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Abstract
Broadband wavelength tunable Laguerre–Gaussian (LG) mode with flexibly manipulated topological charge is greatly desired for large-capacity optical communication. However, the operating wavelengths achieved for the current LG modes are significantly restricted either by the emission spectrum of the intracavity gain medium or by the operation wavelengths of mode-conversion or modulation components. Here, broadband wavelength-tunable LG modes with a controllable topological charge are generated based on a random fiber laser (RFL) and a digital micromirror device (DMD). The RFL can produce broadly wavelength-tunable laser emissions spanning from 1044 to 1403 nm with a high spectral purity and an excellent beam quality, benefiting from the cascaded random Raman gain starting from a ytterbium fiber based active gain. A commercially available broadband DMD is then utilized to excite the LG modes with a flexibly tunable topological charge of up to 100 order through the super-pixel wavefront shaping technique. The combination of the RFL and the DMD greatly broadens the operating wavelength region of the LG modes to be achieved, which facilitates the capacity scaling-up in the orbital angular momentum multiplexed optical communication application.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Vortex beams carrying orbital angular momentum (OAM) have been extensively investigated in the past three decades and have found applications in large-capacity optical communication, particle trapping, and manipulation, super-resolution imaging, etc. [1–3]. Particularly, for the OAM based optical communication, the unbounded topological charge shows great potential in increasing the capacity of communication systems [4–6]. Employing the OAM mode division multiplexing (OAM-MDM) technology, 16 OAM modes are multiplexed to send an intensity encoded gray image through a 3 km distance with strong turbulence [7]. Combined with the wavelength division multiplexing (WDM), 1.6 Tbit/s data flow can be realized in a specially designed vortex fiber and the transmission over 1.1 km has been demonstrated [8]. By further utilizing the three-dimensional multiplexing including OAM, wavelength, and polarization, a 100 Tbit/s free-space data link has been realized [9]. Therefore, the multiplexing techniques in MDM and WDM all place a huge demand in the generation of a broadly wavelength-tunable vortex beam for the development of a high-capacity optical communication system.
As a set of paraxial eigenmodes, the Laguerre-Gaussian (LG) modes can be generally obtained in either a resonant lasing structure (e.g., a solid lasing cavity) or an external light modulator (e.g., a spiral phase plate, q-plate, spatial light modulator (SLM)) [10–12]. It can be inferred that the wavelength response range of the LG modes is mainly restricted by two factors: one is the emission spectrum of the gain medium in the lasing cavity, and the other one is the operation wavelength of the mode-conversion optical components. A first-order optical vortex was generated via an acoustically-induced fiber grating (AIFG), the wavelength of which can be tuned from 1540 nm to 1560 nm [13]. Wavelength- and OAM- tunable vortex laser was also realized in an Er: YAG solid-state laser with a reflective volume Bragg grating [14]. However, the wavelength tuning range and the number of topological charges achieved were greatly limited. Similar results were also reported in the ∼1 µm wavelength band, spanning several tens of nanometres’ tuning range for different orders (up to 14th) of the vortex beam [15]. Recently, supersurface-assisted vortex fiber laser has also been proposed for wavelength tunable OAM beam generation from 1015 to 1075 nm, which is still limited in the available wavelength tuning band [16]. On the other hand, the limited lasing wavelength band also restricts the realization of vortex beam with special wavelengths. For example, the ∼1.3 µm band is an important optical window for bioimaging systems and vortex beam operating at this wavelength band has great potential in increasing the spatial resolution.
For the LG mode generation based on the external modulation method, components such as helical phase plates and mode-selective couplers can only excite individual OAM modes and is improper for the flexible modulation, which would greatly increase the cost and complexity of the system that requires a large amount of OAM modes. Although liquid-crystal based SLM can provide flexible modulation and operate in a real-time regime, the performances in the frame rate, the response wavelength band, the maximum handling power, and the incident light polarizations all hinder the development of high-speed and large-capacity optical communications. In contrast, a binarized digital micromirror device (DMD) shows great potential in providing a broadband spectral response (e.g., from 0.8 µm to 2 µm). Full optical field modulation can be efficiently realized by employing the wavefront shaping technique, such as the super-pixel method [17,18]. In addition, the unique advantages of the DMD, including the faster refresh rate (e.g., ∼12.5 kHz), the excellent power handling capability (e.g., ∼160 W), and polarization-independent operation, all make it the most attractive candidate for flexibly generating the LG modes, especially operating in a broad wavelength region. Thus, the ultimate operating wavelength range of the generated LG modes would be primarily determined by the incident light source.
