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Abstract
Wavelength- and OAM- tunable laser with large tunable range is the key source for the application in large capacity optical communications. In this paper, we demonstrate a wavelength- and OAM-tunable vortex laser in a 1.2 W single mode fiber coupled LD pumped Yb:phosphate laser. A z-type cavity has been used to precisely control the laser mode diameter. A thin film polarizer (TFP) is inserted to finely control the intra-cavity loss and tune the wavelength. Corresponding laser fundamental mode to pump beam ratio has been optimized to decrease the pump threshold for high order HG mode running. A pair of cylindrical lenses has been used to convert the HG mode to vortex output. The vortex beam with OAM-tunable range from 1ħ to 14 ħ with wavelength tuning range of ~36.2 nm for LG0,1 vortex beam, and ~14.5 nm for LG0,14 vortex beam at pump power of only 1.2 W have been realized, which is the largest tuning range of both OAM and wavelength at ~1 W pump power range to the best of our knowledge.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical vortices with helical wavefront structure, carrying orbital angular momentum (OAM) have drawn growing interest in recent years and been widely used in the fields of optical tweezers [1], quantum entanglement [2] and optical communications [3, 4]. Particularly, in the multi-channel optical communications, wavelength- and OAM-tunable vortex lasers with large spectral tunable range are normally preferred for the realization of wavelength division multiplexing (WDM) together with mode-division multiplexing (MDM) [5, 6].
Methods of generating wavelength- and OAM- tunable vortices with volume Bragg grating [6], MEMS-based Fabry-Perot filter integrated with a spiral phase plate [7], metasurfaces [8], and mode converters [9] have been reported. Among them, converting a diagonally aligned Hermite-Gaussian (HG) mode into a Laguerre-Gaussian (LG) mode by astigmatic mode converter (AMC) is efficient, simple and cost saving [9]. Using a pair of cylindrical lenses, a HGn,0 mode can be transferred to LG0,n mode carrying ± nħ OAM [10–12].
Off-axis pumping is a well-known method to produce controllable high-order HG modes in solid-state lasers [11].The availability of the pump power and laser crystal size limit the mode order [9, 13]. The limitation caused by pump power can be avoided by using a high power pump source. Normally, high pump power of tens of Watts are required to excite higher order HG modes [9, 14]. However, the high pump power will result in large heat loading in the laser crystal, which requires the cooling system and might cause thermally induced fracture in the laser crystal [15]. The limitation caused by crystal aperture is normally difficult to be avoided. In [9], the authors suggest to use dual off-axis method to form higher-order mode up to HG15,0 at pump power of more than 30 W. However, the HG mode order cannot be continuously tuned by only increase the off-axis displacement of pump beam. The position of output coupler also needs to be precisely adjusted, which makes the system less practical for OAM-tunable vortex beam generation.
In this paper, we use a single mode fiber coupled laser diode as pump source, which can provide the possibility of tight focusing compared with multimode fiber coupled LD. This characteristic could improve the laser efficiency, decrease the lasing threshold and avoid active cooling system [16]. It is known that, in a TEM0,0 mode running laser, mode-to-pump ratio of about 1.1 can maximize the laser output power at pump power of ~1 W [17]. However, a small laser beam size can compensate the intra-cavity loss induced by the crystal aperture. In order to achieve higher order mode running, theoretically and experimentally, we find that corresponding laser fundamental mode to pump beam ratio needs to be revised to decrease the pump threshold. A z-type cavity can be used to precisely control the laser spot size in order to achieve high order HG modes at even lower pump threshold. Experimentally, by adjusting the cavity, we can decrease the pump threshold for HG6,0 mode from 438 mW to 396 mW, for HG7,0 mode from 638 mW to 408 mW, and for HG8,0 mode from 838 mW to 448 mW. Up to HG14,0 mode has been obtained at pump power as low as 1 W. The order of HG modes can be continuously tuned by only changing the off-axis displacement of pump beam. A pair of cylindrical lens has also been used as π/2 astigmatic mode converter to convert the HGn,0 mode into LG0,n vortex beam. Continuous wavelength tuning is realized by inserting a thin film polarizer (TFP) in the cavity to precisely control the cavity loss. In the experiments, the vortex beam with OAM-tunable range from 1ħ to 14 ħ with wavelength tuning range of ~36.2 nm from 1027.7 nm to 1063.9 nm for LG0,1 vortex beam, and ~14.5 nm from 1033.7 nm to 1050.5 nm for LG0,14 vortex beam at pump power of only 1.2 W have been realized, which is the largest tuning range of both OAM and wavelength at ~1 W pump power range to the best of our knowledge.
