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We report increased wavelength options from Raman lasers for Raman media having two Raman modes of similar gain coefficient. For an external-cavity potassium gadolinium tungstate Raman laser pumped at 532nm, we show that two sets of Stokes orders are generated simultaneously by appropriate orientation of the Raman crystal, and also wavelengths that correspond to sums of the two Raman modes. Up to 14 visible Stokes lines were observed in the wavelength range 555-675nm. The increase in Stokes wavelengths also enables a much greater selection of wavelengths to be accessed via intracavity nonlinear sum frequency and difference frequency mixing. For example, we demonstrate 30 output wavelength options for a wavelength-selectable 271-321nm Raman laser with intracavity sum frequency mixing in BBO. We also present a theoretical analysis that enables prediction of wavelength options for dual Raman mode systems.
©2008 Optical Society of America
1. Introduction
Nonlinear methods for shifting the output wavelength of lasers are needed in a host of industrial and scientific laser applications that require more wavelength specificity than that provided by existing laser sources and their harmonics[1]. Methods based on stimulated Raman scattering have a number of intrinsic advantages including the absence of phase matching constraints, efficient conversion (>80% [2,3]) and improved output beam quality via “Raman beam cleanup”[4]. For a variety of resonator configurations, Raman lasers have been developed in the infrared[5-7], visible[8-11] and ultraviolet[12]. However, a common drawback of Raman shifting is the narrow choice of output lines, which is constrained to wavelengths spaced by the Raman Stokes shift.
An opportunity to increase the choice of output wavelengths arises for Raman materials having multiple Raman active transitions, notably the double metal tungstates, which include potassium gadolinium tungstate (KGW), potassium yttrium tungstate (KYW) and potassium lutetium tungstate (KLW). Their Raman spectra each have two strong Raman modes near 750cm-1 and 900cm-1, which are attributed to 2 stretching modes of the W-O-O-W bridge bond joining WO6 octohedra [13]. As shown in Fig. 1 for propagation along the b-axis in KGW, the two main Raman modes of energy 768 cm-1 and 901 cm-1 have peak gains for crystal orientations approximately orthogonal to each other so that a straightforward rotation of the crystal about the axis of propagation brings about a change in the dominant Raman mode. The relative gain of each mode can be varied, for example by rotating the crystal about b-axis. Findeisen et al reported simultaneous generation of the first Stokes lines of each Raman mode (1159nm and 1177nm) for a KGW Raman laser pumped along the b-axis with 1064nm fundamental polarization set at 45 from the a-axis[14]. Measurements of output spectra for a 532nm-pumped KGW Raman laser [9] exhibited simultaneous generation of first Stokes for the two KGW Raman modes (555nm and 559nm) as well as generation of Stokes lines corresponding to the sum of the two Raman modes (583nm, 612nm and 641nm). However, to our knowledge Raman conversion in materials with more than one principal Raman mode has not been investigated in detail.
Fig. 1. Spontaneous Raman spectra for KGW for pump propagation along the Np axis and polarization aligned parallel and perpendicular to the crystal a-axis. Two strong Raman modes are observed at energies hµ1=768cm-1 and hµ2=901cm-1 (h; Planck’s constant). It should be noted for propagation along the b-axis that peak Raman gain for each mode occurs for the pump aligned with the crystallo-optic axes (Nm, Ng) which are offset by approximately 20 degrees from the crystal axes (a, c)[15].
In this paper we present a study of the wavelength options available for Raman materials that provide simultaneous excitation of two Raman modes. First, the additional Raman lines brought about by the second Raman mode are determined theoretically and the result compared with the performance of a KGW Raman laser externally pumped by a pulsed 532nm laser. For some KGW crystal orientations, up to 10 Stokes lines can be observed simultaneously in the range 555-675nm, whereas only 4 lines are present in the case of a single Raman mode. We also show that that the wavelength options increase many-fold when using intracavity nonlinear mixing. For the KGW Raman laser with intracavity sum-frequency generation (SFG) in BBO, the number of wavelengths in the range 270-321nm increases from 8 for a single Raman mode to up to 23 when two modes are active. Finally, we discuss how multiple Raman mode materials can be used to generate a diverse range of mid and far infrared (IR) output via difference frequency generation (DFG).
