Open Access
Add to BibSonomy
Abstract
For the first time to our knowledge, the operation of a synchronously pumped ultrafast Raman laser that uses a PbMoO4 crystal as the active medium has been demonstrated. We achieved efficient Raman conversion in PbMoO4 from pumping 1063 nm into 1171 and 1217 nm, respectively, at single and combined frequency shifts on stretching and bending Raman modes. The output pulse energy (up to 160 nJ) and peak power (up to 11 kW) of the output picosecond radiation is the highest among all-solid-state synchronously pumped Raman lasers published to date. The strongest pulse shortening at 1217 nm down to 1.4 ps was obtained that is close to the bending mode dephasing time.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Currently, multiwavelength, near-IR (1000-1300 nm), ultrafast lasers and nonlinear-optical devices with both high energy and high repetition rate of femto- or picosecond pulses are getting more and more new applications, such as multicolor two- and three-photon 3D imaging in living tissues [1–3], direct waveguide writing in optical materials [4,5], etc. Extending the laser radiation wavelength beyond the range of the laser source via nonlinear frequency conversion at output peak power of a kW level and average power of a sub-W level can significantly increase efficiency of these applications for different fluorophores in 3D imaging and for different optical materials in direct waveguide writing.
Stimulated Raman scattering (SRS) presents simple and efficient method of nonlinear frequency conversion of laser radiation. Advantage of this method is in the fact that it does not require maintaining of the phase matching condition. Recently, the sub-picosecond and picosecond diamond Raman lasers synchronously pumped by the continuously mode-locked fiber and solid-state lasers [2,3] were expected to be a highly desirable alternative to the high-cost Ti:Sapphire laser systems with nonlinear frequency conversion by optical parametric oscillation for the multiwavelength high-energy high-repetition-rate ultrafast laser applications.
Other interesting alternative can also be an all-solid-state Raman laser with combined frequency shift on both stretching ($\nu _1$) and bending ($\nu _2$) Raman modes in a low-cost tetragonal Raman-active crystal. Such crystal can be synchronously pumped by a low-cost mode-locked Nd doped solid-state laser with the output pulse duration in the range of tens of picoseconds. Strong pulse shortening in the synchronously pumped SRS laser can lead to output pulses shorter than 1 ps [6]. This value is generally limited by the widest bending mode dephasing time. Earlier, alkali-earth tungstate and molybdate Raman-active crystals (MXO$_4$ where M = $Ca$, $Sr$, $Ba$; X = $W, Mo$) having a scheelite-type structure were comparatively studied in the extracavity synchronously pumped Raman laser [7–11]. It was found that the BaWO$_4$ crystal having the most intense Raman modes among these crystals allowed to achieve the most efficient picosecond Raman laser operation – slope efficiencies of 68.8 % and 38.6 % at single ($\nu _1$) and combined ($\nu _1$ + $\nu _2$) Raman shifts, respectively [8]. However, duration of the shortened ($\nu _1$ + $\nu _2$)-shifted SRS pulses was the longest (3 ps) among these crystals because its Raman modes are also the narrowest – the bending mode linewidth of $\Delta \nu _2$ = 3.8 cm$^{-1}$ corresponds to the dephasing time of 1/($\pi$c$\Delta \nu _2$) = 3 ps [10]. SrMoO$_4$ and SrWO$_4$ crystals allowed to obtain the shortest ($\nu _1$ + $\nu _2$) shifted SRS pulses with duration of about 1 ps due to wider Raman modes ($\Delta \nu _2$ $\approx$ 8-10 cm$^{-1}$ and 1/($\pi$c$\Delta \nu _2$) $\approx$ 1 ps), but the SRS oscillation slope efficiencies were not higher than 45 % and 18 % at single ($\nu _1$) and combined ($\nu _1$ + $\nu _2$) Raman shifts, respectively [9–11].
In [12], it was found that one more scheelite-type crystal, namely PbMoO$_4$, can be very efficient like BaWO$_4$, but Raman modes in PbMoO$_4$ are wideband like in SrWO$_4$. It is caused by the fact that the Pb$^{2+}$ cation has a larger mass than Ba$^{2+}$, but it also has small ionic radius similar as Sr$^{2+}$. Therefore, PbMoO$_4$ was proposed as promising Raman-active material for both steady-state and transient SRS modes. However, single-pass picosecond or intracavity nanosecond SRS generation in PbMoO$_4$ was experimentally realized only in several works [12–15]. A limiting factor for efficient SRS generation in PbMoO$_4$ is given by its low optical damage threshold of $\sim$ 0.5 J/cm$^{2}$ corresponding to an upper limit of the pump radiation intensity of $\sim$ 0.4 GW/cm$^{2}$ at 1.4-ns pulse duration [14] and $\sim$ 30 GW/cm$^{2}$, at 20-ps pulse duration [15]. This is a fundamental limiting factor of all the Raman-active molybdates in comparison with the corresponding Raman-active tungstates and therefore tungstates are more popular as the Raman-active media. For example, optical damage threshold of commercial samples of SrMoO$_4$ molybdate is 0.8 GW/cm$^{2}$ at 1064 nm & 4.2 ns that is 2.4 times lower than for the SrWO$_4$ tungstate samples [16]. Keeping in mind higher optical damage threshold intensity for picosecond pumping than for nanosecond pumping, SRS generation in an external cavity under synchronous pumping by repetitive picosecond laser pulses with a repetition period synchronized with the Raman laser cavity round-trip time allows overcoming the limitation of low optical damage threshold. For example, the picosecond extracavity synchronously pumped Raman laser based on the 1.7-cm long SrMoO$_4$ active crystal had SRS oscillation threshold of $\sim$ 0.05 GW/cm$^{2}$ [11] that is essentially two orders of magnitude lower than picosecond optical damage threshold intensity and had no problem with optical damage.
