Transverse mode characteristics of lasers have been extensively investigated with a wide range of applications, such as space-division multiplexing (SDM) optical fiber communications ^[1–3], optical fiber sensing ^[4,5], quantum information ^[6,7], and laser processing of materials ^[8]. With the purpose of improving the transmission capacity in optical communication, the information is modulated at several different higher-order modes ^[9–11]. In an optical fiber sensor, the higher-order modes can achieve high discrimination accuracy for temperature and strain ^[12]. In quantum information technologies ^[13], the higher-order mode at the single photon level has also been exploited for entanglement experiments, quantum cryptography, and high-density information transfer. In laser processing of materials, the higher-order modes can be employed for laser ablation ^[8].

For specific applications, accurate and pure transverse mode emission is commonly required. In a conventional laser, the laser oscillates with both the higher-order modes and the fundamental mode ^[14]. Consequently, it is difficult to customize and prescribe the pure higher-order mode according to the specific application. Recently, attention has been focused on the on-demand mode laser that oscillates in a single transverse higher-order mode, which is a straightforward and efficient way to generate the specific mode directly.

So far, an on-demand mode solid-state laser has been proposed in the 1064 nm band ^[15]. In this scheme, the flexibility of the spatial light modulator (SLM) is utilized to customize and prescribe the pure higher-order mode. In this solid-state laser, an Nd:YAG crystal is employed and end pumped with a multi-mode fiber-coupled laser diode operating at 808 nm. The output mode can be customized and switched by controlling the SLM. This method can generate an accurate and pure transverse mode in the 1064 nm band. However, it is difficult to extend to the 1550 nm band, which is the window of lowest loss for the optical fiber. Therefore, there is an urgent need to realize the on-demand mode in the 1550 nm band. In 1550 nm band, the most frequently used crystal is an Er:glass crystal, whose emission cross section is approximately 3 orders of magnitude less than that of the Nd:YAG operating in the 1064 nm band. As a result, the Er:glass crystal can be used as the gain medium to generate the fundamental mode, despite the fact that it cannot excite the higher-order modes due to insufficient gain. To be specific, in the method proposed in Ref. ^[15], it is difficult to prescribe the higher-order transverse mode in the 1550 nm band. Accordingly, it is necessary to use an erbium-doped fiber (EDF) as the gain medium. Moreover, to eliminate mode conversion loss in the fiber and avoid the required multi-mode pump, it is better to use a single-mode EDF (SM-EDF), rather than a multi-mode EDF.

In this paper, based on the SM-EDF as well as an SLM, a fiber laser for prescribing pure higher-order laser modes in the 1550 nm band is proposed. The SLM is designated to generate higher-order modes. By setting the SLM, the desired higher-order mode and the fundamental mode presenting a different diffraction angle can be separated. Then, the wanted higher-order mode can be exported, while the residual fundamental mode is coupled into the fiber ring oscillator again. As we all know, the fundamental mode, and not the higher-order mode, is a self-reproducing mode of the fiber ring laser. By virtue of this simple and critical design, the gain medium (i.e., the EDF) can be pumped by the single-mode 980 nm laser, no matter what higher-order mode is prescribed. Furthermore, the proposed method is important because the requirement for a higher-order mode pump is avoided, which is usually necessary for mode amplification in SDM optical fiber communications. Simultaneously, the mode conversion loss is also greatly reduced because the fundamental mode oscillates in the fiber laser. Notice that the concept of the superpixel is used in the SLM to enhance the system performance. In conclusion, high-quality higher-order modes from LP01 to LP105 are observed in our proof-of-principle experiment.

The experimental setup is shown in Fig. 1. The laser cavity is a ring cavity with SM-EDF acting as the gain medium. The pump light (980 nm) and oscillating light (1550 nm) are coupled into the SM-EDF through a wavelength-division multiplexing (WDM) coupler. The length of the SM-EDF is 10 m. In the SM-EDF, most of the pump light is absorbed and the oscillating light is amplified. After the amplification in the SM-EDF, the light field enters into free space for wavelength filtering and mode control. The center wavelength of the wavelength filter is 1550±2.4nm. The half-wave bandwidth of the wavelength filter is 12±2.4nm. Therefore, the wavelength is locked in the C and L bands. Then, after the beam passes the half-wave plate (HWP) and polarizer, the polarization direction of the beam is consistent with the functional direction of the SLM, and thus the beam will be shaped by the SLM. The role of the SLM is to load a multi-mode mask for the excitation of on-demand higher-order modes. After the modulation of the multi-mode mask, the beam is split into two sub-beams (one beam with the LP01 mode pattern and one beam with a higher-order mode pattern). The LP01 mode beam is then coupled into a single-mode fiber and amplified again in the SM-EDF. The higher-order mode beam, however, is coupled into a few-mode fiber (FMF) for transmission. The isolators guarantee the light field in the cavity for one-way transmission only.

A multi-mode mask capable of simultaneously exciting several modes is utilized in our scheme. The expression of the multi-mode mask is where φn (n=1,2) denotes the phase of the desired modes and ϕn (n=1,2) denotes a blazed grating being added to each desired mode. The expression of the blazed grating iswhere x denotes the position along the horizontal or vertical axis, Δ denotes the pixel pitch of the SLM, d denotes the grating period, and mod denotes the modulus function. Different blazed gratings make each desired mode present a different propagation direction.

