Experimental determination of the azimuthal and radial mode orders of a partially coherent LG<italic><sub>pl</sub></italic> beam (Invited Paper)

Xianlong Liu; Tengfei Wu; Lin Liu; Chengliang Zhao; Yangjian Cai

doi:doi:10.3788/COL201715.030002

Chinese Optics Letters, 2017, 15 (3): 030002, Published Online: Jul. 25, 2018

Experimental determination of the azimuthal and radial mode orders of a partially coherent LG_pl beam (Invited Paper)

Xianlong Liu ^1,2Tengfei Wu ^1,2Lin Liu ^1,2Chengliang Zhao ^1,2Yangjian Cai ^1,2,*

Author Affiliations

¹ College of Physics, Optoelectronics and Energy & Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China

² Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province and Key Lab of Modern Optical Technologies of Education Ministry of China, Soochow University, Suzhou 215006, China

Figures & Tables

Fig. 1. Distributions of the normalized average intensity and modulus of the correlation functions of a partially coherent LGpl beam with p=1, l=1, ω0=0.57 mm, and δg=0.8 mm in the focal plane. (a) I(r), (b) |μ(r,0)|, (c) |μ(r,−r)|, and (d) |μ(r,2r)|.

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Fig. 2. Distribution of the normalized modulus of the DCF of a partially coherent LGpl beam for different l with p=1. (a) l=0, (b) l=1, (c) l=2, and (d) l=3.

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Fig. 3. Distribution of the normalized modulus of the DCF of a partially coherent LGpl beam for different p with l=6 in the focal plane. (a) p=0, (b) p=1, (c) p=2, and (d) p=3.

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Fig. 4. Experimental setup for generating a partially coherent LGpl beam and measuring the correlation functions. NDF, neutral density filter; BE, beam expander; L1, L2, L3, thin lenses; GAF, Gaussian amplitude filter; CA, circular aperture; PC1, PC2, personal computers.

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Fig. 5. Schematic for the transformations of the intensity matrix. The matrices with green, yellow, and red elements denote the intensity matrix In(x,y), the first sub-matrix In′(x′,y′), and the second sub-matrix In′(2x′,2y′), respectively.

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Fig. 6. Experimental results of the average intensity and square of the normalized modulus of different correlation functions of the generated partially coherent LGpl beam in the focal plane with p=1 and l=1. (a) I(r), (b) |μ(r,0)|2, (c) |μ(r,−r)|2, and (d) |μ(r,2r)|2.

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Fig. 7. Experimental results of the square of the normalized modulus of the DCF of the generated partially coherent LGpl beam with p=1 for different l in the focal plane. (a) l=0, (b) l=1, (c) l=2, and (d) l=3.

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Fig. 8. Experimental results of the square of the normalized modulus of the DCF of the generated partially coherent LGpl beam with l=6 for different p in the focal plane. (a) p=0, (b) p=1, (c) p=2, and (d) p=3.

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Xianlong Liu, Tengfei Wu, Lin Liu, Chengliang Zhao, Yangjian Cai. Experimental determination of the azimuthal and radial mode orders of a partially coherent LG_pl beam (Invited Paper)[J]. Chinese Optics Letters, 2017, 15(3): 030002.

Experimental determination of the azimuthal and radial mode orders of a partially coherent LG_pl beam (Invited Paper)

Fig. 1. Distributions of the normalized average intensity and modulus of the correlation functions of a partially coherent LGpl beam with p=1, l=1, ω0=0.57 mm, and δg=0.8 mm in the focal plane. (a) I(r), (b) |μ(r,0)|, (c) |μ(r,−r)|, and (d) |μ(r,2r)|.

Fig. 2. Distribution of the normalized modulus of the DCF of a partially coherent LGpl beam for different l with p=1. (a) l=0, (b) l=1, (c) l=2, and (d) l=3.

Fig. 3. Distribution of the normalized modulus of the DCF of a partially coherent LGpl beam for different p with l=6 in the focal plane. (a) p=0, (b) p=1, (c) p=2, and (d) p=3.

Fig. 4. Experimental setup for generating a partially coherent LGpl beam and measuring the correlation functions. NDF, neutral density filter; BE, beam expander; L1, L2, L3, thin lenses; GAF, Gaussian amplitude filter; CA, circular aperture; PC1, PC2, personal computers.

Fig. 5. Schematic for the transformations of the intensity matrix. The matrices with green, yellow, and red elements denote the intensity matrix In(x,y), the first sub-matrix In′(x′,y′), and the second sub-matrix In′(2x′,2y′), respectively.

Fig. 6. Experimental results of the average intensity and square of the normalized modulus of different correlation functions of the generated partially coherent LGpl beam in the focal plane with p=1 and l=1. (a) I(r), (b) |μ(r,0)|2, (c) |μ(r,−r)|2, and (d) |μ(r,2r)|2.

Fig. 7. Experimental results of the square of the normalized modulus of the DCF of the generated partially coherent LGpl beam with p=1 for different l in the focal plane. (a) l=0, (b) l=1, (c) l=2, and (d) l=3.

Fig. 8. Experimental results of the square of the normalized modulus of the DCF of the generated partially coherent LGpl beam with l=6 for different p in the focal plane. (a) p=0, (b) p=1, (c) p=2, and (d) p=3.

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Experimental determination of the azimuthal and radial mode orders of a partially coherent LGpl beam (Invited Paper)

Fig. 1. Distributions of the normalized average intensity and modulus of the correlation functions of a partially coherent LGpl beam with p=1, l=1, ω0=0.57 mm, and δg=0.8 mm in the focal plane. (a) I(r), (b) |μ(r,0)|, (c) |μ(r,−r)|, and (d) |μ(r,2r)|.

Fig. 2. Distribution of the normalized modulus of the DCF of a partially coherent LGpl beam for different l with p=1. (a) l=0, (b) l=1, (c) l=2, and (d) l=3.

Fig. 3. Distribution of the normalized modulus of the DCF of a partially coherent LGpl beam for different p with l=6 in the focal plane. (a) p=0, (b) p=1, (c) p=2, and (d) p=3.

Fig. 4. Experimental setup for generating a partially coherent LGpl beam and measuring the correlation functions. NDF, neutral density filter; BE, beam expander; L1, L2, L3, thin lenses; GAF, Gaussian amplitude filter; CA, circular aperture; PC1, PC2, personal computers.

Fig. 5. Schematic for the transformations of the intensity matrix. The matrices with green, yellow, and red elements denote the intensity matrix In(x,y), the first sub-matrix In′(x′,y′), and the second sub-matrix In′(2x′,2y′), respectively.

Fig. 6. Experimental results of the average intensity and square of the normalized modulus of different correlation functions of the generated partially coherent LGpl beam in the focal plane with p=1 and l=1. (a) I(r), (b) |μ(r,0)|2, (c) |μ(r,−r)|2, and (d) |μ(r,2r)|2.

Fig. 7. Experimental results of the square of the normalized modulus of the DCF of the generated partially coherent LGpl beam with p=1 for different l in the focal plane. (a) l=0, (b) l=1, (c) l=2, and (d) l=3.

Fig. 8. Experimental results of the square of the normalized modulus of the DCF of the generated partially coherent LGpl beam with l=6 for different p in the focal plane. (a) p=0, (b) p=1, (c) p=2, and (d) p=3.

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Experimental determination of the azimuthal and radial mode orders of a partially coherent LG_pl beam (Invited Paper)