• Optical Instruments
  • Vol. 44, Issue 6, 36 (2022)
Pengkun ZHENG and Jian CHEN*
Author Affiliations
  • School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
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    DOI: 10.3969/j.issn.1005-5630.2022.006.006 Cite this Article
    Pengkun ZHENG, Jian CHEN. Method for generating highly confined linearly polarized spatiotemporal optical vortices[J]. Optical Instruments, 2022, 44(6): 36 Copy Citation Text show less

    Abstract

    Spatiotemporal optical vortices (STOVs) carrying transverse orbital angular momentum are a new type of optical pulse wave packet, and attract more and more attention from researchers around the world. In this paper, we present a method of generating linearly polarized STOVs with controllable polarization states on the focal plane of a high numerical aperture lens. The incident wave packet is pre-split to overcome the spatiotemporal astigmatism caused by the focusing lens to the STOV. The three dimensional spatiotemporal distributions of the highly confined STOVs with different polarization states are simulated based on Richards Wolf vectorial diffraction theory to analyze their intensity and phase characteristics. The obtained horizontally polarized, vertically polarized and 45° polarized highly confined STOVs manifest the feasibility of the presented method.
    $ {{\boldsymbol{E}}_{ + 1}}(x,y,t) = \left( {\boldsymbolex0} \right)\left( {x + {\rm{i}}}t \right)\exp \left( { - \frac{{{x^2} + {y^2}}}{{{\omega ^2}}} - \frac{{{t^2}}}{{\omega _t^2}}} \right) $(1)

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    $ {{\boldsymbol{E}}_{ - 1}}(x,y,t) = \left( {\boldsymbolex0} \right)\left( {x - {\rm{i}}}t \right)\exp \left( { - \frac{{{x^2} + {y^2}}}{{{\omega ^2}}} - \frac{{{t^2}}}{{\omega _t^2}}} \right) $(2)

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    $ \boldsymbolEx+1(x,y,t)=\boldsymbolE+1(x,y,t)+i\boldsymbolE1(x,y,t)=(\boldsymbolex0)(1+i)(x+t)exp(x2+y2ω2t2ωt2) $(3)

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    $ {\boldsymbol{E}}_y^{ + 1}\left( {x,y,t} \right) = \left( {0\boldsymboley} \right)\left( {1 + {\rm{i}}} \right)\left( {x + t} \right)\exp \left( { - \frac{{{x^2} + {y^2}}}{{{\omega ^2}}} - \frac{{{t^2}}}{{\omega _t^2}}} \right) $(4)

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    $ {\boldsymbol{E}}_{xy}^{ + 1}\left( {x,y,t} \right) = \left( {\boldsymbolex\boldsymboley} \right)\left( {1 + {\rm{i}}} \right)\left( {x + t} \right)\exp \left( { - \frac{{{x^2} + {y^2}}}{{{\omega ^2}}} - \frac{{{t^2}}}{{\omega _t^2}}} \right) $(5)

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    $ \boldsymbolEf(rf,Φ,zf,t)=0α02π\boldsymbolP(θ,ϕ)B(θ)EΩ(θ,ϕ,t)×exp{ik[rfsinθcos(ϕΦ)+zfcosθ]}sinθdθdϕ$(6)

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    $ {E_\varOmega }\left( {\theta ,\phi ,t} \right) = \left( {1 + {\text{i}}} \right)\left( {\sin \theta \sin \phi + t} \right)\exp \left( { - \frac{{{{\sin }^2}\theta }}{{{\omega ^2}}} - \frac{{{t^2}}}{{\omega _t^2}}} \right) $(7)

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    $ {\boldsymbol{P}}\left( {\theta ,\phi } \right) = \left( {(cosθcos2ϕ+sin2ϕ)\boldsymbolex(cosθcosϕsinϕsinϕcosϕ)\boldsymboley(sinθcosϕ)\boldsymbolez} \right) $(8)

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    $ {\boldsymbol{P}}\left( {\theta ,\phi } \right) = \left( {(cosθcosϕsinϕcosϕsinϕ)\boldsymbolex(cosθsin2ϕ+cos2ϕ)\boldsymboley(sinθsinϕ)\boldsymbolez} \right) $(9)

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    $ \boldsymbolP(θ,ϕ)=([cosθcosϕ(sinϕ+cosϕ)+sinϕ(sinϕcosϕ)]\boldsymbolex[cosθsinϕ(cosϕ+sinϕ)+cosϕ(cosϕsinϕ)]\boldsymboley[sinθ(sinϕ+cosϕ)]\boldsymbolez) $(10)

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    Pengkun ZHENG, Jian CHEN. Method for generating highly confined linearly polarized spatiotemporal optical vortices[J]. Optical Instruments, 2022, 44(6): 36
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