1. Introduction

Dual-frequency/dual-wavelength lasers (DFLs/DWLs) have shown great potential in the applications of optical radio frequency (RF) generation [1–6], optical terahertz wave generation [7–12], doppler lidar [13–16], medical diagnose [17–19] and so on. In the recent years, the researches of DFL/DWL have received extensive attentions. So far, the gain media available for DFL/DWL mainly include Nd-doped crystals, Yb-doped crystals and Er-doped glasses, etc. In which, the Nd-doped vanadate crystal is characterized by a high absorption coefficient, a large stimulated emission cross section, and natural birefringence that is favorable for building an efficient diode-pumped solid-state DFL/DWL with linearly polarized output [20]. In 2009, A Mckay produced a tunable dual-frequency (DF) signal with frequency separation up to 0.15 THz by using a vertical cavity Nd:YAG microchip DFL [7]. In 2012, M Hu realized a synchronized DF pulsed signal with frequency separation at 85 GHz by using a dual-doped Nd³⁺:Cr⁴⁺:YAG microchip DFL [21]. The microchip DFLs commonly produce DF signals with frequency separations below 200 GHz, but for larger frequency separations especially above terahertz, the DWLs with two gain media or double-axis in laser cavity are needed. In 2011, P Zhao obtained a dual-wavelength (DW) signal with wavelengths at 1047 nm and 1053 nm, frequency separation at 1.64 THz by using a “Y” type DWL based on $\pi$ and $\sigma$ Nd:YLF crystals [8,9]. In 2012, Y P Huang obtained a pulsed DWL with wavelengths at 1085.7 nm and 1088.5 nm, frequency separation at 0.7 THz based on $\pi$ and $\sigma$ Nd:LuVO₄ crystals [10]. In 2014, A Rolland achieved a DW signal with tunable frequency separation of 0~1.0 THz based on a double-axis Er:Yb:glass DWL [11]. In 2015, Y J Huang obtained a pulsed DWL with wavelengths at 1570.3 nm and 1572.5 nm, frequency separation above 320 GHz based on a diffusion-bonded Nd:YVO₄/ Nd:GdVO₄ crystal [12].

For DFLs /DWLs above, there are two issues worth discussing, namely tunable frequency separation and balanced power distribution. The DFLs/DWLs with tunable frequency separations realize the heterodyne beaten RF or terahertz wave signals with tunable output frequencies but single frequency points, and the balanced power distributions of DFLs/DWLs realize high optical heterodyne beat efficiencies. The double-axis Er:Yb:glass DWL proposed by A Rolland realizes coarse and fine tuning of the frequency separation by etalons and LiNbO₃ crystals [11]. While for the DWL with two gain media, such as linear type Nd:YVO₄/Nd:GdVO₄ DWL and “Y” type Nd:YLF DWL, whose wavelengths are selected by the emission cross section (ECS) spectral peaks and the output power of each wavelength depends on the respective gain coefficient of each crystal, they achieve balanced power distribution by moving the pumping point position [22,23] or tuning the pumping power of each crystal [8].

In this paper, a tunable DWL based on Nd:YVO₄/Nd:GdVO₄ combined crystal is introduced. The balanced power distribution of the DWL is realized by temperature controlling of the combined crystal. As an added benefit, the controlled temperature of the combined crystal enables the DWL frequency separation to tune in a small range. The temperature controlling method for achieving balanced power distribution of the DWL has advantages of more convenient operation and higher stability, and furthermore makes the frequency separation tuning of the DWL possible.

2. Experimental setup and the output spectra of the DWL

The schematic diagram of the DWL setup with combined crystal is shown in Fig. 1(a). An 808 nm fiber-coupled (NA = 0.22) laser diode (LD) is used as a pumping source, and the pumping beam focuses into the combined crystal by a graded index lens (GRIN). The pumping beam waist in the combined crystal is about 400 μm, and the Rayleigh length is about 2.8 mm. A plane mirror with partial reflectivity of 90% at 1064 nm is placed behind the combined crystal to form a simple Fabry-Pérot (F-P) cavity with the front surface of the combined crystal. The cavity length is 10 mm. The focal point of the pumping beam is longitudinally moved near the joint surface of the two crystals to satisfy the DWL threshold. The DWL signal separately feeds into a power meter (30A-BB-18, Ophir Inc.) and a high resolution (0.02 nm) optical spectrum analyzer (OSA, AQ6370B, Yokogawa Electric Co., Ltd., Japan.).