In this paper, for the first time to our best knowledge, a synchronously pumped ultrafast Raman laser based on a PbMoO$_4$ crystal is presented. We demonstrate highly efficient Raman conversion in PbMoO$_4$ with single and combined frequency shifts on stretching and bending Raman modes at the highest pulse energy (up to 160 nJ) and peak power (up to 11 kW) of the output picosecond SRS radiation among all-solid-state synchronously pumped Raman lasers.
2. PbMoO$_4$ Raman crystal characterization
Together with alkali-earth tungstate and molybdate crystals, the PbMoO$_4$ crystal belongs to the scheelite-type tetragonal structure [17,18]. The molecular tetrahedron anionic group of (MoO$_4$)$^{2-}$ with strong covalent bonds Mo-O is a peculiarity of the scheelite structure. Due to weak coupling between the divalent cation and the anionic group, the vibrational modes in spontaneous Raman spectra of the scheelite-type crystals can be divided into two groups – internal and external. The internal vibrations, corresponding to the oscillations inside the anionic group with an immovable mass center, are intense and therefore they are usually used for SRS. The most intense Raman lines with the frequencies of $\nu _1$ and $\nu _2$ correspond to the stretching and bending symmetric internal vibrations of the anionic group. A special and important feature of the spontaneous Raman scattering spectra of the PbMoO$_4$ crystal is essential difference of the dependence of the $\nu _1$ Raman line intensity on the geometry of scattering (E $\parallel$ c or E $\perp$ c). There is also a difference in the Raman lines frequencies from that observed in the spontaneous Raman scattering spectra of other alkali-earth tungstates and molybdates [12,18]. It was explained by very large mass of the Pb$^{2+}$ cation (the cation mass increases in the row Ca$^{2+}$ $\rightarrow$ Sr$^{2+}$ $\rightarrow$ Ba$^{2+}$ $\rightarrow$ Pb$^{2+}$) and a comparatively large degree of covalence of the bond between Pb and O (the cation electronegativity increases in the row Ba$^{2+}$ $\rightarrow$ Sr$^{2+}$ $\rightarrow$ Ca$^{2+}$ $\rightarrow$ Pb$^{2+}$) reducing the effective mass of the oscillating Mo-O pair in the anionic group.
In order to study both $\nu _1$ and $\nu _2$ Raman line characteristics of the PbMoO$_4$ crystal, we measured polarized spontaneous Raman scattering spectra with high spectral resolution in a backscattered scheme. We used double monochromator SPEX-Ramalog 1403 with the excitation by a 510.6-nm copper vapor laser with the spectral resolution of 0.5 cm$^{-1}$ and scanning step of 0.2 cm$^{-1}$. Figure 1 shows the experimental spectra for two excitation polarizations where intensities of the Raman lines are normalized to the most intense Raman line ($\nu _1$ at E $\perp$ c).
Fig. 1. Polarized spontaneous Raman scattering spectra in the vicinities of the $\nu _1$ and $\nu _2$ Raman lines in the PbMoO$_4$ single crystal at exciting light polarization (a) parallel (E $\parallel$ c) and (b) perpendicular (E $\perp$ c) to the crystal optical axis.
It can be seen that the $\nu _1$ and $\nu _2$ Raman lines are located at $\nu _1$ = 870 cm$^{-1}$ and $\nu _2$ = 318 cm$^{-1}$ with linewidths of $\Delta \nu _1$ = 5.4 cm$^{-1}$ and $\Delta \nu _2$ = 7.4 cm$^{-1}$, respectively, at both geometries of scattering (E $\parallel$ c and E $\perp$ c). So, the theoretical limit for the SRS pulse shortening is estimated from the widest ($\nu _2$) Raman line dephasing time and amounts 1/($\pi$c$\Delta \nu _2$) = 1.4 ps.
In an agreement with data in [12] the $\nu _1$ Raman line is the most intense at E $\perp$ c, not at E $\parallel$ c, in contrast to other tetragonal Raman-active crystals [6–11]. On the other hand, the $\nu _2$ Raman line is more intense (by 1.8 times) at E $\parallel$ c than at E $\perp$ c similar to other tetragonal crystals. Intensities of the $\nu _1$ and $\nu _2$ Raman lines (Fig. 1) are distributed as follows: $I_1$ = 1 a.u. at E $\perp$ c, $I_1$ = 0.76 a.u. at E $\parallel$ c, $I_2$ = 0.25 a.u. at E $\perp$ c, and $I_2$ = 0.45 a.u. at E $\parallel$ c. Earlier, for other the tetragonal crystals, an optimal orientation of the crystal in the Raman laser was definitely E $\parallel$ c [7–11] because both the $\nu _1$ and $\nu _2$ lines were more intense at E $\parallel$ c. Now, at first, for PbMoO$_4$ we encounter an ambiguous situation: the $\nu _1$ line is more intense at E $\perp$ c, but the $\nu _2$ line is more intense at E $\parallel$ c. We have to study both to find the optimum for SRS with the combined Raman shift.
