The process of singly resonant second harmonic generation, where a fundamental pump beam is converted into its second harmonic, is known to produce bright squeezed light in the generated frequency-doubled beam [1]. The efficiency by which a squeezed state can be prepared from such a nonlinear optical process depends critically on two parameters that characterize the system. One is the internal passive loss of the fundamental beam [1]. The other is the strength of the non-linearity of the involved nonlinear material. LiNbO₃ is the nonlinear material most often used for frequency doubling at 1064 nm due to its relatively high non-linearity, but considerable improvement of the squeezing efficiency is expected by employing materials with higher non-linearities such as quasi phase matched optical materials. In those materials parametric interaction can be realized without using the critical constraints of natural birefringence phase matching. Phase velocity mismatch between the interacting waves is instead compensated by inverting the second-order susceptibility periodically throughout the material. In this work we have used a quasi phase-matched KTP crystal, which is engineered to access a non-linearity which is approximately four times higher than that of normal birefringence phase matched KTP and approximately two times higher than that of LiNbO₃.

Squeezing in pulsed single pass parametric amplification based on periodically poled LiNbO₃ (PPLN) has been achieved both in a waveguide [2, 3] and in a bulk crystal [4, 5]. In the cw regime Zhang et al. [6] and Lawrence et al. [7] obtained squeezing in PPLN using, respectively, an optical parametric oscillator based on cascaded non-linearities and a second harmonic generator. Owing to the higher non-linearity of PPLN with respect to PPKTP, most attention has been drawn to the PPLN. So far there has been only one report on quadrature squeezing based on a PPKTP crystal. Here short pulses were used to generate squeezing in a single pass PPKTP waveguide optical parametric amplifier [8]. In this letter we present what is to the best of our knowledge the first experimental observation of cw bright squeezed light generated from an intra-cavity periodically poled KTP second harmonic generator.

 

Fig. 1. A schematic diagram of the experimental setup.

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The experimental setup for generating bright squeezed light is depicted in fig. 1. A homemade frequency stable monolithic non-planar ring oscillator based on a Nd:YAG crystal delivers 250 mW of infra-red power at 1064 nm in a single longitudinal and transversale mode [9]. Unfortunately the laser light is influenced by excess amplitude noise at frequencies up to about 20 MHz, mainly because of intrinsic relaxation oscillations in the laser. The presence of these fluctuations are evident from fig. 2, which shows a plot of the noise spectrum for the laser (trace a) together with the standard quantum noise level (QNL) (trace c). To reduce the classical noise an empty cavity (a mode-cleaner) with a narrow line-width was inserted into the laser beam. The laser beam was carefully mode matched into the cavity, and the cavity frequency was actively stabilized to coincide with the laser frequency using the Pound-Drever locking method [10]. Only classical noise within the line width of the cavity passes through the cavity. The spectrum of the laser light after passing the mode-cleaner is shown in fig. 2 (trace b). We see that for this particular power level (approx. 25 mW) the laser light is now QNL at 6 MHz and hence transfers no classical noise into the second harmonic at frequencies higher than 6 MHz. Due to loss in the cavity mirrors and imperfect mode matching the cavity is not impedance matched, which gives rise to reduced power transmission. We measured 40 % power transmission. Besides working as a temporal filter the cavity also acts as a spatial filter. A “cleaned” TEM₀₀ beam is then mode matched into the SHG cavity with an efficiency of 98 % as opposed to 92 % without the mode-cleaner. The SHG cavity is a ring cavity formed as a bow-tie in order to reduce the reflection angles and thereby the astigmatism of the cavity mode. A ring configuration was chosen to avoid possible destructive interference that may result from a double passed linear cavity, and because the circulating beam only encounters the passive loss in the crystal once per round trip [11]. The cavity consists of two curved mirrors of 25 mm radius of curvature and two plane mirrors. Three of the mirrors are highly reflective at 1064 nm, while one has a transmission of 2 % and hence serves as the coupling mirror. The generated green light at 532 nm is freely escaping the cavity since the mirrors are highly transmissive at this wavelength. The crystal is placed in the smallest beam waist, which is located between the two curved mirrors. In order to maximize the conversion efficiency, which corresponds to an optimization of the Boyd-Kleinmann factor [17], we need a beam waist of 20 μm. This size was experimentally approximated by using a total cavity length of about 18 cm and choosing the distance between the two curved mirrors to be 3.2 cm. By measuring the finesse of the cavity we found an overall loss of 1.8 %.

The nonlinear medium for frequency doubling is a 1×5×11 mm periodically poled KTP crystal with both end faces antireflection coated for both the harmonic and the fundamental. The phase matching range of 6.7°C ensures very stable and reliable operation. To access the highest possible component of the susceptibility tensor associated with the KTP-crystal both the fundamental and the second harmonic waves are polarized as extraordinary waves. Frequency doubling in a normal KTP crystal cannot be attained by 90° non-critical phase matching when using a pump wavelength of 1064 nm [18]. Contrary to this case, the periodically poled KTP can easily be non-critically phase matched which in addition to being simple to operate also has the advantage of having no beam walk-off between the two interacting waves. To determine the efficiency of the SHG, the second harmonic conversion efficiency was measured as a function of pump power showing a maximum of 50%. By fitting this curve to theory with the internal conversion coefficient, Γ_nl, as the only fitting parameter, we find Γ_nl = 0.0083W^-1.

