1. Introduction

A continuous-wave (cw) optical parametric oscillator (OPO) is an efficient nonlinear optical device for the generation of bright, spectrally pure, twin beams of light whose intensities are correlated at a level well below the shot noise [1–4]. Potential applications of twin beams in ultrasensitive measurements have been proposed [5,6] and sub-shot-noise spectroscopy has been demonstrated [7]. Similar to quadrature-squeezed states of light, the intensity correlation of twin beams degrade quickly if there are losses within the OPO, along the propagation path, inside the application apparatus, or in the pho-todetection process. It is therefore important to use a strongly correlated twin-beam source and to minimize various losses for a particular application. In addition to the amount of achievable correlation, there are a number of design considerations for the twin-beam generator such as the pump power and the output powers. The amount of observable intensity correlation is dependent on the ratio of the output coupling to the intracavity losses of the OPO. For a cw doubly resonant OPO (DRO), a strong intensity correlation requires a large output coupling which in turn implies a high pump threshold that scales as the square of the total cavity losses. In order to avoid the effects of the pump noise, especially at low rf frequencies, the DRO should generally be pumped well above its threshold [6]. As a result of a high threshold and a high pumping level, the output powers can be substantially greater than the saturation levels of the photodetectors or the power requirements of an experiment. Since attenuation, which degrades the amount of correlation, is not an option, one method is to use a triply resonant OPO (TRO) that reduces the threshold requirement by a factor equal to the finesse of the pump cavity and, at the same time, lowers the output powers.

2. Triply resonant OPO configuration

The advantages of a TRO were amply demonstrated by Mertz et al. [4] in a type-II phase-matched KTiOPO₄ (KTP) OPO with a remarkable intensity correlation of 8.5 dB below shot noise. The measurements were taken using a single-cavity TRO with a 6.3% output coupler, a pump threshold of 430 mW, and a pump level that was less than 10% above threshold. In order to provide design flexibility and separate tuning capability for the pump and downconverted outputs, we have investigated a dual-cavity TRO configuration, as sketched in Fig. 1. The DRO cavity, formed by mirrors M2 and M3, is typically single-ended for the downconverted signal and idler fields with very little outputs through M2. The DRO cavity is usually set up in a double-pass configuration for the pump field that enters the cavity at M2 and is fully reflected by M3 before exiting the cavity through M2. By adding a third mirror M1 to the input side of the DRO cavity, M1 and M3 form the pump cavity that is not affected by the highly transmissive M2. At the same time, the DRO cavity characteristics are unchanged because the signal and idler waves remain confined within the DRO cavity. In this way, the resonances of the pump and downconverted fields can be adjusted and servo locked separately instead of the required simultaneous triple resonance in a single-cavity configuration. Moreover, this arrangement allows us to optimize the pump cavity alignment and finesse without any change to the DRO cavity.

 

Fig. 1. Schematic of a dual-cavity TRO. Signal and idler fields are confined within the DRO cavity formed by mirrors M2 and M3.

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3. Experimental setup

In our experiment, the DRO cavity in Fig. 1 was formed with a 20-cm-radius input mirror M2, coated for maximum reflection at 1064 nm and maximum transmission at 532 nm, and a 2-cm-radius output mirror M3 that was coated for 2.7% transmission at 1064 nm and maximum reflection at 532 nm. The DRO was therefore in a double-pass configuration for the pump. The nonlinear crystal was a 3 × 3 × 10-mm KTP that was antireflection coated at both wavelengths to minimize intracavity losses. The crystal was mounted on a thermoelectric (TE) cooler for fine temperature tuning. In addition, the crystal and the TE cooler were attached to a rotation stage for angle tuning of the crystal that permitted fine adjustment of the DRO resonance modes. Each of the two mirrors was mounted in an aluminum plate that could be attached to a rigid aluminum block. Preliminary DRO cavity alignment was performed by adjusting the two aluminum plates. After the two plates were locked down the final alignment was made with the input pump beam, aided by the weak reflectivity of M2 at 532 nm. In this way we were able to achieve maximum mechanical stability for this three-element DRO by reducing vibration-induced perturbations. The pump cavity comprised the output coupler M3 and a 10-cm-radius input pump mirror M1 with a reflectivity of 90% at 532 nm. Piezoelectric transducers (PZTs) were attached to mirrors M1 and M2 so that each cavity could be tuned and controlled independently. M2 was usually servo controlled to maintain the double resonance of the signal and idler fields within the DRO cavity. The ability to align the two cavities separately was important in this experiment because there was a Poynting vector walkoff (∼0.23°) among the interacting beams in KTP.

