A Power Balanced Dual-Wavelength Nd:GdVO4 Laser With 0.6 THz Frequency Separation

A power balanced dual-wavelength laser (DWL) based on the Nd:GdVO<sub>4</sub> crystal is presented. The orthogonally polarized gain spectral evolution of the Nd:GdVO<sub>4</sub> crystal versus the temperature is studied, and the power balancing conditions of the DWLs are theoretically analyzed firstly. In the experiments, by using two output couplers and a temperature controller, the power balanced Nd:GdVO<sub>4</sub> DWL signals at 1063 nm (π) and 1065 nm (σ) are obtained with the crystal heat sink temperature (<italic>T</italic><sub>c</sub>) from 20 °C to 40 °C. The experimental results show, with the pump power at 9.3 W and <italic>T</italic><sub>c</sub> at 25 °C, the DWL signal of the balanced power at 0.78 W for each wavelength and the frequency separation at 0.62 THz is realized. The beam quality M<sup>2</sup> of the π- and σ-polarized DWL signals are measured between 2.1 to 2.4.

the etalon effect, A Mckay obtained a 20 mW DWL signal with frequency separation at 0.15 THz by using a monolithic microchip Nd:YAG crystal [17]. Y. P. Huang designed a Nd:LuVO 4 DWL with wavelengths at 1086 and 1089 nm by inserting an etalon with free spectral range (FSR) at 0.71 THz [18]. Also, by employing the dual-gain spectral peaks of the Nd-doped vanadate crystals, Pu Zhao achieved a Nd:YLF DWL with the output power of 1.196 W at 1047 nm and 0.608 W at 1053 nm, the frequency separation was 1.64 THz [13]. Wu Bo obtained a Nd:GdVO 4 DWL with output power of 4.0 W at 1065.5 nm and 1.0 W at 1063.1 nm, the frequency separation was 0.63 THz [19].
By employing the DWL signal for heterodyne frequency beating, since the DWL power balance degree is an important factor for the beat-noting efficiency, many researches on the power balanced DWL have been carried out. Florent Pallas achieved the dual-wavelength emission with balanced output power of 200 mW by tilting the output coupler in a c-cut Nd:GdVO 4 laser [20]. However, due to the tilting angle limitation, the power balance degree of the DWL was technically not adjustable. H. C. Liang adjusted the output power balance degree of the DWL by varying the radius of curvature of the input coupler in a Nd:YLF laser [21]. The large radius curvature of the input coupler easily led the DWL cavity to be unstable and the power balance degree was only roughly adjusted yet.
Since the output powers of the two wavelength components in the DWL primarily due to the wavelength dependent ECS values of the gain medium, the output power balance degree of the DWL is adjusted by the tuning the ECS spectra. Also, by considering the natural thermal characteristics of the Nd-doped vanadate crystals, the ECS spectra of the laser gain medium can be tuned by the temperature variation of the gain medium [22].
In this work, the Nd:GdVO 4 DWL with 0.6 THz frequency separation is demonstrated. The temperature dependent ECS spectra of the Nd:GdVO 4 crystal are analyzed in Section II. The power balanced conditions are theoretically analyzed, and the experiment setup is shown in Section III. The experimental results are disscussed in Section IV. The conclusions are given in Section V. by an optical spectrum analyzer. Fig. 1(a) shows the normalized temperature dependent fluorescence spectra in πand σpolarizations of the Nd:GdVO 4 crystal. The solid and dash curves represent the πand σ-polarizations, the different colors represent the different heat sink temperature T c , respectively. The fluorescence spectra with T c from 20°C to 60°C are shown in Fig. 1(a) over the spectral range from 1060 nm to 1068 nm. For each T c , the fluorescence spectra have three peaks, the peak wavelengths locate at 1063 nm in πand σ-polarizations, at 1065 nm in σ-polarization. By employing the Fuchtbauer-Ladenburg equations [23], the expression of the temperature dependent ECS spectrum is expressed as: where σ i (λ,T c ) is the temperature dependent ECS spectrum, I i (λ,T c ) is the temperature dependent fluorescence spectrum, τ i is the fluorescence lifetime, n i is the optical index,λ i is the average emission wavelength. Here, i = 1,2 represent the wavelengths of 1063 nm (π) and 1065 nm (σ). Since the refractive index and the fluorescence lifetime of the Nd:GdVO 4 crystal stay constant over the range of the temperature [24], by (1), the σ i (λ,T c ) evolution only depends on the I i (λ,T c ). The relationship between the ECS of 1063 nm in πpolarization and 1065 nm in σ-polarization are analyzed in depth. Within T c increasing from 20°C to 60°C, the πpolarized ECS spectral peak wavelength shifts from 1063.28 nm to 1063.44 nm and the σ-polarized ECS spectral peak wavelength shifts from 1065.64 nm to 1065.77 nm, the wavelength separation between the two peaks is about 2.3 nm. The relationship between the normalized ECS spectral π peak to σ peak value ratio versus T c is shown in Fig. 1(b). σ 1 and σ 2 represent the normalized ECS spectral peak values of the πand σ-polarizations. σ 1 /σ 2 is the peak value ratio. Within T c from 20°C to 60°C, σ 1 and σ 2 linearly decrease with the slope of 0.682%/°C and 0.182%/°C, σ 1 /σ 2 increases linearly from 5.15 to 7.01.

