High-Capacity Near-Infrared Optical Vortex Sorting and Detection by Nonlinear Dammann Vortex Grating

Abstract

This paper demonstrates the sorting and detection of near-infrared vortex light using a nonlinear Dammann vortex grating. By incorporating a forked structure into the nonlinear Dammann grating, the resulting nonlinear Dammann vortex grating is capable of converting near-infrared Gaussian light into a visible vortex array. The array comprises 49 independent detection channels, each of which can precisely control the inherent topological charge values. When the topological charge value of a detection channel’s vortex light matches that of the incident vortex, the vortex degenerates into a Gaussian spot, thereby enabling the detection of the incident vortex’s topological charge. Our experimental results show that this grating, with its 49 independent detection channels, can detect the topological charge values of vortex light in the near-infrared range from l = −12 to +12 in real-time. Compared to existing solutions, this grating offers enhanced versatility and has potential applications in optical communication systems for the transmission, reception, and multiplexing of OV beams.

1. Introduction

Optical vortices (OVs) have garnered significant attention since 1992 when Allen et al. first demonstrated that photons in a vortex beam with helical phase fronts carry a quantized orbital angular momentum (OAM) of lℏ, where l represents the topological charge [1,2,3]. This groundbreaking discovery highlighted OAM as a robust degree of freedom for measuring light [4], leading to extensive research into its applications across various fields. The distinctive properties of OVs—characterized by their donut-shaped intensity profiles and central phase singularities—make them especially valuable for modern photonics applications [5,6,7].

The orthogonality of OAM modes with different topological charges in Hilbert space forms a crucial foundation for their application in quantum information technologies [8]. This property allows for theoretically unlimited state superpositions, enabling applications such as high-dimensional quantum encoding, superdense coding, and quantum key distribution. Beyond quantum optics, OVs have shown exceptional potential in optical communications [9,10,11], where they facilitate high-capacity data transmission through OAM multiplexing. In optical manipulation, the transfer of OAM to particles enables precise rotational control at the micro- and nano-scales [12], while in remote sensing, OVs enhance imaging capabilities through their unique interaction with scattering media [13].

The accurate measurement of topological charge remains a fundamental challenge that limits the widespread application of optical vortices (OVs). Existing detection methods, such as fork gratings [14,15], spatial light modulators [16], and interferometric techniques [17,18], generally suffer from limited resolutions and are typically constrained to detecting only single.

OAM modes, with particular difficulties in detecting near-infrared beams. Dammann gratings offer an attractive alternative by enabling a uniform energy distribution across diffraction orders, converting the OVs into Gaussian modes that can be readily detected using conventional silicon CCD cameras. This method is especially advantageous for near-infrared OV detection through visible-light imaging. The conservation of OAM in nonlinear processes [19,20], along with the ability to engineer second-order susceptibility (χ⁽²⁾) in nonlinear photonic crystals, opens up further opportunities for efficient frequency conversion and mode transformation in OV detection systems [21,22,23].

In this work, we present a breakthrough in OAM sorting and detection with the development of a nonlinear Dammann vortex grating based on lithium niobate nonlinear photonic crystals. By precisely engineering the χ⁽²⁾ nonlinearity distribution, we have created a device capable of efficient near-infrared to visible frequency conversion through second-harmonic generation [24]. The optical vortex of each channel is precisely arranged and designed to carry a specific OAM. The system detects topological charges ranging from l = −12 to +12 using 49 independent detection channels in the near-infrared region. This advancement provides a practical and efficient solution for OAM-based optical communication systems, significantly enhancing sorting dimensionality and efficiency compared to conventional approaches. These capabilities pave the way for high-dimensional OAM multiplexing and quantum information processing applications.

2. Materials and Methods

The foundation of our work builds upon the classical Dammann grating theory [25,26], which provides an efficient approach for generating multi-beam diffraction patterns with equalized intensities. We have extended this concept to a nonlinear regime by engineering the second-order nonlinear coefficient χ⁽²⁾ within lithium niobate photonic crystals [27]. The effective nonlinear coefficient is expressed as follows [28]:

$$d_{ij}^{\prime }(x)=\sum _m{a}_m\mathit{exp}[im({\displaystyle \frac{2\pi }{\Lambda }}x+l_{\mathrm{c}}\varphi )]$$

(1)

where m denotes the diffraction order, a_m is the m-th Fourier component, Λ is the period, and l_c represents the OAM carried by the structure. The 1D nonlinear Dammann vortex grating design incorporates phase transition points at 0.232, 0.425, and 0.526, enabling the grating to generate equal-intensity diffraction at the ±1, ±2, and ±3 orders. After successfully fabricating the 1D nonlinear Dammann vortex grating, we extended it to a 2D configuration by orthogonally superimposing two 1D gratings [29,30]. By adjusting the intrinsic topological charge values along the x- and y-axes, where l_x = 7 and l_y = 1, the resulting 2D Dammann vortex grating achieves a controllable diffraction efficiency and a well-defined OAM mode distribution.