Another distinctive feature of the PbMoO$_4$ crystal from the previously studied strontium and barium tungstate and molybdate Raman crystals is a high refractive index with a high birefringence. It is important to take this into account for synchronously pumped Raman laser operation because it requires additional tuning of the Raman laser cavity length at rotation of the pump radiation polarization from E $\perp$ c to E $\parallel$ c. In addition, in the case of cascade Raman conversion (2$\nu _1$, or $\nu _1$ + $\nu _2$, or $\nu _1$ + $\nu _2$ + $\nu _2$, etc.), higher refractive index leads to a higher temporal walk-off per cavity round trip between the first and next SRS components that should decrease efficiency of cascade Raman conversion, but it can help to make the SRS pulses shorter. For the negative uniaxial PbMoO$_4$ crystal with the refined data of Sellmeier equations not only for visible-near-IR range up to 1 $\mu$m (usual data from many handbooks), but for the whole transparency range of the crystal ($\lambda$ = 0.40-3.8 $\mu$m) we can use the equations from [19]
The temporal walk-off after transit through the PbMoO$_4$ crystal with a length of L = 5 cm between the ordinary (E $\perp$ c) and extraordinary (E $\parallel$ c) waves at the first Stokes wavelength of $\lambda _1$ = ($\lambda _0^{-1}$ – $\nu _1$)$^{-1}$ = 1.171 $\mu$m ($\lambda _0$ = 1.063 $\mu$m , $\nu _1$ = 870 cm$^{-1}$) amounts $\Delta$t = (n$_o$ – n$_e$)L/c = 16 ps at n$_o$ = 2.296, n$_e$ = 2.198, and n$_o$ – n$_e$ = 0.098. It is comparable with our pump pulse duration of 36 ps and requires tuning of the synchronously pumped Raman laser cavity length to the distance of $\Delta$L = c$\Delta$t = 4.9 mm when the pump radiation polarization is changed from E $\perp$ c to E $\parallel$ c. For example, similar estimation for the SrMoO$_4$ crystal (n$_o$ – n$_e$ = 0.003) gives a very low value of $\Delta$t = 0.4 ps compared to the same pump pulse duration (36 ps).
Estimations of the Raman gain for PbMoO$_4$ at 1.06-$\mu$m pumping are very different in the literature and need to be refined. The Raman gain of $\sim$ 8 cm/GW was presented in [20]. A surprisingly high estimation of 17.5 cm/GW can be found in [12]. In [15] there is a measurement of the single-pass SRS threshold conditions under pumping by the 1064-nm Nd:YAG laser with the laser pulse duration of $\tau _p$ = 18 ps. The PbMoO$_4$ crystal length was L = 1 cm and the pump beam cross-section in the crystal was s$_p$ = 3.01$\cdot$10$^{-3}$ cm$^{2}$. SRS generation threshold took place at the pump pulse energy of E$_{th}$ = 0.55 mJ. Using these data, we can estimate the Raman gain of PbMoO$_4$ by the formula [21]
where I$_{th}$ = E$_{th}$ /($\tau _p\cdot$s$_p$) $\approx$ 10 GW/cm$^{2}$ and $\tau _R$ = 1/($\pi$c$\Delta \nu _1$) $\approx$ 2 ps. According to the given data, we can calculate g $\approx$ 5 cm/GW.In the present work, we have also calculated the Raman gain for PbMoO$_4$ and compared the result to the crystals having known Raman gain which were tested in the same Raman laser system earlier.
3. Experimental setup
The experimental setup is shown in Fig. 2. The Raman laser was synchronously pumped by a laboratory designed Nd:GdVO$_4$ master oscillator – power amplifier (MOPA) generating at the wavelength of 1063 nm which was also used in our previous experiments [7–11]. The master oscillator was based on a 1 at. %. Nd:GdVO$_4$ slab crystal with the dimensions of 2$\times$4$\times$16 mm$^{3}$ in the bounce geometry with continuous-wave laser-diode side-pumping. The oscillator was operated in the continuously mode-locked regime using semiconductor saturable absorber mirror with the modulation depth of 2 % and non-saturable losses < 2 %. The continuously mode-locked train from the oscillator was amplified in the single-pass amplifier (the active element and the pumping geometry of the amplifier are similar as in the oscillator) pumped by a quasi-continuous laser diode. The 500$\mu$s long train with the repetition rate of 50 Hz contained 36 ps pulses (more than 70,000 pulses in the pulse train) with the single pulse energy of up to 330 nJ and the repetition rate of 150 MHz. The MOPA laser system generated linearly-polarized radiation with the beam spatial profile close to the fundamental transversal mode with the M$_x^{2}$ = 1.2 and M$_y^{2}$ = 1.1.
As the active element of the Raman laser, we used two commercial, low-cost (< 500$ \$ $/pc) PbMoO$_4$ samples with dimensions of 3$\times$3$\times$25 mm$^{3}$ each, a-cut, AR-coated (1000-1400 nm), intented for acousto-optic applications (Nanjing Metalaser Photonics Co., Ltd). The external ring cavity of the Raman laser consisted of two concave mirrors PM and M1 with a curvature radius of 100 mm and two flat mirrors. The PM and one of the flat mirrors (OC) were used as a pumping mirror and an output coupler, respectively. We tested two output couplers: OC1 (R = 87 % @1171 nm, R = 85 % @1217 nm) for the $\nu _1$-shifted SRS generation and OC2 (R = HR @1171 nm, R = 90 % @1217 nm) for the ($\nu _1$ + $\nu _2$)-shifted SRS generation. The second flat mirror (M2) was placed on the motorized translation stage for synchronization of the Raman laser cavity round-trip time with the pump pulse repetition period. In order to avoid SRS generation of the 2$\nu _1$-shifted radiation at 1304 nm, the mirrors had high transmissivity at this wavelength. For optimal mode matching between the pump beam and the Raman laser cavity mode, the pump beam was focused into the active element with the focal spot radius of 35$\times$30 $\mu$m$^2$ by a lens SL with a focal length of 100 mm. The pump radiation polarization was controlled by a $\lambda$/2 plate placed in front of the lens SL.