A. Theoretical Analysis for the Balanced Power DWL Operation in Different T c
Based on the space-dependent rate equation [25], the pump threshold ratio between the two wavelengths is expressed as: where P th, R oc and δ are parameters of the pump threshold, the output coupler reflectivity and the geometric deflection loss of the laser cavity, respectively. With the similar cavities, the geometric deflection losses of δ 1 and δ 2 are reasonably considered to be equal as the same loss δ. Therefore, the pump threshold ratio P th,2 /P th,1 depends on the output coupler reflectivity R oc and the temperature dependent ECS spectral peak value σ(T c ). Further, according to the diode-end-pumped laser equation [26], the slope efficiency S e and the output power P out for the specific emission line of the DWL are expressed as: where the parameters η q,i , hv p , s i (r,z) and r p (r,z) are the quantum efficiency, the pump photon energy, the normalized cavity mode intensity distribution and the normalized pump intensity distribution. The subscript i represents the corresponding laser wavelength of the DWL, the parameters λ p and P in are the pump wavelength and the incident pump power. Since the two close wavelength lasers are pumped by the same pump source and transmit between the same upper and lower level, with the similar laser cavities, the parameters η q,i , λ p , s i (r,z) and r p (r,z) of the two wavelengths are reasonably considered to be equal. Therefore, the difference of the slope efficiency S e,i of the two wavelengths only depends on the parameter of R oc,i . Assumption 1 is that the output coupler reflectivity R oc at 1063 and 1065 nm are the same, i.e., R oc,1 = R oc,2 . Since the ECS value σ 1 (T c )>σ 2 (T c ), according to (2), it is easily deduced that P th,2 >P th,1 . The result of P th,2 >P th,1 indicates the DWL first emits at 1063 nm. Also, since the output coupler reflectivity R oc,1 = R oc,2 , as P in increases the output power P out,1 and P out,2 increase at the same slope efficiency S e , which means S e,1 = S e,2 . Therefore, if the pump threshold P th,2 is higher than P th,1 , under the premise of the same slope efficiency S e,1 = S e,2 , the power balancing is impossibly realized at any pump power.
Assumption 2 is that the output coupler reflectivity R oc,1 ࣔR oc,2 , considering the ECS value σ 1 (T c )>σ 2 (T c ), it is consequently necessary to choose the output coupler with high reflectivity at 1065 nm and low reflectivity at 1063 nm. By using the appropriate output coupler reflectivities R oc,2 and R oc,1 , the conditions of R oc,2 >R oc,1 and P th,2 <P th,1 are satisfied. With P in increases, the laser first emits at 1065 nm then simultaneously emits at 1063 nm. Since the output coupler reflectivity R oc,2 >R oc,1 , according to (3), it is deduced that the slope efficiencies S e,2 <S e,1 . Hence, as P in increases, it is always achieved a balanced power DWL operation above the threshold. In addition, under the condition of assumption 2, by slight adjusting the cavity lengths, the geometric deflection losses of δ 1 and δ 2 change accordingly, thereby the pump threshold ratio P th,2 /P th,1 can be finely adjusted.

B. Experimental Setup
The experimental setup is shown in Fig. 2. A 400 μm multimode fiber-coupled laser diode with a wavelength of 808 nm is collimated and focused into the Nd:GdVO 4 crystal by a pair of aspheric lens. The focal length ratio between the collimating and focusing aspheric lens is 2:1. The gain medium is an a-cut, 1.0 at. % Nd:GdVO 4 crystal with the dimension of 3 × 3 × 3 mm 3 . The front surface of the Nd:GdVO 4 crystal is coated high reflectively (HR) at 1064 nm and anti-reflectively (AR) at 808 nm. The rear surface of the crystal is coated HR at 808 nm and AR at 1064 nm. An intracavity Brewster polarizer (BP) separates the two orthogonally polarized laser beams to the respective output couplers. The 1063 nm laser beam of the DWL is πpolarization, and the 1065 nm laser beam is σ-polarization. The front surface of the BP is coated AR at 1064 nm. The end surface of the BP has a coating in such a way that when being placed at a Brewster angle (55.4°) relative to the input beam, the πpolarized beam has a high transmittance of T p = 98% at 1064 nm, whereas the σ-polarized beam has the high reflectivity of R s > 99.9% at 1064 nm. The dimension of the BP is 25.4 × 25.4 × 3 mm 3 . The material of the BP is Corning 7980 with the optical index of 1.45. The reflectivity of the two output couplers at 1063 nm (OC1) and 1065 nm (OC2) are R = 60% and R = 95% at 1064 nm, according to the theoretical analysis in Section III. The cavity lengths are designed to 45 mm at 1063 nm and 1065 nm. In the experiment, the actually used cavity lengths can be appropriately shortened or lengthened to decrease or increase the laser threshold.
To get better thermal contact and proper temperature control of the Nd:GdVO 4 crystal. A thermoelectric cooler (TEC) precisely controls the temperature (T c ) of the crystal heat sink. Meanwhile, the heating surface of the TEC is placed close to a water-cooled aluminum base for heat dissipation. Owing to the combination of the temperature controlling system, the T c change range varies from 0°C to 100°C, and the controlling accuracy is ±0.1°C. The output DWL signal separately feeds into a power meter (PM100A, THORLABS.) and a high-resolution (0.01 nm) optical spectrum analyzer (OSA, Q8384, Advantest.) for powers and optical spectra measurements.

