1 Introduction

Dual-wavelength lasers or lasers with simultaneous output at two different frequencies have been at a focus of several recent studies due to multiple promising applications in biomedicine such as blood analysis, DNA sequencing, flow cytometry, microscopy, and optogenetics [1,2,3,4,5,6,7]. With appropriate wavelength spacing of a dual-wavelength output it can be also converted to a coherent terahertz (THz) radiation through difference frequency generation (DFG) [8]. THz radiation falls into the very attractive spectral range with unique properties and promising potential for THz imaging, sensing, and THz spectroscopy applications [9,10,11].

There are multiple methods to achieve dual-wavelength operation, all of which are based on the balanced round-trip gains at the two wavelengths. Dual-wavelength generation in solid-state lasers can be separated into the three main categories. The first method to obtain dual-wavelength operation is to have two crystals with similar emission cross-sections to have comparable gain at different wavelengths. This method can also be extended to incorporate hybrid laser gain medium [12] or gain medium with multiple dopants [13]. The second method utilized the fact that in some uniaxial or biaxial crystals, the emission peaks for horizontal and vertical polarizations occur at different wavelengths [14]. Therefore, by choosing a proper direction of crystal cut, orthogonally-polarized laser operations can take place [15, 16]. These first two approaches in obtaining a dual-wavelength operation rely on a very strict balance of round-trip gains which is easily disturbed by the cavity conditions such as thermal lensing or fluctuation in the pump power. This can lead to poor control of power ratio between the two oscillating wavelengths. The last type of dual-wavelength generation is obtained by inserting an extra loss element inside the laser cavity. This is generally done using a specific coating of the output coupler (OC) to intentionally have high reflectivity at low gain wavelength of the laser crystal and low reflectivity at high gain wavelength [1, 17]. However, a specific coating of the OC also means that the dual-wavelength laser will again operate on a strict condition of roundtrip-gain equalization and will only work at a certain power level. To allow for more flexibility in the setup, wavelength tunable loss elements such as etalons [18], Fabry–Perot filters [19], or birefringent filters (BRF) [20] are better suited for dual-wavelength generation. The latter approach is a particularly simple one because of ease of use and manufacturing. For example, in case of broadband gain media (such as Ti:sapphire, Alexandrite and Yb:KGW) that are usually used to produce ultrashort pulses [21,22,23,24,25,26,27,28] for various applications [29,30,31,32,33,34,35], the BRF technique was recently successfully used to achieve dual-wavelength operation [36,37,38,39,40]. At the same time, the sharp transition lines of the Nd-ion-doped crystalline gain media [41] in combination with BRF can also be used for multiwavelength operation [42, 43].

Among the gain media for diode-pumped solid-state lasers, the crystals of Nd:vanadate (Nd:YVO4) stand out as suitable candidates for compact and efficient diode-pumped lasers in the medium power range (< 10W) applications since they provide many advantages such as high absorption and emission cross sections, strongly polarized emission, and reasonable thermal conductivity. Considering the observed emission lines at 1064, 1073, and 1085 nm [42], the possible dual-wavelength pairs that Nd:YVO4 can offer are 1064 & 1073, 1064 & 1085, and 1073 & 1085 nm all of which are spaced with a few THz frequency offset. Moreover, the 1073 nm emission line has not been reported in dual-wavelength operation from the Nd:YVO4 crystal even though its stimulated emission cross-section is comparable to the one at 1085 nm. This is possibly due to its proximity to the strongest 1064 nm emission line. In this work, we demonstrated the ability to achieve gain balancing for two of the mentioned wavelength pairs through the use of two intracavity BRF plates.

2 Principle of operation

In our case two quartz BRFs with in-plane optical axes, as seen in Fig. 1 (only one BRF is shown), were placed into the laser cavity at the Brewster’s angle (θB) and introduced tunable wavelength-dependent loss through rotation of the plates around their surface normals [20].