The individual generated Stokes components and pump laser radiation were separated by a long pass filters with the cut-on wavelength of 1100 and 1200 nm (Thorlabs FEL1100 and FEL1200). The radiation spectra were measured by the spectrometer (OceanOptics NIR512, wavelength range 850-1700 nm, FWHM resolution $\sim$ 3 nm). The average power was measured with a power meter (Standa 11PMK-15SH5), pulse energy was determined by calculation from average power, repetition rate, and duty factor of QCW pumping. The output pulses were measured by a laboratory designed non-collinear second harmonic generation (SHG) autocorrelator based on a LiIO$_3$ crystal. For pulse duration calculation we assumed a Gaussian shape of the autocorrelation curves of the measured pulses.
4. Generation of the first Stokes at 1171 nm
Using the output coupler OC1, oscillation was obtained in the Raman laser with one 25 mm long PbMoO$_4$ active crystal at first. In order to decrease SRS oscillation threshold and increase SRS conversion efficiency we used an active element consisting of two such crystals in series (the two-crystal active element), as shown in Fig. 2. In both the cases, only the first Stokes SRS component at a wavelength of 1171 nm corresponding to the Raman shift of $\nu _1$ = 870 cm$^{-1}$ was generated when the Raman laser cavity round-trip time was synchronized with the pump pulse repetition period. No higher order Stokes components or Stokes components with different shifts were observed. The output radiation spectrum of the PbMoO$_4$ Raman laser with the OC1 is shown in Fig. 3 (blue line) and it was the same for both excitation light polarizations.
Fig. 3. Output radiation spectra of the synchronously pumped PbMoO$_4$ Raman laser with output couplers OC1 (blue line) and OC2 (green line).
Figure 4 shows dependences of the output SRS pulse energy and average power on the input pump pulse energy in the 50mm-long PbMoO$_4$ Raman laser with the OC1 at the excitation light polarizations E $\perp$ c and E $\parallel$ c. Changing the polarization of the excitation light was accompanied by adjusting the cavity length for ideal synchronous pumping. As expected, SRS threshold was lower at E $\perp$ c than at E $\parallel$ c (82 nJ against 108 nJ) by 1.32 times because the $\nu _1$ Raman mode is more intense at E $\perp$ c than at E $\parallel$ c by $\sim$ 1.3 times (see Fig. 1(b)). Interesting phenomena was also essentially higher slope efficiency at E $\perp$ c than at E $\parallel$ c (65.3 % against 42.3 %) even though the losses of the Raman laser were not changed. Therefore, we achieved highly efficient operation of the all-solid-state PbMoO$_4$ Raman laser having the two-crystal active element (overall length of 50 mm) at E $\perp$ c at slope efficiency of 65.3 % and optical-to-optical efficiency of up to 49 %. The obtained output pulse energy of 160 nJ is the highest among other all-solid-state synchronously pumped Raman lasers. Despite the quasi-continuous-wave pumping mode, the output SRS radiation average power reached 0.6 W with the duty cycle of 2.5 % because of high energy of the individual repetitive pulses that is enough for the high-energy high-repetition-rate ultrafast laser applications.
Fig. 4. Dependences of the output SRS pulse energy and average power on the input pump pulse energy in the synchronously pumped PbMoO$_4$ Raman laser with the two-crystal active element (overall length of 50 mm) with the OC1 for excitation light polarizations E $\perp$ c and E $\parallel$ c.
For comparison, using only one 25 mm-long crystal, not only the SRS threshold pump energies (103 and 128 nJ at E $\perp$ c and E $\parallel$ c, respectively), but also slope efficiencies (44.7 and 25.6 % at E $\perp$ c and E $\parallel$ c, respectively) were lower than for the 50mm-long two-crystal active element. Note that, slope efficiency was essentially lower at E $\parallel$ c than at E $\perp$ c too with no change of losses. Furthermore, the intrinsic losses are higher when the active crystal is longer that should decrease slope efficiency of lasing. We believe it is a synchronous pumping effect resulting in higher slope efficiency of oscillation at higher single-pass gain of the active element. Earlier, we had similar results of essentially higher slope efficiency of the synchronously pumped Raman laser using longer (36 mm against 14 mm) SrWO$_4$ active crystal [10,11], and it was accurately confirmed in the comparative study of GdVO$_4$ active crystals with different lengths of 16, 20, and 40 mm [22].
