Generation of higher-dimensional modal entanglement using a three-waveguide directional coupler

In this paper, we propose a method for the generation of higher-dimensional modal entanglement through a type II spontaneous parametric down-conversion process using a three-waveguide directional coupler in a periodically poled lithium niobate substrate. We show that by a proper design, it is possible to achieve an output state of two photons occupying three different spatial modes. The advantage of using such waveguide structure is its flexibility and the design space availability to achieve desired characteristics of the photon pairs generated in the down-conversion process.

Figure 1

Schematic diagram of an array of three identical single-mode waveguides and the field distributions of the three normal modes.

Figure 2

Schematic of the channel waveguide of three-waveguide coupler having QPM grating of period Λ.

Figure 3

Schematic of waveguide structure describing how the modes are separated at output.

Figure 4

Normalized transverse modal field distributions along $y$ direction in a three-waveguide coupler: (a) fundamental symmetric normal mode (0) at pump, signal, and idler wavelengths; (b) fundamental symmetric mode normal mode (0) at pump wavelength and the first excited antisymmetric normal mode (1) at signal and idler wavelengths; (c) fundamental symmetric mode normal mode (0) at pump wavelength and the second excited symmetric normal mode (2) at signal and idler wavelengths

Figure 5

Square of the normalized transverse modal intensity distributions along $y$ direction in a three-waveguide coupler: (a) fundamental symmetric normal mode (0) at pump, signal, and idler wavelengths; (b) fundamental symmetric mode normal mode (0) at pump wavelength and the first excited antisymmetric normal mode (1) at signal and idler wavelengths; (c) fundamental symmetric mode normal mode (0) at pump wavelength and the second excited symmetric normal mode (2) at signal and idler wavelengths.

Figure 6

Variation of the efficiency of the three down-conversion processes (a) as a function of signal wavelength, and (b) as a function of QPM grating.

Figure 7

Variation of the efficiency of the three down-conversion processes as a function of signal wavelength having grating period (a) $\Lambda =6.874\mu \mathrm{m}$, (b) $\Lambda =6.974\mu \mathrm{m}$.

Figure 8

Square of the normalized transverse modal field distributions along $y$ direction in a three-waveguide coupler: (a) first excited antisymmetric normal mode (1) at pump and idler wavelength and the fundamental symmetric normal mode (0) at signal wavelengths in a three-waveguide coupler; (b) first excited antisymmetric normal mode (1) at pump and signal wavelength and the fundamental symmetric normal mode (0) at idler wavelengths; (c) first excited antisymmetric normal mode (1) at pump and signal wavelengths and the second excited symmetric normal mode (2) at idler wavelength; (d) first excited antisymmetric normal mode (1) at pump and idler wavelengths and the second excited symmetric normal mode (2) at signal wavelength.

Figure 9

Variation of the efficiency of the four down-conversion processes (a) as a function of signal wavelength, and (b) as a function of QPM grating

Figure 10

(a) Schematic of three-waveguide coupler. (b). Corresponding separable refractive index profile.