IV. EXPERIMENTAL RESULTS AND DISCUSSION
The DWL output powers versus the pump power with T c in the range of 20°C to 40°C are presented. The output powers of πand σ-polarized laser signals and the total output power versus the pump powers under different T c are shown in Fig. 3. In all T c , the σ-polarized 1065 nm light lases prior to the π-polarized 1063 nm light, and the balanced DWL signals are always achieved with the pump power increasing. As T c increases from 20°C to 40°C, the maximum balanced output power is 0.78 W × 2 with the pump power of 9.3 W and T c of 25°C. The maximum total output power is 1.75 W with the pump power of 11.1 W and T c of 25°C, the total output power optical-to-optical slope efficiency is up to 15.2%.
Since the Nd:GdVO 4 crystal ECS spectral peaks linearly decrease as T c increases, the threshold pump powers P th,1 and P th,2 increase as T c increases. However, Fig. 3(e) shows the P th,2 increasing and the P th,1 decreasing as T c increases. A good explanation is modes competition between the two wavelength components. Further, as shown in Fig. 3(b), for T c = 25°C, the output power of the σ-polarized 1065 nm light initially increases linearly as the pump power increases from 2.3 W (P th,2 ), and reach its maximum power of 0.88 W with the pump power of 7.9 W. When the pump power continues to increase to 6.2 W (P th,1 ), the π-polarized 1063 nm light starts to increase as the pump power increases. The gain competition between the πand σ-polarized laser leads to the output power of the 1065 nm light decreases when the pump power exceeds 7.9 W, and the output power of the 1063 nm light rises with higher slope efficiency. The balanced output power of 0.78 W × 2 is obtained with the pump power of 9.3 W. Similar laser performances are observed for other T c , as shown in Fig. 3(a), (c) and (d). The relationship between the threshold pump powers P th and the pump powers at the power balanced points P in, bal versus T c are shown in the Fig. 3(e). As T c increases from 20°C to 40°C, the P in, bal linearly decreases from 9.5 W to 7.1 W with a slope of −0.13 W/°C. The P th,1 linearly decreases from 6.4 W to 5.8 W with  dual-polarized lights are mainly due to the intracavity Brewster polarizer, which degrades the beam quality. The output beam transverse intensity profiles are depicted in the inset of Fig. 4, which exhibits the πand σ-polarized laser signals operating in a good fundamental mode.
The evolution of the lasing spectra with pump power increasing for T c = 25°C is shown in Fig. 5. The laser signal only oscillates at 1065.50 nm (σ-polarized) with the pump power at 2.9 W. With the pump power increases to 6.1W, the laser signal at 1063.28 nm (π-polarized) also appeared. When the pump power reaches 9.3 W, the output intensities of the πand σ-polarized light are maintained to be 1:1 and the wavelengths locate at 1063.31 nm and 1065.65 nm with the line widths of 0.04 nm and 0.06 nm, respectively. The wavelength separation is of 2.34 nm and the frequency separation is calculated as 0.62 THz. At the maximum pump power of 11.5 W, the output intensity of 1065.69 nm (σ-polarized) is lower than that of 1063.34 nm (π-polarized), which was resulted from the mode competition. When the pump power increases from 2.9 to 11.5 W, the wavelength of the π-polarized light shifts from 1063.28 to 1063.34 nm and the wavelength of the σ-polarized light shifts from 1065.50 to 1065.69 nm. The frequency separation of the DWL is tuned from 608.9 to 622.1 GHz. With the phonon theory by Sardar and Yow [27], the laser wavelength shifts with the pump powers varying is explained as follows. Though the temperature controlling systems are employed, the increasing of the pump power results in the increasing of the laser crystal temperature [24]. With the temperature increasing, the πand σ-polarized ECS spectral wavelengths red shift, which causes the wavelengths of the two polarized light to red shift [28]. The different red shift rates of the two wavelengths with the laser crystal temperature change lead to the variation in the frequency separation with the temperature.

V. CONCLUSION
In conclusion, based on the temperature dependent ECS spectrum of the Nd:GdVO 4 crystal, by choosing different reflectivities of the output coupler, a power balanced Nd:GdVO 4 DWL with 0.6 THz frequency separation at T c in the range of 20°C to 40°C is successfully realized. When the pump power of 9.3 W and T c of 25°C, the maximum balanced output power is 0.78 W × 2, and the frequency separation is 0.62 THz. The πand σ-polarized laser signals operate in a good fundamental mode. Such simultaneous Nd:GdVO 4 DWL is desirable for scientific and practical applications, especially for the development of terahertz sources.