Chapter 11 Domain-Engineered Ferroelectric Crystals for Nonlinear and Quantum Optics

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1 Chapter 11 Domain-Engineered Ferroelectric Crystals for Nonlinear and Quantum Optics Marco Bellini, Pablo Cancio, Gianluca Gagliardi, Giovanni Giusfredi, Pasquale Maddaloni, Davide Mazzotti, and Paolo De Natale 11.1 Introduction Nonlinear optics studies the class of phenomena occurring when an intense light field, typically from a laser source, modifies the optical properties of a transparent material in a nonlinear way [1 3]. The polarization P (x,t) of the material can be written as a power series in the field strength E(x,t): P = χ (1) E + χ (2) E 2 + χ (3) E 3 + (11.1) where χ (i) is the i-order optical susceptibility of the material. Nonlinear phenomena arise from the non-zero value of the χ (2) susceptibility in non-centrosymmetric crystals. A large class of nonlinear materials (among them LN, KTP, BBO and LBO) has been studied and used since 1960s for up/down-conversion of the existing laser sources to wavelength regions which are not directly accessible otherwise [4]. Some of these materials also belong to ferroelectrics and this feature can be exploited to engineer the orientation of their nonlinear susceptibility. One of the earliest [5] and most commonly used material is LiNbO 3 (LN), because of its high nonlinear coefficient (d pm/v) and its wide transparency range from the UV to the mid IR (0.3 5 µm). A technique giving access to d 33 in LN for optimizing nonlinear conversion processes, named quasi-phase-matching (QPM) [6], was thought even M. Bellini P. Cancio G. Giusfredi D. Mazzotti (B) P. De Natale Istituto Nazionale di Ottica del CNR (CNR-INO), Largo Fermi 6, Firenze, FI, Italy davide.mazzotti@ino.it M. Bellini P. Cancio G. Giusfredi D. Mazzotti P. De Natale European Laboratory for Nonlinear Spectroscopy (LENS), Via Carrara 1, Sesto Fiorentino, FI, Italy G. Gagliardi P. Maddaloni Istituto Nazionale di Ottica del CNR (CNR-INO), Via Campi Flegrei 34, Pozzuoli, NA, Italy P. Ferraro et al. (eds.), Ferroelectric Crystals for Photonic Applications, Springer Series in Materials Science 91, DOI / _11, Springer-Verlag Berlin Heidelberg

2 286 M. Bellini et al. before the first fabrication of this material. About 20 years later the first experimental demonstration of this idea was obtained [7] and nowadays periodic poling of ferroelectrics crystals is a widely spread technology making these devices worldwide used and commercially available Classification of Nonlinear Processes Depending on the optical configurations in which the input/output waves interact through the χ (2) susceptibility, different class of processes can be identified. Each kind of process always involves 3 optical waves named pump, signal and idler (with decreasing frequencies ν p >ν s >ν i ). The energy conservation law for the discrete conversion of a pump photon into a signal/idler photons pair (or viceversa) requires: ν p ν s ν i = 0 (11.2) It is obvious that the frequency tunability of the output wave(s) as well as its/their linewidth(s) are strictly bound by this law. The spatial modes and the power of the output wave(s) depends on the focusing and overlapping of the input wave(s). When the input waves are signal and idler and the output wave is the pump, the process is named sum-frequency generation (SFG). This is an up-conversion process, in which the generated frequency is higher than the two generating ones. In the degenerate case, when ν s = ν i and ν p = 2ν s the process is named secondharmonic generation (SHG) and consists in an optical frequency doubling. When the input waves are pump and signal and the output wave is the idler, the process is named difference-frequency generation (DFG). This is a down-conversion process, in which the generated frequency is lower than the two generating ones. When the input wave is the pump and the output waves are signal and idler, the process is named optical parametric generation (OPG). This is a down-conversion process, in which the two generated frequencies are lower than the generating one. When one of the generated wave, either signal or idler (or even both), resonates in an optical cavity, the process is named optical parametric oscillation (OPO) and, similarly to what happens in a laser cavity, a threshold pump power exists for the oscillation to occur Phase Matching Equation (11.2) is not the only conservation law binding the nonlinear process. The momentum conservation law, better called phase matching (PM) condition, is another physical condition determining the direction of the process (direct/inverse), i.e. if photons will emerge from the crystal at the frequency of the pump/signal/idler: k p k s k i = 0 (11.3)

