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We report frequency doubling of an extended-cavity diode laser in an a-cut KTP crystal. Continuous-wave, single-mode green light at 540 nm with a power of 22.8 mW was generated from an input of 44.2 mW by type II non-critical phase matching. Stable operation with intensity fluctuations smaller than 1 % peak-to-peak for more than two hours was achieved by employing resonant optical feedback. The optical feedback also reduced the fundamental-wave linewidth to the upper limit of 41 kHz.
©2004 Optical Society of America
Laser diodes (LDs) are compact, reliable and low-cost light sources for various optical sciences. Especially, continuous-wave single-frequency LDs are widely used in applications demanding good spectral quality such as spectroscopy and metrology [1]. Although the wavelength range accessible with LDs has been extended to violet region recently [2], no LD is commercially available in some wavelength regions yet. For instance, it is still difficult to generate wavelengths between 440 nm and 630 nm [3]. To generate coherent light in these regions from a LD, the standard way is frequency doubling of an infrared LD in a nonlinear crystal place in an enhancement cavity [4–6]. In order to achieve high conversion efficiency, it is advantageous to use diode taper amplifiers with a single-mode power of several hundred milliwatts [4–5], and/or periodically-poled materials with a large χ (2) nonlinearity [3,5,7]. For example, Schwedes et. al. obtained 205 mW of blue light at 461 nm by frequency doubling of a 520-mW taper amplifier in a 20-mm-long periodically-poled KTP crystal [5]. However, cost-efficient setups consisting only of easily available components are desired for easy access to the short wavelengths. In this report we demonstrate a simple frequency doubling setup for efficient and stable generation of high-quality green light. We use a 50-mW extended-cavity diode laser (ECDL) and a normally phase-matched KTP crystal. For efficient doubling, the fundamental wavelength of 1080 nm is selected to exploit the non-critical phase matching (NCPM) of an a-cut KTP crystal. Additionally, resonant optical feedback is employed for simple and stable locking of the ECDL to the cavity and also for linewidth reduction.
One of the most essential factors to limit the conversion efficiency in frequency doubling is walk-off of the interacting beams. This degrades the second harmonic beam shape as well as the conversion efficiency [8]. The fundamental solution is to choose a wavelength for NCPM. KTP is a popular crystal for frequency doubling of Nd:YAG lasers at 1064 nm, but the performance is limited by non-zero walk-off [8]. Better performance is expected at 1080 nm, where the type II NCPM in an a-cut KTP is possible. This fact was dramatically demonstrated by Ou et al. [8]. They achieved a conversion efficiency of 85% for doubling of a continuous-wave (CW) Nd:YAlO3 laser at 1080 nm. We realized a more compact and more stable setup with a 50-mW ECDL as the fundamental source. The combination of a single-stripe diode laser and a bulk nonlinear crystal is advantageous in simplicity and cost.
Our experimental setup is illustrated in Fig. 1. The laser is a commercial ECDL in the Littrow configuration with a specified maximum power of 50 mW at 1080 nm [1]. The elliptical beam from the ECDL is first circularized with a prism pair (PP) after passing through the first half-wave plate (HWP1). Then the beam is mode-matched to the cavity by a lens (L1) with a focal length of 400 mm. Because the type II phase matching requires both ordinary and extraordinary beams, the polarization of the beam is tilted about 45° with respect to the horizontal plane by the second half-wave plate (HWP2). A neutral density filter (NDF) is used to vary the input power. Note that no optical isolator is inserted in between the ECDL and the cavity. This enables self-locking of the ECDL to a resonant frequency of the cavity by optical feedback and also delivery of the fundamental power without notable loss. About 90% of the power emitted from the ECDL was brought to the input port of the cavity. Tiny tilt of the KTP crystal in the cavity was carefully adjusted, so that the scattering on the crystal surface gives proper amount of the counter-propagating mode responsible for optical feedback. The path length between the ECDL and the cavity is set manually by the mirror mounted on a piezoelectric transducer (PZT-ϕ). The enhancement cavity is a ring cavity made up with two plane mirrors (M1, M2) and two curved mirrors (M3, M4, r=50 mm). The measured transmission of the input mirror (M1) for 1080 nm is T1=0.85%. The other mirrors were coated with high reflectivity (>99.8%) for 1080 nm. The transmission of the output coupler (M4) for second harmonic is T2=98%. One of the plane mirrors (M2) is mounted on a PZT (PZT-C) for adjusting the cavity length. The nonlinear crystal is an a-cut KTP crystal in a dimension of 3 mm×3 mm×10 mm. The both surfaces were anti-reflection coated for both wavelengths. The crystal is mounted in an oven made of aluminum, and its temperature is stabilized by a controller with a specified stability of ±0.005 °C. The generated second harmonic is separated from the leakage of the fundamental beam by a harmonic separator (HS), and the power is measured by a calibrated power meter (PM1). The 1080-nm leakage from the cavity arriving at PM1 was less than 1µW. The reflected fundamental beam at the cavity input port is simultaneously measured by another power meter (PM2) in order to evaluate the coupling to the cavity.
