Research Article Vol. 28, No. 16 / 3 August 2020 / Optics Express 24095

Direct generation of 1108 nm and 1173 nmLaguerre-Gaussian modes from a self-RamanNd:GdVO4 laserYUANYUAN MA,1 ANDREW J. LEE,2 HELEN M. PASK,2

KATSUHIKO MIYAMOTO,1,3 AND TAKASHIGE OMATSU1,3,*

1Graduate School of Engineering, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan2MQ Photonics Research Centre, Department of Physics and Astronomy, Macquarie University, Sydney,NSW 2109, Australia3Molecular Chirality Research Center, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan*omatsu@faculty.chiba-u.jp

Abstract: We demonstrate a continuous-wave self-Raman Nd:GdVO4 Laguerre-Gaussian (LG)mode laser based on different Raman shifts of 382 cm−1 and 882 cm−1 by shaping the pumpingbeam with the use of an axicon lens and a focusing lens. Selective generation of LG mode beamsat 1108 nm or 1173 nm, or simultaneously 1108 nm and 1173 nm, was achieved by carefullyadjusting the alignment of the laser cavity. The maximum Raman LG mode output powers at thewavelengths of 1108 nm (the first-Stokes emission of the 382 cm−1 Raman shift) and 1173 nm (thefirst-Stokes emission of the 882 cm−1 Raman shift) were measured to be 49.8mW and 133.4mWat the absorbed pump power of 5.69 W, respectively. The generated LG modes, formed via theincoherent superposition of two LG mode beams with positive and negative topological charges,carry zero orbital angular momentum. Such LG mode laser sources have the potential to fill inthe wavelength gap of lasers in the visible and infrared regions.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Laguerre-Gaussian (LG) beams [1–4] possesses a ring-shaped spatial form and an orbital angularmomentum (OAM), associated with its on-axis phase singularity characterized by a topologicalcharge `, and they have attracted significant research interests in a myriad of fields, such asoptical 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 maypropagate further through air turbulence with less degradation than conventional Gaussian beams,and thus, have potential application in environmental optics [21–23]. For the above-mentionedapplications, wavelength-versatile LG mode sources are strongly desired.

Stimulated Raman scattering (SRS) is a well-known third-order nonlinear frequency conversionprocess. When combined with second-order nonlinear frequency conversion processes, such assecond harmonic generation (SHG) and sum-frequency generation (SFG), it enables us to fillin 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-Ramanlasers, in which they act as both laser and Raman gain media, thereby realizing ultra-compactlaser 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 nmowing to the 882 cm−1 transition in GdVO4 [25,40], by employing an output coupler with a lasermicro-machined damage spot. However, there are still no reports of LG mode laser sourcesoperating at 1108 nm, corresponding to the 382 cm−1 transition in GdVO4, because the 382

#400007 https://doi.org/10.1364/OE.400007Journal © 2020 Received 11 Jun 2020; revised 24 Jul 2020; accepted 25 Jul 2020; published 30 Jul 2020

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cm−1 shift has a ∼6.4 times smaller Raman gain than that of the 882 cm−1 shift. Also, whenusing mirrors with engineered damage spots, it is difficult to achieve stable operation and reliablepower scaling of high quality LG modes due to severe thermal effects and further damage to themirror itself at high pump powers. Furthermore, the beam quality of LG mode is degraded at ahigh 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 incoherentsuperposition of two LG modes with positive and negative topological charges, that is thegenerated LG mode carries zero OAM, from a self-Raman Nd:GdVO4 laser, which uses a shapedpumping 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 outputcoupler. Maximum LG mode output powers of 49.8 mW and 133.4 mW at the wavelengths of1108 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 outputmaintains 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-longNd3+-doped (0.3 at.% Nd doping) GdVO4 a-cut crystal was used as the laser gain medium, and itwas wrapped with indium foil and mounted inside a water-cooled copper holder to maintain itstemperature at 20 C.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 usinga focusing lens (CL, f = 25 mm). The collimated pump beam was transformed into a ring-shapedbeam by an axicon lens with an axicon angle of 5 (Thorlab, AX125-B) and it was then focusedinto 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 thec-axis of the crystal, so as to maximize the absorption (absorption efficiency ∼76%) of the pumpin the laser crystal. This geometry allows shaping of the pump beam with a central intensitydip, to improve the spatial overlap between the pump beam and the LG mode. To consider the3-dimensional spatial overlap between laser mode and pumped region, the effective pumpedregion g(r) in the laser crystal can be calculated using following formula,

g(r) ∝∑

iP(r,∆z · i)(1 − exp(−α∆z))i(α∆z), (1)

where r is the radial coordinate along the cylindrical coordinate, α is the absorption coefficientof the pump beam in the crystal, ∆z is the infinitesimal displacement along the z axis, i is theinteger, and P (r, ∆z· i) is the spatial intensity profile of the pumped beam at a position of ∆z· ialong 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 lasercrystal. The g(r) was estimated by employing Eq. (1) and features a central shallow dip whichenables the laser to selectively operate at an annular mode with a central dark core and suppresslasing 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],

g(r) ∝ exp

(−2r2

ω20

) (a tanh2

(r2

h2

)+ (1 − a)

), (2)

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

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Fig. 1. (a) Experimental setup for direct generation of LG mode output from a Self-RamanNd: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 thepump beam inside the laser crystal. (c) Effective pumped region in the crystal. (d) Modelledpumped region for estimating spatial overlap efficiency. The red broken and black solidlines correspond to those at a= 0 and 0.15, respectively. (e) Simulated spatial overlappingefficiency as a function of dip depth a.