2. Stokes generation with two Raman modes
2.1 Calculated spectrum
For a single Raman mode of frequency µ1, the output Stokes spectrum is given by νi=νf-iµ1 where i is a non-negative integer and νf is the fundamental (ie., pump) frequency. The cascade of energy to higher Stokes orders is governed by coupled equations involving the pump intensity, Raman gain coefficient, and frequency dependent loss terms (see for example ref [16]) that apply to a variety of configurations including single or double pass Raman generators, Raman lasers pumped by an external pump laser (external cavity Raman lasers) and Raman lasers which share or are coupled to the resonator of the pump laser (intracavity Raman lasers, coupled-cavity Raman lasers), as reviewed in references [17-20]. For Raman lasers, the maximum Stokes order n m is determined by the characteristics of the optical resonator such as the bandwidth of mirror and AR coatings as well as the Raman gain.
Considering a material with 2 Raman modes µ1 and µ2 which act independently on any pump or Stokes fields, the possible Stokes output wavelengths combinations become νij=νf-iµ1-jµ2 where i and j are positive integers. The resulting spectra for the single and dual Raman modes are shown in Fig. 2 for the examples of n m≤4 where nm is the maximum number of Raman modes generated in the medium for a single pump photon. Note nm here corresponds to the maximum number of Stokes shifts for both Raman modes. The spectrum may include the two separate Stokes spectra (νi0 and νoj) and mixtures of the two Raman modes (νij where i and j are nonzero) as reported in ref [9] and verified below in the present study. The maximum number of Stokes wavelengths that can be generated as a function of n m is thus For example for nm=2, the 5 Stokes lines ν10, ν01, ν11, ν20 and ν02 are generated. For nm up to 5, which is typically the highest order of Raman excitation observed in our experiments, the ns values are listed in Table 1. The theory may be further generalized to consider three Raman modes if needed.
Table 1. The calculated number of Stokes lines and harmonic wavelength options as a function of nm.
2.2 Experimental details
The experiments were performed for an external-cavity KGd(WO4)2 Raman laser with intracavity nonlinear mixing crystal BBO as previously described in ref 12, but with the KGW crystal placed in a mount which provided rotation about the laser propagation axis (refer Fig. 3). The 5×5×50mm long KGW crystal was cut for propagation along the b-axis with the minor facets cut parallel and perpendicular to the c-axis. The arrangement enabled the relative gain of the two Raman modes to be varied without realigning the resonator. Following Mochalov[15], maximum gain for the 901cm-1 Raman mode is obtained for pump polarization aligned with the Nm crystallo-optic axis, which is offset approximately 24 degrees from the a-axis, and maximum Raman gain for the 768cm-1 mode is obtained for the pump polarization aligned with the Ng crystallo-optic axis which is offset by 20 degrees from the c-axis. The BBO crystal is cut for Type I phase matching for second harmonic generation near 300nm (theta=40°) and is mounted to enable angle tuning in the range 260-330nm. The input mirror M1 is highly reflecting at the Stokes wavelengths (555-650nm) and highly transmitting at the pump wavelength (532nm), and the end mirror M2 is highly reflecting at the pump and Stokes wavelengths (530-650nm). The output coupler M3 is highly transmitting at the Stokes wavelengths (530-700nm) and highly reflecting in the range 270-320nm. The curvatures of the end mirror (2m radius) and input coupler (1m radius) are selected to obtain good spatial overlap between the Raman mode and the 200µm-diameter pump mode in the KGW crystal.
The Raman laser is pumped with the TEM00 532nm output from a frequency-doubled electro-optic Q-switched Nd:YAG laser pulsed at 10Hz and generating pulses of duration 10ns full-width half-maximum. Raman laser output spectra are measured using a 200-900nm fiber spectrometer (USB2000, Ocean Optics). Output pulse energies were measured by separating the UV beam from the visible leakage from the resonator using a Pellin-Boca prism in combination with a laser energy joulemeter (Gentec ED100).
2.3 Results - Stokes generation
The visible output spectrum for the Raman laser with the BBO crystal angle detuned from all phase-matching (to ensure negligible conversion to the ultraviolet) is shown in Fig. 4 for nominal pump energies of ~2mJ. The initial orientation of the KGW crystal is designated ϕ=0° and corresponds to the pump polarization parallel to the crystal c-axis. As the KGW crystal rotation angle is increased, we observe a continuous evolution of Raman spectra between a pure single-Raman mode spectrum (νf-iµ2 where i≤4) for when the pump polarization is aligned to Nm (ϕ~115°) and intermediate states that include more complex Raman spectra involving both modes. Two types of pattern are observed in the dual mode spectra.