Fig. 1
figure 1

A drawing of the birefringent plate, angles, and the corresponding notations

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Regarding the dual-wavelength operation itself, in order for two wavelengths to ‘start’ oscillating at the same time, it is required that the threshold pump power Pth levels for both wavelengths, e.g. 1064 and 1073 nm, were the same [13, 44]. From the threshold pump power expression given in [45], the condition for the same threshold pump power for the two laser wavelengths becomes,

$$\frac{{{L_{1064}} - \ln \left( {1 - {T_{{\text{oc}}}}} \right)}}{{{\sigma _{1064}}{\eta _{1064}}}}=\frac{{{L_{1073}} - \ln \left( {1 - {T_{{\text{oc}}}}} \right)}}{{{\sigma _{1073}}{\eta _{1073}}}},$$
(1)

where L is the round trip intracavity loss, Toc is the transmission of the output coupler, σ is the emission cross-section at the laser wavelength, and η is the quantum efficiency. This condition is possible even with a single intracavity BRF plate as demonstrated in [42], where the transmission at 1064 nm at a certain angle of a BRF exactly equals the required transmission at which the two wavelengths experience the same Pth. However, the ‘first’ problem is that the angular tolerance of such a condition is very small (~ 0.1°), making it hard to perfectly achieve and control in practice, thus leading to unstable power ratio at the two wavelengths over a long period of time.

It is also worth noting that equal threshold condition described by Eq. (1) does not automatically translate into the equal output power ratio between the oscillating wavelengths above the threshold which is the ‘second’ problem. Unlike other methods of dual-wavelength generation, the benefit of using BRF plates is that they enable not only to select the correct threshold condition via changes in the L1064 and L1073 losses (i.e. BRF introduced losses) but also to reach 50% power ratio at all power levels which is generally much more complicated [19].

To illustrate the problem of gain balancing at power levels at and beyond Pth, we recall that the laser output power (Pout) is described by [46]

$${P_{{\text{out}}}}=\frac{{ - \ln (1 - {T_{{\text{oc}}}})}}{{ - \ln (1 - {T_{{\text{oc}}}})+{L_\lambda }}}\frac{{{v_L}}}{{{v_p}}}\left( {{P_{{\text{abs}}}} - {P_{{\text{th}},\lambda }}} \right),$$
(2)

where λ refers to the laser wavelength, v L is the laser frequency, v p is the pump frequency, and Pabs is the absorbed pump power. This equation also shows the expanded form of slope efficiency (ηs) of a given laser system (Pout = ηs (Pabs − Pth,λ)). With this in mind, let us consider a scenario when there is no intracavity BRF plate in the laser cavity. In such a case the intracavity losses are the same at both wavelengths (L1064 = L1073) whereas Eq. (1) dictates that Pth,1064 < Pth,1073 because of the difference between the emission cross-sections (σ1064 > σ1073). This laser operation is schematically drawn in Fig. 2a. As Pabs increases, the output power (Pout) at 1064 nm also increases with the slope efficiency (ηs,1064) described by the Eq. (2) with no dual-wavelength operation. The emission at 1073 nm will not be observed due to a higher threshold.

Fig. 2
figure 2

Simple illustrations of the change in output power versus the absorbed pump power of single- and dual-wavelength lasers for various conditions involving birefringent filter tuning

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In the next step (Fig. 2b), we introduced an additional intracavity loss from a single BRF plate which helps to fulfill the exact condition described by Eq. (1) (LBRF,1064 > LBRF,1073) and leads to Pabs = P′th,1064 = P′th,1073. This point is shown as the starting point (white circle) in Fig. 2b. Equation (2) shows, however, that the higher loss introduced at 1064 nm (high LBRF,1064 and, ultimately, high L1064) to achieve the same threshold pump power will result in the lower slope efficiency (η′s,1064) at this wavelength than at 1073 nm (η′s,1073). Therefore, above the threshold at Pabs > P′th,1064 = P′th,1073, the levels of Pout at the two wavelengths will start to diverge. As shown by the two lines in Fig. 2b, this means that the dual-wavelength operation with equal power ratio for the oscillating wavelengths can only be achieved at a certain level of Pabs. This describes the second problem mentioned earlier.