Self-homodyne detection of the generated green light was employed in order to verify the quantum noise limit at the particular power level. A pair of identical photo detectors based on Si photodiodes (Hamamatsu S3072) were designed with the special requirements of high quantum efficiency, relatively high power handling and low noise amplification. The quantum efficiency was measured experimentally to 80 %. Low noise amplification of the photo currents was obtained using a monolithic amplifier (HP-INA01170) [14] and a notch filter at 600 kHz was inserted in the detector electronics to avoid saturation of the amplifier due to the relaxation oscillations of the laser. The amplified ac photo currents from the two detectors were subsequently sent to passive 0° and 180° power splitters and finally to a spectrum analyzer for analysis in frequency space. Because the detectors were optically balanced by the use of a good 50/50 BS the reproduced sum signal is the intensity noise while the difference signal is a measure of the standard quantum noise limit [12].

 

Fig. 2. Amplitude noise of our Nd:YAG laser as a function of frequency. Trace a is the noise power spectrum of the laser field before it enters the mode-cleaner, trace b is the noise spectrum of the mode-cleaner output field and trace c is the quantum noise limit. The dip at low frequencies is caused by the notch filter in our detectors while the modulation at 19.5 MHz is for locking the cavity. RBW=300kHz, VBW=1kHz.

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We pumped the second-harmonic generator with mode matched power of 65 mW, which was the maximum available after passing the different optical components. However, higher pump powers are expected to increase the squeezing. Figure 3 shows the spectrum of the squeezed signal together with the quantum noise level at frequencies from 1 MHz to 30 MHz. Noise in the detector electronics was found to be 11 dB below the QNL and hence negligible. Noise reduction below the QNL is evident from 6 MHz to 17 MHz and from about 25 MHz the squeezing vanishes due to the limited line-width of the second harmonic cavity. The squeezing was also monitored at a single frequency (Ω = 10 MHz), which is shown in figure 4. A maximum of 0.6± 0.1 dB (0.87± 0.02 on a linear scale) of squeezing was obtained.

Applying the input-output formalism of Gardiner and Collett [13] and the semi-classical theory for single resonance SHG developed by Collett and Levien [15] and Paschotta et al. [1] an equation for the second harmonic spectrum normalized to the QNL, which is set to 1, can be found. We have

where P_c is the circulating power inside the SH cavity which can be determined using standard nonlinear optics. Γ_nl is the internal conversion efficiency, Ω is the noise frequency, T and L are the transmission of the coupler mirror and the passive losses at the fundamental frequency, respectively, and τ is the resonator lifetime. By inserting the experimental values (T=2 %, L=1.8 %, Γ_nl = 0.83 %W^-1) and with an input power of 65 mW we find V=0.85 at 10 MHz. The small discrepancy with the observed squeezing ratio of 0.87 results from losses in the detection process and transmission losses down stream from the SHG to the homodyne detector. The expected amount of degraded squeezing is V_l = ηV + (1 - η) where η is the efficiency by which the squeezed state is measured. This quantity is measured to η=0.80 and by insertion we find V_l = 0.88, which is in excellent agreement with the experimentally obtained value.

 

Fig. 3. Spectra of the amplitude noise for the squeezed second harmonic field and for the vacuum field. The latter defines the QNL. Spectra are obtained with RBW=3MHz and VBW=1kHz.

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Fig. 4. Amplitude noise power and QNL is observed at 10MHz in zero span mode with RBW=300 kHz and VBW=300 Hz.

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The generation of squeezed light at relatively low input powers is one of the main advantages of using quasi phase matched materials. Using normal phase matched LiNbO₃ with γ_nl = 0.4 %/W [16] and otherwise the same parameters as in our experiment the theory above predicts that squeezing of 0.6 dB will require an input power of 160 mW. This is more than twice as high as the power we used. Such high pump powers give rise to a very bright squeezed beam (around 80 mW) which makes it more difficult to measure because of saturation of the photodiodes.

We stress that the relatively low squeezing obtained in our device is mainly a result of the high intra-cavity losses. Replacing the PPKTP crystal with a normal birefringence phase matched KTP is anticipated to reveal a degraded squeezing performance. On the other hand, keeping the PPKTP in place and using higher quality mirror and crystal coatings, much higher degrees of squeezing might be observed. Intra-cavity losses of only 0.3% in a similar frequency doubling system has been achieved in ref. 17.

In summary, we have observed bright amplitude squeezing of green light which is produced by a singly resonant frequency doubler employing a periodically poled KTP crystal as the nonlinear material. We put emphasis on the influence of the non-linearity for squeezed light production. With intra-cavity losses of 1.8 % we obtained a noise reduction of 13 %. Using high quality mirror coatings [18], efficient AR coatings on the crystal and a mode-cleaner with a narrower line width [19] a squeezing degree of approximately 3 dB at 5 MHz is expected at low powers. Using higher pump powers, say 300 mW, direct detection of almost 5 dB of squeezing is achievable in a relatively simple system.

The PPKTP crystal was kindly made available on a loan from ASAH Medico A/S. Financial support for this research was provided by a Ph.D. stipend from the Technical University of Denmark.