Fig. 4. Visible output spectra of the Raman laser as a function of the rotation angle ϕ about the propagation axis. The lower plot corresponds to the rotation angle ϕ=0 deg and the pump electric field vector aligned to the c -axis as shown in the inset. Plots sequentially offset in the vertical direction correspond to 10-degree increments in ϕ.
For ϕ=0-40°, which corresponds to angles yielding near maximum gain at µ1, we observe the νf - iµ1 spectrum, the first Stokes of the µ2 Raman mode and the first Stokes shifted by up to 4 orders by the µ1 Raman mode. The Raman spectrum appears as a pair of wavelengths spaced in frequency by µ2 - µ1 (ie., at 555 and 559nm) and repeated up to 4 times at longer wavelengths up to 670nm by higher order Stokes shifting at µ1. Ten Stokes lines are observed having wavelengths as listed in Table 2 and identified as νf - (i - 1)µ1 - jµ2 where j≤1 and i+j≤5. The simultaneous appearance of the µ1 and µ2 modes are consistent with the similar gains deduced from the spontaneous Raman spectrum for E perp a (ie., ϕ~0) in Fig. 1, though the Raman gain coefficient for µ1 is slightly higher than µ2 since only 1 µ2 mode was excited per pump photon, compared to up to 5 for µ1.
Table 2. Visible Stokes orders observed for three KGW rotation angles.
For ϕ=50-70° (or 140-150°), we observe Raman lines that include many of those seen for ϕ=0-40° as well as Stokes lines corresponding to the excitation second and third order excitation of the µ2 Raman mode (refer also Fig. 4 and Table 2). It is noted, however, these additional lines are at the expense of the higher-order lines at wavelengths >640nm. Ten wavelengths are observed having wavelengths that correspond to νf - (i - 1)µ1 - jµ2 where j≤3 and i + j≤4. We deduce that for these ϕ values there is approximately equal gain for the µ1 and µ2 Raman modes.
In total, up to 14 wavelengths were observed in the range 555-675nm with n m values up to 5. Of the 20 predicted lines, the 6 not observed correspond to very high order Stokes lines of wavelength longer than 645nm (where resonator losses become significant) and in particular those that involve a combination of the two Raman modes. All the above Stokes wavelengths are linearly polarized with orientation parallel to the pump laser.
As the resonator is not optimized for efficiency, the conversion efficiency from the pump laser is less than a few percent. The output coupling at the output visible wavelengths is <2%, which is lower than the combined losses at other resonator interfaces including in particular the facets of the BBO crystal. Optimization of visible output can be achieved by tailoring the output coupler spectrum as discussed in further detail in Sec. 4 Discussion).
3. Dual-mode Raman lasers with intracavity sum frequency mixing
3.1 Background and calculated spectra
The cascade to higher order Stokes wavelengths inside a Raman resonator is rapid and good temporal overlap is obtained between the intracavity fields within a 10ns pump pulse. This enables conversion to other wavelength regions via second-harmonic, sum and difference frequency generation. Ammann[21] first reported a Raman laser with intracavity sum frequency mixing in an arclamp pumped Nd:YALO laser which included an intracavity lithium iodate crystal which simultaneously acted as a Raman and nonlinear harmonic generation. Ammann showed that by changing the angle of the lithium iodate crystal up to 5 visible wavelengths were generated spanning the range 540nm to 655nm. Recently, systems that use separate Raman and nonlinear crystals, along with the increased availability of high quality Raman materials and diode pumped solid-state lasers, has seen wavelength switchable lasers in the visible[22] and in the ultraviolet (270-320nm)[12]. In all of these systems, wavelength selectability arises from the cascading of energy from the fundamental into higher Stokes orders and the nonlinear output coupling at the selected harmonic combination by appropriate configuration of the phase-matching conditions in the nonlinear harmonic mixing crystal (eg., by temperature or angle tuning). Ideally, the resonator is designed to allow efficient cascading of the intracavity fields amongst Stokes orders, so that a number of possible output wavelength combinations are available according to the selected phase matching conditions in the nonlinear medium; additionally the nonlinear coupling to the output harmonic beam must be sufficiently large to prevent power loss to unwanted higher-order Stokes generation[22]. As far as the authors are aware, only sum frequency (SF) and second harmonic (SH) wavelengths have been demonstrated to date, however, the concept can be extended to generate long wavelengths via difference frequency (DF) generation.