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

η = ∫ g(r) · I(r)2πrdr, (3)

I(r) = r2 |` |exp

(−2

r2

ω2l

), (4)

where I(r) is the intensity profile of the LG mode, `(=1) is the topological charge, and ω` [∼180µm, this value was estimated using ABCD resonator modelling (LASCAD software)] is the beamradius of the cavity mode. The key outcome from this modelling is shown in Fig. 1(e), where itis seen that, the LG mode with a central dark core possesses higher spatial overlap with the pumpregion 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 250mm concave output coupler (OC) with ultra-high reflection (R> 99.99%) for 1063 nm, and highreflectivity (R= 99.99% and 99.00%) for 1108 nm and 1173 nm. Such an extremely high Qcavity allowed us to efficiently generate the fundamental (1063 nm), and Stokes outputs (1108nm or 1173 nm). The OC was mounted on an x-y-z translation stage, thereby allowing the systemto operate selectively on various lasing modes by carefully aligning the OC along the x and yaxes. The cavity length was fixed at 17 mm. The fundamental and Stokes outputs were spatiallyseparated by a diffraction grating (GR25-0608), and they were observed simultaneously using alaser 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 maximumpower 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 severalhigh-order transverse modes, resulting from the extremely high Q factor of the cavity. Theseresults are well supported by the simulated spatial overlap. The Stokes output then showed aperfect annular LG mode profile with a central dark spot in both the near and far-fields, owing tobeam 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 foundthat the Stokes output carries effectively zero OAM, manifesting the incoherent superpositionof two optical vortices with positive and negative topological charges owing to the cylindricalsymmetry of the laser cavity. Also, it is worth mentioning that the topological charge of thegenerated LG mode was then assigned by two branches of fork-shaped fringes. The fringesproduced by the incoherent superposition of two positive and negative LG modes are given asfollows:

I(x, y) ∝

�����((x + ∆x) + iy) · exp

(−(x + ∆x)2 + y2

ω2`

)+ eikx ·x)

�����2+

�����((x − ∆x) − iy) · exp

(−(x − ∆x)2 + y2

ω2`

)+ eikx ·x)

�����2,(5)

where ∆x is the lateral displacement of the wavefront, and kx is the carrier frequency of thefringes. 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 modeis formed of the coherent coupling Hermite-Gaussian HG01 and HG10 modes with a relativephase equal to π/2 or -π/2. However, the spectral broadening effects of the fundamental field in

Research Article Vol. 28, No. 16 / 3 August 2020 / Optics Express 24099

intracavity Raman lasers induces frequently microsecond time-scale laser power fluctuation like arelaxational oscillation even in the continuous-wave operation [44], thereby switching temporallythe relative phase of HG01 and HG10 modes between π/2 and -π/2 (termed ‘unlocked doughnutbeam generation’ [45]).

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

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

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

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

Figures 3 and 4 summarize the experimental spatial forms and the power scaling characteristicsof the fundamental (1063 nm), and 1108 nm and 1173 nm Stokes outputs. The 1173 nm Stokesoutput 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 higherthan that of 1108 nm output. In fact, the experimental fundamental outputs deviated slightlyfrom the fitted yellow line at a pump power of >4 W, manifesting the efficient Raman conversion.

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

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

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Figure 5 also shows the experimental laser spectra of the fundamental and Stokes outputs capturedusing a high-resolution optical spectrometer (Ocean Optics HR4000).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. Suchsimultaneous LG mode operation occurred within the absorbed pump power region of 3.46–3.97W.

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

4. Conclusion

We have successfully demonstrated direct generation of LG mode outputs at 1108 nm and1173 nm from a CW self-Raman Nd:GdVO4 laser by employing a shaped pumping geometrycomprising an axicon and a focusing lens. Maximum LG mode output powers of 49.8 mW and133.4 mW were achieved at 1108 nm and 1173 nm, respectively, for the absorbed pump power of5.6 W. This approach offers many benefits, for instance, stable and robust operation of a systemwith low cost and without damage. Further frequency extension of the system in combinationwith second harmonic generation or sum-frequency generation will allow us to pave the waytowards efficient Bottle beam laser sources with a 3-dimensional dark core in the ultraviolet andvisible regions for super-resolution microscopes [50,51].

Funding

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

Disclosures

The authors declare no conflicts of interest.

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