2. Experiment setup and theoretical analysis
The experimental setup is shown in Fig. 1(a). A single mode fiber coupled 1.2 W laser diode (LD) is used as pump source. The output pump beam from the single mode fiber is collimated and focused to a 2 × 8 × 2.5 mm3 10% doped Yb:phosphate (Yb:QX) glass by two focusing lenses L1 and L2 with 18.53 mm and 60 mm focal length respectively. The Yb:QX glass is placed at Brewster angle. The pump beam waist at the focus is calculated as about 19.4 μm. The pump coupling system is mounted together in a 3-adjuster mirror mount in order to precisely control the pump beam path in the gain crystal. Off-axis pumping technique is used to excite high order Hermite Gaussian modes. OC is a 1.5% output coupler. M1 and M2 are concave dichroic mirror of radius of curvature 100 mm. M3, M4 and M5 are folding mirrors. A thin film polarizer (TFP) is inserted inside the cavity to adjust the intracavity loss and control the effective spectral gain profile of the Yb:phosphate laser. It is clear that the peak wavelength of the gain spectrum depends on the cavity loss [18], hence continuously wavelength tuning can be realized by fine tuning of intra-cavity loss (i.e., rotation of the TFP). The z-type cavity is used to cancel the astigmatism caused by the Brewster angle placed gain material. The position of curved mirror M2 is finely adjusted in order to achieve higher order HG mode emission.
It is already known that a z-type cavity can be simplified as an equivalent two-mirror resonator as shown in Fig. 1(b). The equivalent radii of curvature of curved mirrors are given by [19]:
where d1 and d2 are the distance between curved mirrors M1 and OC, M2 and M4 respectively; f is the focal length of M1 and M2; Δ is a parameter, which characterizes the range of stable operation.
Endo’s method [20, 21] has been used to simulate the HG mode generation in the equivalent two-mirror cavity. Figure 2(a)-2(c) shows the simulated HGn,0 modes excited by shifting the position of tight beam focus laterally from the central axis of the laser cavity. Mode number n increase from 0 to 8 with increasing shift d from 0 to 103 μm, where the pump beam position was adjusted to the position of the brightest outermost spots [11]. Figure 2(d)-2(f) shows the mode changing from HG7,0 to HG9,0 by fine tune the cavity length t, equivalent to translating curve mirror M2 in the laser setup, while d is kept constant as 103 μm in the simulation. When the position of M2 is changed, the fundamental mode size changes, i.e. the fundamental mode-to-pump ratio changes, which will affect the laser mode. In order to understand the modes changing, pump power threshold for different modes has been calculated.
Fig. 2 Simulation of HG mode generation: (a) HG0,0 mode generation by pointing the pump beam at x = 0 μm, y = 0 μm; (b) HG2,0 mode generation by pointing the pump beam at x = 39 μm, y = 0 μm; (c) HG8,0 mode generation by pointing the pump beam at x = 130 μm, y = 0 μm; fine tune the equivalent cavity length t to generate (d) HG7,0 mode (e) HG8,0 mode and (f) HG9,0 mode.
It is already known that the pump power threshold for TEMn,0 mode can be calculated as [22]:
where Ae is the mode effective area, γ is the cavity loss, Isat is the saturation intensity, L is the length of the gain medium, ηp = ηtηa(υl/υp) as ηt is the quantum efficiency, ηa is the absorption coefficiency, and υl and υp are frequency of laser and pump respectively. sn,0 is the normalized laser intensity distribution and rp is the normalized pump intensity distribution. Here wl is the corresponding fundamental mode size of HGn,0 mode:Figure 3 shows the simulation results. It is clear from Fig. 3(a) that the pump threshold is dependent on the laser intensity distribution. Higher order HG modes will result in higher threshold. However we find that if the pump beam size and position at the laser crystal keeps unchanged, by changing the corresponded fundamental laser mode size, pump threshold for HG9,0 could be smaller than pump threshold for HG8,0, as shown in Fig. 3(b). This is because that if the corresponding fundamental laser mode size gets smaller, the position of the outermost spot HG mode will become closer to the original axis of the laser crystal, which compensates the intra-cavity loss induced by the crystal aperture. But a too small fundamental laser mode, will again increase the threshold and decrease the output power due to the bad overlap efficiency [22]. So in order to design a high-order HG mode laser, corresponding fundamental mode-to-pump beam size ratio should be optimized to minimize the limitation effect by crystal size.
Fig. 3 Simulation results of (a) HGn,0 mode dependent pump threshold; (b) corresponding fundamental mode-to-pump beam size ratio dependent pump threshold for HG8,0 mode and HG9,0 mode.
