Ghost Polarization Communication

There is an increasing and demanding interest in the realization of secure communication schemes. Here, we conceive and realize an approach for a message-encoding scheme between two parties, Alice and Bob, by exploiting the infinite number of polarization states of unpolarized thermal light on the Poincaré sphere together with their correlation properties to camouflage and recover a message, thus realizing ghost polarization communication. At first, we investigate the second-order correlation coefficient $g^{(2)}(\tau )$ of classical unpolarized broadband amplified-spontaneous-emission light emitted by an erbium-doped fiber amplifier at 1550 nm by manipulating its instantaneous polarization state utilizing various polarization optics in the beam paths of a Hanbury-Brown and Twiss like ghost polarimetry setup using ultra-fast two-photon absorption in a photomultiplier tube. The observed polarization state modifications are in excellent agreement with our developed model based on the Stokes vector dynamics and a Glauber protocol for $g^{(2)}(\tau )$. On the basis of these results we then proceed towards the realization of a message-encoding scheme. By changing the instantaneous polarization state using a half-wave plate, Alice encodes and subsequently transmits a message. The camouflaged message can be recovered uniquely by Bob measuring the second-order correlations of the modified instantaneous polarization state with his reference beam. By using the agreed keypad of the communication scheme, he is able to retrieve the bit values of the encoded message. Finally, we address real-world implementation of this first proof-of-principle demonstration and discuss its security issues. This scheme demonstrates a method of establishing a secure communication link between two parties directly on the physical layer based on polarization correlations of classical light. It is expected that by the realization of this correlated photon modality not only avenues for ghost modalities, in general, are opened but also insight into polarization, even more than 175 years after Stokes will be achieved.

Figure 1

Experimental setup enabling a secure message transfer from Alice to Bob by exploiting polarization correlations of photons. Top: Alice encodes her message as a rotation angle of the half-wave plate. The resulting IPS change can be measured by Bob using the two-photon absorption of a PMT (TPA PMT) and exploiting the polarization correlation between reference beam and object beam. Further components depicted are as follows: erbium-doped fibre amplifier, quarter-wave plate, beam-splitter cube (BS), linear polarizer (${\mathrm{LP}}_R$) in the reference arm, linear polarizer (${\mathrm{LP}}_O$) in the object arm and fiber coupler (FC). Below the EDFA, there is a schematic depiction of the Poincaré sphere, which is spanned up by the three Stokes parameters $S_1$, $S_2$, and $S_3$ and the temporal IPS dynamics on its surface is illustrated by the red-dot curve. Bottom: extraction of the $g^{(2)}(\tau )$ coefficient [right, (b)] from a measured fringe-resolved interferometric autocorrelation function [left, (a)].

Figure 2

Polarization correlations for LPs. Values of $g^{(2)}(\tau =0)$ as a function of the rotation angle of the linear polarizer ${\mathrm{LP}}_R$ in the reference arm for a fixed rotation angle of ${\mathrm{LP}}_O$ (solid black triangles). Placing an additional half-wave plate oriented at ${45}^{\circ }$ with respect to the fixed ${\mathrm{LP}}_O$ and measuring the $g^{(2)}(\tau =0)$ values yields the data points indicated by open blue squares. Continuous lines show the fits using Eqs. (1) and (3). The precision of the depicted $g^{(2)}(\tau =0)$ measurement results is defined by the statistical error resulting from five subsequent measurements and is indicated in all experimental data sets by the error bars.

Figure 3

Polarization correlations for LP and QWP. Values of $g^{(2)}(\tau =0)$ as a function of the linear polarizer ${\mathrm{LP}}_R$ rotation angle in the reference arm. The $g^{(2)}(\tau =0)$ values for a quarter-wave plate rotation angle of $0^{\circ }$ indicate an unpolarized IPS (solid red circles), whereas the $g^{(2)}(\tau =0)$ values for rotation angles of ${30}^{\circ }$ and ${45}^{\circ }$ show an elliptical IPS (closed orange triangles) and a circular IPS (open green diamonds), respectively. The continuous lines are fitted to the data points using Eq. (4).

Figure 4

Communication keypad. Values of $g^{(2)}(\tau =0)$ measured by Bob as a function of the HWP (Alice) and QWP (Bob) rotation angle. The dashed lines indicate the two HWP angles used for encoding: ${30}^{\circ }$ represent a “0” (green dashes) and ${60}^{\circ }$ represent a “1” (purple dashes). The data points across the dashed lines are the data in Fig. 6.

Figure 5

Simulated communication keypad. Simulated map of $g^{(2)}(\tau =0)$ values as a function of the HWP and QWP rotation angles for the case of a HWP with a nonideal retardation value of 0.55, calculated according to Eq. (A17). See Fig. 4 for comparison with the experimental data.

Figure 6

Polarization correlations for QWP and HWP. $g^{(2)}(\tau =0)$ values for two distinct rotation angles of the HWP (blue squares for an HWP angle of ${30}^{\circ }$ and red circles for an HWP angle of ${60}^{\circ }$) as chosen by Alice plotted as a function of the rotation angle of Bob’s QWP. The continuous lines are fitted to the data points using Eq. (A17) with a phase retardation of 0.55 for the HWP.

Figure 7

Eve’s correlation results. $g^{(2)}(\tau =0)$ values for rotation angles of the HWP and QWP as measured by Eve while tapping the communication between Alice and Bob. Inset: entire map of all HWP rotation angles and all QWP rotation angles.