Tunable near-infrared optical vortex parametric laser with versatile orbital angular momentum states

Roukuya Mamuti; Shungo Araki; Shigeki Nishida; Katsuhiko Miyamoto; Takashige Omatsu

doi:10.1364/AO.57.010004

1. INTRODUCTION

An optical vortex beam with a helical wavefront possesses unique properties, such as a ring-shaped spatial intensity profile and an orbital angular momentum (OAM) of $ℓ ℏ$ [1–6] due to a phase singularity arising from its azimuthal phase term $e^{i ℓ ϕ}$ , where $ℓ$ is an integer and is known as the topological charge. The optical vortex beam also exhibits a handedness assigned by the sign of the OAM. Such an optical vortex beam twists the surface of various materials such as metals, semiconductors, and polymers [7–12] to establish chiral micro/nanostructures and provide novel technologies including chiral-sensitive nanoscale imaging systems (e.g., atomic force microscopes with chiral sensitivity) and planar metamaterials for chemical reactions on plasmonic nanostructures.

The properties of an optical vortex beam mean that it could be potentially utilized in a variety of fields, such as optical trapping and manipulation [13–17], quantum computing [18–21], stimulated emission depletion microscopy [22–24], material processing. [9,25,26], and coronagraphic techniques for astrophysics [27–29]. These applications require strong wavelength tunability and controllable OAMs for versatility with optical vortex sources.

To date, nonlinear frequency extension techniques, such as second-harmonic generation [30–32], sum-frequency generation [33,34], and stimulated Raman scattering [35], have been conducted and investigated to achieve laser sources with extended lasing wavelengths. The optical parametric oscillator (OPO) [36–39], in which a pump photon is divided into signal (higher energy) and idler (lower energy) photons, is a particularly efficient method to develop a continuously tunable vortex source with a large wavelength range.

In recent years, we have successfully demonstrated a near infrared octave-band tunable optical vortex laser source with a millijoule level pulse energy formed from a 532 nm vortex pumped ${LiB}_{3} O_{5}$ (LBO) OPO with a simple linear cavity configuration, in which asymmetric topological charge transfer occurred from the pump beam to the signal or idler beam [40]. We have also extended the system to develop an ultrabroadband tunable vortex source within the wavelength region of 0.67–2.57 μm with little frequency gap by employing a nanosecond diode-pumped solid-state laser as a pump source [41]. However, these systems have enabled the generation of only two OAMs for the signal or idler output, for instance, vortex ( $ℓ = 1$ ) and Gaussian ( $ℓ = 0$ ) outputs. These systems have not provided an upconverted OAM state, that is, a vortex output with a higher topological charge than that of the pump beam.

Here, we give a first demonstration of the selective generation of a signal (idler) output with $ℓ = 0 - 2 (1 - - 1)$ , including an upconverted (negative) OAM, from a nanosecond vortex-pumped LBO-OPO (optical vortex parametric laser) by appropriate shortening (or extending) of the cavity. The system with a compact cavity configuration also allows the generation of a signal (idler) output with $ℓ = 1 - 3 (0 - - 2)$ by simply tuning the signal wavelength.

This system provides new insights on the direct generation of OAM modes in OPOs, which has potential for use in numerous applications.

2. PARAMETRIC GAIN

To control the OAM states in a noncritical phase-matching (NCPM) LBO OPO, we designed a singly resonant cavity for the signal output, in which there is nonlinear interaction between pump and signal electric fields. The resulting nonlinear gain is then governed by the spatial overlap efficiency $η_{ℓ_{s}} (L)$ between the pump $E_{p}$ and resonating signal $E_{s}^{ℓ s}$ with a topological charge $ℓ_{s}$ [37] as follows:

η_{ℓ_{s}} (L) = \frac{\int_{0}^{\infty} E_{P} E_{S}^{ℓ_{s}} \cdot 2 π r \cdot d r}{\int_{0}^{\infty} E_{P} E_{S}^{0} \cdot 2 π r \cdot d r} \propto \frac{\int_{0}^{\infty} r^{| ℓ_{P} |} \exp (- \frac{r^{2}}{ω_{P}^{2}}) \cdot r^{| ℓ_{S} |} \exp (- \frac{r^{2}}{ω_{S}^{2} (L)}) \cdot 2 π r \cdot d r}{\int_{0}^{\infty} r^{| ℓ_{P} |} \exp (- \frac{r^{2}}{ω_{P}^{2}}) \exp (- \frac{r^{2}}{ω_{S}^{2} (L)}) \cdot 2 π r \cdot d r},

where

L

is the cavity length;

r

and

ϕ

are the radial and azimuthal axes in cylindrical coordinates;

ℓ_{p} (= 1)

and

ℓ_{s}

are the topological charges of the pump and signal, respectively;

ω_{p}

is the mode field size (

\sim 0.38 mm

) of the incident pump beam size, and

ω_{s} (L)

is the mode field size of the signal output at various cavity lengths estimated using LASCAD software (LAS-CAD GmbH). Also note that

η_{ℓ_{s}} (L)

is normalized by that between the pump and resonating Gaussian signal output; thus,

η_{ℓ_{s}} (L) > 1

indicates that the vortex mode with the topological charge of

ℓ_{s}

possesses higher parametric gain in comparison with that of the Gaussian mode, and it is allowed to selectively lase.