For a typical laser, the wavelength tuning range is mainly determined by the gain spectrum and the wavelength-selection component in the resonant cavity. In contrast to conventional active gain based lasing structures where the lasing wavelength is restricted by the active rare-earth-ion-dopants’ gain spectrum (e.g., ytterbium or erbium ions), stimulated Raman scattering (SRS) based lasing structure can theoretically excite any wavelength of interest combined with a proper pump source and effective feedback of the corresponding Raman Stokes. However, traditional resonant cavity still suffers from wavelength-dependent feedback originating from the narrow band reflectors and additional optical components. A random fiber laser (RFL) [19,20] is considered to be an ideal candidate for producing laser emissions at a special wavelength [21–23] since the Rayleigh scattering can provide effective optical feedback in an open cavity structure. Random vortex beams have also been studied based on the SLM [24], the long-period fiber grating (LPFG) [25], and the mode-selective coupler (MSC) [26]. It has been demonstrated that by combining a tunable ytterbium doped fiber (YDF) based RFL source and the cascaded random Raman Stokes generation, the lasing wavelength can cover a super-broad wavelength band ranging from 1 to 1.9 µm [27]. Taking advantage of this technique, the lasing wavelength has been broadened into the mid-infrared region by further combing with the nonlinear frequency conversion technique [28,29]. Therefore, it is naturally anticipated that the broadband wavelength-tunable RFL can be incorporated with a DMD based wavefront shaping technique to achieve broadband wavelength-tunable LG modes.
Here, we propose and demonstrate the generation of broadband wavelength- and OAM-tunable Laguerre–Gaussian (LG) modes based on a wavelength-tunable RFL and the super-pixel wavefront shaping. A wavelength tuning range of more than 350 nm (from 1044 to 1403 nm) for the LG modes with an attainable topological charge of up to 100 has been simultaneously obtained. The broadband wavelength-tunable RFL is realized in an integrated structure composed of a wavelength-tunable YDF RFL seed and the cascaded random Raman Stokes. The broadband lasing is then modulated by the wavefront shaping technique based on a DMD with broad spectral response. The proposed broadband wavelength- and OAM-tunable Laguerre–Gaussian (LG) modes can have great prospects in increasing the capacity of vortex mode based optical communication, as well as some particular applications that require vortex beams at a special wavelength.
2. Experimental setup
The proposed schematic diagrams for generating the broadband wavelength-tunable LG modes as well as their characterization section are shown in Fig. 1. The broadband light source is based on a wavelength-tunable YDF RFL seed light and the corresponding cascaded random Raman Stokes in a half-opened cavity, as described in the dashed box in Fig. 1. For the wavelength tunable YDF RFL seed, we employ the passive feedback assisted half-open random lasing structure, where the optical feedback is provided by a fiber loop mirror composed by a 3 dB coupler (coupler 1) and the random distributed Rayleigh scattering along a piece of 3 km long SMF (G652D). To realize the wavelength tuning function, a pig-tailed bandpass filter in the 1 µm region is inserted into the loop mirror. A piece of 5 m YDF (LMA-YDF-10/130-M, Nufern) provides the optical amplification for the selected random lasing wavelengths and the pump laser is a multimode 976 nm laser diode (LD1, maximum output power of 60 W). An isolator is deployed at the distal end of the SMF to prevent any potential feedback from the following sections and keep the RFL seed stable. The RFL seed was injected through a 3 dB coupler (coupler 2) into the following section comprising a classic half-opened cavity structure to activate the cascaded random Raman Stokes. The other input port of coupler 2 was connected with another 3 dB coupler (coupler 3) based fiber loop mirror. Another piece of 5 m YDF (LMA-YDF-10/130-M, Nufern) was pumped by a high-power 976 nm LD through a signal/pump combiner to largely boost the optical power of the injected RFL seed. At the distal end, a piece of angle-cleaved 10 km dispersion shifted fiber (DSF, zero dispersion wavelength of ∼1480 nm) is used to provide the optical feedback based on Rayleigh scattering only and the SRS nonlinear gain. The cascaded random Raman Stokes can then be excited in the forward output direction. A cladding power stripper (CPS) is inserted between the YDF and the DSF to strip the unabsorbed pump light. It is worth noting that the DSF is extremely important to extend the lasing wavelength beyond 1.3 µm, since the modulation instability initiated spectral broadening would lead to the supercontinuum generation and prevent the further power transfer into laser emissions at a longer wavelength once a traditional SMF was used here instead [30].