The measured data of the SRS oscillation threshold can be used to estimate the Raman gain of PbMoO$_4$. The calculation will be also based on data obtained from the previously studied GdVO$_4$ active crystals having known Raman gain of g$_{GdVO_4}$ = 4.5 cm/GW at 1.06-$\mu$m pumping [23]. The output coupler OC1 reflectivity for both these crystals was the same and equal to 87 % and therefore the cavity losses can be considered approximately the same. GdVO$_4$, similarly as PbMoO$_4$, has comparatively wide Raman modes and $\tau _p$/$\tau _R$ > 10 for both these crystals at $\tau _p$ = 36 ps. Therefore, the SRS regime is close to quasi-steady-state with the Raman amplification increment of g$\cdot \textrm{I}_p \cdot \textrm{L}_{eff}$, where I$_p$ is the pump intensity and L$_{eff}$ is the effective interaction length. We can write an equation:
where $(E_{th}L_{eff})_{GdVO_4}$ and $(E_{th}L_{eff})_{PbMoO_4}$ are the products of the threshold pump pulse energy $E_{th}$ and the effective interaction length $L_{eff}$ for the GdVO$_4$ and PbMoO$_4$ crystals, respectively. The effective interaction length can be calculated as where $L_R=\pi w_p^2 n_p/(\lambda_p M_{p}^2)$ is the Rayleigh length of the pump beam, $w_p$ is the pump beam waist radius, $n_p$ is the refractive index, $\lambda_p$ is the pump wavelength, $M_p^2$ is the pump beam quality factor [10]. The measurement results from [22] and from this work are presented in Table 1. As a result, using formula (4) for PbMoO$_4$ we obtain = 5$\pm$0.3 cm/GW for input polarization $\textbf{E} \perp$ c. This value is close to the result above estimated from the data [15] and it is lower than the results presented in [12,20].
Table 1. Measurement results of SRS oscillation threshold for GdVO$_4$ [22] and for PbMoO$_4$ [this work].
Figure 5 shows the output pulse energy, peak power, and pulse duration in dependence on the cavity length detuning. The first Stokes SRS oscillation was observed for the cavity length detuning range from –270 to +60 $\mu$m (zero detuning corresponds to the maximal output energy), but the detuning with at least half of output energy maximum was achieved only between –100 and +30 $\mu$m. The detuning full width at half-maximum amounting 130 $\mu$m characterizes an acceptable temporal delay of $\Delta$t$_{max}$ = 0.9 ps between a pair of the radiation components interacting by SRS at the pump pulse duration of 36 ps. The SRS pulse duration monotonously decreased with the cavity length detuning, the shortest pulse with the duration of 22.5 ps was measured at the detuning of +50 $\mu$m. The maximum output peak power of 5 kW was observed at the maximum output pulse energy (160 nJ) because pulse shortening of the SRS radiation was weak using the OC1.
Fig. 5. Output energy E$_p$, peak power P$_p$, and pulse duration $\tau _p$ in dependence on cavity length detuning $\Delta$L in the synchronously pumped PbMoO$_4$ Raman laser with the two-crystal active element and with the OC1 at the pump pulse energy of 330 nJ for excitation geometry E $\perp$ c.
5. Generation of combined Stokes component at 1217 nm
The output radiation spectrum of the PbMoO$_4$ Raman laser with the OC2 is shown in Fig. 3 (green line) and it was the same for both the excitation light polarizations. It can be seen that, an additional Stokes SRS component at 1217 nm with the combined ($\nu _1$ + $\nu _2$) Raman shift oscillated due to secondary intracavity short-shifted SRS conversion from the 1171-nm long-shifted first Stokes SRS component. Because the cavity with the OC2 was high-Q at 1171 nm, the second long-shifted (2$\nu _1$) Stokes component at 1304 nm also oscillated, but with very low efficiency.
Figure 6 presents the output energy characteristics of the synchronously pumped PbMoO$_4$ Raman laser with the combined ($\nu _1$ + $\nu _2$) frequency shift in dependence on the input pump pulse energy at both excitation light polarizations (E $\perp$ c and E $\parallel$ c). The laser was based on the two-crystal active element and the OC2.
Fig. 6. Dependences of the output SRS pulse energy and average power on the input pump pulse energy in the synchronously pumped PbMoO$_4$ Raman laser with the two-crystal active element with the OC2 for excitation light polarizations E $\perp$ c and E $\parallel$ c.
In spite of higher intensity of the bending ($\nu _2$) Raman mode at E $\parallel$ c than at E $\perp$ c (Fig. 1), SRS oscillation threshold of the secondary 1217-nm $\nu _2$-shifted Stokes component was lower (88 nJ against 111 nJ) at E $\perp$ c than at E $\parallel$ c (Fig. 6). It can be explained as follows. At E $\perp$ c the stretching $\nu _2$ Raman mode is more intense than at E $\parallel$ c (Fig. 1), therefore SRS oscillation of the first 1171-nm $\nu _1$-shifted Stokes component had higher efficiency being the pump wave for the secondary 1217-nm SRS oscillation, which became more efficient too. We can also see from Fig. 6 that the difference in slope efficiencies for E $\perp$ c and E $\parallel$ c (27.5 % against 21.8 %) was not as large as in the previous case (Fig. 4). It is because of relatively high intensity of the bending ($\nu _2$) Raman mode at E $\parallel$ c (Fig. 1). We obtained the highest output pulse energy of 67 nJ (overall conversion efficiency of 20 %) in the secondary Stokes component with the combined ($\nu _1$ + $\nu _2$) shift as compared to the synchronously pumped second-Stokes Raman lasers not only with the combined long-short shift [7–11], but also with the double long shift [24–26]. The average output power at 1217 nm reached 0.25 W.