Figure 1 shows the spatial overlap integrals at various cavity lengths. The topological charge of the pump beam was then fixed to be $+ 1$ . When the cavity was sufficiently compact (cavity length $< 70 mm$ ), $η_{2}$ was estimated to be larger than $η_{1}$ , that is, the parametric gain of the second order vortex mode is higher than that of the first order vortex mode. Thus, the signal output will be interestingly expected to lase in the second order vortex mode (with upconverted OAM), and the resulting idler output would lase with the negative first order vortex output (with negative OAM), according to conservation of the OAM. When the cavity is extended (the cavity length is 70–155 mm), $η_{1}$ exceeds $η_{2}$ . The signal output is thus encouraged to lase in the first order vortex mode, which results in a Gaussian idler output.

Fig. 1. Spatial overlap efficiency as a function of the cavity length when the pump beam is the first order optical vortex.

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A further extended cavity with a cavity length of 155–250 mm will yield spatial overlap $η_{1}$ below 1, so that the signal output will lase with a fundamental Gaussian mode. Note that even further cavity extension (cavity $length > 250 mm$ ) would make the cavity unstable and prevent efficient lasing of the signal output. Such multiple OAM states of the signal and idler outputs can thus be selectively generated simply by shortening or extending the OPO cavity.

3. EXPERIMENTS

Figure 2 shows a schematic diagram of the tunable optical parametric laser system. A frequency-doubled, diode-pumped, $Q$ -switched Nd:YAG laser (wavelength, 532 nm; pulse duration, 10 ns; pulse repetition frequency, $PRF = 100 Hz$ ; $M^{2} = 1.1$ ) was used as a pump source, and its output was converted into an optical vortex with a topological charge of $+ 1$ [Figs. 2(a) and 2(b)] using 16 segmented spiral phase plates formed of silica glass. A NCPM LBO crystal ( $θ = 90 °, φ = 0 °, 3 mm \times 3 mm \times 45 mm$ , antireflective-coated for 532 and 1064 nm) used as a nonlinear crystal was mounted on an oven, so that its temperature could be controlled within the range of 110.6–157.3°C with a stability of $\pm 1 ° C$ (Fig. 3).

Fig. 2. Schematic diagram of experimental setup. (a) Incident pump beam profile with a topological charge of 1, and (b) self-interference fringes. SPP: spiral phase plate.

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Fig. 3. Output wavelength tunability according to crystal temperature.

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The singly resonant cavity for the signal output was formed by a flat input mirror with high reflectivity for wavelengths of 0.65–1.05 μm and a concave output mirror (curvature radius, 500 mm) with 90% reflectivity for 800 nm.

The signal and idler outputs were separated by a dichroic mirror and were observed using Si and InGaAs cameras, respectively. The cavity length was tuned within 50–250 mm to control the topological charge sharing between the signal and idler outputs. The topological charges of the signal and idler outputs were assigned by employing a self-referenced interferometer, in which the first order and negative first order beams were diffracted with a transmission grating (10 lines/mm) and overlapped by a lens on the CCD camera to form self-interference fringes. At first, the topological charge of the pump beam was then fixed to be $+ 1$ .

A cavity with a length of 120 mm forced the signal to lase at a vortex mode with $ℓ = + 1$ , as evidenced by the annular spatial form with a small dark core and a pair of $Y$ -shaped forks, as shown in Figs. 4(a) and 4(b). The resulting idler exhibited a Gaussian spatial profile without any phase singularities. The extended cavity with a length of 230 mm prevented lasing of the signal in the vortex mode, thereby yielding a Gaussian signal and vortex idler with $ℓ = + 1$ , as shown in Figs. 4(g) and 4(h) and as reported in our previous publication [41].

Fig. 4. (a), (c) Spatial profiles and (b), (d) self-interference fringes for the 0.93 μm signal and 1.24 μm idler outputs from a compact cavity with a length of 120 mm. (e), (g) Spatial profiles and (f), (h) self-interference fringes for the 0.93 μm signal and 1.24 μm idler outputs from an extended cavity with a length of 230 mm.