We have evaluated the DRO without the pump cavity by removing mirror M1. Mirrors M2 and M3 were separated by 1.9 cm which yielded a free spectral range of 5.58 GHz for the DRO cavity. As the DRO cavity length was scanned, the outputs exhibited a series of narrow resonances with a width of ∼1 nm in the cavity length. Each resonance corresponded to the simultaneous resonance of the signal and idler fields. We stabilized the DRO’s cavity length by the usual side locking technique. The roundtrip power losses excluding the 2.69% output coupling was found to be 0.46% for the extraordinary polarization and 0.66% for the ordinary polarization for nearly degenerate operation of the DRO. The primary source for the losses was the antireflection coatings on the KTP crystal, which was also the cause of the difference in the losses for the two polarizations. Assuming an average roundtrip loss of 0.56% a quick estimate of the expected intensity correlation at low rf frequencies yields 7.6 dB below shot noise for unity detection quantum efficiency. The detection efficiency of our system was measured to be 89.5%, limited primarily by the InGaAs photodetectors. The schematic of the experimental setup in Fig. 2 shows that the detectors were tilted (∼45° angle of incidence) to reduce reflection losses, and we measured a detector quantum efficiency of 91.2%. At an overall detection efficiency of 89.5% and ignoring electronics noise, the maximum intensity correlation for the DRO system is expected to be 5.9 dB.

The pump was a krypton ion laser at 531 nm and was intensity stabilized to yield a residual intensity noise of 0.5% (peak-to-peak). We measured that the intensity noise spectrum of the pump laser was shot-noise limited for frequencies greater than 5 MHz. Without any frequency stabilization, the frequency jitter of the pump laser was ±20 MHz, mostly at the noise band of 400 Hz caused by the structural vibration of the laser’s plasma tube that was induced by the cooling water. In the absence of pump mirror M1, we observed an oscillation threshold of 350 mW. By use of the PZT-mirror M2 we were able to intensity lock the DRO to maintain its double resonance condition even in the absence of pump laser frequency stabilization. We have observed an intensity correlation of 3.5 dB below shot noise, which is significantly lower than expected. After thorough measurements of the losses of the DRO and the photodetection system, we concluded that the weak correlation was due to the ±20-MHz frequency jitter of the pump laser, even though the DRO was able to track the frequency jitter of the pump. In order to stabilize the pump laser a PZT-mounted back mirror replaced the original back mirror of the krypton ion laser. Unfortunately, the resultant output power was reduced due to lower reflectivity of the new back mirror and was barely at the pump threshold value, which led to our use of a TRO.

 

Fig. 2. Schematic of the experimental setup. HWP: half-wave plate, PBS: polarizing beam splitter.

