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A compact and electric tuning microwave source based on a diode-pumped composite Nd:YAG-LiNbO3 cavity microchip laser is demonstrated. The electro-optical element introduces an electric tuning intra-cavity birefringence which causes a tunable frequency difference between two spilt orthogonal polarization states of a longitude mode. Thus a continuously tunable microwave signal with frequency up to 14.12 GHz can be easily generated by beating the two polarization modes on a high speed photodetector.
©2012 Optical Society of America
1. Introduction
Among different architectures for optical generation of microwave, dual-wavelength laser sustaining the oscillation of two orthogonal polarizations is a good candidate, in particular when high purity and continuous frequency tunability are required. Several effective methods based on this principle have been reported. By rotating the relative angles of the two quarter-waveplates which worked as phase-anisotropic components, a widely tunable microwave signal could be tuned linearly from a few gigahertzes to 150 GHz using a helicoidally polarized ceramic laser [1]. Mechanical stress-induced birefringence has also been used to generate a tunable dual frequency laser with frequency difference up to 3.4 GHz in good linear relationship [2]. The major drawback of these approaches is that the frequency separation between the two polarization modes depends on mechanical tuning, which dramatically limits the system flexibility. To overcome this limitation, several alternative methods based on electrical tuning were proposed. J. L. Gouët et al. have demonstrated an electro-optically tunable microwave signal with a dual-frequency single-axis Nd:YAG laser [3], utilizing an intra-cavity voltage-controlled anisotropic etalon made of lead lanthanum zirconate tantalate (PLZT) ceramic. This configuration allowed step by step tuning from 11 to 127 GHz. The key limitation associated with this method is the narrow continuous tuning range which is restricted to ± 200MHz around the discrete steps. To expand the continuous tuning range and simplify the system complexity, several composite microchip laser structures containing an active medium and a birefringence crystal, such as Nd:YAG + MgO:LiNbO3 [4] and Er:Yb:glass + LiTaO3 [5], were presented. The heterodyning signal of the two orthogonal polarization modes was tunable thermo-optically up to tens of gigahertz. However, the thermal tuning has its response time in order of milliseconds, much slower than electro-optical (EO) tuning which can respond within nanoseconds, and needs a sophisticated feedback control to stabilize the operation.
In this paper, we propose a composite-cavity dual-polarization microchip laser for generation of electrically and widely continuous-tunable microwave signal. The laser cavity consists of Nd:YAG crystal acting as active medium and LiNbO3 as tuning component. By controlling the voltage applied on the LiNbO3, the beat frequency of the two modes can be tuned continuously. In this configuration, the two optical modes share the same cavity and experience the same phase fluctuations, thus a high quality heterodyning signal is expected due to the good phase coherence.
2. Principle and experiments
Birefringence in laser cavity may result from several sources, such as mechanical or thermal stress, inserting a number of waveplates, or applying voltage on intra-cavity electro-optic (EO) components. As a result of birefringence, the effective cavity lengths for the two orthogonal polarization modes are different, and each longitudinal mode will split into two simultaneously oscillating modes, with the resonance frequency separation expressed as
where ν is the oscillation frequency, L is the cavity length, and δ is the optical path difference due to phase anisotropy.The conceptual diagram for the dual-polarization microchip laser is shown in Fig. 1 . The size of the composite-cavity is 3 mm × 3 mm × 2 mm, which consists of a 1 mm-long Nd:YAG (1 atom% doped) gain medium and a 1 mm-long LiNbO3 tuning section. The Nd:YAG crystal and the LiNbO3 crystal were face-glued, and two dielectric mirror stacks were directly deposited to form a resonance cavity. The pump-side face was coated with high-reflection (HR) film at 1064 nm and anti-reflection (AR) film at 808 nm, while the output face was HR coated at 1064 nm with reflectivity over 95%. The cavity length is L = 2 mm, corresponding to a free spectral range (FSR) of 36 GHz. A fiber coupled 808 nm LD with maximum output power of 500 mW is used as the pump source. The pump output beam is collimated and refocused to the microchip laser active medium by a lens pair.