Fig. 1. The setup for frequency doubling of an ECDL in an a-cut KTP placed in an enhancement cavity. Abbreviations are HWP, half-wave plate; PP, prism pair; NDF, neutral density filter;PZT, piezo-electric transducer; PD, photo diode; PM, power meter; HS, harmonic separator.
The type II phase matching demands that both ordinary and extraordinary beams are simultaneously resonant on the enhancement cavity. This situation cannot be realized automatically, since the optical length in the crystal is generally different for the two modes. There are basically two ways to solve this problem [6,8]. One way is to control the crystal temperature at which the both beams are brought to resonance by chance, with a precision as high as a few millikelvins [8]. Another way is to put a half-wave plate inside the cavity to rotate the polarization 90° so that the beams exchange the cavity lengths every round trip, but at the cost of a larger intra-cavity loss [6]. We adopted the former method to achieve higher conversion efficiency. Without the cavity the phase matching width (full width at half maximum) was 22.1 °C centered at 63.1 °C. The doubly-resonant temperature nearest to the center was found at 67.0 °C. The stability of the temperature controller was marginal for the reported tolerance of 20 mK [8]. Instead of pursuing better temperature stability, the fundamental-wave frequency was servo-controlled to track the double resonance frequency, which is primary determined by the crystal temperature. For this purpose PZT-C was dithered at 40 kHz and the green light leaking from the cavity was monitored by a photo diode. The error signal was derived by a lock-in amplifier and it was directly fed back to PZT-C via a piezo driver. This kept the cavity length to the doubly-resonant frequency. Although the ECDL frequency was left constant, it automatically followed the cavity frequency by optical feedback. The feedback path length was set to an appropriate value by PZT-ϕ at the beginning, and was left constant during the operation. Theoretically, the perfect servo for optical feedback is simultaneous control on the ECDL frequency and on the feedback phase [9,10], but our simplified electronic servo was enough to keep constant power for hours mainly owing to the large locking range of about 800 MHz by strong optical feedback.
Fig. 2. Measured dependence of (a) generated second harmonic power, (b) reflected fundamental power, on the input power. The dots are measured data. The curves are calculated from Eq. (3) and (2), respectively.
Figure 2(a) shows generated second harmonic power as a function of the input power. The dots represent raw values measured with PM1. For small input powers bellow 18 mW, stable operation was not obtained due to insufficient optical feedback. No thermal effect was observed at large input powers. For 44.2 mW input, 22.8 mW of green light was emitted out from the cavity. This corresponds to a conversion efficiency of 51.6%. Similar efficiency (50%) was reported in frequency doubling of a diode laser in a setup with a KNbO3 crystal [11], however, optical feedback was not properly managed to result in stable operation in the report. When only the in-coupled fundamental power is taken into account, as is often done in evaluating the efficiency [4], our conversion efficiency corresponds to 64.5%. The high efficiency is comparable to those obtained by frequency doubling of a taper amplifier, where input power as large as a few hundred milliwatts is used [4, 5].