 

Fig. 1 (a) Schematic diagram of the DWL setup; (b) Nd:YVO₄/Nd:GdVO₄ combined crystal structure; (c) Temperature controlling system of the combined crystal.

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As shown in Fig. 1(b), the bonded combined crystal is composed of an Nd:YVO₄ crystal and an Nd:GdVO₄ crystal. Both crystals are a-cut with Nd³⁺ doping concentration of 1.0 at.%, and the crystallographic axes are vertically placed. The dimension of the combined crystal is 3 mm × 3 mm × (1 + 5) mm, wherein the thicknesses of the front-end Nd:YVO₄ crystal and the rear-end Nd:GdVO₄ crystal are 1 mm and 5 mm, respectively. For the front-end Nd:YVO₄ crystal, the 1mm thickness ensures the pumping light pass through the Nd:YVO₄ crystal and still maintains sufficient pumping power density when entering the rear-end Nd:GdVO₄ crystal. For the rear-end Nd:GdVO₄ crystal, since the ECS value is smaller than that of the Nd:YVO₄ crystal, 5 mm thickness increases the effective gain length, which facilitates the balanced power distribution of the DWL signal. All the crystal surfaces are coated. The front surface of the Nd:YVO₄ crystal is coated with high-reflection film at 1064 nm and antireflection film at 808 nm. The rear face of the Nd:GdVO₄ crystal is coated with antireflection film at 1064 nm. The joint surfaces of the both crystals are coated with antireflection film at 808 nm and 1064 nm. In order to prevent interference, the joint surfaces are designed with inclined angles of 8°.

As shown in Fig. 1(c), in order to well control the temperature of the combined crystal, the liquid metal is applied between the combined crystal and the heat sink. Since the liquid metal offers full thermal contact, very good temperature controlling of the combined crystal is realized. The heat sink temperature (T_c) is controlled by a thermoelectric cooler (TEC), meanwhile, the heat surface of TEC is close to a water cooled aluminum base for heat dissipation. Due to the combination of the temperature controlling system, the T_c adjustment range is from 0 °C to 100 °C and the temperature stability over an hour period is measured better than ± 0.1 °C.

The fluorescence spectra of the separated Nd:YVO₄ and Nd:GdVO₄ crystals with the same parameters as the combined crystal are measured under different temperature conditions firstly. Then the acquired fluorescence spectra are converted to ECS spectra by the temperature dependent Fuchtbauer–Ladenburg (FL) equation [24]. As shown in Fig. 2, when T_c is controlled at 15 °C, the ECS spectra of the Nd:YVO₄ and Nd:GdVO₄ crystals are curved, the spectral wavelengths of which are 1064.23 nm and 1062.95 nm, respectively.

 

Fig. 2 Normalized ECS spectra of the Nd:YVO₄ and Nd:GdVO₄ crystals with T_c at 15 °C.

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Since the linear type DWL cavity length is 10 mm (the combined crystal length is 6 mm), the DWL is multi-longitudinal mode operating. If necessary, an etalon can be disposed in the resonator to make the DWL oscillate in a single longitudinal mode in both wavelengths. The wavelengths of the DWL are selected by the ECS spectral peak of each crystal. Due to the thermal-induced ECS spectra evolution of the crystals, the power and wavelength of each component of the DWL signal changes with the crystals temperatures varying in the experiments, respectively. According to the previous researches [25], with the temperature increasing, the ECS spectral wavelengths of the Nd:YVO₄ and Nd:GdVO₄ crystals red-shift and the ECS spectral peak values decrease, which causes the DWL wavelengths to red-shift and output powers to decrease consequently. From the formula: ∆v = c/λ₁- c/λ₂, where ∆v is the frequency separation, λ₁ and λ₂ are the wavelengths of the DWL, it deduces the different shifting rates of λ₁ and λ₂ cause the frequency separation ∆v to vary further.