The LiNbO3 crystal is z-cut, and deposited along x axis with gold layers as electrodes. Subjecting the EO crystal to a dc electric field via the two electrodes, the corresponding refractive index can be written as,
where no is refractive index of the ordinary mode in LiNbO3 crystal, is the EO coefficient, and Ex is the electric field along x axis, respectively.Thus a tunable birefringence is obtained as a result of the EO anisotropy. Due to this voltage-induced birefringence, the longitudinal mode will split into two orthogonal polarization modes. The polarizations of each mode align with the resulting optical axis x′ and y′, respectively, and the frequency difference of the two modes can be given as,
where is the longitude mode frequency, L is the length of the laser cavity, Loe is the length of the electro-optic crystal, V is the applied voltage, and d is the distance between the electrodes. The LiNbO3 crystal was provided by Cryslaser Inc., Chengdu, China, and the values for no and to be 2.28 and 6 × 10−12 mV−1, respectively. The calculated tuning scale factor is about 3.37 MHz/V. The tunable beat note signal between these two polarization modes is generated by placing a polarizer at the output of the laser, with its optical axis oriented at 45 degree with respect to each mode, and the resulting light beam is then directed to a photodiode followed by an electric spectrum analyzer (ESA), as shown in Fig. 2 .3. Result and discussion
The laser threshold power and efficiency are measured in stable dual-polarization mode operation. Figure 3 shows the total laser output power as a function of the pump input. The laser threshold is measured at the pump power of about 137 mW, and the power efficiency is about 12%. Although high pump power could provide higher signal power, it may also cause some problems in the experiment, such as multi-wavelength oscillating [6, 7], enhanced thermal lens effect that leads average laser power rolling off, and a serious long-term frequency drift for heterodyning signal. Especially, when there exist multi-modes in the cavity, the beat notes between them would produce unexpected frequency spectra at the output. To overcome this limitation, a single mode operation should be maintained. With appropriate pump power, the short pump absorption length enables us to get a single mode oscillating at 1064.36 nm, as shown in Fig. 4(a) . Increasing the pump power, another excited emission induced by transition with high emission cross section was observed at 1061.71 nm with pump of 245 mW, as shown in Fig. 4(b). The second longitudinal mode starts to oscillate with pump of 318 mW, as shown in Fig. 4(c), which can be attributed to the spatial-hole burning effect.
Fig. 4 Optical spectra of the laser with a 2 mm-long cavity at the pump power of (a) 140 mW, (b) 245 mW, and (c) 381 mW, respectively.
The frequency separation between two mutually orthogonal polarizations was detected with the polarizer set at 45 degree to both polarizations for maximum amplitude. In our experiment, it is observed that there is a low frequency beat note about 16 MHz without voltage applied on the LiNbO3. It can be attributed to the residual birefringence caused by the stresses in the crystal and optical coatings derived from the manufacture process, and the misalignment of the components. Moreover, the EO coefficient and birefringence of electro-optical component often depend on temperature, which offers another beat frequency adjustment [4]. Thus the total frequency difference from Eq. (1) can be expanded as
where is the initial frequency difference at zero voltage, and are electrical and thermal tuning factors, respectively. The values for a and b are determined by several factors, such as properties of the active material, cavity structure and so on. In our experiment, the measured value for a is about 3.02 MHz/V, and the value for b has been investigated by R. Wang et al. [4], which is about 2.38 GHz/°C with 1.5mm MgO:LiNbO3 inside a 2.5 mm-long cavity.To reduce the thermal influence and focus on the electro-optical tuning, in our experiment, the cavity was fixed on a thermal conductor, and the thermal conductor was mounted on a thermoelectric cooler (TEC) which made it possible to control the cavity temperature. The beat frequency versus the applied voltage can be measured without any possible extra birefringence introduced by power-induced temperature fluctuation. As shown in Fig. 5(a) , the beat note produced from the frequency separation behaves a linear relationship with the applied dc voltage. The measured tuning sensitivity is about 3.02 MHz/V which closes to the calculated value of 3.37 MHz/V. It can be seen that the beat note frequency basically agrees with the theoretical results of Eq. (3), and can be tuned continuously by varying the voltage within the FSR. In the linear dual-polarization arrangement, especially for EO crystal laser, tuning the beat frequency beyond half FSR of the cavity allows a possible second longitudinal mode to oscillate and induces mode hopping consequently [4, 8]. As a result, the maximum frequency difference is about 14.12 GHz at the applied voltage of 4800 V.