3. Experimental results and discussion
Figure 4(a) shows the measured pump threshold for different HG modes with increasing off-axis displacement. Initially, the laser cavity, which was strictly co-axial, has been optimized for lowest threshold of fundamental mode TEM0,0 (HG0,0). As the off-axis displacement is increased and the pump power increases accordingly, higher order HG modes can be achieved. However, at this cavity configuration, the highest mode is limited to HG8,0. Then we transverse curved mirror M2 to fine tune the laser mode distribution. After optimization, we could decrease the pump threshold for HG6,0 mode from 438 mW to 396 mW, for HG7,0 mode from 638 mW to 408 mW, and for HG8,0 mode from 838 mW to 448 mW, as shown in Fig. 4(b). However, the pump threshold for HG modes order lower than 6 becomes larger than before. This is due to the better mode matching for higher order modes, which results in worse mode matching for lower order modes. With increasing pump power to 1 W and off-axis displacement, the order of HGn,0 mode can be scaled up to n = 14, as shown in Fig. 5. The order of HG mode can be continuously tuned by just adjusting the pump coupling system.
Fig. 4 (a) Measured pump threshold for different HGn,0 mode with increasing off-axis displacement; (b) HGn,0 mode dependent pump threshold -●- measured results at laser cavity optimized for lower order mode,-■- measured results at laser cavity optimized for higher order mode.
A pair of cylindrical lens has been used as π/2 astigmatic mode converter to convert the HGn,0 mode into corresponding LG0,n vortex beam with OAM nħ. The experimental setup is shown in Fig. 6. Lens L1 is a mode-matching lens. The π/2 mode converter includes two identical convex-plane cylindrical lens of focal length 50 mm with separation of 70.7 mm. L4 is a collimating lens. After the mode converter, donut shape beam can be formed. An interference experiment with the vortex beam and a plane wave to characterize the spatial phase of the converted vortex has also been performed. Part of the HG beam has been used as reference plane wave, which then interfered with the converted LG vortex beam. Figure 7 shows both the simulation and experimental interference pattern for the LG0,1, LG0,2, LG0,6, LG0,10, LG0,14 modes. The experimental results agree well with the simulation ones. Note that LG modes from 1 to 14 can be continuously tuned with controlled corresponding HG mode generation. Here we only show part of them for simplicity.
Wavelength tuning of the generated LG modes have also been realized by rotating the TFP inside the cavity. For LG01 mode, the wavelength can be tuned continuously from 1027.7 nm to 1063.9 nm at pump power of 1.2 W, as shown in Fig. 8(a). As cavity loss is introduced by the TFP, the output power at different wavelength changes from 82 mW at 1027.7 nm to 14.5 mW at 1063. 9 nm. Maximum output power of 128 mW is obtained at laser wavelength of 1040.6 nm. With increasing HG mode order, the tuning range is decreased, as shown in Fig. 8(b). For LG14 mode, the wavelength can be tuned from 1033.7 nm to 1050.5 nm. This is due to the extra cavity loss introduced by the off-axis pumping.
Fig. 8 (a) Wavelength tuning for LG0,2 mode; (b) LG0,n mode dependent wavelength tuning: -●- upper limit of tuning wavelength, -■- lower limit of tuning wavelength, -▲- wavelength tuning range.
4. Conclusion
In summary, we use a 1.2 W single mode fiber coupled laser diode as pump source to achieve wavelength- and OAM- tunable vortex beam. Hermite-Gaussian modes have been generated by off-axis pumping technology, while the vortex LG modes have been obtained by cylindrical lens pair mode converter. In order to obtain high order HG mode emission from the laser cavity, fundamental mode-to-pump beam ratio needs to be optimized to compensate the intra-cavity loss induced by the crystal aperture. By proper design of the z-type cavity, in the experiments we have achieved a large OAM-tunbale range from 1ħ to 14ħ at pump power of only 1.2 W. Wavelength tuning has also been realized by simply inserting a TFP inside the cavity to precisely control the cavity loss. The wavelength tuning range is as large as ~36.2 nm for LG0,1 vortex beam, and ~14.5 nm for LG0,14 vortex beam. The OAMs are also experimentally verified by the interferograms, which is in good agreements with the simulation results. This work provides a method to achieve vortex beam with large tuning range of both OAM and wavelength at low pump power, which can be applied to high-capacity optical communications with spatial- and wavelength- division multiplexing techniques and other novel researches.
Funding
National Natural Science Foundation of China (Grant Nos. 61605133, 61505129); Sichuan Province International Cooperation Research Program, China (Grant No. 2016HH0033); Chengdu Science and Technology Program, China (Grant No. 2015-GH02-00021-HZ).
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