Figure 1a shows the binary phase mask of the lithium niobate domain for the Dammann vortex grating, where the nonlinear coefficients of the positive and negative regions are defined as d_ij and −d_ij, respectively. Figure 1b presents the simulated diffraction pattern of the nonlinear Dammann vortex grating, generating 49 distinct vortex channels with topological charges ranging from −24 to +24, labeled in white text beneath each vortex. When an incident optical beam carrying an orbital angular momentum of l = q interacts with the nonlinear Dammann vortex grating, each diffraction order acquires a modified topological charge. The resulting OAM at a given diffraction position is expressed as n_xl_x + n_yl_y + 2q, where n_x and n_y represent the diffraction orders along the orthogonal axes; it is noteworthy that if the condition n_xl_x + n_yl_y + 2q = 0 is satisfied, the optical vortex degenerates into a fundamental Gaussian mode. Given that the frequency-doubled output falls within the visible spectrum, this degeneration appears as a bright spot, observable with the naked eye at the corresponding diffraction order. This phenomenon facilitates the direct visual detection of OAM beams in the near-infrared region.

3. Experiment

The 7 × 7 DVG was fabricated through electric field poling on a z-cut lithium niobate crystal (15 mm × 15 mm × 0.5 mm, x × y × z). A 120 nm thick aluminum electrode, patterned with the DVG design, was first deposited onto the +z face of the crystal using photolithography, followed by vacuum evaporation and lift-off processing [31]. Domain inversion was then achieved by applying high-voltage pulses to the crystal, systematically reversing the spontaneous polarization to establish the predetermined periodic domain structure. Figure 2b presents an optical microscope image (Olympus BX53) of the fabricated nonlinear DVG in lithium niobate, where the precisely patterned domain structure created using electric field poling is clearly visible. Figure 2c shows a photograph of the fabricated lithium niobate crystal sample containing the nonlinear DVG. Figure 2b presents the microscopic observation corresponding to the area outlined by the black dashed box in Figure 2c.

Figure 2a illustrates the experimental setup used for detecting the orbital angular momentum of near-infrared optical vortices [32]. The system utilizes a Ti–sapphire laser (Chameleon Ultra II, Coherent), which generates 141 fs pulses at 900 nm with an 80 MHz repetition rate as the fundamental light source. The laser’s original output beam has a diameter of 1.2 mm. The initial Gaussian beam is directed by a mirror into a polarizer for polarization control, and then guided to a reflective spatial light modulator (SLM, PLUTO-2.1-NIR-118, Holoeye) to be converted into a focused optical vortex. The inset in the upper right corner of Figure 2a shows the optical vortex phase pattern used for the SLM, corresponding to a vortex carrying a topological charge of 1. The generated optical vortices are then focused by a 200 mm focal length lens and are projected onto the sample along the z-axis at a normal incident, with an incident pulse energy of approximately 18 nJ. The second-harmonic far-field diffraction pattern is captured using a visible-band CCD camera positioned 2 cm behind the sample. A spectral filter is placed before the CCD to block residual fundamental wavelength radiation.

4. Results

Figure 3 presents both simulated and experimental results of 7 × 7 s-harmonic vortex arrays generated through nonlinear Raman–Nath diffraction [33,34], using Gaussian beams and vortex beams carrying different orbital angular momenta as the fundamental waves. The second-harmonic vortices were produced via nonlinear frequency conversion in the Dammann vortex grating. As shown in Figure 3b, when illuminated by a Gaussian beam, the DVG effectively converts the plane wave into multiple OAM modes. Our beam propagation method simulations (Figure 3a) accurately predict this behavior, demonstrating excellent agreement with experimental observations.