3 11 Domain-Engineered Ferroelectric Crystals 287 that for collinear waves is equivalent to n p ν p n s ν s n i ν i = 0 (11.4) Because of the dispersion in transparent media (n p >n s >n i ), this condition is not automatically satisfied and suitable optical properties overcoming this naturally occurring phase mismatch must be exploited. Birefringent Phase Matching Most of the nonlinear optical materials with a non-zero χ (2) are also birefringent (apart from crystals with cubic symmetry). For example, the birefringence of uniaxial crystals can be exploited to achieve PM due to the existence of ordinary/extraordinary refraction indexes n o and n e along different directions with respect to the optical axis. A careful tuning of the orientation angle and temperature of the crystal can give the desired PM condition. In special cases named non-critical PM, where the crystal orientation angle is either 0 or 90, an unwanted walk-off between the interacting waves is also avoided and the efficiency is higher. With this kind of PM the polarization of the 3 waves involved in the nonlinear process cannot be all the same, since these waves are both ordinary and extraordinary. Hence birefringent PM (BPM) gives access to small off-diagonal nonlinear coefficients (i.e. the d ij elements with i j) only. Quasi-phase Matching For not all nonlinear mixing processes a suitable crystal with noncritical PM at a certain temperature can be found. This can be overcome with a special class of crystals, whose ferroelectric domains are periodically poled. The phase mismatch of the interacting waves is quasi-compensated every half period by the inversion of the χ (2) susceptibility. The QPM gives access also to the large diagonal nonlinear coefficients (i.e. the d ii elements), increasing the efficiency of optical mixing processes by about a factor of 20 with respect to BPM Nonlinear Optics for Spectroscopic Applications Since its early appearance, laser spectroscopy has shown to be a powerful tool to investigate atomic and molecular physics with great precision and sensibility. While present laser sources cover most of the visible/near-ir spectrum of light, there is a lack of available coherent sources in the µm region. However this spectral window is of the utmost importance for trace gas detection, because here lie the fundamental ro-vibrational bands of many molecular species of atmospheric interest.

4 288 M. Bellini et al Coherent Sources for Mid-IR Spectroscopy and Metrology Several coherent sources exist with emission in the mid-ir. Now, let us shortly describe their features in terms of frequency tunability, power and linewidth. Gas lasers (e.g. He Ne, CO, CO 2 ) are generally powerful, but poorly tunable coherent sources: this seriously limits the probability to find coincidences between their discrete emission frequencies and molecular spectra. Quantum cascade lasers (QCLs) [8 10] are carefully engineered semiconductor lasers directly emitting in the mid-ir even more than 5 W average power [11]. Room-temperature and single-frequency continuous-wave (CW) operation is available in the spectral range µm [12, 13]. The tunability of a distributedfeedback (DFB) device is rather poor (<10 cm 1 ) and it is only achievable with wide changes in the operation temperature. Nevertheless, similarly to conventional semiconductor lasers, broad-gain QCLs mounted in an external-cavity configuration with a feedback grating can achieve wider tuning ranges (>400 cm 1 )[14]. Optical parametric oscillators (OPOs) are powerful and widely tunable (2 4.5 µm) sources based on χ (2) optical processes occurring in nonlinear crystals within singly or doubly resonant cavities [15]. They often suffer from uncontrolled mode-hops and requires cavity locking with servo loops. Alternatively, coherent sources based on DFG rely on nonlinear optical processes and can generate narrow-linewidth and tunable radiation in the same spectral region, with IR powers ranging from a few µw [16 18] uptoafewmw[19, 20]. DFG source do not requires resonant cavities and are intrinsically mode-hop free. Periodically-poled LiNbO 3 (PPLN) is one of the most efficient nonlinear crystals for the mid-ir [4]. Its transparency range allows down-conversion processes from visible/near-ir lasers to the µm range. For many years, mid-ir metrology has been limited to a few frequency references, mainly gas lasers stabilized onto molecular transitions, such as He Ne/CH 4 at 3.39 µm or CO 2 /OsO 4 at 10.6 µm [21]. The advent of optical frequency-comb synthesizers (OFCSs), based on mode-locked fs lasers, has suddenly led to new advances in the field of precision spectroscopy [22, 23]. By acting as a bridge between the radio-frequency (RF) and the optical domain, an OFCS allows to count the optical cycles of a CW laser directly with respect to an absolute frequency standard, such as an atomic clock. This has represented an immediate breakthrough for accurate frequency metrology in the visible/near-ir spectrum where the first OFCSs worked, enabling for measurements of atom energies with a relative precision approaching [24 26]. In this frame, new perspectives have been opened recently by the demonstration of OFCSs operating in the UV, based on high-order harmonic up-conversion [27 33]. On the other hand, further extension of OFCSs to the IR region is crucial for absolute frequency measurements on molecular ro-vibrational spectra. So far, direct broadening of the spectrum of fs mode-locked lasers through highly-nonlinear optical fibers has succeeded in extending combs up to a 2.3-µm wavelength [34]. For longer wavelengths, a few alternative schemes have been devised, essentially based on parametric generation processes in nonlinear crystals. A 270-nm-span frequency comb at 3.4 µm has been realized by DFG between two