Fig. 1. Schematic diagram of the broadband wavelength tunable LG mode generation and characterization. LD, laser diode. YDF, ytterbium doped fiber. SMF, single mode fiber. ISO, isolator. CPS, cladding power stripper. DSF, dispersion shifted fiber. DMD, digital micromirror device. BS, beam splitter.
To excite the vortex beam and characterize its spiral phase profile, the output of the random lasing is split into two paths using a 3 dB coupler. Both of the two outputs are collimated by a convex lens (focal length of 6.2 mm). One of the collimated light beams is incident on the surface of the DMD (DLP650LNIR, Texas Instruments) via a high-reflection mirror. A binarized hologram pattern is created in advance using the super-pixel wavefront shaping method and loaded on the DMD to regulate the light field of the incident RFL. The corresponding vortex beam is then obtained by deploying an iris diaphragm at the Fourier plane of the 4f system to select the first-order diffracted light. The other output beam from the 3 dB coupler (coupler 4) is used as a reference light to constitute a Mach-Zehnder (MZ) interferometer for the spiral phase verification. The two beams are combined through a cubic beam splitter (BS) and the output profile is measured by a charge coupled device (CCD) camera.
3. Experimental results
Firstly, the lasing characteristics of the wavelength tunable RFL are investigated, as shown in Fig. 2. The output spectrum of the RFL is measured by an optical spectrum analyzer (AQ6370D, Yokogawa). For the convenience of revealing the evolutionary process of the wavelength tunable RFL, we fixed the center wavelength of the bandpass filter to 1070 nm, as shown in Fig. 2(a1) to 2(a3). A smooth and stable spectral profile appears when the power of LD1 pump exceeds the lasing threshold of ∼0.465 W while the LD2 pump is turned off, as shown in Fig. 2(a1). The low lasing threshold benefits from the active gain of the random lasing structure [31]. The maximum output power of the RFL seed reaches ∼1000 mW when the power of LD1 pump is increased to 4.902 W, which was then fixed for the following power boosting and the activation of cascaded random Raman Stokes emissions. Representative output spectra of the high-order random Raman Stokes are given in Fig. 2(a2) and 2(a3), corresponding to the third- (central wavelength is 1252 nm, the LD2 pump power is 9.65 W) and fifth- (central wavelength is 1403 nm, the LD2 pump power is 29.8 W) order Raman Stokes, respectively. Compared with the ∼0.224 nm 3 dB spectral width of the RFL seed that was determined by the bandpass filter, the output spectrum of the high-order Raman Stokes emissions was slightly broadened. For instance, the spectral widths were enlarged to 1.032 and 3.200 nm for the 1252 and 1403 nm Stokes wavelengths, respectively. It can be also seen that, although residual Raman Stokes emissions exist in both cases, the spectral contrast between the dominant and the secondary lasing emissions is 18.47 and 15.97 dB, respectively, representing a reasonably high spectral purity. It is worth noting that the spectral purity of the random lasing can be further increased by further optimizing the length of the DSF [22,32].
Fig. 2. Characteristics of the wavelength tunable RFL. (a1 - a3) Optical spectral evolution at different pump powers. (b1 - b3) Short-time temporal domain traces corresponding to spectrum curves of 4.902 W in (a1) and those in (a2) and (a3). (c) Output powers for different order Raman Stokes lights with respect to pump power. The pump wavelength is 1070 nm in this case. (d) Output spectra plotted for approximately every 50 nm from 1044 to 1403 nm.
The wavelength-tunable RFL operates in a continuous-wave regime, which can be seen from the short-time temporal traces at different pump powers, as shown in Fig. 2(b1) to 2(b3). The std/mean value (the standard deviation divided by the mean value) is used to quantitatively characterize the temporal dynamics. It is observed that the corresponding std/mean values grow larger as higher order Raman Stokes emissions are excited, resulting from the spectral broadening effect as shown in Fig. 2(a). To evaluate the characteristics of power transfer, the central wavelength of the bandpass filter is fixed to be 1070 nm, while the power of the LD1 pump is maintained at 4.902 W. Then, the output powers for different orders of Raman Stokes lasers versus the LD2 pump power are shown in Fig. 2(c). The maximum output power of the fifth-order random Raman Stokes is 1.703 W under a pump power of 30.8 W. When the pump power reaches 31.6 W, the output power of the sixth-order random Raman Stokes starts to increase rapidly. It is worth noting that the RFL seed in Fig. 2(c) refers to the random lasing initiated by the active gain from ytterbium ions, i.e., the 1070 nm, while the 1st to 6th lasing all corresponds to the cascaded Raman Stokes.