An interesting property of the oscillating ($\nu _1$ + $\nu _2$)-shifted Stokes component at 1217 nm is significantly shorter pulse duration of 7 ps (in the case of perfect synchronization of pumping) in comparison with the pump (36 ps) and the first Stokes (33 ps) pulses. As a result, the peak power of the output SRS radiation is increased to a level that is even higher than the input pump pulse peak power. Earlier, a similar result has been achieved for the BaWO$_4$ crystal [8]. On the other hand, the second 2$\nu _1$-shifted Stokes component didn’t have this property [7,25]. As defined in [25], in the synchronously pumped Raman laser with single cavity the second 2$\nu _1$-shifted Stokes generation mechanism is due to parametric Raman interaction. Therefore, the pulse duration of the parametrically generated second (2$\nu _1$) Stokes is equal to duration of the temporal region of overlap of the pump and the first Stokes pulses [27] which is close to these pulses’ duration because of synchronization of pumping. The ordinary mechanism of cascade secondary SRS oscillation is inefficient here because of a long temporal delay after the transit through the active crystal between the long-shifted second Stokes pulse and the first Stokes pulse due to dispersion of the active crystal. For PbMoO$_4$ from formula (1) we have n$_o$(1171nm) = 2.2955, n$_o$(1217nm) = 2.2929, and n$_o$(1304nm) = 2.2885; therefore, the temporal delay between the 1171-nm and 1304-nm waves after transit through the 50-mm long PbMoO$_4$ crystal is $\Delta$t = 1.16 ps that is longer than the acceptable temporal delay of $\Delta$t$_{max}$ = 0.9 ps defined above. In the case of SRS with the combined shift (at the wavelength of 1217 nm), the parametric Raman mechanism cannot be maintained because of difference of Raman shifts ($\nu _1$ and $\nu _2$), but the temporal delay between the 1171-nm and 1217-nm waves (again for the 50-mm PbMoO$_4$ crystal) is only $\Delta$t = 0.44 ps that is shorter than the acceptable temporal delay ($\Delta$t$_{max}$ = 0.9 ps), and therefore the mechanism of cascade SRS with the combined shift took place. Thus, strong pulse shortening of the 1217-nm ($\nu _1$ + $\nu _2$)-shifted Stokes radiation is caused by the mechanism of ultrashort light pulse formation by intracavity SRS generation with the pulse duration close to the Raman mode inverse linewidth that was predicted in [28].
Figure 7 shows dependences of output energy, peak power, and pulse duration on the cavity length detuning in the synchronously pumped 50mm-long PbMoO$_4$ Raman laser with the OC2 at E $\perp$ c.
Fig. 7. Output energy E$_p$, peak power P$_p$, and pulse duration $\tau _p$ in dependence on cavity length detuning $\Delta$L in the synchronously pumped PbMoO$_4$ Raman laser with the two-crystal active element and with the OC2 at the pump pulse energy of 330 nJ for excitation geometry E $\perp$ c.
It can be seen that, the ($\nu _1$ + $\nu _2$)-shifted Stokes pulses at 1217 nm had strong self-shortening in the whole range of cavity length detuning and didn’t exceed 8 ps at negative and zero detuning of the cavity length. As in the previous case, the SRS pulse duration monotonously decreased with the cavity length detuning, but this decrease is significantly stronger at the positive detuning: from 7 ps for the zero detuning down to 1.42 ps for the maximum detuning of +50 $\mu$m. The maximum peak power of SRS radiation was obtained at the detuning of +10 $\mu$m and amounted 10.8 kW (65 nJ in 6 ps). It is higher than the input pump peak power of 9.2 kW (330 nJ in 36 ps) due to strong pulse shortening, and it is the highest output peak power among the known synchronously pumped Raman lasers. Increasing the detuning up to +50 $\mu$m led to strong decreasing of the SRS pulse energy by 17 times down to 4 nJ, but the output peak power decreased only by 3.9 times down to 2.8 kW due to the shortest SRS pulse (1.42 ps). We checked the shortest pulse duration (at +50 $\mu$m) for all cases of different crystal lengths (50 and 25 mm) and excitation geometries (E $\perp$ c and E $\parallel$ c). We have measured values of 1.42 and 1.49 ps for the 50-mm crystal (overall length) at E $\perp$ c and E $\parallel$ c, respectively; 1.33 and 1.41 ps for the 25-mm crystal at E $\perp$ c and E $\parallel$ c, respectively. For the long crystal, the shortest pulse duration is slightly longer that can be explained by the group velocity dispersion effect. But all the measured data are very close to the dephasing time of the bending ($\nu _2$) Raman mode in PbMoO$_4$ amounting 1/($\pi$c$\Delta \nu _2$)= 1.4 ps.
