Phase coherent division of optical frequencies by two and three is of high interest for precision metrology spanning wide optical ranges [1
1. N. C. Wong, “Optical frequency counting from the UV to the near IR,” Opt. Lett. 17, 1155 (1992). [CrossRef] [PubMed]
]. Promising candidates for phase coherent division with high efficiency are continuous-wave (CW) optical parametric oscillators (OPOs). Division by two or by three of the pump laser frequency is, e.g., achieved with the idler frequency at one half or one third of the pump frequency. An exact ratio of 1:2 as required for phase coherent by-two-division can be maintained by electronically phase-locking the signal-idler beat note to zero (or the frequency of a stable radio-frequency oscillator) via a piezo or electro-optic servo control of the OPO cavity length [2
2. D. Lee and N. C. Wong, “Tunable optical frequency division using a phase-locked OPO,” Opt. Lett. 17, 13 (1992). [CrossRef] [PubMed]
]. By-three-division requires that one frequency-doubles the idler wave before a radio-frequency (RF) beat with the signal wave can be observed and used for a servo control [3
3. T. Ikegami, S. Slyusarev, and Shin-ichi Ohshima, “Realization of a 3:1 optical frequency divider using a CW optical parametric oscillator,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, Washington DC, 1999), pp. 10–11.
]. Although electronic phase-locking is a well established technique [4
4. H. R. Telle, D. Meschede, and T. W. Hänsch, “Realization of a new concept for visible frequency division: phase locking of harmonic and sum frequencies,” Opt. Lett. 15, 532 (1990) [CrossRef] [PubMed]
], there are also disadvantages. These are the shot noise and electronic noise associated with any beat measurement [5
5. I. Andonovic and D. Uttamchandani, Principles of modern optical systems (Artech House, Norwood, 1989), Chap. 5.
], and the approximately 1-GHz bandwidth limit of photodetectors, electronic circuits, and amplifiers required for electronic phase-locking.
To avoid such disadvantages and reduce the residual phase noise, frequency division is of interest which solely relies on optical methods to stabilize the phase of the OPO output waves with respect to each other. Such optically phase-locked by-two-division has, in fact, been observed with a type-I CW-OPO at degeneracy [6
6. C. D. Nabors, S. T. Yang, T. Day, and R. L. Byer, “Coherence properties of a doubly-resonant monolithic optical parametric oscillator,” J. Opt. Soc. Am. B 7, 815 (1990). [CrossRef]
], where optical injection-locking of the signal by the idler wave (and vice versa) stabilized the phase difference of these waves, which is similar to injection-locking of lasers [7
7. A. E. Siegman, Lasers (University Science Books, Mill Valley, 1986), Chap. 29.
]. This also stabilized the signal and idler phase with respect to that of the pump laser, which is equivalent to parametric oscillation in one of their two phase eigenstates. Recently, also a type-II OPO (with the signal and idler polarization perpendicular to each other) was used for frequency by-two-division, where an intracavity half-wave-plate was used to gradually vary the signal-idler injection efficiency and thus the optical locking range [8
8. E. J. Mason and N. C. Wong, “Observation of two distinct phase states in a self-phase-locked type II phase-matched OPO,” Opt. Lett. 23, 1733 (1998). [CrossRef]
]. A phase coherent frequency by-three-division using solely optical techniques has not been reported so far. Such division should be possible using a CW-OPO whose idler frequency is set to about one third of the pump frequency. The idler frequency is then simultaneously frequency-doubled inside the OPO cavity in order to injection-lock the signal frequency for phase coherent oscillation. In this contribution we report, for the first time to our knowledge, on the observation of such self-injection-locking of a CW-OPO.
