1 5 µm, f =2 1 5 µm, v =3µm, w =.48µm to.53µm; Object plane( x, y ) : 1µm 1µm, integral reference plane( u, u ): 3µm 3µm, η( u, u ) is a white noise.the matrix is of size 256 by 256 pixels. x y x As the rough surface is the determining factor of the diffraction pattern, and its height is Gaussian distributed in natural situations, we simulate a series of rough surfaces whose height distributions are Gaussian. Figure 3 shows cross section of a rough surface and shows height statistical histogram of the surface. y Height/µm v =3µm, w =.5µm Height value frequency/µm Height statistical histogra Height stastistical histogram -.$ Middle cross section Height value range/µm Figure 3.A rough surface whose height distribution is Gaussian a) Middle cross section of the rough surface b) Height statistical histogram of the rough surface A laser beam transmits through a rough transparent body, with different hx (, y ) distributions, different modulated laser beam emerging as different diffraction patterns. Figure 4 shows two different diffraction patterns we get.. Figure 4.Two different diffraction patterns. a) v =3µm, w =.53µm b) v =3µm, w =.48µm. Proc. of SPIE Vol U-3

4 In a multimode fiber, we sum different diffraction patterns of rays (Figure 4. shows) to simulate the instantaneous speckle formed by a multimode fiber [7]. The key point is the phase distributions of the rough surfaces. We use 6 different w to generate the rough surfaces, after the diffraction procedure producing 6 different diffraction patterns; parameters w obeys the Gaussian distribution, whose mean value ' u w ' is.µm, mean square error ' σ w ' is.2µm. Figure 5 shows the instantaneous speckle formed by a multimode fiber we simulate Middle cross section of the input Gaussian beam Middle cross section of the instantaneous speckle Intensity Absolute difference.2 Figure 5.The instantaneous speckle. a) Speckle intensities. b) Middle cross section of speckle intensities Middle cross section/pixel The number of pixels Speckle intensities Figure 6. Intensities statistical histogram of the speckle The speckle formed by a multimode fiber is circular and its intensities are exponential probability density distributed [8]. The instantaneous speckle we simulate has the same characteristics (shown in Figure5 and Figure (6)), so we can use the instantaneous speckle we simulate to study some aspects of the real speckle formed by a multimode fiber. Proc. of SPIE Vol U-4

5 3. SPECKLE SUPPRESSION 3.1 Implementation of speckle suppression: Phase Modulation The speckle we see or recorded by a CCD are the speckle intensities homogenizing effect in our visual persistence time or in the CCD s exposure time, so we could study speckle intensities superposition. A laser beam with a specific phase could form its unique speckle. The speckle we observed is the superimposed effect over time; without modulating the phase of input beam, the same speckle would appear as high-contrast speckle. When modulating the phase contribution of input beam dynamically, the homogenizing effect over time makes the contrast of speckle to turn lower. That means, no matter what actually the method you adopt, as long as the essence of your work is exerting disturbance in the process of the speckle formation, speckle will be suppressed. In our simulation, we take 6 instantaneous speckles superposing to simulate the speckle under disturbance. The 6 different speckle intensities are created by different w. The superposed speckle is shown in Figure 6. Table 1.Six sets of w ; the parameters are Gaussian - random numbers Groups u w (um) σ (um) w Middle cross section of the input Gaussian beam Middle cross section of the supposed speckle Intensity Absolute difference Middle cross section /pixel Figure 7. Superposed speckle. a) Speckle intensities. b) Middle cross section of speckle intensities. Figure 5 shows the instantaneous speckle from a multimode fiber we simulate. If no disturbance in the process of the speckle formation, so the speckle intensities homogenizing process doesn t affect the speckle we see or record by a CCD. Then the contrast of the superposed speckle is the same as the contrast of the instantaneous speckle. Figure 5 shows the cross section of the instantaneous speckle and the input Gaussian beam. Figure 7 shows when exerting disturbance, speckle recede. Figure 7 shows the cross section of the superposed speckle and the input Gaussian beam. From the two figures, we could easily see that the superposed speckle has more uniform intensity than the instantaneous speckle. Proc. of SPIE Vol U-5

6 3.2 Illustrative test We verify the speckle suppression by modulating the phase distribution of input beam experimentally. In our experiment the light beam transmit through a rotating phase plate. Laser(635nm):lP635-SF8 diode laser Micro-objective: SINGMA 1x Fiber:fiber diameter D=3μm,Plastic CCD: HV1351UC,pixels: Phase Plate:quartz material, the phase distribution is of Kolmogorov,modulation depth:d=16μm [9] Collimation & expander system 准直扩束系统 CCD1 CCD1 Micro-objective 显微物镜 CCD2 CCD2 Laser Rotating phase 相位板 plate Computer 计算机 Figure 8. Schematic diagram of experimental set-up. The laser beam is expanded and collimated, then coupled to a multimode fiber uses an objective. CCD1 monitors the input beam; CCD2 receives the speckle, recorded by computer. The speckle we get is shown in Figure 8. When we place a rotating phase plate in the middle of collimating & expanding system and objective lens, and set its rotating rate to 7 rounds per minute, the speckle is shown in Figure 8. The rotating phase plate modulates the phase of input beam. In the experiment, with the rotating rate increasing from to 7 rounds per minute, light spot intensity gets more and more homogenized. Figure 9.Speckle under phase modulation in our lab.a) Rotating rate is r/min. b) Rotating rate is 7r/min. Proc. of SPIE Vol U-6

7 Y X Figure 1. Speckle cross section in our experiment a) Rotating rate is r/mi. b) Rotating rate is 7r/min. 4. CONCLUSION From diffraction patterns formed by different rough surfaces, we simulate the speckle from a multimode fiber. Adopting an appropriate combination of the rough surfaces to modulate the laser beam, their diffraction patterns form the instantaneous speckle. And then we superpose different instantaneous speckle to study the suppression of the speckle after modulating the phase of the input beam. The result shows exerting disturbance in the process of the speckle formation is an effective way to suppress speckle. ACKNOWLEDGEMENTS This work is supported by the National Natural Science Foundation of China (Grant No ). Proc. of SPIE Vol U-7

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