Direct generation of 1108&#x2005;nm and 1173&#x2005;nm Laguerre-Gaussian modes from a self-Raman Nd:GdVO<sub>4</sub> laser

Yuanyuan Ma; Andrew J. Lee; Helen M. Pask; Katsuhiko Miyamoto; Katsuhiko Miyamoto; Takashige Omatsu; Takashige Omatsu

doi:10.1364/OE.400007

1. Introduction

Laguerre-Gaussian (LG) beams [1–4] possesses a ring-shaped spatial form and an orbital angular momentum (OAM), associated with its on-axis phase singularity characterized by a topological charge ℓ, and they have attracted significant research interests in a myriad of fields, such as optical trapping and manipulation [5–8], quantum information and communication [9–12], super resolution microscopy [13–15], and nano/micro-fabrication [16–20]. The LG beams may propagate further through air turbulence with less degradation than conventional Gaussian beams, and thus, have potential application in environmental optics [21–23]. For the above-mentioned applications, wavelength-versatile LG mode sources are strongly desired.

Stimulated Raman scattering (SRS) is a well-known third-order nonlinear frequency conversion process. When combined with second-order nonlinear frequency conversion processes, such as second harmonic generation (SHG) and sum-frequency generation (SFG), it enables us to fill in wavelength gaps in solid-state laser sources [24–26] across visible and near-infrared regions. Several laser host crystals with strong Raman activity, such as YVO₄ [27–30], GdVO₄ [25,30–33], SrWO₄ [34,35], and BaWO₄ [36,37], and PbWO₄ [38,39] allow the development of self-Raman lasers, in which they act as both laser and Raman gain media, thereby realizing ultra-compact laser systems with versatile lasing wavelengths and high beam quality.

To date, we and our co-workers have successfully demonstrated Nd:GdVO₄ self-Raman LG mode laser sources, which carries OAM with a topological charge of 1 and operate at 1173 nm owing to the 882 cm⁻¹ transition in GdVO₄ [25,40], by employing an output coupler with a laser micro-machined damage spot. However, there are still no reports of LG mode laser sources operating at 1108 nm, corresponding to the 382 cm⁻¹ transition in GdVO₄, because the 382 cm⁻¹ shift has a ∼6.4 times smaller Raman gain than that of the 882 cm⁻¹ shift. Also, when using mirrors with engineered damage spots, it is difficult to achieve stable operation and reliable power scaling of high quality LG modes due to severe thermal effects and further damage to the mirror itself at high pump powers. Furthermore, the beam quality of LG mode is degraded at a high pump region (M²>2.5 at the pump power of 6W).

In this work, we propose a novel approach to generating LG modes, formed via the incoherent superposition of two LG modes with positive and negative topological charges, that is the generated LG mode carries zero OAM, from a self-Raman Nd:GdVO₄ laser, which uses a shaped pumping geometry by employing an axicon lens and an objective lens.

Interestingly, the system allows the selective generation of a first-order LG mode at 1108 nm or 1173 nm or both 1108 nm and 1173 nm by subtly changing the alignment of the laser output coupler. Maximum LG mode output powers of 49.8 mW and 133.4 mW at the wavelengths of 1108 nm and 1173 nm were achieved for the absorbed pump power of 5.69 W. Furthermore, even at high pump region (absorption power of 5.7W (pump power >7.5W), the Stokes output maintains a perfect LG mode spatial profile without degradation.

2. Experiments

Figure 1(a) shows the experimental setup for our self-Raman LG mode laser. A 10-mm-long Nd³⁺-doped (0.3 at.% Nd doping) GdVO₄ a-cut crystal was used as the laser gain medium, and it was wrapped with indium foil and mounted inside a water-cooled copper holder to maintain its temperature at 20 ^◦C.

Fig. 1. (a) Experimental setup for direct generation of LG mode output from a Self-Raman Nd:GdVO₄ laser. LD: 879 nm fiber-coupled laser diode (nLight element e06); Col. L: collimation lens (f = 25 mm); PBS: polarizing beam splitter; HWP: half-wave plate; IL: lens (f = 25 mm); ICO: NIR infinity-corrected objective (f = 200 mm, 10X / 0.26); HR: high-reflection coating for 1033-1263 nm; OC: output coupler. (b) Beam propagation of the pump beam inside the laser crystal. (c) Effective pumped region in the crystal. (d) Modelled pumped region for estimating spatial overlap efficiency. The red broken and black solid lines correspond to those at a = 0 and 0.15, respectively. (e) Simulated spatial overlapping efficiency as a function of dip depth a.