6. Conclusion
In conclusion, for the first time to our knowledge, we have demonstrated a synchronously pumped all-solid-state Raman laser based on a PbMoO$_4$ crystal. The laser operated at both stretching (a long Raman shift of $\nu _1$ = 870 cm$^{-1}$) and bending (a short Raman shift of $\nu _2$ = 318 cm$^{-1}$) anionic group symmetric vibrations in the PbMoO$_4$ crystal under extracavity pumping at 1063 nm by the 330 nJ, 36 ps, quasi-continuously mode-locked Nd:GdVO$_4$ laser. In contrast to other tetragonal Raman crystals, the PbMoO$_4$ crystal has intense Raman modes at both the E $\perp$ c and E $\parallel$ c excitation geometries where the stretching Raman mode is more intense at E $\perp$ c than the bending Raman mode at E $\parallel$ c. In the present work, we have found that for PbMoO$_4$ the E $\perp$ c excitation geometry is better than E $\parallel$ c for synchronously pumped SRS not only on the single stretching ($\nu _1$) Raman mode, but also with the combined ($\nu _1$ + $\nu _2$) frequency shift on the stretching and bending mode. Using different output couplers, the Raman laser efficiently generated either at the 870 cm$^{-1}$-shifted first Stokes wavelength of 1171 nm (slope efficiency up to 65.3 %, output pulse energy up to 160 nJ, and peak power up to 5 kW), or at the 870 cm$^{-1}$ + 318 cm$^{-1}$-shifted Stokes wavelength of 1217 nm (slope efficiency up to 27.5 %, output pulse energy up to 67 nJ, and peak power up to 10.8 kW). The obtained output pulse energy and peak power are the highest among other synchronously pumped Raman lasers both on the single and cascade Raman shifts. Significantly higher peak power of 10.8 kW at 1217 nm (even higher than the input pump peak power of 9.2 kW) is caused by strong pulse shortening of the secondary Stokes component with the combined ($\nu _1$ + $\nu _2$) Raman shift due to cascade SRS under high-intensity intracavity pumping by the 1171-nm first Stokes radiation. As for other tetragonal Raman crystals, in PbMoO$_4$ the strongest pulse shortening of the ($\nu _1$ + $\nu _2$)-shifted Stokes component was observed at the positive cavity length detuning. The shortest pulse duration was 1.4 ps at 1217 nm for the detuning of +50 $\mu$m that is equal to the bending Raman mode dephasing time.
Funding
European Regional Development Fund (CZ.02.1.01/0.0/0.0/16_019/0000778); Russian Foundation for Basic Research (19-02-00723).
Disclosures
The authors declare no conflict of interest.
References
1. C. Stringani, L. Abdeladim, G. Malkinson, P. Mahou, X. Solinas, I. Lamarre, S. Brizion, J.-B. Galey, W. Supatto, R. Legouis, A.-M. Pena, and E. Beaurepaire, “Multicolor two-photon imaging of endogenous fluorophores in living tissues by wavelength mixing,” Sci. Rep. 7(1), 3792 (2017). [CrossRef]
2. E. P. Perillo, J. W. Jarrett, Y.-L. Liu, A. Hassan, D. C. Fernée, J. R. Goldak, A. Bonteanu, D. J. Spence, H.-C. Yeh, and A. K. Dunn, “Two-color multiphoton in vivo imaging with a femtosecond diamond Raman laser,” Light: Sci. Appl. 6(11), e17095 (2017). [CrossRef]
3. J. Trägårdh, M. Murtagh, G. Robb, M. Parsons, J. Lin, D. J. Spence, and G. McConnell, “Two-color, two-photon imaging at long excitation wavelengths using a diamond Raman laser,” Microsc. Microanal. 22(4), 803–807 (2016). [CrossRef]
4. A. A. Khalil, J.-P. Bérubé, S. Danto, J.-C. Desmoulin, T. Cardinal, Y. Petit, R. Vallée, and L. Canioni, “Direct laser writing of a new type of waveguides in silver containing glasses,” Sci. Rep. 7(1), 11124 (2017). [CrossRef]
5. I. Alexeev, K. Cvecek, J. Genser, and M. Schmidt, “Direct waveguide writing with high energy high repetition rate picosecond laser pulses,” Phys. Procedia 39, 621–627 (2012). [CrossRef]
6. M. Frank, S. N. Smetanin, M. Jelínek, D. Vyhlídal, V. E. Shukshin, P. G. Zverev, and V. Kubeček, “860 fs GdVO4 Raman laser at 1228 nm pumped by 36 ps, 1063 nm laser,” Laser Phys. Lett. 16(8), 085401 (2019). [CrossRef]
7. M. Frank, M. Jelínek, D. Vyhlídal, V. Kubeček, L. I. Ivleva, P. G. Zverev, and S. N. Smetanin, “Multi-wavelength picosecond BaWO4 Raman laser with long and short Raman shifts and 12-fold pulse shortening down to 3 ps at 1227 nm,” Laser Phys. 28(2), 025403 (2018). [CrossRef]
8. M. Frank, S. N. Smetanin, M. Jelínek, D. Vyhlídal, L. I. Ivleva, P. G. Zverev, and V. Kubeček, “Highly efficient picosecond all-solid-state Raman laser at 1179 and 1227 nm on single and combined Raman lines in a BaWO4 crystal,” Opt. Lett. 43(11), 2527–2530 (2018). [CrossRef]
9. M. Frank, S. N. Smetanin, M. Jelínek, D. Vyhlídal, A. A. Kopalkin, V. E. Shukshin, L. I. Ivleva, P. G. Zverev, and V. Kubeček, “Synchronously-pumped all-solid-state SrMoO4 Raman laser generating at combined vibrational Raman modes with 26-fold pulse shortening down to 1.4 ps at 1220 nm,” Opt. Laser Technol. 111, 129–133 (2019). [CrossRef]
10. M. Frank, S. N. Smetanin, M. Jelínek, D. Vyhlídal, V. E. Shukshin, L. I. Ivleva, P. G. Zverev, and V. Kubeček, “Efficient synchronously-pumped all-solid-state Raman laser at 1178 and 1227 nm on stretching and bending anionic group vibrations in a SrWO4 crystal with pulse shortening down to 1.4 ps,” Opt. Laser Technol. 119, 105660 (2019). [CrossRef]
11. M. Frank, S. N. Smetanin, M. Jelínek, D. Vyhlídal, V. E. Shukshin, L. I. Ivleva, E. E. Dunaeva, I. S. Voronina, P. G. Zverev, and V. Kubeček, “Stimulated Raman scattering in alkali-earth tungstate and molybdate crystals at both stretching and bending Raman modes under synchronous picosecond pumping with multiple pulse shortening down to 1 ps,” Crystals 9(3), 167 (2019). [CrossRef]
12. T. T. Basiev, P. G. Zverev, A. Y. Karasik, V. V. Osiko, A. A. Sobol’, and D. S. Chunaev, “Picosecond stimulated Raman scattering in crystals,” J. Exp. Theor. Phys. 99(5), 934–941 (2004). [CrossRef]
13. A. A. Kaminskii, S. N. Bagayev, K. Ueda, H. J. Eichler, J. Garcia-Sole, D. Jaque, J. J. Romero, J. Fernandez, R. Balda, A. V. Butashin, and F. Agullo-Rueda, “Multiple Stokes and anti-Stokes picosecond generation, cw laser action at wavelengths of two stimulated-emission channels 4F3/2 → 4I11/2 and 4F3/2 → 4F13/2, and nanosecond self-SRS lasing in undoped and Nd3+-doped tetragonal PbMoO4 crystals,” Laser Phys. 11, 1142–1146 (2011).
