Wavelength- and OAM-tunable vortex laser with a reflective volume Bragg grating

Qiyao Liu; Yongguang Zhao; Manman Ding; Weichao Yao; Xuliang Fan; Deyuan Shen

doi:10.1364/OE.25.023312

1. Introduction

Phase-twisted vortex beams have spurred widespread interest in recent decades due to their unique properties like doughnut-shaped intensity distribution, helical wavefront structure and the ability to carry orbital angular momentum [1–3]. These beams have found several uses, such as atom manipulation [4], high-dimensional quantum entanglement [5], super-resolution microscopes [6], and in particular increasing the channel capacity in optical communications since they can provide an additional degree of freedom [7,8]. Through the so called “OAM mode-division multiplexing” (OAM-MDM) technique, the grayscale image of Mozart encoded in the intensity patterns of 16 OAM modes superposition was successfully transmitted through 3 km of strong turbulence over the city of Vienna [9]. When combining with the traditional wavelength division multiplexing (WDM) technique, 1.6 terabits-per-second data can be transmitted over 1.1 km in specially designed vortex fiber [10], which indicates the prospect of large capacity optical communications. Undoubtedly, laser sources that supporting narrow-band multi-wavelength extracting and meanwhile enable each wavelength carrying OAMs, are essential for the realization of WDM together with MDM. The common method used to produce OAMs is passing traditional Gauss beams through OAM generators, such as spatial light modulators (SLMs) [8], Q-plats [11], spiral phase plates (SPPs) [10], “fork” gratings [7], etc., in which, however, the OAM generators are generally designed for a certain wavelength and seem hard to integrate with wavelength selection. Most recently, simultaneous wavelength and OAM multiplexing/demultiplexing was demonstrated by using a MEMS-based Fabry-Perot filter integrated with a SPP [12], however, it still belongs to a type of external cavity elements and cannot completely integrate with laser devices. In addition, these specially designed extra-cavity optical elements usually suffer from drawbacks of low laser damage threshold and high production cost.

Modulating the wave-front phase during the beam oscillating process is a probable way to realize packable and robust devices with simultaneous modulation of wavelengths and OAMs. Nowadays, generation and modulation of OAMs have been widely researched inside the laser cavity by using various techniques, such as spot-defect mirror [13], annular shaped beam pumping [14,15], and intra-cavitary SPP [16], etc. However, simultaneously modulating with wavelengths in resonant cavity has never been reported. The commonly used spectrum discrimination filters in the solid-state laser cavity are prism and Lyot filter [17,18]. Unfortunately, the introduced additional losses make them not the preferred candidate in high-order modes resonator, and on the other hand, the selected spectrum is usually not sharp. Volume Bragg Gratings (VBGs), via a holographic process exposing UV light onto photo-thermal-refractive (PTR) glass doped with silver, cerium and fluorine, have currently gained much attention for serving as perfect spectrum selectors because of their high diffraction efficiency, large damage threshold and excellent thermal stability [19,20]. Employing intracavity VBG has been demonstrated an effective way of wavelength selection and spectral narrowing for Gaussian laser beams in many researches [21–23]. However, the effects of VBG on OAM beams have not been explored.

In this letter, we theoretically analyzed that reflective VBG used as a folding mirror would not bring any phase errors to destroy the helical wavefront structure of vortex laser, meaning the initially carried OAM could be preserved during the wavelength-tuning process. Then by combining the usage of an uncoated YAG plate, synchronously tunable wavelength and OAM were experimentally realized in a compact z-shaped Er:YAG resonator. TEM₀₀, LG_{0, ± 1}, and LG_{0, ± 2} beams were respectively excited, and the linewidth of the output spectrum was narrowed down to under 0.04 nm. This tunable vortex laser capable of simultaneously selecting both wavelength and OAM in 0, ± ħ, and ± 2ħ region was expected to improve the transmission capacity of communication systems by multiplexing multiple channels based on MDM and WDM techniques, especially for certain dielectric mediums like water, air, etc., which have special requirements on wavelength and spectrum for transmission light source [24,25].