Fig. 5 (a) Measured and calculated beat note frequency as a function of the voltage applied to the electro optic crystal; and (b) Stability of the beat frequency.
Without any active thermal stabilization, the short-term stability in well-controlled lab environment for beat note at 14 GHz is about 1 MHz, as shown in Fig. 5(b), and the long-term drift is in several tens of MHz range. This is probably due to the fact that the localized temperature variation in the crystal induced by the pump power concentration results in refractive index change, and produces frequency deviation, while the temperature-induced birefringence causes the frequency shift. Therefore, to minimize frequency variation, stable laser diode pump and temperature control components (such as TEC) are required.
Typical beat note spectra observed with 1 Hz resolution bandwidth are shown in Fig. 6 . The 3 dB linewidths of the signals at 6.22 GHz, 10.24 GHz, and 14 GHz are all measured to be less than 12 kHz, and the signal-to-noise ratio at low frequency is better than 30 dB. Thanks to the continuous electrical tunability, this microchip laser can be phase-locked with an external reference at microwave frequency, which will effectively reduce the phase noise and improve the signal spectral purity. It has been verified that an optical phase-locked loop enables one to reach a very narrow linewidth less than 10 Hz [9]. We simply measured the phase noise directly from ESA (Agilent 8563EC) according to follow formula [10],
where Pc and Pm are signal power at center frequency and offset frequency Δf, respectively, BnT is the resolution bandwidth, and C is the correction value, which is typically 2.5 dB for the ESA. The phase noises from 1 kHz to 100 kHz are shown in Fig. 6. It can be seen that at 10 kHz offset frequency, the phase noises of 6 GHz, 10 GHz and 14 GHz signals are about −100 dBc/Hz, −88 dBc/Hz, and −82 dBc/Hz, respectively.Fig. 6 Frequency spectra and phase noise measurement of the beat note signals at (a) 6.16 GHz, (b) 10.45 GHz, and (c) 14.09 GHz, respectively.
However, as we can see, the peak power of the generated signal is very low. It is mainly limited by the single mode operation condition of this system. To solve this problem, the most effective method for this structure is to shorten the cavity length. When the cavity length is short enough, the frequency interval between adjacent longitudinal modes would extend the gain spectral bandwidth of the active medium, and there would be only one longitudinal mode oscillating in the cavity. Thus we can build a more compact microwave source with much higher output power. However, in this case, excellent heat dissipation and temperature control are very important for system performance.
Basically, the beat note power will experience logarithmic reduction with the increase of frequency [11], which can be attributed to the coupling phenomenon between the two polarization modes. It can be seen that the peak power at 14GHz suffers more decrease about 15 dB than that at lower frequency. As mentioned in [12], each polarization mode will induce a population grating for ions along its own polarization and another weak grating in the orthogonal polarization which is out of phase with the normal population inversion-intensity interactions. Thus the coupled component would contribute constructively to the intensity of the orthogonal mode. With the frequency difference between the two modes increasing, the coupling will decrease due to the decreasing spatial overlap of the coupled component with orthogonal states, and the beat power between the two modes will decrease consequently.
Furthermore, the voltage sensitivity can be increased by reducing the distance between two electrodes, or using new medium with a higher EO coefficient. It will effectively lower the requirement for the applied voltage. In addition, due to the maximum frequency difference is limited to the half FSR, the tuning range can be further extended by shortening the cavity length.
4. Conclusion
A widely electrically tunable dual frequency single-axis laser with power efficiency of 12% and tuning sensitivity of 3.02 MHz/V is demonstrated theoretically and experimentally. The microchip composite structure provides an opportunity to realize integrated design, such as miniaturized dual wavelength laser and compact microwave source. By tuning the voltage applied on the EO crystal in the composite cavity, the variable intra-cavity birefringence results in a continuously tunable frequency difference between two polarization modes. The experimental results verify that the beat note signals with frequency up to 14 GHz have low phase noise without any phase-lock.
Acknowledgment
This work was supported by the National Natural Science Foundation of China (grant Nos. 61071059, 60971060 and 60871011), the National Basic Research Program of China (grant No. 2012CB315703), and the Natural Science Foundation of Zhejiang Province of China (No. R1090354).
References and links
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