For a single Raman mode, the possible SF and SH frequencies available are νi+νj and difference frequencies |νi-νj|. For n m Stokes orders, there are 2n m possible unique SF/SH wavelengths available (since each additional Stokes order provides an additional SH wavelength and a unique wavelength by SF generation with the next lowest order) and n m unique DF wavelengths.
For two Raman modes, the possible output frequencies are the various combinations of νij+νkl where i+j, k+l are less than or equal to nm. It can be readily shown that the number of unique wavelengths available as function of n m is For DF mixing, the number of unique wavelengths νij-νkl is As listed in Table 1, the number of SF/SH and DF wavelengths available increase more than 5-fold up to 45 and 28 respectively when using SF and DF mixing compared to that for a single Raman mode. Indeed, for DF dual Raman modes offer the biggest increase in wavelength options (~8 times for n m=5).
3.2 Results for sum frequency mixing in BBO
SF and SH outputs of the laser were determined as a function of the BBO rotation angle in the phase matching plane. We found that the available UV wavelengths depend on the KGW rotation angle as expected according to the visible Stokes subharmonics oscillating in the resonator listed in Table 2.
The UV wavelengths observed as the BBO crystal was rotated are listed in Table 3. For ϕ=20°, 22 ultraviolet (UV) laser lines were observed in the range 271 to 321nm. For ϕ=50°, a similar number of UV output lines are observed but with wavelengths consistent with the different set of Stokes subharmonics. Twenty lines were observed with UV output wavelengths involving second and third order excitation of the µ2 Raman mode. In comparison, 7 wavelengths are observed for a single Raman mode (ie., ϕ~110°). For some BBO angles, the Raman laser is able to also generate the very closely spaced lines (eg, 292.0 nm and 293.1nm) simultaneously. Analysis of the phase-matching requirements suggests the dual lines result from the spread of ray angles passing through the BBO which overlaps the phase-match angles of two neighboring UV lines. In total, up to 31 wavelengths in the range 271 – 321nm can be selected by appropriate orientation of the BBO and KGW Raman crystal. The numerous wavelength choices across the 50nm tuning band is of interest for a diverse range of applications including biosensing, defence, environmental sensing and in medicine.
Table 3. Output wavelengths for the KGW Raman laser with intracavity SF mixing.
The last column of Table 3 provides an indication of the relative efficiency of lines for ϕ=160°. The values are rankings (from 1-10) of the efficiency of each output line as determined from relative efficiencies and thresholds. As a general rule, the second-harmonics have the lowest threshold and are the most efficient. Also, the stronger lines tend to consist of only 1 Raman mode (ie., no Raman mode mixing) or at most correspond to excitation of one quantum of the secondary Raman mode. The output on each line is influenced by the Stokes cascading dynamics of the subharmonics as well as the temporal overlap in the Raman crystal, and these vary notably for some harmonics. As shown in Fig. 5 for example, the 283.4nm line (ν10+ν20) rises above threshold at 0.4mJ and increases rapidly for pump energies up to 1.5mJ, above which the output saturates. Saturation is attributed to a decrease in the Stokes subharmonics due to the cascading of energy to higher Stokes orders. In contrast the 284.5nm line (ν01+ν20), which contains subharmonics corresponding to different Raman modes, the threshold is more than twice as high (1.0 mJ) and output increases much more linearly up to the maximum pump energy of 3mJ. The higher threshold and the offset of saturation to higher input energies are attributed to a slightly weaker gain on the µ2 Raman mode.
The conversion efficiency from the input pump energy for each Raman line is typically about 0.5%. The efficiencies are limited by energy loss to Stokes orders not used in generating the output beam ie., Stokes lines of higher order than the output subharmonics and, if the output beam involves only one Raman mode (eg., µ1), Stokes lines involving the unwanted (µ2) Raman mode. As noted in ref [12], efficiency is likely to be substantially improved by increasing the nonlinear coupling for SF/SH mixing. Also, tailoring the resonator to have high loss at the wavelengths of the higher Stokes orders could increase the efficiency of specific wavelengths (but at the sacrifice of wavelength choice).
