High-power femtosecond cylindrical vector beam optical parametric oscillator

Jun Zhao; Jintao Fan; Jintao Fan; Ruoyu Liao; Na Xiao; Minglie Hu; Minglie Hu

doi:10.1364/OE.27.033080

1. Introduction

Laser beams with spatially inhomogeneous polarization states, also named as vector beams, have drawn growing interest during the last decade [1]. One particular example is cylindrical vector beam (CVB) with cylindrical symmetry in polarization distribution. It turns out that the CVBs are vector-beam solutions of Maxwell’s equations and obey axial symmetry in both amplitude and phase [2]. In general, such beams can be classified as azimuthally polarized, radially polarized, and hybridly polarized beams according to the spatial distribution of the polarization [3–4]. Owing to the unique axial polarization symmetry, CVBs present many interesting propagating and focusing properties [5–10]. For example, a tightly focused radially polarized beam has a sharp focal spot that is smaller than achievable with linearly polarized light. Femtosecond (fs) lasers, on the other hand, because of the characteristics of ultrahigh peak power and ultrafast pulses, are showing increasing importance in many applications and have become pivotal tools in scientific research [11]. As a result, fs-CVB laser, which combines the superiority of CVB and the ultrafast laser pulse, has spawned numerous applications in modern optics [12–15], including high-resolution microscope [16–17], optical trapping and manipulation [18], laser machining [19–22], second harmonic generation [23–24], and optical communication [25].

Motivated by the fantastic features and great application potential of fs-CVB laser, a large number of schemes and systems for the generation have been reported over the past decade including inserting laser intracavity devices [26–31] or applying devices with spatially variant polarization properties in free space [32], such as Q-plate, liquid crystal spatial light modulator and vortex retarder. As compared to the CVB generated outside the laser cavity, fs-CVB emitted directly from the laser cavity has advantages of low cost, high compactness and high efficiency. Despite that various efforts have been made to produce fs-CVB directly at source, restricted by the limited gain bandwidth, the output radiation commonly works at specific discrete wavelengths [26,28]. Indeed, to meet the requirement of practical applications, a novel laser source that can delivery fs-CVB with broadband wavelength tunability need to be developed. For instance, SHG imaging for different nano-materials, fs-CVB with different central wavelengths is highly demanded [23–24]. We show that a femtosecond optical parametric oscillator (OPO) can offer such a unique capability.

Over the last decade, OPOs have been recognized as versatile sources providing high power and broad wavelength coverage, in all time-scales from the continuous-wave to the femtosecond domain [33–35]. In this paper, we demonstrate a new type of fs-OPO, which is capable of providing high power tunable fs-CVB. By introducing a half-wave plate (HWP) and a vortex half-wave plate (VWP) into the OPO’s cavity, the OPO could directly produce fs-CVB tunable over 1375-1650 nm. At 1505 nm, CVB with a maximum output power of 614 mW and a pulse duration of 133 fs has been achieved at 2 W pump power. By controlling the polarization state of the signal inside the OPO cavity, the fs-CVBs with desired spatial distributions of the polarization have been generated. The measured polarization extinction ratios of CVBs with different wavelengths are around 19 dB, confirming high polarization purity for the output beam. Furthermore, high order fs-CVBs can be flexibly produced by changing the order of the VWP in this system. To our best knowledge, this is the first example of high-power tunable fs-CVB OPO. The presented results offer an intriguing route to produce high power fs-CVB at on demand polarization state together with arbitrary wavelengths.

2. Theoretical analysis

In this work, we insert a VWP (Thorlabs, WPV10L-1550, Inc.), a specially designed half-wave plate with fast axes rotating along the azimuthal direction with high transmission efficiency (up to 96%), inside an OPO cavity to convert Gaussian beam into CVB. The VWP has a constant retardance across the clear aperture but the orientation of its fast axis rotates continuously over the area of the optic, which can be expressed as:

(1)$$\theta (\varphi ) = \frac{m}{2}\varphi + {\varphi _0}$$

where φ is the azimuthal angle and φ₀ is the orientation of the fast axis at φ = 0. The positive integer m is the order of the VWP, defining the polarization order of the CVB, with an m×2π polarization rotations along the clockwise circular direction. The VWP’s Jones Matrix can be written as [32]:

