Dichroism for orbital angular momentum using parametric amplification

We theoretically analyze parametric amplification as a means to produce dichroism based on the orbital angular momentum (OAM) of an incident signal field. The nonlinear interaction is shown to provide differential gain between signal states of differing OAM, the peak gain occurring at half the OAM of the pump field.

Figure 1

Signal gain $G_s$ (solid line) and net gain (dashed line) versus the OAM difference $m_1-m_2/2$ for a LBO crystal of length $L=2$ mm, pump intensity $I_2=2$ GW/$\mathrm{cm}{}^2$, and ring radius $R=35\mu \mathrm{m}$. The discrete data points are connected by a solid line as a visual aid.

Figure 2

(a) Signal gain $G_s$ versus the OAM difference $\Delta =m_1-m_2/2$ for $m_2=0$ (dotted line) and $m_2=11$ (solid line) and (b) same as (a) but for the net gain $G$. The parameters used are for LBO and $m_r=11,w_0=15\mu \mathrm{m}$, giving $R=35\mu \mathrm{m}$, an input pump power of $P_2\left(0\right)=264$ kW, and a signal power of $P_{\mathrm{sig}}=0.2P_2\left(0\right)=52.8$ kW, giving a peak intensity $I_p=8.8$ GW/$\mathrm{cm}{}^2$. The discrete data points are connected by a solid line as a visual aid.

Figure 3

Signal gain $G_s$ versus the OAM difference $\Delta =m_1-m_2/2$ for the same parameters as in Fig. 2 with $m_2=11$ and a pump intensity of $I_p=8.8$ GW/$\mathrm{cm}{}^2$ (solid line) and $I_p=4.4$ GW/$\mathrm{cm}{}^2$ (dashed line), the signal power being held constant at $P_{\mathrm{sig}}=0.2P_2\left(0\right)=52.8$ kW. The discrete data points are connected by a solid line as a visual aid.

Figure 4

Examples of the (a) and (b) fundamental and (c) and (d) SH output transverse intensity profiles for two different values of the pump power: (a) and (c) $P_2\left(0\right)=264$ kW and (b) and (d) $P_2\left(0\right)=2.64$ kW, with $P_{\mathrm{sig}}=0.2P_2\left(0\right)$, all other parameters being the same as in Fig. 2. The winding numbers of the fundamental and SH fields were chosen as $m_1=8$ and $m_2=11$ so that $\Delta =2.5$ and the generated idler will have winding number $m_3=m_2-m_1=5$.

Figure 5

Plot of the signal gain $G_s$ (solid line) and net gain $G$ (dashed line) as functions of the signal beam winding number $m_1$ for a pump winding number (a) $m_2=11$ and (b) $m_2=0$. The parameter values are $m_r=11$ and $w_0=15\mu \mathrm{m}$, giving $R=35\mu \mathrm{m}$, an input pump power of $P_2\left(0\right)=264$ kW, and a signal power of $P_{\mathrm{sig}}=0.2P_2\left(0\right)=52.8$ kW. The discrete data points are connected by a solid line as a visual aid.