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An 879 nm fiber-coupled laser diode (nLight, element e06) with a core diameter of 200 μm and a numerical aperture of 0.22 was used as a pump source, and its output was collimated using a focusing lens (CL, f = 25 mm). The collimated pump beam was transformed into a ring-shaped beam by an axicon lens with an axicon angle of 5 ^◦ (Thorlab, AX125-B) and it was then focused into the laser crystal using a lens (IL, f = 25mm) and a NIR infinity-corrected objective lens, ICO (f = 200 mm, 10X / 0.26 NA). The pump beam was linearly polarized to be parallel to the c-axis of the crystal, so as to maximize the absorption (absorption efficiency ∼76%) of the pump in the laser crystal. This geometry allows shaping of the pump beam with a central intensity dip, to improve the spatial overlap between the pump beam and the LG mode. To consider the 3-dimensional spatial overlap between laser mode and pumped region, the effective pumped region g(r) in the laser crystal can be calculated using following formula,

(1)$$g(r )\propto \mathop \sum \limits_i P({r,\Delta z\cdot i} ){({1 - \textrm{exp}({ - \alpha \Delta z} )} )^i}({\alpha \Delta z} ),$$

where r is the radial coordinate along the cylindrical coordinate, α is the absorption coefficient of the pump beam in the crystal, Δz is the infinitesimal displacement along the z axis, i is the integer, and P (r, Δz· i) is the spatial intensity profile of the pumped beam at a position of Δz· i along the z axis. These profiles were measured experimentally as shown in Fig. 1(b), and thus, they reflected beam transformation, diffraction and absorption effects of pump beam in the laser crystal. The g(r) was estimated by employing Eq. (1) and features a central shallow dip which enables the laser to selectively operate at an annular mode with a central dark core and suppress lasing of Gaussian modes [Figs. 1(c) and 1(d)].

We found that the pumped region g(r) was well-described by the following analytical approximation [41],

(2)$$g(r )\propto \textrm{exp}\left( {\frac{{ - 2{r^2}}}{{\omega_0^2}}} \right)\left( {a\;{{\tanh }^2}\left( {\frac{{{r^2}}}{{{h^2}}}} \right) + ({1 - a} )} \right),$$

where ω₀ (∼260 μm) is the pump beam radius, h ( = 0.1 ω₀) is the point defect radius in the pump beam, and a (0 ∼ 1) is the depth of the gain dip.

The modeled pumped region (a = 0.15) was plotted in Fig. 1(d). The spatial overlap η is then given by,

(3)$$\eta = \smallint g(r )\cdot I(r )2\pi rdr,$$

(4)$$I(r )= {r^{2|\ell |}}\textrm{exp}\left( { - 2\frac{{{r^2}}}{{\omega_l^2}}} \right),$$

where I(r) is the intensity profile of the LG mode, ℓ(=1) is the topological charge, and ω_ℓ [∼180 μm, this value was estimated using ABCD resonator modelling (LASCAD software)] is the beam radius of the cavity mode. The key outcome from this modelling is shown in Fig. 1(e), where it is seen that, the LG mode with a central dark core possesses higher spatial overlap with the pump region for a > 0.1 in comparison with that of the fundamental Gaussian mode.

The self-Raman laser consisted of the input crystal facet with an ultrahigh reflection coating (R > 99.99%)) for 1033-1263 nm and high transmission (T > 99.933%) for 879 nm and a 250 mm concave output coupler (OC) with ultra-high reflection (R > 99.99%) for 1063 nm, and high reflectivity (R = 99.99% and 99.00%) for 1108 nm and 1173 nm. Such an extremely high Q cavity allowed us to efficiently generate the fundamental (1063 nm), and Stokes outputs (1108 nm or 1173 nm). The OC was mounted on an x-y-z translation stage, thereby allowing the system to operate selectively on various lasing modes by carefully aligning the OC along the x and y axes. The cavity length was fixed at 17 mm. The fundamental and Stokes outputs were spatially separated by a diffraction grating (GR25-0608), and they were observed simultaneously using a laser beam profiler (Spiricon SP620U).

3. Results and discussions

The 1108 nm Stokes output lased at the absorbed pump power of 3.52 W, and its maximum power of 49.8 mW was obtained at a maximum absorbed pump power of 5.69 W. At this power, the fundamental output operated at a mixed mode with a central dark spot, formed of several high-order transverse modes, resulting from the extremely high Q factor of the cavity. These results are well supported by the simulated spatial overlap. The Stokes output then showed a perfect annular LG mode profile with a central dark spot in both the near and far-fields, owing to beam clean-up effects, in which the self-Raman gain itself acts as an intracavity spatial aperture [42].

Wavefront analysis of the Stokes output was performed using a self-referenced, laterally sheared interferometer, as reported in our previous publication [43]. Interestingly, it was found that the Stokes output carries effectively zero OAM, manifesting the incoherent superposition of two optical vortices with positive and negative topological charges owing to the cylindrical symmetry of the laser cavity. Also, it is worth mentioning that the topological charge of the generated LG mode was then assigned by two branches of fork-shaped fringes. The fringes produced by the incoherent superposition of two positive and negative LG modes are given as follows:

(5)$$\begin{aligned}I({\textrm{x},\textrm{y}} )&\propto {\left|{({({x + \Delta x} )+ iy} )\cdot \textrm{exp} \left( { - \frac{{{{({x + \Delta x} )}^2} + {y^2}}}{{\omega_\ell^2}}} \right) + {e^{i{k_x}\cdot x}})} \right|^2}\\ &\quad + {\left|{({({x - \Delta x} )- iy} )\cdot \textrm{exp} \left( { - \frac{{{{({x - \Delta x} )}^2} + {y^2}}}{{\omega_\ell^2}}} \right) + {e^{i{k_x}\cdot x}})} \right|^2},\end{aligned}$$

where Δx is the lateral displacement of the wavefront, and k_x is the carrier frequency of the fringes. In fact, the simulated fringes support well the experimental fringes, as shown in Fig. 2. The mechanism of the zero-OAM LG mode generation is as follows: The first order LG mode is formed of the coherent coupling Hermite-Gaussian HG₀₁ and HG₁₀ modes with a relative phase equal to π/2 or -π/2. However, the spectral broadening effects of the fundamental field in intracavity Raman lasers induces frequently microsecond time-scale laser power fluctuation like a relaxational oscillation even in the continuous-wave operation [44], thereby switching temporally the relative phase of HG₀₁ and HG₁₀ modes between π/2 and -π/2 (termed ‘unlocked doughnut beam generation’ [45]).

Fig. 2. Fringes of (a) 1108 nm and (b) 1173 nm Stokes outputs. Insets show the spatial intensity profile of the Stokes output. (c,d) Simulated fringes of incoherent superposition of two LG modes with positive and negative topological charges.

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In the future, we will explore prospects for controlling handedness of the LG mode (sign of the LG mode topological charge) by means of an intracavity etalon or nanoscale aluminum stripes for azimuthal symmetry breaking [46–49]. Also, this future work will completely reveal the mechanism of the zero-OAM LG mode generation.

Most previously reported Nd:GdVO₄ self-Raman lasers operated at 1178 nm, this being due to the high gain associated with the 882 cm⁻¹ Raman mode [32]. It is noteworthy that we obtained selectively stable laser operation at1108 nm. SRS gain competition effects between the strongest transition at 882 cm⁻¹ and a weaker transition at 382 cm⁻¹ occurred, however, once the laser was well aligned by appropriately adjusting the OC, we obtained selectively stable LG mode operation at wavelengths of 1108 nm or 1173 nm. Such selective operation of 1108 nm and 1173 nm or both 1108/1173 nm LG mode should be induced by an optional transmission loss of the slightly inclined output coupler.

Figures 3 and 4 summarize the experimental spatial forms and the power scaling characteristics of the fundamental (1063 nm), and 1108 nm and 1173 nm Stokes outputs. The 1173 nm Stokes output exhibited a relatively high lasing threshold (3.97 W) arising from high transmission loss (∼1%), however, its maximum power reached up to 133.4 mW. This value was 2.7 times higher than that of 1108 nm output. In fact, the experimental fundamental outputs deviated slightly from the fitted yellow line at a pump power of >4 W, manifesting the efficient Raman conversion. Figure 5 also shows the experimental laser spectra of the fundamental and Stokes outputs captured using a high-resolution optical spectrometer (Ocean Optics HR4000).

Fig. 3. Spatial intensity profiles of (a) the fundamental (1063 nm), and (b) 1108 nm Stokes output in the near-field. Corresponding far-field patterns of (c) the fundamental and (d) the Stokes outputs. Spatial intensity profiles of (e) the fundamental (1063 nm), and (f) 1173 nm Stokes outputs in the near-field. Corresponding far-field patterns of (g) the fundamental and (h) 1173 nm Stokes outputs.

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Fig. 4. Output powers of fundamental and Stokes outputs as a function of pump power.

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Fig. 5. Normalized emission spectrum of the output modes.

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Interestingly, the laser system could also produce LG mode emission simultaneously at both 1108 nm and 1173 nm by carefully aligning the OC; mode profiles are shown in Fig. 6. Such simultaneous LG mode operation occurred within the absorbed pump power region of 3.46–3.97 W.

Fig. 6. Spatial intensity profiles of (a) fundamental, and both (b) 1108 nm and (c) 1173 nm Stokes outputs in the near-field. The pump power was then ∼3.6 W.

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4. Conclusion

We have successfully demonstrated direct generation of LG mode outputs at 1108 nm and 1173 nm from a CW self-Raman Nd:GdVO₄ laser by employing a shaped pumping geometry comprising an axicon and a focusing lens. Maximum LG mode output powers of 49.8 mW and 133.4 mW were achieved at 1108 nm and 1173 nm, respectively, for the absorbed pump power of 5.6 W. This approach offers many benefits, for instance, stable and robust operation of a system with low cost and without damage. Further frequency extension of the system in combination with second harmonic generation or sum-frequency generation will allow us to pave the way towards efficient Bottle beam laser sources with a 3-dimensional dark core in the ultraviolet and visible regions for super-resolution microscopes [50,51].

Funding

Japan Society for the Promotion of Science (JP16H06507, JP17K19070, JP18H03884); Core Research for Evolutional Science and Technology (JPMJCR1903).

Disclosures

The authors declare no conflicts of interest.

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Direct generation of 1108 nm and 1173 nm Laguerre-Gaussian modes from a self-Raman Nd:GdVO₄ laser

Abstract

1. Introduction

2. Experiments

3. Results and discussions

4. Conclusion

Funding

Disclosures

References

Cited By

Figures (6)

Equations (5)

Optics Express