(2)$$M(\theta ) = \left[ {\begin{array}{{cc}} \begin{array}{l} \cos 2\theta \\ \sin 2\theta \end{array} &\begin{array}{l} \sin 2\theta \\ - \cos 2\theta \end{array} \end{array}} \right]$$

When applied to a linear polarization light beam $\left( {\begin{array}{{c}} {\cos \alpha }\\ {\sin \alpha } \end{array}} \right)$ where α represents the orientation of the incident linearly-polarized beam with respect to the x-axis, the output result E should satisfy:

(3)$$E = M(\theta )\left( {\begin{array}{{c}} {\cos \alpha }\\ {\sin \alpha } \end{array}} \right) = \left( {\begin{array}{{c}} {\cos (m\varphi + 2{\varphi_0} - \alpha )}\\ {\sin (m\varphi + 2{\varphi_0} - \alpha )} \end{array}} \right)$$

Equation (3) shows that each point on the transverse plane of the output beam is linear polarized, but the polarization direction depends on the azimuthal angle φ. Therefore, a linearly-polarized Gaussian beam will become a CVB through a VWP. Moreover, because each point on the VWP is a half-wave retarder, a linearly-polarized Gaussian light can be recovered after propagating forward and then reflecting backward through the same VWP. The reflected result ${E_r}$ can be derived as:

(4)$${E_r} = M(\theta )E = \left( {\begin{array}{{c}} {\cos \alpha }\\ {\sin \alpha } \end{array}} \right)$$

Here, taking the generation of first-order CVB as an example, we will explain the mode conversion in detail. Using the VWP with m = 1, Fig. 1 illustrates four representative CVB polarization patterns from different orientations linearly-polarized light passing through the VWP. In this case, set the initial orientation of the fast axis φ₀ as 0°. Specifically, as we all know, the Jones Matrix of horizontal and vertical polarization are $\left( {\begin{array}{{c}} {1}\\ {0} \end{array}} \right)$ and $\left( {\begin{array}{{c}} 0\\ 1 \end{array}} \right)$ when α is equal to 0° and 90°, respectively. Then, the output polarization distribution ${E_{{0}^\circ }}$ and ${E_{{90}^\circ }}$ in Eq. (3) can be expressed as

(5)$${E_{{0}^\circ }} = \left( {\begin{array}{{c}} {\cos \varphi }\\ {\sin \varphi } \end{array}} \right), \;{E_{{90}^\circ }} = \left( {\begin{array}{{c}} {\sin \varphi }\\ { - \cos \varphi } \end{array}} \right)$$

corresponding to the radial and azimuthal polarization CVBs in Fig. 1(a) and (c). After the CVBs reflected back by mirror and passing the VWP again, it’s clear that the light turn to be horizontal $\left( {\begin{array}{{c}} {1}\\ {0} \end{array}} \right)$ and vertical $\left( {\begin{array}{{c}} 0\\ 1 \end{array}} \right)$ polarization again, respectively. In the same way, bring the + 45° linear polarization $\frac{1}{{\sqrt 2 }}\left( {\begin{array}{{c}} {1}\\ {1} \end{array}} \right)$ and −45° linear polarization $\frac{1}{{\sqrt 2 }}\left( {\begin{array}{{c}} {{ - 1}}\\ {1} \end{array}} \right)$ into Eq. (3), the output CVBs polarization distribution ${E_{ + 45^\circ }}$ and ${E_{ - 45^\circ }}$ are written as

(6)$${E_{ + 45^\circ }} = \frac{1}{{\sqrt 2 }}\left( {\begin{array}{{c}} {\cos \varphi + \sin \varphi }\\ {\sin \varphi - \cos \varphi } \end{array}} \right), \;{E_{ - 45^\circ }} = \frac{1}{{\sqrt 2 }}\left( {\begin{array}{{c}} {\cos \varphi - \sin \varphi }\\ {\sin \varphi + \cos \varphi } \end{array}} \right)$$

corresponding to the clockwise polarization in Fig. 1(b) and anticlockwise polarization in Fig. 1(d), respectively. The light beam can be reversal to $\frac{1}{{\sqrt 2 }}\left( {\begin{array}{{c}} {1}\\ {1} \end{array}} \right)$ and $\frac{1}{{\sqrt 2 }}\left( {\begin{array}{{c}} {{ - 1}}\\ {1} \end{array}} \right)$ after reflected as well. Therefore, when VWP is inserted, the beam mode and the polarization state of the signals inside OPO cavity keep consistent in each cavity roundtrip.