2. Theoretical analysis and experiment

The effect of a given grating on the electric-field amplitude of incident beams could be analyzed by the beam-propagation method [26], which relies on the assumption that the behavior of beam in the grating still satisfy the scalar Helmholtz equation:

\nabla^{2} E + {(\frac{ω}{c})}^{2} n^{2} (\bar{x}) E = 0,

where

n (\bar{x}) = n + δ n (\bar{x})

was designated as the refractive-index profile of the gating structure,

\bar{x}

is an arbitrary vector, and

δ n (\bar{x})

is the refractive-index variation assumed much smaller than the median refractive index n. In cylindrical coordinates with the optical axis aligned along the z-axis, the electric field situated at an infinitesimally small axial distance

Δ z

from the origin can be expressed in terms of the electric field at z = 0 by means of direct differentiation:

E (r, φ, Δ z) = \exp [- i Δ z {(\nabla_{⊥}^{2} + {(\frac{ω}{c})}^{2} {(n + δ n)}^{2})}^{\frac{1}{2}}] E (r, φ, 0),

here

\nabla_{⊥}^{2} = \frac{1}{r} \frac{\partial}{\partial r} (r \frac{\partial}{\partial r}) + \frac{1}{r^{2}} \frac{\partial^{2}}{\partial φ^{2}}

is the Laplacian operator in cylindrical coordinate. With appropriate approximation on the exponential term appearing in Eq. (2),

{(\nabla_{⊥}^{2} + {(\frac{ω}{c})}^{2} {(n + δ n)}^{2})}^{\frac{1}{2}} ~ \frac{\nabla_{⊥}^{2}}{{(\nabla_{⊥}^{2} + k^{2})}^{1 / 2} + k} + k + \frac{ω}{c} δ n,

variable of

δ n

can be separated from.

n

As one eigen solution of wave equation, we define the field of Laguerre-Gaussion mode [27]:

E_{L} (r, φ, z) = ε (r, z) \exp (i l φ) \exp (- i k z) = ε' (r, φ, z) \exp (- i k z),

where

(r, φ, z)

are cylindrical coordinates, l is a signed integer called the topological charge,

k = \frac{2 π}{n λ} = \frac{n ω}{c}

is the wavenumber and λ is the wavelength. Inserting Eq. (4) to Eq. (2), then

ε' (r, φ, z)

could be shown as

\begin{array}{l} ε' (r, φ, Δ z) = \exp (- i Δ z k \frac{δ n}{n}) \exp {- i Δ z [\frac{\nabla_{⊥}^{2}}{{(\nabla_{⊥}^{2} + k^{2})}^{1 / 2} + k}]} ε' (r, φ, 0) + 0 (Δ z^{3}) \\ = \exp (- i Δ z k \frac{δ n}{n}) \exp {- i Δ z [\frac{\nabla_{⊥}^{2}}{{(\nabla_{⊥}^{2} + k^{2})}^{1 / 2} + k}]} ε (r, 0) \exp (i l φ) + 0 (Δ z^{3}) . \end{array}

We can see that in beam-propagating procedure, the refractive-index variation

δ n

only imposes a phase variation along the z direction on the electric field

ε' (r, φ, Δ z)

comparing to that propagating in homogeneous medium (setting

δ n = 0

in Eqs. (2) and (3)). The unique exponential term

\exp (i l φ)

of LG mode is not deteriorated, which means that the OAM and helical wavefront will be maintained after passing through the gating element. To verify this analysis, we exploited a VBG as a cavity element for our vortex laser.

The experimental setup is schematically shown in Fig. 1. The pump source is provided by a commercial laser diode (LD) locked at 1532 nm with a linewidth of 0.2 nm (FWHM) to match the narrow absorption spectrum of the Er:YAG crystal (~1 nm around 1532 nm). Tailored by a specially fabricated mirror (M), it was reformatted with a hollow intensity profile for matching the targeted LG₀₁ mode laser [28]. A 0.5 at. % Er:YAG crystal with 3 × 3 × 24.5 mm³ dimension was used as the gain medium, both facets of which were anti-reflection coated at the lasing wavelength. In order to reduce the thermal damage, this gain medium was embedded in a water-cooled aluminum heat-sink maintained at 17 °C. The z-shaped free space cavity was constituted by an input coupler (IC), a plano-concave folding mirror, a reflective VBG and an output coupler. The IC was anti-reflective coated at 1532 nm and high-reflective at 1600-1700 nm, and the high-reflective folding mirror (HR) coated at 1600-1700 nm has a curvature of 200 mm radius, while the output coupler was employed with transmissions of 5% at the lasing wavelength. The VBG reflector (Optigrate Inc.) with 6 mm × 8 mm aperture and 3.2 mm length was broadband antireflection coated at ~1.5-1.7 μm on both front and back surfaces, and covered by indium foil and mounted in a copper heat sink for heat removal. The internal grating structure had reflectivity of >95% when Bragg condition is met and was designed with a line center (λ₀) of 1650 nm for normal incidence to the grating and a spectral reflection bandwidth of 0.5 nm (FWHM). The feedback wavelength from VBG could be adjusted (i.e. synchronously rotating the VBG and OC) to match resonating conditions with the fixed input hollow pump beam.