Efficient frequency doubling is achieved by good impedance matching. In order to check our frequency-doubling parameters, we analyzed the data by the standard model for frequency doubling in a cavity [8]. Because mode matching is usually not perfect for LDs, we have extended the method to account for the mode matching factor m (0≤m≤1). It is straightforward to derive formulas for intra-cavity fundamental power Pc, reflected fundamental power Pref, second harmonic power emitted out from the cavity P2, as a function of input power P1. They are given by
where T1, L, ENL, T2 are transmission of the input coupler (M1) for 1080 nm, round trip linear loss for 1080 nm, single-pass conversion efficiency and transmission of the output coupler (M4) for 540 nm, respectively. We used the formulas to simulate the data in Fig. 2(a) and 2(b) with measured values of T1=0.85%, T2=98%. This resulted in estimation of L=0.36%, ENL=1.9×10-3 W-1, m=0.80, respectively. The solid lines shown in Fig. 2 are calculated with these parameters. Both curves fit very well to the measured data. The impedance matching is achieved by the optimum input transmission Topt=L/2+(L 2/4+m ENL P1)1/2. For our estimated parameter values Topt is calculated to 1.0% for 44mW input. Since the actual transmission T1 is very close to Topt, the impedance matching is almost achieved with the current parameter setting. This is also indicated by the flat behavior of the reflected power shown in Fig. 2(b). The most of the reflected power comes from mode mismatch, and this could not be made smaller due to the quality of the ECDL beam. The value of ENL can be adjusted by spot size of the cavity, but our estimated value is already very close to the optimum value of 2×10-3 W-1 for a 10-mm a-cut KTP crystal [8]. From this analysis we concluded that the current setup realizes almost the best doubling efficiency for the given set of ECDL, KTP crystal and enhancement cavity. Further improvement of the efficiency would be realized by having a larger fundamental-wave power with the accompanying optimized transmission Topt.
The observed stability of the generated second harmonic power is shown in Fig. 3. Each point was recorded every second by averaging the power meter readout 40 times. In the specific data set in Fig. 3, the power stayed within 0.3% peak-to-peak for 160 minutes with the electronic servo on. Typical fluctuation was smaller than 1% per hour. Gradual power decrease was observed for longer operation, but the initial value was immediately recovered by adjusting PZT-ϕ and the ECDL grating PZT. This recovering process would be automated by servo control on both PZT actuators [10]. Surprisingly, even without any electronic servo the ECDL stayed locked to the cavity, and the second harmonic was generated for more than 70 minutes as shown in the lower trace in Fig. 3. This demonstrates the robust nature of the optical feedback, and shows an advantage over other electronic locking methods [4–6,8].
Fig. 3. Observed intensity stability of the generated second harmonic power. Even without electronic servo the diode laser frequency stayed locked to the cavity for more than an hour. By adding slow electronic servo the power stayed within 0.3% peak-to-peak for more than two hours.
Reduction of the linewidth is another nice feature of the optical feedback [9,10]. The spectrum of the fundamental wave was observed with a Fabry-Perot cavity, since no cavity for 540 nm was available this time. A laboratory-made confocal cavity was used to observe the spectrum. Fig.4 shows the spectrum taken by a scan with a sweep time of 0.3 msec. The frequency scale was calibrated by the separation of 4 MHz between the sidebands generated with an electro-optic modulator. The observed spectrum fits to a nice Lorentzian line shape with a full-width at half maximum of 41 kHz. This linewidth is much smaller than the free-running width of about 1 MHz. The measurement was limited by the resolution of the Fabry-Perot cavity, and the width gives the upper limit of the fundamental-wave linewidth. From this we estimated that of the second harmonic linewidth to be 82 kHz.
Fig. 4. Spectrum of the fundamental wave observed with a non-confocal Fabry-Perot spectrum analyzer. The curve is the fit with a lorenzian.
As a practical application we used the green light to pump a CW triply-resonant optical parametric oscillator (OPO), which also uses an a-cut KTP crystal as the nonlinear gain medium. In a semi-monolithic cavity described in ref. 12, we achieved a threshold pump power of 2.5 mW and an output power (signal and idler, around 1080 nm) of 5.1 mW for 16 mW pump [12]. The nice Gaussian beam shape of the second harmonic contributes to the small threshold power. The intensity fluctuation of the OPO output was as small as 1% peak-to-peak for more than 10 minutes with a simple electronic servo. The OPO output exhibited even non-classical nature; noise reduction in the intensity difference between the signal and the idler beams 4.3 dB below the shot-noise level was successfully observed at the detection radio frequency of 3 MHz. These quantum-correlated twin beams are used in quantum optics experiments, in which their quantum nature is fully exploited [13,14]. This example clearly demonstrates the excellent properties of our green light.
In summary we have generated 22.8 mW of single-mode green light at 540 nm by frequency doubling of a 50-mW extended-cavity diode laser in an a-cut KTP crystal. Conversion efficiency of 51.6% was demonstrated. Stable operation with intensity fluctuation 0.3% peak-to-peak for two hours was achieved by employing resonant optical feedback. The upper limit of the linewidth reduced by optical feedback was inferred 82 kHz from the measurement of the fundamental-wave linewidth by Fabry-Perot cavity. The green light was successfully applied to generation of the quantum-correlated twin beams from an optical parametric oscillator.
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