To solve both of these problems, an extra loss element can be used with lower angular sensitivity, which can be found in thin BRF plates featuring broad transmission linewidths [20]. The effect of having two BRFs with different thicknesses in the cavity is shown in Fig. 2c. The introduced extra loss from a thin BRF reduces the slopes and increases the thresholds for both wavelengths. Most importantly, with proper alignment of a thin BRF, it can shift the threshold of 1073 nm to a higher value of the absorbed pump power than that for 1064 nm. Therefore, by breaking the condition of equal thresholds and due to the different slopes of the two wavelengths, one can achieve equal power dual-wavelength oscillation well above the threshold. As a side effect, at each pump power level this regime would require a slightly different amount of the introduced intracavity loss which can be conveniently found by rotation of a thin BRF.

For example, let us consider the transmissions at 1064 and 1073 nm wavelengths with the 4-mm-thick intracavity BRF plate kept at a constant angle of rotation of 27.0° (ϕ4 mm = 27.0°) while the second, 0.5-mm-thick, BRF plate is rotated from ϕ0.5 mm = 0° to ϕ0.5 mm = 90°. The choice of the plate thicknesses was based on our previous discrete wavelength tuning work in Nd:YVO4 lasers [42, 43]. The transmission through both BRF plates is shown in Fig. 3 which was obtained from Jones matrix calculations [20]. At ϕ0.5 mm = 0° point, there is no loss introduced by the BRF plate at 1073 nm (LBRF,1073 = 0) while LBRF,1064 = 0.32. The required transmission at 1064 nm (blue dashed line) in Fig. 3 is the transmission level at 1064 nm that is required to fulfill the condition given by Eq. (1). The overlapped sections (in red circles) of the 1064 nm transmission and the required transmission at 1064 nm represent Pth,1073 ≈ Pth,1064 condition and will have the largest angular tolerance when the slopes of both lines are at the minimum. As can be seen, this occurs at 0° and 90° of rotation angles of the 0.5-mm-thick BRF plate and can be compared to the ϕ0.5 mm ≈ 38° case which has a very tight angular tolerance (~ 0.1°). Fine tuning of the starting condition can then be accomplished by rotating the thin BRF away from 0° and 90°. Therefore, two birefringent filters allow for more precise control over the conditions of the two oscillating wavelengths thus solving the ‘first’ problem and allowing for higher long-term stability. Similar to the drawing in Fig. 2b, the discussed parameters result in a dual-wavelength operation only around the threshold pump power which is not practical.

Fig. 3
figure 3

Transmissions of the 1064 and 1073 nm wavelengths through both 4-mm-thick and 0.5-mm-thick BRF plates as well as the required transmission at 1064 nm (blue dashed curve) for dual-wavelength operation. The crossing points of the 1064 nm (black) and the required (blue dashed) curves indicate the condition of equal thresholds for 1064 and 1073 nm wavelengths. The fixed angle of the 4-mm-thick BRF plate is indicated in the graph as ϕ4 mm

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The ‘second’ problem of how to maintain the equal power ratio far above the threshold (Pout,1064 = Pout,1073 at Pabs >> Pth) can also be solved by the rotation of the thin BRF further away from the starting positions at either ϕ0.5 mm = 0° or ϕ0.5 mm = 90°. Qualitatively, since by rotating the 0.5-mm-thick BRF plate we are simultaneously reducing transmission at both wavelengths (i.e. increasing losses by ΔLBRF,1064 ≈ ΔLBRF,1073 ≈ ΔLBRF as seen in Fig. 3), the Eq. (1) tells us that this causes the P″th,1073 to be higher than P″th,1064. This happens because the right side of Eq. (1) is much more sensitive to the change of intracavity loss which was previously kept at the minimum value. Equation (2) also makes sure that the resulting slope η″s,1064 after the rotation of the thin BRF (with ΔLBRF,1064 ≈ ΔLBRF,1073 ≈ ΔLBRF) is still lower than η″s,1073 due to the larger total intracavity loss (L1064 = Lin + LBRF,1064 + ΔLBRF > L1073 = Lin + ΔLBRF).