Fig. 1 Experimental setup of tunable Er:YAG crystal vortex laser.

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3. Results and analysis

For generating the first order LG mode vortex beams, the total laser cavity length was designed of 345 mm, and a small incident angle (<5°) on the curve mirror was taken to minimize the astigmatism. The radius of the laser mode in the Er:YAG crystal medium and the VBG was calculated about 238 μm and 448 μm, respectively. A homemade Mach–Zehnder interferometer was employed to interfere the output beam with a spherical reference wave, which could verify vortex beams and investigate the carried OAM of the output vortex beam. A Brewster plate (BP) was inserted into resonator after the Er:YAG crystal to polarize the output vortex. In order to control the handedness of vortex mode, an uncoated tilted YAG plate with 1-mm-thick was used to introducing differential Fresnel loss for opposite-handed LG mode beams, thus the one suffering less loss would oscillate preferentially while the other was suppressed at last [28]. An infrared CCD (Xeva-1.7) was used to image the output intensity distribution and interference pattern, which have been given as Fig. 2(a). It can be seen that the output beam has a doughnut-shape intensity profile, a typical property of LG₀_l mode, with two clear helical interference fringes of opposite directions indicating carrying relatively pure + ħ and –ħ of OAM. For each interference pattern, the number of spiral arms indicates the mode’s |l|, while the handedness indicates the sign of l.

Fig. 2 (a) The output intensity distributions of LG_{0, ± 1} modes and corresponding interference fringes; (b) the wavelength tuning ranges; measured spectra of vortex with (c) OAM of + ħ and (d) OAM of –ħ.

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In the case of certain stable OAM, we rotated the VBG cooperating with the OC to switch the wavelength. Under ~21.2 W pumping level, the obtained whole tunable ranges were given as the scattered points in the Fig. 2(b), blue for LG_{0, + 1} while pink for LG_0,-1, whose profiles were coincident well with the emission spectrum at 1645 nm of Er:YAG crystal. It should be pointed out that in order to optimize the output performance, fine-tuning the tilt YAG was needed to shift its transmission peak to match with one given wavelength, and in this work the tilt angle was finely adjusted in ± (3°~4°) range for effective handedness-selecting. Due to the lower multiplicity of the Stark levels, the gain spectrum of Er:YAG is sharp and narrow, only about 11.5 nm [29]. Thus the obtained total tuning ranges were only about 6.8 nm, from 1642.2 nm to 1649 nm. Before designing the laser size to excite the LG₀₁ mode, we noted the Gaussian-shaped TEM₀₀ mode was first output and had a wavelength tuning range measured about 8.4 nm. Although the tuning range became narrower after granting the output beams OAM, it offers a new degree of spatial freedom that could fold increase the signal channels of light source for optical communication system. We monitored the interference patterns in the tuning process, the interference fringes were found stable at one certain handedness in the whole tunable range. This work proved that the reflective VBG could be used as an effective wavelength-selector without destroying the helical wavefront and the carried OAM of vortex beams.

On the other side, the etalon effect of YAG plate synergistically functioned with VBG’s periodical structure dramatically narrowed the linewidth of the output, kept <0.04 nm in all wavelength range. The spectrum was measured by an optical spectrum analyzer (AQ6370C, Yokogawa) with a resolution of 0.02 nm. Figure 2(c) and 2(d) gives the measured 3dB linewidths of two LG₀₁ modes near the emission peak, respectively 0.04 nm at 1645.5 nm of LG_{0, + 1} and 0.03 nm at 1645.4 nm of LG_0,-1. But limited to the resolution of the spectrometer, more accurate data of linewidths were not obtained in this work. Such property should be an obvious advantage for optical communication, for narrow bandwidth will reduce the crosstalk and require less wavelength spacing between two channels suitable for dense wavelength division multiplexing (DWDM) system. Besides, it has been reported that Er:YAG laser with a narrow bandwidth operating at around 1645 nm can accurately avoid the absorption of methane in the atmosphere and thus is beneficial to applications requiring free-space propagation over long distances [20].