shows the experimental setup. The frequency to be divided is provided by a single frequency diode master-oscillator power-amplifier (MOPA) system. This system is similar to the one employed in a recent investigation [9
9. M. Scheidt, B. Beier, K.-J. Boller, and R. Wallenstein, “Frequency-stable operation of a diode-pumped continuous-wave RbTiOAsO4 optical parametric oscillator,” Opt. Lett. 22, 1287 (1997). [CrossRef]
] for the frequency stable operation of a CW-OPO. The 10-mW radiation from a grating-stabilized single-stripe AlGaAs diode laser (SDL 5311-G1) is amplified by a AlGaAs diode tapered power-amplifier (SDL 8630-E). After passing beam correction optics and an optical 60-dB isolator a single-frequency, nearly diffraction-limited output beam with a maximum power of 350 mW at a wavelength of 812 nm is available. The spectral bandwidth of the MOPA output is less than 1 MHz (FWHM, resolution limited). The diode MOPA wavelength can be grating-tuned over several nanometers. Additionally, the diode frequency can be tuned without mode hops over 1 GHz via a piezo control of the diode oscillator cavity length. For the investigations of OPO self-injection- locking we use a pump-enhanced, idler resonant two-mirror OPO based on quasi-phase- matching (QPM) in a 40-mm long periodically poled LiNbO3
(PPLN) crystal. The crystal carries two different poling periods for cascading a second harmonic generation (SHG) process to the parametric oscillation. The first 30-mm long section of the crystal is poled with a domain grating of 21.2 µm to obtain QPM for idler frequencies close to one-third of the pump frequency. The corresponding idler wavelength of 2436 nm is approximately twice the signal wavelength of 1218 nm. The second, 10-mm long section of the PPLN crystal is poled with a period of 34.1 µm to provide QPM for frequency doubling of the idler wave. For temperature tuning of the OPO wavelengths the crystal is placed in an oven equipped with an electric heater and a thermoelectric element. The temperature of the crystal can be set to values of up to 200 °C and is held constant by an electronic control with an estimated stability of 10 mK.
Fig. 1. Experimental setup for self-injection locking of a CW-OPO with its idler frequency set to a third of the pump frequency (FR: Faraday rotator, EOM: electro-optical modulator, PD: photodiode, PZT: piezo transducer, FPI: confocal scanning Fabry-Perot interferometer).
The OPO consists of two mirrors with 30-mm radius of curvature each, in a distance of 77 mm, with the PPLN crystal placed at the beam waist. The free spectral range (FSR) of the OPO resonator is 1.2 GHz. The pump input mirror, M1, is coated for a power transmission of 3 % at the pump wavelength and for high reflectivity at the signal and idler wavelengths. The signal output mirror, M2, is coated for high reflectivity at the pump and idler wavelengths and for 90 % transmission at the signal wavelength. The pump beam is mode-matched to the OPO cavity with a spherical lens of 100-mm focal length. The beam radius in the crystal is 35 µm. The observed maximum pump input coupling is 80 % at a pump power below the OPO threshold and 50% at the maximum pump power of 350 mW. To provide a CW output from the OPO, the cavity length is stabilized to the pump wavelength using the Pound-Drever-Hall (PDH) technique [10
10. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97 (1983). [CrossRef]
]. The required frequency modulation (FM) side bands (at 32.5 MHz) are generated with an electro-optic modulator placed between the diode oscillator and the diode amplifier. The PDH error signal is obtained by detecting the AC component in the reflected pump light from the OPO cavity with a Si-diode (bandwidth of 100 MHz) and demodulating this signal with a balanced mixer. The mixer output is filtered (low-pass <1 MHz) and amplified to control the resonator length via a piezo transducer at M2. The servo bandwidth of the PDH loop is about 500 Hz as limited by the piezo transducer. Fig. 2
shows the power output characteristic of the OPO. The pump power at threshold is 150 mW and the maximum signal wave output power (behind M2) is 46 mW at a pump power of 350 mW. The maximum output power of the frequency-doubled idler is about 1 mW. The maximum idler wave output is less than 1 mW due to the high reflectivity of the OPO mirrors at the idler wavelength. The signal wave is single-frequency as monitored with a confocal scanning Fabry-Perot interferometer (FPI) of 1-MHz resolution.
Fig. 2. Signal wave output power of the OPO with a crystal temperature of 167 °C as a function of pump power. The pump, signal, and idler wavelength are 812 nm, 1218 nm, and 2436 nm, respectively.
During temperature tuning of the signal wavelength close to the frequency-doubled idler wavelength we observe the OPO spectrum with a double grating optical spectrum analyzer (OSA, Ando AQ-6315A) with a resolution of 100 GHz and, in addition, with a confocal scanning FPI with a FSR of 7.5 GHz and a resolution of 250 MHz. Fig. 3
shows emission spectra of the OPO near 1218 nm recorded with the OSA for three different values of the crystal temperature. At about 167 °C the two nonlinear processes (OPO and idler-SHG) are simultaneously phase-matched. At a temperature of 167.12 °C the signal wavelength coincides with the wavelength of the frequency-doubled idler radiation within the 100-GHz resolution interval of the OSA and also within the 250-MHz resolution interval of the FPI.
