图 1  (a)通过传统SPP产生的涡旋光束, 入射光具有高斯强度分布; (b)通过由电光晶体制成的平板产生涡旋光束, 其中局部折射率由微电极板阵列控制, 从而部分调制入射光的相位

Fig. 1.  (a) The generation of optical vortex beams through a traditional SPP, the incident light has a Gaussian intensity distribution; (b) the generation of optical vortex beams through a flat plate made of electro-optical crystals, where the local refractive index is controlled by a micro-electrode plate array so that the phase of the incident light is partially modulated.

图 2  电场施加区域之一的示意图. XYZ坐标是没有施加电场的KDP晶体的所谓主轴坐标. 晶体的光轴沿Z方向. 当施加外部电场时, 由于 Pockels效应^[29], 主轴围绕Z轴旋转45°

Fig. 2.  Schematic of one of the electric-field-applied regions. The XYZ coordinate is the so-called principal-axis coordinate of the KDP crystal with no applied electric field. The crystal is prepared cut so that the optical axis is in the Z direction. When an external electric field applies, the principal axes rotate 45° about the Z-axis due to the Pockels effect ^[29].

图 3  所有入射光穿过板时, 透射光在自由空间中传播时的光强分布. 第1列中的黑色圆圈表示具有高斯模式的入射光的调制区域, 白色值表示方位角调制的光学相位, 其相应的施加电压可以通过(4)式计算, 未调制区域相应的光学相位为${{\text{π}}/4}$　(a) $ 2{\text{π }} $相移; (b)$-2{\text{π }} $相移; (c) $ 4{\text{π }} $相移; (d) $ -4{\text{π }} $相移; (e) $ {\text{π }} $相移

Fig. 3.  The intensity distribution of the transmitted light propagating in free space for the case that the whole incident light passing through the plate. The black circles in the first column denote the modulation regions of the incident light with Gaussian mode, and the white values represent the azimuthally modulated optical phase whose corresponding applied voltages can be calculated by Eq. (4). The corresponding optical phase of the unmodulated region is${{\text{π}}/4}$: (a)$ 2{\text{π}} $ phase shift; (b)$ -2{\text{π}} $phase shift; (c)$ 4{\text{π}} $phase shift; (d)$-4{\text{π}} $phase shift; (e)$ {\text{π}} $phase shift.

图 4  所有入射光穿过板时, 透射光在自由空间中传播时的相位分布. 每一行的相位调制方案与图3中的相位调制方案一致　(a)$ 2{\text{π }} $相移; (b)$-2{\text{π }} $相移; (c) $ 4{\text{π }} $相移; (d) $ -4{\text{π }} $相移; (e) $ {\text{π }} $相移

Fig. 4.  The phase distribution of the transmitted light propagating in free space for the case that the whole incident light passing through the plate. The phase modulation scheme of each row is consistent with those of Fig. 3: (a)$ 2{\text{π }} $ phase shift; (b)$ -2{\text{π }} $phase shift; (c)$ 4{\text{π }} $ phase shift; (d) $ -4{\text{π }} $ phase shift; (e)$ {\text{π }} $ phase shift.

图 5  只有调制区域的入射光通过板时, 透射光在自由空间中传播时的光强分布. 第1列显示了调制方案　(a) 没有施加电场; (b) $ 2{\text{π }} $相移; (c) $ -2{\text{π }} $相移; (d) $ 4{\text{π }} $相移; (e) $ -4{\text{π }} $相移; (f) $ {\text{π }} $相移

Fig. 5.  The intensity distribution of the transmitted light propagating in free space for the case that only the modulated regions of the incident light passing through the plate. The first column shows the modulation schemes for (a) absence of applied electric field; (b)$ 2{\text{π }} $phase shift; (c) $-2{\text{π }} $ phase shift; (d) $ 4{\text{π }} $phase shift; (e) $ -4{\text{π }} $phase shift; (f) $ {\text{π }} $phase shift.

图 6  只有调制区域的入射光通过板时, 透射光在自由空间中传播时的相位分布. 每一行的相位调制方案与图5中的相位调制方案一致　(a) 没有施加电场; (b) $ 2{\text{π }} $相移; (c) $ -2{\text{π }} $相移; (d) $ 4{\text{π }} $相移; (e) $ -4{\text{π }} $相移; (f)$ {\text{π }} $相移.

Fig. 6.  The phase distribution of the transmitted light propagating in free space for the case that only the modulated regions of the incident light passing through the plate. The phase modulation scheme of each row is consistent with that in Fig. 5: (a) Absence of applied electric field; (b) $ 2{\text{π }} $phase shift; (c) $ -2{\text{π }} $phase shift; (d) $ 4{\text{π }} $phase shift; (e) $ -4{\text{π }} $phase shift; (f) $ {\text{π }} $ phase shift.

图 7  所有入射光通过板时, 不同调制方案的OAM模式光谱 (a)—(e) 的调制方案分别与图3(a)—(e) 中的相同; (f) 插入显示调制方案的模式频谱, 其中也实现了$ 2{\text{π }} $相移, 但调制区域的面积大于 (a) 中的区域

Fig. 7.  OAM-mode spectra with different modulation schemes for the case that the whole incident light passing through the plate. The modulation schemes of (a)–(e) are the same as in Fig. 3 (a)-(e), respectively. (f) The mode spectrum with the insert showing the modulation scheme, in which a $ 2{\text{π }} $ phase shift is also achieved but the area of modulated regions is more than the one in (a).

图 8  仅调制区域的入射光通过板时, 具有不同调制方案的OAM模式谱. (a)—(f)的调制方案分别与图7(a)—(f)相同

Fig. 8.  OAM-mode spectra with different modulation schemes for the case that only the modulated regions of the incident light passing through the plate. The modulation schemes of (a)–(f) are the same as in Fig. 7 (a)-(f), respectively.