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The signal and idler outputs with multiple OAM states were tuned in the wavelength regions of 0.81–0.98 and 1.12–1.55 μm, respectively (Fig. 5). Note that the signal and idler outputs exhibit a fractional vortex mode within the wavelength region of 0.98–1.12 μm due to the double resonance of the signal and idler outputs, as previously reported [41].

Fig. 5. Tunability of the signal and idler outputs from further compact and extended cavities.

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A compact cavity with a length of 60 mm allowed both signal and idler outputs to lase in vortex modes with upconverted and negative topological charges of $+ 2$ and $- 1$ , as evidenced by the pair of downward and upward tree-armed fringes for the signal and a pair of upward and downward $Y$ -shaped fringes for the idler (Fig. 6).

Fig. 6. (a), (d) Spatial profiles and (b), (e) self-interference fringes for the 0.93 μm signal and 1.24 μm idler outputs from a further compact cavity with the length of 60 mm. (c) Magnified image of self-fringes for 0.93 μm signal output near its dark core.

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These experiments concerning selective control of the OAM states of the signal and idler outputs by shortening or extending the OPO cavity can be well supported by the theoretical parametric gain analyses. The wavelengths of the signal and idler outputs were then measured to be 0.93 and 1.24 μm, respectively. The maximum signal and idler output energies of 2.16 and 1.55 mJ were observed at a pump energy of 9.3 mJ, which corresponds to optical efficiencies of 23.2% and 16.7% (Fig. 7).

Fig. 7. Power scaling of the signal and idler outputs in a further compact cavity.

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4. DISCUSSION

Note that the compact cavity configuration interestingly enables the signal (idler) output to be produced with various OAMs by simply tuning the wavelength of the signal output and without changing the cavity length. When the signal output was tuned in the wavelength region below 0.80 μm, the system allowed the signal output to lase in an unexpected third order (further upconverted) vortex mode. The signal output with a wavelength above 950 nm was also forced to operate in a first order vortex mode. The generated idler output was then the negative second order vortex or Gaussian mode (Figs. 8 and 9). Also, note that the tilted focusing method based on Laguerre Gaussian–Hermite Gaussian mode conversion was performed to assign the topological charges of the signal and idler outputs [42].

Fig. 8. Tunability of signal and idler outputs.

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Fig. 9. (a)–(c) Spatial profiles of the signal outputs with various wavelengths of 770, 880, and 952 nm. (d)–(f) Spatial profiles of idler outputs with various wavelengths of 1206, 1345, and 1721 nm. (g), (h) Focused beam profiles of the 770 nm signal and 1721 nm idler outputs by a tilted lens.

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This phenomenon can be understood qualitatively by employing the spatial overlap efficiency $η_{ℓ_{s}}$ between the pump and signal at various signal wavelengths. The blueshift (redshift) of the wavelength of the signal output induces a higher spatial overlap efficiency (i.e., parametric gain) for the third (first) order vortex when compared with that for the second order vortex mode due to the shrinkage (expansion) of the cavity (Fig. 10). The cavity length was then fixed to be 60 mm. To fully understand this phenomenon, further investigation including intracavity loss mechanism and nonlinear effects such as gain competition between longitudinal and spatial modes will be necessary.

Fig. 10. Spatial overlap efficiency as a function of the signal wavelength.

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5. CONCLUSION

We have successfully demonstrated, for the first time, selective generation of signal and idler outputs with multiple OAMs from a tunable vortex parametric laser based on a singly resonant OPO formed by a NCPM-LBO crystal. This system with a compact cavity configuration allows vortex modes to be produced with six different OAMs ( $ℓ = 3 - - 2$ ) of the signal or idler output, simply by tuning the signal wavelength to establish the OAM conservation law. This system with versatile OAM states will be extremely useful in various fields, such as materials processing, as well as tunable optical vortex generation in the mid-infrared or terahertz region. Further OAM versatility in this system will be possible by utilizing a shorter nonlinear crystal with a large parametric gain, for instance, a periodically poled crystal.

Funding

Scientific Research on Innovative Areas “Nano-Material Optical-Manipulation,” Japan Society for the Promotion of Science (JSPS) (JP 15H03571, JP 16H06507, JP 17K19070, JP 18H03884).

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Tunable near-infrared optical vortex parametric laser with versatile orbital angular momentum states

Abstract

1. INTRODUCTION

2. PARAMETRIC GAIN

3. EXPERIMENTS

4. DISCUSSION

5. CONCLUSION

Funding

REFERENCES

Cited By

Figures (10)

Equations (1)

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