The two restrictions set by the Eqs. (1) and (2) above mean that at all pump power Pabs levels beyond the starting point at threshold (Pabs > P′th,1064 = P′th,1073), it would be always possible to find a Pout,1064 = Pout,1073 situation since there will always be an intersection between the two output power lines as shown in Fig. 2c. This can be ensured providing that the introduced ΔLBRF intracavity loss by rotation of the thin BRF plate shifts the threshold condition away from the starting point. This also means that for a specific intracavity loss introduced by the two BRFs it would be possible to find the equal power dual-wavelength regime simply by adjusting the pump power level rather than the loss. Therefore, equal power regime can be stabilized either by the proper level of loss or pump power.

Therefore, two birefringent filters allow for a more precise control over the initial conditions (P′th,1064 = P′th,1073) of the two oscillating wavelengths thus allowing for a higher long-term stability as well as helping in maintaining the equal power ratio at subsequent output power levels.

As a side note, the overlapping of the transmission at 1064 nm and the required transmission at the starting point as shown in Fig. 3 can be ensured by two factors. First, by changing between the different values of ϕ4 mm (for example, to other values besides 27.0°), the starting points of 1064 nm transmission can be discretely selected (black arrows in Fig. 3) while keeping the transmission at 1073 nm still at the maximum. Second, it is worth noting that aside from changing the ϕ4 mm rotation angle, the insertion angle can be also purposefully chosen slightly off from the Brewster’s angle, therefore, increasing Lin and changing the level of the required transmission at 1064 nm (blue arrows). This should be used with caution because any deviation from the Brewster’s angle also affects losses at 1073 nm. With these two factors chosen carefully, the starting points displayed in Fig. 3 can be easily achieved. Finally, similar conditions can also be found in the case of dual-wavelength operation between the 1064 and 1085 nm.

3 Experimental details

A 5 mirror-cavity shown in Fig. 4 was used in the experiments with cavity lengths adjusted to accommodate the thermal lensing effect of about 160 mm [47]. The laser used a 20-mm-long, 1.5% doped crystal of an a-cut Nd:YVO4. The crystal was pumped by up to 16.7 W of pump power at 914 nm from a fiber-coupled laser diode. This low quantum defect pump wavelength was chosen to minimize the effect of thermal lensing [48] and maximize laser efficiency [49,50,51,52]. The pump spot size diameter in the crystal was 550 µm. About 67% of the incident pump power was absorbed by the crystal. Two birefringent quartz filter plates, the 4 and 0.5-mm-thick, were used at the Brewster’s angle in the laser cavity.

Fig. 4
figure 4

Experimental setup for dual-wavelength operation

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The 4-mm-thick birefringent filter plate was inserted into the cavity first and rotated until the 1073 nm (or 1085 nm) laser output was observed. This birefringent plate ensured that the 1064 nm line fell into the low transmission band of the filter. The second plate with 0.5 mm thickness was then inserted and adjusted until both wavelengths were present. Further fine optimization of rotation angles of both plates was necessary to achieve the highest output power. Among the multiple OCs available, the one with the 2.1% transmission in the 1040–1090 nm range was found to provide the highest output power in dual-wavelength operation.

4 Results and discussions

Dual wavelength oscillation was maintained within the range of 3–5 degrees of rotation of ϕ0.5 mm. At 11.2 W of absorbed pump power (16.7 W of incident pump power), the dual-wavelength operation with > 1 W of output power was observed at the 1064.1 & 1073.1 nm and 1064.1 & 1085.3 nm wavelength pairs after carefully adjusting of the BRFs. The laser output power with 1:1 power ratio at every pump power level is presented in Fig. 5.