For the OAM detection experiments, near-infrared vortex beams were generated by programming various spiral phase patterns onto a spatial light modulator (SLM). According to our detection principle, when the condition n_xl_y + n_yl_y + 2q = 0 is satisfied, the vortex beam degenerates into a Gaussian spot at the corresponding diffraction order. This phenomenon allows for direct OAM measurement through simple intensity observation. Figure 3 demonstrates three representative detection cases: For an l = +1 input (Figure 3d), the vortex-to-Gaussian conversion occurs at the n_xl_y + n_yl_y = −2 position, as predicted by our beam propagation method simulation (Figure 3c). Similarly, for l = +3 and l = +7 inputs (Figure 3f and Figure 3h, respectively), characteristic Gaussian spots appear at the n_xl_y + n_yl_y = −6 and −14 positions. Corresponding simulations (Figure 3e,g, with marked positions) confirm these experimental findings. The remarkable agreement between simulations and experiments validates the reliability of our Dammann vortex grating for OAM detection. This method offers a straightforward and effective approach for OAM measurement, eliminating the need for complex interferometric setups.

To quantitatively evaluate the performance of our Dammann vortex grating, we first calculated the normalized Root Mean Square (RMS) relative error, which quantifies the deviation in the intensity at each diffraction point from the average intensity. The specific formula is given by:

$$Normalized RMS={\displaystyle \frac{\sqrt{\frac{1}{N}\sum _{i=1}^{48}{(I_i-\overline{I})}^2}}{\overline{I}}}$$

(2)

where $I_i$ is the intensity at the i-th diffraction order, and $\overline{I}$ is the average intensity of the 48 diffraction points, excluding the intensity of the central point. The final normalized RMS was 27.2%.

Subsequently, the energy distribution across the various diffraction orders of the nonlinear DVG was thoroughly analyzed. Figure 4a,b present the normalized intensity profiles for the experimental (corresponding to Figure 3b) and theoretical (corresponding to Figure 3a) diffraction patterns, respectively, generated under Gaussian beam illumination. We introduce a normalized uniformity metric, defined as: $\eta =\left({\displaystyle \frac{I_{max}-{ I}_{in}}{I_{ax}}}\right)\times 100\%$, where I_max and I_min denote the peak and valley intensities in the diffraction pattern. Our measurements reveal η = 80.46% for the experimental results (Figure 4a), compared to η = 74.95% for the theoretical prediction (Figure 4b). The observed reduction in intensity at higher diffraction orders in the experimental results (Figure 4a) compared to theoretical predictions (Figure 4b) can primarily be attributed to two factors: (i) domain imperfections introduced during electric field poling fabrication, and (ii) an insufficient incident beam power in the experimental setup. Finally, the overall second-harmonic conversion efficiency of the nonlinear DVG was measured. Under the Gaussian beam incidence, the obtained overall second-harmonic conversion efficiency was 6.901 × 10⁻⁵.

The optical vortex mode purity in the generated array was quantitatively analyzed using modal decomposition. As shown in the inset in Figure 5, we isolated a single vortex with a topological charge of l = +1 from the experimental array (corresponding to Figure 3b) for detailed characterization. The decomposition was performed using Laguerre–Gaussian (LG) modes as basis functions, taking advantage of their orthogonality properties. The program begins by reading the input optical vortex image and performing frequency domain analysis using a Fourier transform to extract the phase information, thereby reconstructing the complex amplitude field. The reconstructed complex amplitude field contains both the amplitude and phase information. After extracting the phase, the program constructs LG modes with different topological charges as basis functions. In this implementation, the radial index p = 0 is assumed, meaning only variations in the topological charge l are considered, and modes are computed for topological charge values ranging from 1 to 10. The program calculates the inner product between the reconstructed complex amplitude field and each LG mode for every topological charge l, obtaining the coefficients of each mode. Based on these coefficients, the purity of each topological charge mode is computed, representing the power contribution of each mode. The analysis demonstrates excellent agreement with the design parameters, showing a dominant contribution from the desired LG mode: l = 1.

5. Discussion and Conclusions

In conclusion, we have successfully fabricated a nonlinear Dammann vortex grating in periodically poled lithium niobate and demonstrated its application in sorting and detecting near-infrared optical vortices through nonlinear diffraction. The device generates a 49-channel vortex array, extending the detection range of near-infrared optical vortices from −12 to +12. By precisely sorting the vortex modes in the array, the system enables the rapid, real-time detection of near-infrared vortices through a nonlinear process. Additionally, the system not only enhances communication capacity but also simplifies the detection process for near-infrared vortex beams. This method enhances detection accuracy and provides significant potential for applications in OAM-based optical imaging, communication systems, and quantum information processing. Future research could optimize conversion efficiency by increasing the fundamental pulse energy or by integrating three-dimensional nonlinear photonic crystal technology to compensate for longitudinal phase mismatch, further enhancing the system’s performance. This work presents an efficient and practical solution for both sorting and detecting optical vortices, contributing to advancements in high-dimensional optical manipulation and multiplexing techniques.