5 11 Domain-Engineered Ferroelectric Crystals 289 spectral peaks emitted by a single uniquely-designed Ti:Sa fs laser [35]. In a different approach, the metrological performance of a Ti:Sa OFCS has been transferred to the 9-µm region by using two diode lasers at 852 and 782 nm as intermediate oscillators, with their frequency difference phase-locked to a CO 2 laser. Then, the CO 2 laser has been used for saturated absorption spectroscopy to provide absolute frequency measurements of several CO 2 lines [36]. A two-branch mode-locked Er:fiber pump source has been used to produce single-pass DFG radiation by using a MgO:PPLN crystal, delivering femtosecond pulses, with an average power of up to 1 mw of mid-ir radiation tunable in the wavelength range between 3.2 and 4.8 µm at a repetition rate of 82 MHz [37]. A fiber-laser-pumped OPO based on a fan-out MgO:PPLN crystal has provided a high-power frequency comb in the mid-ir spectral region, generating up to 0.3-µm-wide idler spectra, which are continuously tunable from 2.8 to 4.8 µm, with an average power of up to 1.5 W [38]. Other synchronously-pumped OPOs have provided mid-ir frequency combs with similar schemes (see, e.g., Refs. [39, 40]) OFCS Extension to the Mid-IR We report two different schemes which exploit a DFG process to transfer the metrological performance of a visible/near-ir OFCS to the mid-ir. In one scheme, the DFG near-ir pumping lasers are phase-locked to their associated closest tooth in the comb. Then, the generated mid-ir radiation is used for saturated-absorption spectroscopy providing absolute frequency measurements of CO 2 lines at µm with a relative uncertainty down to about In the second scheme, a frequency comb is directly created at 3 µm by nonlinear mixing of a near-ir fiber-based OFCS with a CW laser. In the latter case, the generated comb can be employed both as a frequency ruler and as a direct source for molecular spectroscopy. 4-µm Experiment The setup implemented to lock the DFG radiation to the visible/near-ir OFCS, described into details in previous works [41, 42], is shown in Fig The pump source is an external-cavity diode laser (ECDL) operating between 830 and 870 nm with a maximum power of 130 mw. The signal laser source is a monolithic-cavity Nd:YAG laser at 1064 nm seeding an Yb fiber amplifier with a maximum power of 5 W. The diffracted (1)-order beam coming from an acousto-optic modulator (AOM) is then used for the DFG process. The latter takes place in a PPLN crystal (with a period around 23 µm) and produces about 200 µw of idler radiation at 4.2 µm. The OFCS is based on a Kerr-lens mode-locked Ti:Sa laser and covers an octave in the visible/near-ir region ( nm). Its repetition rate (f r = 1 GHz) is locked to a high-stability reference oscillator. The latter consists of a 10-MHz quartz which is locked to a GPS-disciplined Rb clock. The measured stability of such a system

6 290 M. Bellini et al. Fig Schematic of the experimental apparatus: C = fiber collimator, AOM = acousto-optic modulator, HWP = half-waveplate, DM = dichroic mirror, AL = achromatic lens, L = lens, Ge-F = germanium filter, M = mirror, PLL = phase-locked loop, PBS = polarizing beam splitter, G = diffraction grating, PD = photodiode. The 4-µm radiation is phase-locked to the Ti:Sa comb through the DFG pumping lasers and used either for sub-doppler or cavity-ring-down spectroscopy providing absolute frequency measurements of ro-vibrational molecular transitions against a Cs-fountain-disciplined H maser limits the OFCS precision to at 1 s and its accuracy to After nonlinear mixing, RF beat notes (f p and f s ) are generated between the pump/signal beams and their associated closest teeth (with orders N p and N s, retrieved by a wave-meter) in the comb are used to phaselock the mid-ir radiation to the OFCS. For this purpose, two phase-locked-loop (PLL) circuits are used to feed appropriate frequency corrections back to the lasers. Then, the frequency of the generated idler radiation is given by ν i = (N p N s )f r ± f p ± f s (11.5) and its stability is limited by the OFCS. Frequency scans across a molecular resonance are performed by sweeping the beat-note frequency of one of the pumping lasers. Simultaneously, the beat-note frequencies f p and f s for each data point in the spectrum are recorded to yield an absolute frequency scale following (11.5). Then, the line center absolute frequency is measured by fitting a suitable theoretical function to the experimental line shape. For transitions with a sufficiently high dipole moment, precision of measurements can be further improved by performing saturated-absorption spectroscopy which reduces the observed linewidth δν thus increasing the quality factor Q = ν/δν. An example of spectrum is given in Fig. 11.2, which shows the Lamb-dip profile for