Fig. 5
figure 5

Dual-wavelength output power at 1:1 power ratio versus absorbed pump power

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The maximum output power when each wavelength had a similar spectral intensity (1:1 power ratio) was 1.44 W in case of 1064 & 1073 nm operation. The slope efficiency was 16.53%. The output power reached 1.46 W in case of 1064.1 & 1085.3 nm dual-wavelength operation with the slope efficiency of 16.2%. Figures 6 and 7 show the output spectra for 1064.1 & 1073.1 nm and 1064.1 & 1085.3 nm operations, respectively. As expected, power ratio could be adjusted either by the rotation of the BRFs or pump power level.

Fig. 6
figure 6

Dual-wavelength operation spectra at 1064.1 and 1073.1 nm. a–c show the change in power ratio between the two output wavelengths by adjusting the rotation angle of the 0.5-mm-thick BRF plate

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Fig. 7
figure 7

Dual-wavelength operation spectra at 1064.1 and 1085.3 nm. a–c show the change in power ratio between the two output wavelengths by adjusting the rotation angle of the 0.5-mm-thick BRF plate

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Although the power ratio of the dual-wavelength output was still sensitive to the change in the pump power level of the laser and specific power ratio could only be maintained within a limited range of output power without the change in cavity parameters, it could be adjusted back to 1:1 throughout all of the output power levels by rotating the 0.5-mm-thick birefringent plate. The long-term stability of the average laser output power at the highest power level was better than 1% over 2 h with the fluctuation in the spectral power ratio of 2.14% as was obtained from the optical spectrum analyzer data. This measurement started from 1:1 power ratio and the maximum deviation of spectral intensity at 1073 nm over 1064 nm was recorded (ΔI1073/I1064). In both dual-wavelength regimes the linewidths of each wavelength were ~ 0.1 nm and were limited by the resolution of the available spectrometer. When the 0.5-mm-thick birefringent filter plate was rotated until the laser was operating at a single laser wavelength again, the output powers were increased to 4.61 W, 3.83 W and 3.74 W for 1064.1, 1073.1, and 1085.3 nm wavelengths, respectively.

To compare the results achieved in this work, Table 1 shows a summary of the results of dual-wavelength Nd-doped lasers operating on the similar laser transitions.

Table 1 Performance results of dual-wavelength Nd-doped lasers
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As can be seen from Table 1, our result is the first dual-wavelength operation with two wavelength pairs at 1064 & 1073 nm and 1064 & 1085 nm achieved with the same laser setup without the need to replace any optical elements. The highest optical-to-optical efficiencies with controllable spectral power ratio were also demonstrated for both wavelength pairs which is desirable for the generation of THz radiation. At the same time, we have also achieved the highest output power in dual-wavelength regime. We believe that the output power can be scaled even further by more careful optimization of BRF thicknesses and owing to the reduced thermal lensing offered by the low quantum defect pumping at 914 nm. The dual-wavelength operation at 1073 & 1085 nm was not observed in the experiment. Most likely this was caused by the close proximity of the strong 1064 nm line which made it difficult to suppress by the currently available combination of the BRF plates.

5 Conclusions

In conclusion, we have presented a method and explanation on how multiple BRFs can be used to achieve the power ratio tunable dual-wavelength operation of a Nd:YVO4 laser. To the best of our knowledge, the results shown in this work were the first demonstration of the dual-wavelength Nd:YVO4 laser operating at the 1064.1 & 1073.1 nm and 1064.1 & 1085.3 nm wavelength pairs with adjustable output power ratios and high output power stability. Both dual-wavelength pairs could be obtained with one setup with minor adjustments to the BRFs. The observed dual-wavelength output features > 1.4 W of output power and is very promising for applications in THz generation because the frequency difference of the oscillating wavelengths corresponds to the desirable range of THz radiation (1–10 THz). The high output power and efficiency of this method could lead to an efficient source of THz radiation. Finally, it is worth mentioning that multiple BRF plates can also be used to generate a more complex transmission shape and ultimately to balance the gain for more than one pair of wavelengths at a time.

This can lead to even tri-wavelength or multiwavelength operation [39] which is much harder to achieve with other tuning methods.