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Without adjusting the DRO cavity, pump mirror M1 was installed in such a way that the mode matching for the DRO cavity was preserved for the pump field. We then stabilized the pump laser to a reference cavity and obtained an estimated linewidth of 50 kHz, well below the cavity linewidth of the DRO. We obtained a finesse of 55 for the pump cavity and the threshold for the TRO was ∼50 mW, although we observed a threshold range from as low as 40 mW to as high as 80 mW, depending on alignment. The pump cavity was stabilized by dithering M1 at 10 kHz, detecting the back-reflected pump light, and locking the cavity to the peak of the resonance with a lock-in amplifier. In this way, the pump and the DRO cavities were aligned and servo locked separately. The relatively low finesse of the pump cavity presented a problem in stabilizing the DRO outputs. A small variation of the pump cavity length due to dithering of M1 caused the internal pump power to vary. As a result the DRO output powers were found to vary at twice the dither frequency and at a significantly larger percentage due to the smaller cavity linewidth of the DRO. The small pump reflection of M2 also contributed to the problem. However, we were able to maintain a robust servo lock of both the DRO cavity and the pump cavity with stable and mode-hop-free operations. The added fluctuations in the DRO cavity lock did not seem to affect the time-averaged quantum noise measurements. For the DRO servo that had a unity gain frequency of 5 kHz, the ∼10% rms noise at 20 kHz was filtered out resulting in a dc output noise level of 1.5% rms. This dither-induced noise problem can be eliminated in the future by using frequency-modulation sideband locking technique that does not require dithering of the pump cavity mirror. We have also servo locked the pump cavity with a side locking technique but found that it was inferior to the dither-and-lock method.

As shown in Fig. 2 the TRO outputs were collimated with a lens, passed through a half-wave plate HWP1, and separated with a polarizing beam splitter (PBS) into two channels for difference-intensity correlation measurements. The vertically polarized output was further rotated by another half-wave plate HWP2 into horizontally polarized light to take advantage of the reduced reflection from the tilted photodetector. Typically the photocurrent at each detector was ∼1.0 mA. Because the intracavity losses for the signal and idler were not equal, the output powers were also different and were observed to have a variation of ∼10%. The dc portion of one of the photocurrents was used to intensity-stabilize the DRO cavity. The ac portion of each photocurrent was amplified with a Comlinear CLC425 transimpedance amplifier and the two voltages were differenced and amplified with another CLC425 amplifier. One of the channels had an adjustable 4-dB electronic gain to balance the signals from the two channels in order to maximize the common mode rejection at a particular rf frequency. We could typically obtain a common mode rejection of 30 dB at a specific frequency and between 20-25 dB over a broader range of several MHz. The difference-photocurrent output was then sent to a rf spectrum analyzer for data analysis and storage.

The purpose of HWP1 in Fig. 2 was to allow the measurement of either the signal-idler intensity correlation or the shot noise. If the fast axis of HWP1 was aligned parallel to the KTP’s c-axis (pure-mode setting), then the two optical channels from the PBS outputs would consist of signal and idler beams and their intensity correlation would be measured. By setting HWP1’s fast axis at an angle of 22.5° relative to the KTP’s c-axis (mixed-mode setting), the signal and idler beams would be rotated by 45° and the two optical channels would contain equal parts of signal and idler beams. The resultant difference-intensity noise measurements would yield the shot-noise level because the sub-shot-noise signal-idler correlation was destroyed by the mixed-mode setting while retaining the classical noise correlation. In this way, excess noise in the two beams was cancelled and the shot-noise level could be conveniently measured [1].

4. Experimental results

Figure 3 shows typical difference-intensity noise spectra of the TRO under (a) mixed-mode and (b) pure-mode settings for a sum photocurrent of 2.0 mA, averaged over 10 traces and with a resolution bandwidth of 10 kHz. The TRO was pumped at 80 mW and the threshold was 60 mW. As noted earlier the pump laser had excess noise up to 5 MHz and hence the TRO outputs also contained significant excess noise below 5 MHz. The large increase in noise power below 2 MHz in traces (a) and (b) of Fig. 3 was entirely due to pump excess noise [6]. For Fig. 3 the adjustable electronic gain was set to optimize common mode rejection at 4 MHz. Owing to the presence of excess noise and incomplete common mode noise rejection (except around a specific rf frequency) we observed that the setting of the adjustable electronic gain could change the slope and shape of the noise power spectrum for frequencies below 5 MHz. As a result we believe that the mixed-mode spectrum of Fig. 3(a) yielded the shot-noise level only for frequencies above 2.5 MHz. The shot-noise level was verified by injecting a 1064-nm YAG laser light into the unused port of the PBS. In addition, a white light source from a light bulb was used to confirm the shot-noise level to within +0.1 dB. (The shot noise had a slight slope due to nonuniform electronic gain.) Figure 3(c) is the electronic noise floor of the detection system. The signal-idler intensity correlation in Fig. 3(b) was 5.0 dB below shot noise for frequencies above 2.5 MHz, falling slightly to 4.9 dB at 8 MHz.