Fig. 3. Output of the OPO (on a logarithmic scale) vs. wavelength for different crystal temperatures. The emission peaks show the signal wavelength and one-half of the idler wavelength.
A higher spectral resolution is provided by a beat measurement of the signal and frequency-doubled idler wave. In our experiments we use a Ge-photodiode (bandwidth of 2 GHz) followed by a broadband RF amplifier (gain of 33.5 dB from 10 MHz to 2 GHz) and a RF spectrum analyzer (Advantest R3261A, bandwidth of 2.6 GHz). Fine variations of the pump laser frequency and the crystal temperature are used to stepwise tune the two 1218-nm fields via longitudinal mode hops until their beat frequency is observed on the RF spectrum analyzer. A measured RF spectrum showing a beat frequency of 560 MHz is given in Fig. 4
(black trace). All measurements are performed with a spectral resolution of 100 kHz and a sweep time of 30 ms. The spectral width of the beat is 2 MHz over an integration time of 100 ms. To distinguish the beat and other noise peaks, a measurement in the max-hold mode for an integration time of one minute is also shown as the red trace in Fig. 4
. In the max-hold mode the maximum values at all frequencies in the measurement interval are recorded and stored until a higher value occurs in the next sweepings. The max-hold trace thus shows a fluctuation of the measured signal vs. RF frequency. The flat distribution of the peak of the beat signal vs. RF frequency in the red trace in Fig. 4
indicate a frequency fluctuation in the range of typically 10 MHz for a minute. This fluctuation is probably caused by acoustically or thermally induced instabilities of the OPO cavity length. Two sidebands located symmetrically at 32.5 MHz from the beat carrier are caused by a residual FM transferred from the pump spectrum to the OPO output waves and show the same 10-MHz wide frequency fluctuation. In contrast, other peaks in the black trace are caused by noise fluctuating only in amplitude, since their width in frequency does not increase in a max-hold measurement.
Continuous tuning of the OPO frequencies via the pump frequency is then used to further reduce the beat frequency, until the beat frequency is close to zero. The observation of near zero beat frequencies is now performed at the upper FM sideband such that indicated frequencies are higher by 32.5 MHz compared to the actual beat frequency. This technique is commonly used to move out of the typically 10 kHz to 1 MHz wide noise band of analogue RF analyzers around zero frequency. The observation interval of the beat signal is about 5 MHz centered at 32.5 MHz. As in Fig. 4
, the beat frequency is seen to randomly fluctuate within this interval. A measurement with the RF analyzer in the max-hold mode (integration time of over 2 minutes) is shown in Fig. 5
as the black trace. The trace shows a flat distribution of the beat signal over most of the 5-MHz interval except a small interval around 32.5 MHz. The sharp peak at 32.5 MHz is caused by electronic pick-up from the FM driver as can be seen also from the red trace obtained with the photodiode blocked. In addition, however, the black trace shows a significant dip (approximately 10 dB) centered at 32.5 MHz, extending over a width of about 500 kHz. This dip proves that beat signals within the 500-kHz frequency interval around zero do not occur with the same strength or probability, as do beat signals outside this interval. It is also observed in this interval that the beat is pulled in frequency to zero and simultaneously suppressed in amplitude. This is exactly what is expected from injection-locking of the signal wave by the frequency-doubled idler wave: at sufficiently close proximity of the two frequencies, injection-locking suppresses the free running signal and idler frequencies (as they would be observed without idler-SHG) and replaces them by oscillation at the same frequency such that the beat frequency becomes zero. Thus the 500-kHz wide range of beat suppression should correspond to the locking range of the OPO. The measured range is in good agreement with the locking range we calculate by numerically integrating the coupled amplitude equations of the OPO with cascaded SHG using known experimental parameters. A detailed analysis of the experimental and theoretical OPO locking ranges is currently under investigation.
Fig. 4. RF beat frequency of the signal and the frequency-doubled idler wave as recorded with an RF spectrum analyzer. For details, see text.
Fig. 5. Signal-idler beat recorded around the upper sideband in the max-hold mode (integration time of over 2 minutes, black trace). For reference, the red trace is recorded with the photodiode blocked.
In conclusion the experimental data show, to our knowledge, the first evidence of self-injection-locking of a CW-OPO by using a cascaded SHG nonlinearity. This is the most important step for the experimental realization of all-optical phase coherent by-three-division. Further work should investigate in detail the degree of phase coherence, e.g., by beating the frequency-tripled idler wave with the pump wave.