Ultimately, a wavelength tunable YDF based RFL seed is constructed with a tunable bandpass filter, covering the operation wavelength from 1044 to 1090 nm. Then, by further increasing the LD2 pump power, the output spectrum can be extended to a longer wavelength range benefiting from the cascaded stimulated Raman Stokes. Representative random lasing wavelengths from 1044 to 1403 nm are given in Fig. 2(d), spanning over 350 nm. Technically, the tuning range of the cascaded random Raman fiber laser is mainly determined by the zero dispersion wavelength (ZDW) of the employed Raman fiber. Notable spectral broadening would be excited if the lasing wavelength is near the ZDW of the anomalous dispersion region, which restricts the power transfer into the next order of Raman Stokes with a longer wavelength. In addition, the random lasing with a reasonably high spectral purity can also limit the tuning range in practice considering the properties of the employed optical components. Here, to achieve laser emissions with a reasonably high spectral purity and density, we fixed the wavelength tuning range to be from 1044 to 1403 nm for the following vortex beam generation section. It is anticipated that by carefully optimizing the critical parameters of the Raman fiber (e.g., the length, the zero dispersion wavelength), the wavelength tuning range can be expanded to as broad as 900 nm [27].
The wavefront shaping method is then applied to yield the broadband wavelength- and OAM-tunable LG modes. Here, the created hologram pattern and its theoretical performance are shown in Fig. 3. The theoretical optical field of the LG mode is defined as [33]:
Fig. 3. Theoretical analysis of the super-pixel based wavefront shaping. The target intensity (a) and phase (b) profiles of the LG modes with topological charges of 1, 5, 10, 50, and 100. (c) The corresponding binarized hologram patterns loaded on the DMD. Numerically calculated intensity (d) and phase (e) profiles of the LG modes. (f) Interference patterns calculated by the LG modes and a spherical wave.
The super-pixel wavefront shaping process can be implemented based on the following two steps: Firstly, the target intensity (Fig. 3(a)) and phase (Fig. 3(b)) profiles are generated by the defined optical field of the LG modes depicted in Eq. (1). Secondly, the binarized hologram patterns (Fig. 3(c)) are then created through a precalculated lookup table which links the object plane on the DMD and the image plane of the LG modes. Although the topological charge to be created theoretically can be extremely large, in practice it is mainly restricted by the available number of pixels in the modulator. Therefore, the feasibility of the generated hologram can be theoretically identified by the wave optics theory as the calculated intensity and phase profiles shown in Fig. 3(d) and 3(e) respectively. The maximum topological charge is specified as 100, which is approaching the performance limit of the employed DMD. It is anticipated that by using a DMD with more modulation pixels, the achieved topological charge can be greatly improved using the same technique. The interference patterns between the LG modes and a spherical wave are calculated and given in Fig. 3(f) for convenience in verifying the spiral phase front in the experiment. It is clear that the number of spiral lines outwards from the center corresponds to the value of the topological charge.
In the LG mode generation experiment, we used the 1070 nm random lasing as the representative incident light to verify the generation of LG modes, as shown in Fig. 4(a). Here, the LG modes with topological charges of 1, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100 are generated respectively. We can see that the annular radius of the LG modes gradually grows with the topological charge. Even the LG mode with the highest topological charge can show a clear and sharp intensity profile. In addition, to quantitatively evaluate the evolution process of the LG modes with different topological charges, the annular radius and its annulus width in both the theoretical targets and the experimental ones are calculated and shown in Fig. 4(b) and 4(c). The different individual values between the theory and the experiment come from the 4f system, where the involved two lenses can affect the size of the final annulus to a certain degree. However, their evolution obeys the same tendency, as shown in Fig. 4(c) and 4(d). The radius grows gradually with the topological charge while the annulus width remains almost unchanged. This also verifies that the experimentally obtained LG modes with different topological charges are of good quality benefiting from the super-pixel wavefront shaping technique.
