• Acta Photonica Sinica
  • Vol. 49, Issue 7, 726001 (2020)
Qi-hao ZHANG1、2, Ling-xuan ZHANG1, Zhong-yu LI1, Wei WU1、2, Guo-xi WANG1、2, Xiao-chen SUN1、2, Wei ZHAO1、2, and Wen-fu ZHANG1、2、*
Author Affiliations
  • 1State Key Laboratory of Transient Optics and Photonics, Xi''an Institute of Optics and Precision Mechanics, Chinese Academy of Science, Xi''an 710119, China
  • 2University of Chinese Academy of Sciences, Beijing 100049, China
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    DOI: 10.3788/gzxb20204907.0726001 Cite this Article
    Qi-hao ZHANG, Ling-xuan ZHANG, Zhong-yu LI, Wei WU, Guo-xi WANG, Xiao-chen SUN, Wei ZHAO, Wen-fu ZHANG. Antenna Array Initial Condition Calibration Method for Integrated Optical Phased Array[J]. Acta Photonica Sinica, 2020, 49(7): 726001 Copy Citation Text show less

    Abstract

    To solve the problem that the phase error of the optical phased array is difficult to calibrate, rotating element electric field vector calibration method is modified. Comparing with the traditional method, the new method modifies the algorithm and corrects the phase immediately after measuring the phase error of one unit, then measures and corrects the phase of the next unit. Possible π phase error in traditional method is avoided when large initial phase distribution and finite optical power measurement accuracy present. The simulation results show that the main lobe intensity calibrated with the original method reaches at most 70.8% of the ideal value on average, and the standard deviation is at least 19.1%. While after calibration with the modified method the main lobe intensity reaches at least 87.6% of the ideal value on average, the maximum standard deviation is 7.3%. The modified method produces statistically more accurate and predictable calibration result. A 9×9 optical phased array chip is manufactured. The initial grating lobe suppression ratio ofthe chip is 2.12 dB. Calibrated with this modified method the ratio reaches 4.68 dB. The effectiveness and practical application value of this method are proved.
    $ {{\boldsymbol E}_n} = {A_n}\left( {\alpha , \beta , r} \right){\rm{exp}}\left( {{\rm{i}}\omega t - {\rm{i}}{{\boldsymbol k}_n} \cdot {{\boldsymbol r}_n} + {\rm{i}}{\varphi _n}} \right) \cdot {\boldsymbol e} $ (1)

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    $ {E_0} = \mathop \sum \limits_{n = 1}^N {A_n}{\rm{exp}}\left( {{\rm{i}}\omega t - {\rm{i}}k{r_n} + {\rm{i}}{\varphi _n}} \right) = {\rm{exp}}\left( {{\rm{i}}\omega t} \right)\mathop \sum \limits_{n = 1}^N {A_n}{\rm{exp}}\left( {{\rm{i}}{\phi _n}} \right) $ (2)

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    $ {I_0} = {\left| {{E_0}} \right|^2} = {\left| {{\rm{exp}}\left( {{\rm{i}}\omega t} \right)} \right|^2} \cdot {\left| {\mathop \sum \limits_{n = 1}^N {A_n}{\rm{exp}}\left( {{\rm{i}}{\phi _n}} \right)} \right|^2} = {\left| {\mathop \sum \limits_{n = 1}^N {A_n}{\rm{exp}}\left( {{\rm{i}}{\phi _n}} \right)} \right|^2} $ (3)

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    $ I\left( {{\rm{\Delta }}\varphi } \right) = {\left| {\mathop \sum \limits_{n = 1}^N {A_n}{\rm{exp}}\left( {{\rm{i}}{\phi _n}} \right) - {A_m}{\rm{exp}}\left( {{\rm{i}}{\phi _m}} \right) + {A_m}{\rm{exp}}\left( {{\rm{i}}{\phi _m} + {\rm{i\Delta }}\varphi } \right)} \right|^2} $ (4)

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    $ {E_{ - m}} = \mathop \sum \limits_{n = 1}^N {A_n}{\rm{exp}}\left( {{\rm{i}}{\phi _n}} \right) - {A_m}{\rm{exp}}\left( {{\rm{i}}{\phi _m}} \right) = {A_{ - m}}{\rm{exp}}\left( {{\rm{i}}{\phi _{ - m}}} \right) = {v_m} + {\rm{i}}{w_m} $ (5)

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    $ I\left( {{\rm{\Delta }}\varphi } \right) = v_m^2 + w_m^2 + A_m^2 + 2{v_m}{A_m}{\rm{cos}}\left( {{\phi _m} + {\rm{\Delta }}\varphi } \right) + 2{w_m}{A_m}{\rm{sin}}\left( {{\phi _m} + {\rm{\Delta }}\varphi } \right) $ (6)

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    $ {\rm{\Delta }}\varphi + {\phi _m} = \left\{ {\begin{array}{*{20}{c}} {{\rm{arctan}}\left( {{w_m}/{v_m}} \right)}\\ {{\rm{ \mathsf{ π} }} + {\rm{arctan}}\left( {{w_m}/{v_m}} \right)} \end{array}} \right. $ (7)

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    $ {\left. {\frac{{{{\rm{d}}^2}I}}{{{{\left( {{\rm{d\Delta }}\varphi } \right)}^2}}}} \right|_{{\rm{\Delta }}\varphi = {\rm{arctan}}\frac{{{w_m}}}{{{v_m}}} - {\phi _m}}} = - 2{A_m}\sqrt {v_m^2 + w_m^2} < 0 $ (8)

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    $ {{I}_{\text{max}}}=I\left( \text{arctan}\frac{{{w}_{m}}}{{{v}_{m}}}-{{\phi }_{m}} \right)={{\left( \sqrt{v_{m}^{2}+w_{m}^{2}}+{{A}_{m}} \right)}^{2}}={{\left( \left| {{E}_{-m}} \right|+\left| {{E}_{m}} \right| \right)}^{2}} $ (9)

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    $ \delta {\varphi _{m + 1}} \le {\rm{arcsin}}\frac{{\left| {{A_{m + 1}}} \right|}}{{\left| {{E_0}} \right|}} $ (10)

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    $ \delta {\varphi _2} \le {\rm{arcsin}}\frac{{{A_2}}}{{\left| {{E_0}} \right|}} \le {\rm{ \mathsf{ π} }}/2 $ (11)

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    $ \delta {\varphi _3} \le {\rm{arcsin}}\frac{{{A_3}}}{{\left| {{E_0}} \right|}} \le {\rm{ \mathsf{ π} }}/4 $ (12)

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    $ {{\phi }_{\text{e}}}=\text{arctan}\left[ {\text{sin}\left( \Delta {{\varphi }_{\text{pmax}}} \right)} \bigg /{\left( \text{cos}\left( \Delta {{\varphi }_{\text{pmax}}} \right)+\dfrac{\sqrt{{{p}_{\text{max}}}/{{p}_{\text{min}}}}-1}{\sqrt{{{p}_{\text{max}}}/{{p}_{\text{min}}}}+1} \right)}\; \right] $ (13)

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    Qi-hao ZHANG, Ling-xuan ZHANG, Zhong-yu LI, Wei WU, Guo-xi WANG, Xiao-chen SUN, Wei ZHAO, Wen-fu ZHANG. Antenna Array Initial Condition Calibration Method for Integrated Optical Phased Array[J]. Acta Photonica Sinica, 2020, 49(7): 726001
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