Fig. 1. The mode transformation of the linear polarization light with different orientations propagate forward and then reflect backward through the VWP (m = 1). (a) 0° linear polarization (b) +45° linear polarization (c) 90° linear polarization (d) −45° linear polarization.

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3. Experimental setup

Based on the theoretical analysis above, a high-power wavelength-tunable femtosecond CVB OPO is designed. Figure 2 is the schematic illustration of the experimental setup. The pump source is a homemade Yb-doped large-mode-area photonics crystal fiber femtosecond laser with 2 W output power at 53 MHz repetition rate. The central wavelength is located around 1040 nm with an FWHM of 40 nm, and the pulse duration is 108 fs. The average power incident into the nonlinear crystal can be adjusted with a combination of an HWP and a polarizing beam-splitter cube. The high-quality beam from the fiber laser source with a Gaussian special profile is used to pump the linear cavity OPO. M1 and M2 are gold-coated concave mirrors with a curvature of 200 mm. The laser beam is focused into the OPO crystal using M1 and then re-collimated using M2. We deploy a quasi-phase-matched (QPM) nonlinear crystal to achieve high gain. The crystal is a 3-mm long, 12.3-mm wide, and 1-mm thick 5% MgO-doped periodically poled LiNbO₃ (MgO:PPLN, HC Photonics, Taiwan), which consists of 10 gratings with periods ranging from 27.58 to 31.59 µm. Both faces of the crystal are antireflection coated for 1000 nm-1100 nm (R < 1%) and 1420 nm-2000nm (R < 1.5%). M3-M5 are dichroic mirrors, which exhibit 99% reflectance over 1400 nm ∼ 2100 nm, 95% transmissivity for the pump wavelength at 1.04 µm, and high transmission for idler wave. This design ensures the singly-resonant oscillation for the signal. M5 is mounted on a delay line for fine tuning of the cavity length. M6 is an output coupler with 70% transmittance for the signal laser. The combination of an HWP (Thorlabs, WPH05M-1550, Inc.) and a VWP is inserted into the OPO’s cavity to generate controllable CVB. Here, the HWP is used to adjust the orientation of the linear polarization beam before the VWP. Then the signal beam profile is captured by a CCD camera (Beamage-4M-IR, 238215). The total optical length of the OPO cavity is ∼2.83 m, corresponding to a repetition rate of 53 MHz.

Fig. 2. Experimental setup of the OPO for CVB generation. M1-M2: gold-coated concave mirrors; M3–M5: mirrors; M6: output coupler; HWP: halfwave plate; PBS: polarizing beam-splitter; VWP: vortex half-wave plate; CCD: charge-coupled device.

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4. Results and discussion

Firstly, we characterize the performance of the OPO with regard to the output power and the pulse duration of CVB signals across the tuning range. A VWP with m = 1 is employed to generate the first-order CVB. At first, we examine the CVB signal wavelength tuning property of the OPO by switching poling periods of PPLN, which can be realized by the linearly mechanical translation of the crystal, while keeping the orientation of the HWP at θ=0°. As explained before, since the polarization inside OPO cavity realizes a completely reversible cycle, the OPO could stably outputs CV modes from the output coupler. Optimizing the cavity to make it operate with maximum signal output power at each poling period of the PPLN crystal, the central wavelength of the CVB signals could be continuously tuned from 1405 to 1601 nm. Moreover, the spectra can be further extended to cover 1375–1650 nm. Figure 3(a) displays the recorded spectra, where the spectral bandwidths at full-width at half-maximum (FWHM) are around 25 nm. The spectra are noisy at the shorter wavelengths, induced by the water absorption lines. The maximum CVB powers are measured across the tuning range. The signal power changes from 74 mW at 1405 nm to 268 mW at 1601 nm with a constant average pump power of 2 W. A maximum output power of 614 mW is generated at 1505 nm, corresponding to a signal extraction efficiency of ∼30.7%. The decreasing signals power at shorter or longer wavelengths can be ascribed to the reduction in parametric gain of the nonlinear crystal and the mirrors’ coating [36]. What’s more, as evident from Fig. 3(a), all the signal beams have doughnut-shaped intensity patterns in the whole tuning range.