4. Discussion
The results show that simultaneous Stokes laser action on the two main Raman modes can be achieved for a large range of KGW rotation angles. This suggests that the interaction between the Raman modes is small in this case, and in particular, that gain competition brought about by depletion of the pump beam does not act strongly enough to suppress excitation of the second mode. The conversion efficiencies to the Stokes output beam are low in the present case, as the output coupling in the visible well below optimum. Conversion efficiency dependence on output coupling in external cavity solid-state Raman lasers has been widely discussed (eg., [3,8,9]) and modeled by Ding et al[23]. As a general rule, the optimum output coupling is 30-70% for Q-switched laser pumped systems, and the resonator should be designed to efficiently cascade energy to the selected Stokes order while suppressing higher orders. Conversion efficiencies to a selected Stokes wavelength may be as high as 60%[3]. The same principles apply in the present case, except with the addition that energy flow amongst multiple “branches” in the Stokes spectrum must be considered. For example, higher efficiencies are favored for the ν21 Stokes line for resonator losses of the higher order ν31 and ν22 lines large enough to ensure they do not reach threshold. Though additional constraints are placed on the output coupler design, efficiencies similar to that observed for single-Raman mode devices and that approach the quantum limit are likely to be possible.
Using intracavity SF/SH mixing, we have demonstrated UV Raman laser generation over an increased number of lines for relatively low pulse rate and output power (10Hz, ~100µW). The device should easily scale to higher average powers by increasing the pulse repetition rate. Pulse rates up to 5kHz and average powers up to 45mW have been previously demonstrated previously for a single Raman mode[12] without limitations from thermal effects. For the present device, UV average output powers higher than 10mW output are projected at most wavelengths using a high repetition rate pump laser and there is substantial scope to further increase power by using the above method for boosting converter efficiency in combination with more powerful pump sources.
Table 4. Difference frequency wavelengths available for a dual-Raman mode KGW laser with n m=2.
A corollary of the present work is a method for generating output in the mid-IR to terahertz range where there is presently strong demand in medical, remote sensing and defence applications. Previously, Raman lasers have been used to generate IR output via DFG[24,25], however, the output wavelengths are limited to integer multiples of the Raman shift. With a second Raman mode, the difference frequencies extend much lower and the number of options is greatly increased (refer Table 1). For example, the above KGW Raman laser operating with n m as small as 2 is capable of 9 unique DFG wavelengths spanning 5 - 75µm as listed in Table 4. In contrast, the single mode spectra consist of either 13.0µm (901cm-1) or 11.1µm (768cm-1) and their integer fractions. For higher n m values, the range and number of available wavelengths increases rapidly (refer also Table 1). The intrinsic Raman features of spatial beam-cleanup, narrowband output and freedom from phase-matching constraints are potential advantages over current methods involving either optical parametric oscillators [26] or DFG of multiple lasers (see for example [27]).
The concepts encompassed by the above examples apply to other Raman materials and pump sources, as well as a variety of resonator configurations, which can be tailored according to the wavelength and output pulse requirements. The slightly disparate Raman mode frequencies for KGW, KLW and KYW provide a method to bring about slight changes in the output spectrum that may be useful for targeting particular wavelengths. It is likely that other crystals may offer sufficient gain on two modes simultaneously, however, a more detailed survey of Raman material spectra as functions of crystal orientation is required. In addition to external cavity arrangement of the present example, the concepts are applicable to Raman laser variants such as intracavity Raman laser and coupled cavity arrangements [28].
5. Conclusion
A large increase in output wavelength options is obtained for Raman lasers operating simultaneously on two Raman modes. Calculations show that many-fold increases in the number of wavelengths are available via direct Stokes generation and via nonlinear mixing of the Stokes wavelengths. For an external-cavity potassium gadolinium tungstate Raman laser pumped at 532nm, we demonstrated up to 14 visible Stokes lines in the wavelength range 555-675nm and up to 30 wavelengths via sum frequency to the UV. Dual Raman mode lasers are thus promising for targeting a diverse range of wavelengths spanning the ultraviolet to the terahertz regions.
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