By fixing the pumping beam power at 3.0 W and waist at 400 μm, controlling the heat sink temperature T_c from 5 °C to 70 °C with an interval of 5 °C, the DWL output spectra are recorded by OSA and the frequency separations are calculated. In Fig. 3(a), the DWL signals with two spectral peaks locate around at 1063 nm and 1064 nm are shown. As T_c increases from 5 °C to 70 °C, the both wavelengths of the short-wavelength component and the long-wavelength component red-shift as a whole, while the output powers show a downward trend. It is noticed when T_c reaches 40 °C, the short-wavelength component experiences a “mode hopping”, which is mainly caused by the different red-shifting rates between the ECS spectrum and laser wavelength of the Nd:GdVO₄ crystal with T_c increasing. Since the “mode-hopping” is not suitable for stable tuning of the frequency separation, only the DWL spectra with T_c in the range of 5~40 °C are analyzed in Fig. 3(b).

 

Fig. 3 (a) The DWL spectra with T_c ranging from 5 °C to 70 °C; (b) The wavelengths and frequency separations of the DWL with T_c ranging from 5 °C to 40 °C.

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The relationship between the DWL wavelengths and the frequency separations versus T_c are shown in Fig. 3(b). With T_c increasing from 5 °C to 40 °C, the DWL wavelengths are linearly red-shifting. The short-wavelength component shifts from 1062.87 nm to 1063.21 nm with shifting rate of 9.70 pm/°C, and the long-wavelength component shifts from 1064.20 nm to 1064.41 nm with shifting rate of 6.12 pm/°C. The frequency separation linearly decreases from 351.11 GHz to 316.15 GHz with a slope of −0.95 GHz/°C.

3. Frequency separation and peak power ratio tuning of the DWL

From the section 2, since the DWL wavelengths are selected by the ECS spectra of the crystals [25], the DWL frequency separation tuning characteristics is ultimately decided by the ECS spectra evolution of the crystals.

Accordingly, the temperature dependent ECS spectra evolution of the combined crystal is studied firstly. With the pumping beam power at 3.0 W and waist at 400 μm, when T_c is precisely controlled from 5.0 °C to 95.0 °C, the fluorescence spectra of the combined crystal are collected by the OSA. With the modified FL equation [24], the temperature dependent ECS spectra are deduced from the fluorescence spectra and curved in Fig. 4(a) with T_c at 10 °C, 45 °C and 80 °C. The spectra are normalized by the ECS peak value at 10 °C. As shown in the Fig. 4(a), when T_c increases, the ECS spectral wavelengths red-shift and the ECS spectral peak values decrease. The relationships among the wavelengths and the peak values of the ECS spectra versus T_c are shown in Fig. 4(b). When T_c increasing from 5 °C to 95 °C, the ECS spectral wavelengths linearly red-shift, while the normalized peak values decrease. For the left spectral peak (Nd:GdVO₄), the wavelength shifts from 1062.91 nm to 1063.09 nm with a shifting rate of 2.31 pm/°C and the normalized peak value decreases from 100% to 69.68% with a rate of 0.34%/°C. For the right spectral peak (Nd:YVO₄), the wavelength shifts from 1064.13nm to 1064.27 nm with a shifting rate of 2.34 pm/°C and the normalized peak value decrease from 80.34% to 57.56% with a rate of 0.25% /°C.

 

Fig. 4 (a) The ECS spectra of the combine crystal with T_c at 10 °C, 45 °C and 80 °C; (b) The wavelengths and normalized peak values of the ECS spectra with T_c from 5 °C to 95 °C.

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During the ECS spectra measurement experiments, since the thermal generated by quantum losses and deposited inside the combined crystal can be negligible, the central temperature of the combined crystal is approximately equal to the heat sink temperature T_c. On the contrary, when the DWL is stably operating, the thermal deposited inside the combined crystal is proportional to the DWL output power and much more than the former, the central temperature of the combined crystal is hence higher than T_c. With the finite element analysis method and based on the experimental setup parameters, the temperature distribution of the combine crystal is calculated when the DWL is operating. The results show the central temperature of the combined crystal has a positive relationship with T_c. The difference between the central temperature of the Nd:GdVO₄ crystal and T_c is 23.7 °C, as well the difference between the central temperature of the Nd:YVO₄ crystal and T_c is 52 °C. Thus, in the experiments, when T_c varies from 5 °C to 40 °C, the central temperature of the Nd:GdVO₄ and Nd:YVO₄ crystals are 28.7 °C-63.7 °C and 57 °C-92 °C, respectively.