In the experimental scheme, φ1=0 and ϕ1=0 are set. Thus, Eq. (1) is simplified as follows:

After using the multi-mode mask, part of the light is still in the LP01 mode without being shaped. However, other light is shaped and then converted into a higher-order mode. The propagation direction of the higher-order mode is changed, while that of LP01 is not. The coefficients A and B in Eq. (3) are related to the power distribution between modes. Parameters of A=1 and B=3 are set to achieve a power balance between two modes.

In Eq. (1), φn is defined as the phase of the desired modes. However, the converted mode after pure phase modulation is not exactly the same as the desired mode. The difference lies in the amplitude distribution. Thus, the method of the superpixel that realizes combined amplitude and phase modulation is utilized to generate φn. Superpixels correspond to small areas on the SLM, each of which has a checkerboard pattern with two independent pixel values [Fig. 2(a)]. After being reflected by the superpixel, the intensity of the light can be controlled by the difference in the pixel values, and the phase shift can be set through the individual phase shifts. In previous work, the intensity modulation function of our SLM was measured ^[16], and the expression is where Δθ=a−b [Fig. 2(a)] denotes the difference between two independent pixel values. The multi-mode mask for the excitation of the LP21 mode using the superpixel is shown in Fig. 2(b). The simulation results clearly demonstrate the feasibility of our scheme for the simultaneous and accurate excitation of the LP01 and LP21 modes [Fig. 2(c)]. At the same time, the excitation of the LP74 and LP105 modes is also given [Figs. 2(d) and 2(e)].

In addition, the excitation of higher-order modes is demonstrated in the experiment. The experimental results of simultaneous excitation of the LP01 and LP21 modes are shown in Fig. 2(f). By controlling the multi-mode masks loaded on the SLM in real time, the excitation of other higher-order modes is also demonstrated (Fig. 3). The output mode fields from the laser are coupled into four-mode FMF in transmission. The intensity distribution of the output beam after propagating 100 m in FMF is captured using CCD. The intensity distributions of the modes before and after propagation in FMF are shown in Fig. 4.

In order to analyze the spectrum of the output laser, the multi-mode masks for the excitation of two LP01 modes are loaded onto the SLM. Then, after injecting light into the optical spectrum analyzer, we obtain the spectrum diagram, as shown in Fig. 5(a). Obviously, the center wavelength obtained and the bandwidth of the output laser are 1575.9 and 1 nm, respectively. In addition, to analyze the polarization state of the output from the fiber laser, the output LP01 mode is also coupled into the polarization synthesizer to obtain the polarization data. The output laser is linearly polarized light, and the degree of polarization remains stable (Visualization 1). Finally, for the LP21 mode, the quantum efficiency is presented in Fig. 5(b). It can be clearly seen that the output power increases linearly with the pump power. The laser threshold is only 26.6 mW, and the power of the output laser is 52.3 μW. The maximum output power of the LP21 mode is 4.196 mW, because the output power is limited by the maximum pump power of 288.2 mW.

The SLM used in the experiment contains 1920×1080 pixels with an 8 μm pixel pitch and 256 (8 bit) gray level. The resolution is sufficient to achieve the accurate excitation of many lower-order modes. The experimental results are clear, with a weak distortion at the periphery of the excited modes (Figs. 3 and 4). The weak distortion can be filtered out through beam propagation in FMF (Fig. 4) or by using a 4f filter system. For higher-order modes (LP74 and LP105, for example), a bright spot exists at the center of the light field, which does not appear in the simulation results shown in Figs. 2(d) and 2(e). It can be derived from the inaccurate modulation of the SLM and can be eliminated by utilizing a SLM with high modulation accuracy or phase plates.

In a few-mode erbium-doped fiber amplifier (FM-EDFA), to boost the power of signals carried by modes, pumping in a higher-order mode is preferred to significantly reduce the mode-dependent gain. Before coupling into the FM-EDFA, the 980 nm pump light is transformed by an optional phase plate ^[17]. To get rid of the requirement on the higher-order mode pump and mode conversion, the SM-EDF is the best choice, and also greatly reduces the loss in the laser cavity. Under sufficient pump power and the proper doping concentration of erbium ions in SM-EDF, the gain of a 1550 nm laser can well overcome the loss of the ring cavity. Finally, the stable output of the higher-order modes is achieved.

In conclusion, we propose a method to effectively excite transverse laser modes based on an SM-EDF and an SLM. The SM-EDF is employed to be the gain medium, and the SLM is designated to convert the fundamental mode to the desired higher-order mode. The desired higher-order mode is exported, while the residual fundamental mode is coupled into the ring cavity. In general, the experimental implementation is simple but efficient. The propagation of the LP01, LP11, LP21, and LP02 modes from a laser in a four-mode FMF is also demonstrated. Because of it characteristics of being on-demand and flexible, the on-demand laser will play an important role in a variety of interesting applications.

Acknowledgment. The authors thank the FiberHome Corporation for providing single-mode erbium-doped fiber and four-mode few-mode fiber in the experiment. We also thank Liaocheng University for providing the spatial light modulator in the test.