Fig. 3. (a) CVB signals wavelength tuning range of the OPO and average output power of the signal with a variation of central wavelength. (b) Measured pulse durations (filled circles) and corresponding calculated transform-limited pulse durations (empty circles) across the tuning range. (c) A typical autocorrelation of CVB signal at 1505 nm.

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Comparison between the measured and calculated transform-limited pulse durations of CVBs signal across the tuning range is displayed in Fig. 3(b). The filled circles represent the experimentally determined pulse durations of the signals changing from 137 fs to 204 fs at different wavelengths. The supported transform-limited pulse durations are all around 100 fs (the empty circles in Fig. 3(b)). Obviously, the measured pulse durations are a little longer than the calculated transform-limited ones, which is caused by the group-delay dispersion introduced by the nonlinear crystal and the mirrors in the cavity. The Fig. 3(c) provides a typical autocorrelation profile (black line) of signal pulse at 1505 nm. FWHM of the autocorrelation trace is 188 fs. With a Gaussian pulse shape assumption, the pulse duration is approximately 133 fs. The red line shows the calculated transform-limited autocorrelation trace at 1505 nm, and the pulse duration is 101 fs.

In order to study the CV mode output properties in detail, we fix poling period of the MgO:PPLN at Λ = 29.5 µm for further study, corresponding to the output signal wavelength of 1505 nm. First of all, we contrast the Gaussian beam and the first order CVB signal output power dependences on the pump power. When the HWP and VWP are absent, the OPO outputs the signal with Gaussian mode. The black dots in Fig. 4(a) imply that the Gaussian signal power can be scaled up to 660 mW at 2 W pump power, corresponding to a conversion efficiency of 33% (the black dots in Fig. 4(b)). The threshold pump power is measured to be ∼ 483 mW. Then the combination of VWP (m = 1) and HWP is employed into the cavity in the following step. The OPO could be re-oscillated by slightly adjusting the length of the cavity. As the red dots shown in Fig. 4(a), the CVB signal power increases from 13 mW at a pump power of 0.5 W to a maximum of 614 mW with 2 W pump power. Despite the extra loss induced by the HWP and VWP, the threshold of the first order CVB mode lasing is only slightly raised to 489 mW. The conversion efficiencies exhibit saturation when the pump power is higher than 1.2 W for both cases, as shown in Fig. 4(b). Such high conversion efficiency of the CVB signals can be attributed to the Gaussian mode of the pump beam, the low loss introduced by the VWP and the HWP, and high output ratio of the coupler.

Fig. 4. (a) The experimentally measured output powers of the Gaussian beam and the first order CVB at 1505 nm are shown in black and red dots, respectively. (b) The conversion efficiencies of Gaussian beam and the first order CVB as a function of incident pump power.

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According to Eq. (4–7), four representative CVBs (radial, clockwise, azimuthal, and anticlockwise polarizations) at different angle θ of the HWP, are shown in Fig. 5. Apparently, all the CVB intensity profiles share doughnut patterns. In principle, the generated CVBs are superimposed with corresponding cylindrically-arranged polarization patterns, which can be verified by the transmitted intensity profiles after an oriented linear polarizer. Hence, a linear polarizer is arranged in front of the CCD to analyze the polarization distribution of the output CVBs. As the HWP is set in an angle of θ=0°, orienting the linear polarizer at the angles of 0, 45°, 90°, and 135°, the donut-shaped vector beam splits into two lobes parallel to the orientation of the linear polarizer (depicted by double-end arrows) as shown in Figs. 5(a₂)–5(a₅), indicating the formation of radial vector beams. When the HWP is set in an angle of θ=45°, the azimuthal polarization is characterized by the two-lobed structure perpendicular to the orientation of the linear polarizer (Figs. 5(c₂)–5(c₅)). The intensity distributions of the other two CVBs after linear polarizer are demonstrated in Fig. 5(b) and 5(d). As is evident, the experimentally generated CVBs are in excellent agreement with the theoretical modes shown in Fig. 1. Benefitted from the laser cavity design, when the angle of the HWP varies, the output pulse properties remain the same except for the polarization state.

Fig. 5. Donut-shape intensity profiles and corresponding polarization patterns are depicted for four representative 1^st-CVBs. The second to fourth column: Transmitted intensity distributions after a linear polarizer with horizontal (0°), counter-diagonal (45°), vertical (90°) and main-diagonal (135°) orientations, as depicted by the double-ended arrows.