14. T. T. Basiev, S. V. Vassiliev, M. E. Doroshenko, and V. V. Osiko, “Laser and self-Raman-laser oscillations of PbMoO4:Nd3+ crystal under laser diode pumping,” Opt. Lett. 31(1), 65–67 (2006). [CrossRef]
15. T. T. Basiev, M. E. Doroshenko, S. N. Smetanin, M. Jelínek, V. Kubeček, H. Jelínková, A. N. Shekhovtsov, and M. B. Kosmyna, “Multi-wave SRS oscillation in PbMoO4 and PbMo0.5W0.5O4 crystals under 18 picosecond laser pumping,” Laser Phys. Lett. 9(12), 853–857 (2012). [CrossRef]
16. Eksma, “Crystals for stimulated Raman scattering,” [retrieved 3 November 2020], https://eksmaoptics.com/nonlinear-and-laser-crystals/crystals-for-stimulated-raman-scattering/.
17. R. K. Khanna, W. S. Brower, B. R. Guscott, and E. R. Lippincott, “Laser induced Raman spectra of some tungstates and molybdates,” J. Res. Nat. Boreou of Stand. 72A(1), 81–84 (1968). [CrossRef]
18. T. T. Basiev, A. A. Sobol, Y. K. Voronko, and P. G. Zverev, “Spontaneous Raman spectroscopy of tungstate and molybdate crystals for Raman lasers,” Opt. Mater. 15(3), 205–216 (2000). [CrossRef]
19. G. M. Loiacono, J. F. Balascio, R. Bonner, and A. Savage, “Crystal growth and characterization of lead molybdate,” J. Cryst. Growth 21(1), 1–11 (1974). [CrossRef]
20. J. A. Piper and H. M. Pask, “Crystalline Raman lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 692–704 (2007). [CrossRef]
21. S. N. Smetanin, “Determination of the stimulated Raman scattering threshold for a pump pulse of arbitrary width,” Opt. Spectrosc. 121(3), 395–404 (2016). [CrossRef]
22. M. Frank, S. N. Smetanin, M. Jelínek, D. Vyhlídal, V. E. Shukshin, P. G. Zverev, and V. Kubeček, “Laser output radiation characteristics controlled by the GdVO4 crystal length in the extracavity synchronously pumped Raman laser with combined Raman shift resulting in generation of 860 fs pulses at 1228 nm,” OSA Laser Congress 2019 (ASSL, LAC, LS&C), Vienna, Austria, 28 September – 03 October 2019: OSA Technical Digest. Optical Society of America, 2019. – Paper JTh3A.32.
23. A. A. Kaminskii, K. I. Ueda, H. J. Eichler, Y. Kuwano, H. Kouta, S. N. Bagaev, T. H. Chyba, J. C. Barnes, G. M. A. Gad, T. Murai, and J. Lu, “Tetragonal vanadates YVO4 and GdVO4 – new efficient χ(3)-materials for Raman lasers,” Opt. Commun. 194(1-3), 201–206 (2001). [CrossRef]
24. E. Granados, H. M. Pask, E. Esposito, G. McConnel, and D. J. Spence, “Multi-wavelength, all-solid-state, continuous wave mode locked picosecond Raman laser,” Opt. Express 18(5), 5289–5294 (2010). [CrossRef]
25. A. M. Warrier, J. Lin, H. M. Pask, R. P. Mildren, D. W. Coutts, and D. J. Spence, “Highly efficient picosecond diamond Raman laser at 1240 and 1485 nm,” Opt. Express 22(3), 3325–3333 (2014). [CrossRef]
26. M. Murtagh, J. Lin, J. Trägårdh, G. McConnell, and D. J. Spence, “Ultrafast second-stokes diamond Raman laser,” Opt. Express 24(8), 8149–8155 (2016). [CrossRef]
27. S. N. Smetanin, M. Jelínek, V. Kubeček, H. Jelínková, and L. I. Ivleva, “Parametric second Stokes Raman laser output pulse shortening to 300 ps due to depletion of pumping of intracavity Raman conversion,” Appl. Phys. B 122(10), 260 (2016). [CrossRef]
28. S. K. Isaev, L. S. Kornienko, N. V. Kravtsov, and V. N. Serkin, “Formation of ultrashort light pulses in a laser with a bleachable filter by intracavity generation of Raman emission,” Sov. J. Quantum Electron. 11(3), 365–370 (1981). [CrossRef]