Figure 4 shows the noise power spectrum under (a) mixed-mode setting and (b) pure-mode setting for a 75-mW-threshold TRO that was pumped at 130 mW. The two traces were taken at a resolution bandwidth of 10 kHz, averaged over 25 traces, and for a sum photocurrent of 2.0 mA. For Fig. 4 we set the adjustable electronic gain to balance the two channels (performed under the pure-mode setting) to obtain a common mode rejection of ∼30 dB at 3 MHz. Trace 4(a) represents the shot-noise level for frequencies between 2.8 and 6 MHz. We believe that for frequencies below 2.8 MHz the shot-noise level is lower than that shown in Fig. 4(a) due to excess pump noise and insufficient common mode rejection at those frequencies. This is evident from the slopes of the two traces in Fig. 4 between 2-3 MHz. Trace 4(b) shows that the noise power became smaller toward 2 MHz. The slope of trace (b) in Fig. 4 is more reliable because the common mode rejection was optimized at 3 MHz under the pure-mode setting. On the other hand, the slope of trace (a) in Fig. 4 does not show similar features. Since the common mode rejection was not optimized under the mixed mode, this suggests that the noise spectrum of Fig. 4(a) between 2 and 2.8 MHz was above shot noise. The maximum correlation occurred around 3 MHz showing a suppression of 5.5 dB below the shot-noise level. Corrected for the electronic noise and the quantum efficiency of the detection system, the inferred suppression was 7.4 dB at 3 MHz, in good agreement with the expected value.

 

Fig. 3. Noise power spectrum of (a) mixed signal-idler mode (HWP1 angle at 22.5°), (b) pure signal-idler mode (HWP1 angle at 0°), and (c) photodetection electronics noise floor.

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Fig. 4. Noise power spectrum of output difference-intensity correlation for (a) mixed signal-idler mode (HWP1 angle at 22.5°) and (b) pure signal-idler mode (HWP1 angle at 0°). Maximum noise suppression is 5.5 dB at 3 MHz.

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It is instructive to compare our dual-cavity TRO results with the single-cavity TRO results of Mertz and coworkers [4]. The intracavity losses in both experiments were ∼0.6% that were limited by crystal absorption and the antireflection coating for the KTP crystal. If we were to increase the output coupler from our current 2.69% to 6.3% that was used by Mertz and coworkers, then the inferred noise correlation would have been identical (91%) in both cases and our threshold would have increased to 328 mW, compared with 430 mW for the Mertz experiment. (If we use our typical threshold values of ∼60 mW in our current setup, the threshold for a 6.3% output coupler would be even lower at 262 mW.) This lower threshold value is a direct result of a higher pump cavity finesse in our setup. This comparison highlights an important advantage of a dual-cavity TRO in that the finesse of the pump cavity can be varied easily by simply changing the mirror M1 which does not require ultralow-loss, dual-wavelength coatings that could be costly and difficult to make.

5. Conclusions

In summary, we have demonstrated a dual-cavity TRO that permitted separate adjustments and servo controls of the pump and DRO cavities. We have inferred an intensity noise correlation of 7.4 dB below shot noise at 3 MHz for a TRO that had a threshold of 75 mW and an output coupling of 2.69%. The modest result in this experiment should be adequate for a variety of applications. In applications where more substantial correlation is necessary, one can double the output coupling, which should increase the threshold by a factor of ∼3.3, and an inferred correlation of 10 dB at the output should result. Further improvements in the detection system are necessary to exploit the strong quantum noise correlation. This work also serves as a useful starting point in the observation of saturated optical parametric amplification [8].