Fig. 4. OAM modulated LG modes of the 1070 nm random lasing. (a) Experimentally measured intensity profiles corresponding to LG0,l (l = 1, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100). The radius r0 and width Δr of the theoretical target intensity (b) and the experimentally measured ones (c) as a function of the topological charge.
One of the most attractive features of the RFL is its excellent temporal stability shown in Fig. 2(b). Therefore, the stability of the measured LG modes at 1070 nm with a topological charge of 10 is characterized, as shown in Fig. 5. Here, four individual pixels on the measured patterns are selected, while the corresponding intensity and the mean intensity of each pattern are listed and calculated every 30 seconds. For the overall 20-minute’ time window, all the intensity variation curves show relatively good stability, which comes from the intrinsic features of the RFL.
Fig. 5. The intensity of four individual pixels on the measured patterns and the mean intensity value of each pattern versus time.
We can see that the operating wavelength of the tunable RFL spans more than 350 nm. However, traditional silicon-based CCDs can only cover the visible and near-infrared band shorter than ∼1.1 µm and the optical responsivity and sensitivity at longer wavelengths would be dramatically reduced. Therefore, to monitor the intensity profiles of the LG modes and the corresponding interference patterns, a phosphor-coated CCD camera was employed here which can further extend the wavelength response to 1.6 µm. Here, we used a classical silicon-based CCD (DCU224M, Thorlabs) for the measurement of two random lasing wavelengths which are located at 1044 and 1123 nm. Both the mode field profiles and the corresponding interference patterns were measured by the MZ interferometer and are provided in Fig. 6. The outward spiral fringes are all in agreement with those numerically calculated interference patterns in Fig. 2(f). It is also noted that for the 1044 nm lasing case all the interference fringes are clear and sharp, while for the 1123 nm situation, it becomes a bit weak and blurry, especially for the LG modes with a high topological charge. This can be attributed to the dramatically reduced optical response efficiency of the silicon based CCD. The features in Fig. 6 verify again the feasibility and effectiveness of generating the broadband wavelength- and OAM-tunable LG modes based on the super-pixel wavefront shaping technique. To further verify the LG modes at longer wavelengths, a phosphor-coated CCD camera (U3-VIS NIR, BeamOn) is used and representative lasing wavelengths at 1.2, 1.3, and 1.4 µm are selected and shown in Fig. 7. Here, the intensity profiles of the LG modes versus the topological charge are similar with those in Fig. 6. The reduced contrast between the LG modes and the background also results from the dramatically reduced optical response in the longer wavelength region even for the phosphor-coated CCD camera. Distortions of the measured intensity profiles of the LG modes with higher-order topological charges are observed in Fig. 6 and 7, which is caused by the unoptimized light collimation condition for different lasing wavelengths. By precisely adjusting the relative positions of each optical component for an individual lasing wavelength and topological charge, the existing distortion can be eliminated.
Fig. 6. The measured results of LG0,l beam (l = 1, 5, 10, 50, 100) generated by super-pixel wavefront shaping under different wavelength conditions. (a) and (c) are the experimentally measured intensity profiles. (b) and (d) are the interference fringe.
Fig. 7. Experimentally measured intensity profiles of LG0,l beam (l = 1, 5, 10, 50, 100) at different wavelengths.
4. Conclusions
In conclusion, we propose a method to generate the LG modes with both the wavelength and OAM tunability based on a random fiber laser (RFL) light source and digital micromirror device (DMD). By using the super-pixel technique, the Gaussian beam is flexibly converted into the OAM-tunable LG modes, with an achieved topological charge of as high as 100. The topological charge can be manipulated by changing the DMD pattern, and the spiral phase front is verified by the coaxial interference between the LG mode and the reference beam. Wavelength tunability was demonstrated from 1044 to 1403 nm. High spectral purity and power stability are guaranteed throughout the wavelength tuning range. This work is conducive to the realization of high-capacity optical communication with spatial, mode and wavelength division multiplexing techniques and other new researches.
Funding
National Natural Science Foundation of China (123004478); Guangdong Basic and Applied Basic Research Foundation (2020A1515110471, 2020A1515111143); Natural Science Foundation of Guangdong Province (2021A1515011532, 2022A1515010326); Shenzhen Government's Plan of Science and Technology (JCYJ20220818100019040, RCYX20210609103157071); Natural Science Foundation of Top Talent of SZTU (20221061010038).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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