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The polarization purity of CVB signals with different wavelengths is investigated by analyzing the intensity profile of the two-lobe structure at a radius r as a function of the azimuthal angle θ in this work. For instance, for a pure radially polarized beam, the intensity at an arbitrary radius r and azimuthal angle θ is given by [37]

(7)$$I(r,\theta ) = {I_{\max }}(r){\cos ^2}(\theta - {\theta _0})$$

where θ₀ is the angle orientation of the transmission axis of the linear polarizer. The black dots in Fig. 6(a) show the experimental intensity data of radially polarized beam at 1550 nm which are extracted from the intensity pattern image shown in the inset. The red line is the simulated result, which shows a good agreement with the experiment data. The polarization extinction ratio ($EXT = 10log\left( {\frac{{{I_{\max }}}}{{{I_{\min }}}}} \right)$) is measured to be 20.7 dB, confirming high radial-polarization purity for the output beam. Furthermore, the polarization extinction ratios of the radially polarized beam at different poling periods of the PPLN are illustrated in Fig. 6(b). The different extinction ratios at different wavelengths could be ascribed to the specific designed at 1550 nm of VWP.

Fig. 6. (a) Azimuthal-intensity profile for radius r of the beam after passing through a horizontally oriented polarizer at 1550 nm. (b) The polarization extinction ratios of radially polarized beam at different wavelengths.

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Moreover, this technique is not limited to the generation of the first order CVB modes. Replacing the VWP of m = 1 with VWP of m = 2, we have generated second-order CVBs with well-defined annular beam profile as shown in Fig. 7(a₁) and 7(b₁). The measured intensity distributions after the linear polarizer consists of four intensity lobes, depicted in Fig. 7(a) and 7(b). This implies that the polarization direction along the circumference of the doughnut beam rotates twice. Besides, the measured output power of second order CVB is around 552 mW and the threshold pump power raises to 497 mW. In fact, higher orders of CVB can be equivalently realized by changing the number of the cascading first- and second-order VWPs and HWPs [38]. Hence, as an example, by cascading VWPs with m = 1, m = 2 and two HWPs at the same time in the cavity, the third order CVB also can be produced as illustrated in Fig. 7(c₁). The annular output of the third order CVB leads to a six lobes intensity distribution after a linear polarizer, revealing the polarization direction rotates three times. It is obvious that the central hole of doughnut profiles gets bigger as the order increasing. Due to the loss of mode conversion, the measured power of third order CVB reduces to 420 mW.

Fig. 7. Donut-shape intensity profiles and corresponding polarization patterns are depicted for on-demand generated (a)–(b) 2^nd-CVBs. (c) 3^rd-CVB. The second to fourth column: Transmitted intensity distributions after a linear polarizer with horizontal, counter-diagonal, vertical and main-diagonal orientations, as depicted by the superimposed double-ended arrows.

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5. Conclusions

In summary, we have demonstrated the first high-power femtosecond CVB OPO with wide wavelength tunability, to the best of our knowledge. In view of the Jones matrix of the CVB converters, a VWP and an HWP are inserted into an OPO cavity, enabling the OPO to directly output the CVB. We have produced tunable femtosecond CVB from 1375 to 1650 nm. The maximum average output power is 614 mW at 1505 nm with a 2 W pump laser, corresponding to 30.7% conversion efficiency. All the output CVBs show annular intensity patterns and characteristic intensity patterns after a linear polarizer, confirming high polarization purity of CVB signals. High order CVB can be generated using this system by simply changing the order of VWP. Such a flexible laser source, which can generate high power CVB with a well-define donut-intensity profile and controllable polarization distribution tunable across the near-IR wavelength range, may be practical applied in optical communication, material processing, superfocusing, etc.

Funding

Tianjin Research Program of Application Foundation and Advanced Technology of China (17JCJQJC43500); National Natural Science Foundation of China (61535009, 61827821).

Disclosures

The authors declare no conflicts of interest.

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High-power femtosecond cylindrical vector beam optical parametric oscillator

Abstract

1. Introduction

2. Theoretical analysis

3. Experimental setup

4. Results and discussion

5. Conclusions

Funding

Disclosures

References

Cited By

Figures (7)

Equations (7)

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