To further expand the OAM freedom, our work put the focus on the generation of higher-order vortex beams by changing the cavity conditions. When the cavity length was stretched to about 370 mm, the waist radius of laser mode in cavity was diminished and the LG₀₂ mode laser beams was then directly excited instead. These transverse mode selection scheme was based on the mode-matching principle, the mode having largest overlapping area with the ring-shaped pump beam will have the lowest threshold [30]. The wavelength tunable range was measured from 1643.1 nm to 1648 nm, as shown by the scattered points in Fig. 3. The inset patterns are corresponding intensity distribution and interference fringes for indicating the vortex beams have topological charge of l = ± 2. Taken together, in the range of 1643.1 nm~1648 nm, the beams can be modulated in five OAM states (i.e. 0, ± ħ, and ± 2ħ) with continuously tunable wavelength while preserving the integrality of topological charge. Given employing DWDM with 100 GHz spacing and OAM-MDM techniques with this vortex laser, it would be expected to supply up to 30 signal channels for information multiplexing. When merely using TEM₀₀ mode as light source with DWDM technique, although having a comparatively wider wavelength spanning range, but could supply only 10 signal channels. What’s more, this proposed laser also has the ability to merge with polarization division multiplexing, which could be realized in our setup by adding basic arrangement, consisting of a quarter-wave plate (QWP) and polarization beam splitter (PBS) after OC (as in Fig. 1). Passing through the QWP, the output beam would first be transformed to elliptical polarization state and then divided by the PBS into 2 branches of the x- and y-polarizations with random intensity radio (decided by the rotation of QWP). Specially, when the polarization direction of the output is aligned azimuthally at 45° with x-axis incident into the QWP, two orthogonal-polarized signals would be produced with equal intensities after PBS.

Fig. 3 The scattered points are the output power of LG₀₂ mode as a function of wavelength under the maximum incident pumping level of 21.2 W. The inset are the corresponding intensity distribution and interference fringes.

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The output power characteristics at ~1645.5 nm of five OAM states as a function of the incident pump power were also recorded, as shown in Fig. 4. The laser produced TEM₀₀ beam of a maximum output power of 3.5 W with a slope efficiency of 19.9%, LG₀₁ beam of a maximum output power of 2.4 W with a slope efficiency of 14.7%, while LG₀₂ beam of a maximum output power of 1.3 W with a slope efficiency of ~11.5%. The laser performances suffered from power leakage at the VBG (>95% reflectivity) and the inserting loss caused by BP and YAG, while was expected to be further scaled by using higher-reflective VBG and higher-power pump source. The tuning range tended to be narrower when the order of the targeted mode was higher, which could be contributed to different gains which proportional to the overlap efficiencies with the pump beam. The one with higher gain will support more longitudinal modes to oscillate, thus has wider tuning wavelength range. It should be noted that the tilt angle of YAG also affected the power scale, for example, the TEM₀₀ mode had the highest slope efficiency, besides the high mode-matching efficiency with pump, it also suffered less Fresnel loss from the YAG plate because there was no need to choose handedness.

Fig. 4 Output powers of beams with five OAM states at emission peaks.

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4. Conclusions

In summary, this article reports the design of a wavelength-tunable and narrow-linewidth vortex laser in Er:YAG systems with five OAM states. In a z-shaped resonator compromising a reflective VBG as a folding element, vortex beams with OAM of 0, ± ħ, and ± 2ħ were respectively obtained. The VBG could function as an effective wavelength selector and narrower for vortex laser without deteriorating the OAM integrity, the obtained wavelength tunable ranges for TEM₀₀, LG₀₁, LG₀₂ modes were respectively 1641.4~1649.8 nm, 1642.2~1649 nm, and 1643.1~1648 nm. The wavelength tunable range was limited by the emission band of Er³⁺ ion, which was expected much wider if using other rare ions laser systems like Yb³⁺, Tm³⁺. We consider this proposed z-shaped laser compact, integrated, and providing the selection of a particular wavelength with reliable transformation of topological charge (in 0, ± 1, ± 2 region), which can be beneficial in future to high-capacity optical communications with spatial- and wavelength- division multiplexing techniques. This work is an important step toward integrated spatial multiplexing for optical communications.

Funding

National Natural Science Foundation of China (No. 61505072); Natural Science Foundation of Jiangsu Province, China (No. BK20150240); Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 15KJB510009).

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Wavelength- and OAM-tunable vortex laser with a reflective volume Bragg grating

Abstract

1. Introduction

2. Theoretical analysis and experiment

3. Results and analysis

4. Conclusions

Funding

References and links

Cited By

Figures (4)

Equations (5)

Optics Express