Increasing the central temperature of the Nd:GdVO₄ and Nd:YVO₄ crystals by 23.7 °C and 52 °C in the ECS measurement experiments to compensate the temperature difference with the combined crystal when DWL is stably operating. The compensated ECS spectral wavelengths comparing with the DWL wavelengths in same temperature range are shown in Fig. 5(a). It shows the compensated ECS spectral wavelengths are consistent with that of the DWL spectra overall, the slight deviation is caused by the measurement error. The frequency separations obtained from the ECS spectra and the DWL spectra are shown in Fig. 5(b). With T_c increasing from 5 °C to 40 °C, the ECS spectral frequency separation decreases from 357.68 GHz to 315.20 GHz, and the DWL frequency separation decreases from 351.11 GHz to 316.15 GHz, the standard error is 3.30 GHz. Therefore, in Nd:YVO₄/Nd:GdVO₄ DWL, the conclusion that the frequency separation tuning is caused by the different shifting rates of the ECS spectral wavelengths of the combined crystal is confirmed.

 

Fig. 5 (a) The wavelengths of the ECS spectra and DWL spectra versus T_c; (b) The frequency separations of the ECS spectra and DWL spectra versus T_c.

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With T_c increasing, it is also found the ECS spectral peak values of the Nd:YVO₄ and Nd:GdVO₄ crystals decrease in different rates, which leads the power ratio of the DWL to change [25]. For the purpose of high optical heterodyne beat efficiencies, the DWL must offer balanced power distribution. Defining the power ratio as R_p = P_L/P_R, where P_L and P_R represent the powers of the short-wavelength and long-wavelength components. The closer R_p is to 1, the better balanced power distribution of the DWL signal is achieved.

Figure 6(a) shows the normalized peak values of DWL spectral with T_c from 5 °C to 95 °C according to Fig. 3(a). With T_c increases, the normalized peak values decrease. For the left spectral peak (Nd:GdVO₄), the normalized peak value decreases with a slope of −1.88%/°C. For the right spectral peak (Nd:YVO₄), the normalized peak value decreases with a slope of −0.83%°C. Figure 6(b) shows the relationship between R_p and the heat sink temperature T_c. When T_c increases from 5 °C to 40 °C, R_p linearly decreases, and the relationship is fitted as R_p = −0.0158T_c + 1.51, from which the temperature point of balanced power distribution can be calculated as 32.28 °C. Since the accuracy of the temperature controller is 0.1 °C, the balanced power distribution of the DWL signal is obtained with T_c at 32.3 °C.

 

Fig. 6 (a) The normalized peak value of DWL spectral with T_c from 5 °C to 95 °C; (b) The power ratio R_p versus T_c.

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As shown in Fig. 7, when T_c at 30.0 °C, 32.3 °C and 35.0 °C, the normalized peak powers of short-wavelength and long-wavelength component decrease, the R_p is calculated as 1.09, 1 and 0.94. The frequency separations are measured as 327.10 GHz, 324.29 GHz and 322.11 GHz. When T_c is kept at 32.3 °C, a 435 mW power-balanced DWL signal is achieved with frequency separation at 324.29 GHz, and the wavelengths are at 1063.10 nm and 1064.33 nm, respectively. The closer R_p approaches to 1, the smaller tunable range of the frequency separation is obtained.

 

Fig. 7 The DWL spectra with T_c at 30 °C, 32.3 °C and 35 °C.

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4. Conclusion

The tunable DWL with frequency separation above 310 GHz and tuning rate of −0.95 GHz/°C is realized. The wavelengths of the DWL are determined by the ECS spectral wavelengths of the combined crystal. The different thermal-induced ECS spectral wavelength shifting rates of the each crystal realize the frequency separation tuning mechanism. By selecting different gain media as well as controlling the temperature of the combined crystal, the balanced-power DWL signal with tunable frequency separation can be finally achieved, which provides a new idea for obtaining terahertz wave by means of heterodyne beat frequency.