7 11 Domain-Engineered Ferroelectric Crystals 291 Fig Experimental recording of the CO 2 ( ) R(60) saturated-absorption line at cm 1. The enhancement optical cavity is filled with pure gas at a pressure of 27 µbar and the first-derivative signal is obtained by modulation of the Nd:YAG laser frequency. The experimental data points, the fitting curve and the residuals are shown. The line center is measured by fitting the experimental line shape with a theoretical model taking into account the various broadening effects. This yields the value (1) MHz, corresponding to a relative uncertainty of the ( ) R(60) CO 2 transition at cm 1 recorded by a liquid-n 2 - cooled InSb detector. The first-derivative signal was obtained by modulation of the Nd:YAG laser frequency at a rate of a few khz. Due to the limited DFG power, in this experiment the 4-µm beam was coupled to a confocal Fabry-Perot enhancement cavity (free spectral range FSR = 1.3 GHz, finesse F 500) filled with pure gas at a pressure of 27 µbar. The reflection signal from the cavity was also detected by a second InSb detector and used to actively control its length (by means of a PZT transducer) in order to keep the cavity mode resonant with the IR frequency during the scan. The line center was measured by fitting the experimental line shapes to a theoretical model taking into account several broadening effects, the main contributions coming from collisions ( 100 khz) and transit time ( 400 khz). The measured value is (1) MHz, which corresponds to a relative uncertainty of Moreover, this uncertainty can be further reduced by repeating the above procedure many times over a long period (a few months) and taking the weighted-average value [41]. Absolute frequency measurements can also be extended to very weak transitions by using the OFCS-referenced DFG radiation in high-sensitivity detection schemes. Indeed, cavity ring-down spectroscopy (CRDS) has also been performed by coupling the 4-µm beam to a high-finesse optical cavity (FSR = 150 MHz, finesse > 24000). In this configuration, when a given threshold for the intra-cavity photon filling is achieved, a digital oscilloscope starts acquiring the signal transmitted through the cavity and the corresponding trigger signal makes the acousto-optic modulator on the Nd:YAG laser rapidly ( 1 µs) switch off the DFG beam. As an example, in

8 292 M. Bellini et al. Fig Doppler-broadened ( ) P(19)e ro-vibrational transition of 13 CO 2 at cm 1 (linestrength S = cm), recorded by means of CRDS at a gas pressure of 9 mbar. Here, L is the cavity mirror spacing and α the absorption coefficient. The Gaussian fit gives the line-center absolute frequency with a relative uncertainty of Fig we show the Doppler-broadened ( ) P(19)e ro-vibrational transition of 13 CO 2 at cm 1 with linestrength S = cm, recorded with a gas pressure of 9 mbar. The Gaussian fit curve is also shown, giving for the line center the absolute frequency value of (1) MHz. In this case, the higher relative uncertainty ( ) is basically due to the lower quality factor Q of measurements performed in Doppler broadening regime. More recently, the spectral features of the 4-µm DFG source to the OFCS were improved [18] by introducing a phase-locking scheme [43]. The pump radiation from the ECDL is phase-locked to the signal radiation from the Nd:YAG laser across a frequency gap of about 70 THz, by using the OFCS as a transfer oscillator, while canceling out any frequency-noise contribution coming from the two OFCS parameters f 0 and f r. Figure 11.4 depicts a schematic of this new OFCS-referenced DFG source. A loose phase-locked-loop (PLL), not shown in figure, with a low bandwidth ( 10 Hz) is used to remove the frequency drift of the Nd:YAG laser, by locking it to the OFCS. A tight PLL circuit, shown in Figure, with a much higher bandwidth ( 2 MHz) locks the pump frequency to the signal one, by feeding correction signals back to the ECDL current and PZT voltage. The final achievement of the DDS-based locking scheme is an idler frequency which is related to the signal one only, according to the following equation: ( ) Np ν i = ν p ν s = 1 ν s (11.6) N s For all Fourier frequencies below 10 Hz, ν s traces the N s -th comb tooth around 1064 nm and thus ν i traces the reference oscillator of our OFCS, whose stability and accuracy has been reported above. For all Fourier frequencies above 10 Hz, ν s traces the free-running Nd:YAG laser frequency and thus all fast frequency fluctuations of the idler radiation are a fraction (N p /N s 1) of signal ones. This ultra-stable mid- IR source was used to demonstrate a new spectroscopic technique, named saturatedabsorption cavity ring-down (SCAR) [44]. This technique requires CW radiation

9 11 Domain-Engineered Ferroelectric Crystals 293 Fig OFCS-referenced DFG IR source with the OFCS used as a transfer oscillator to phase-lock the ECDL directly to the Nd:YAG laser. DM, dichroic mirror; PPLN, periodically-poled LiNbO 3 crystal; Ge, germanium filter; PLL, phase-locked loop; DDS, direct-digital synthesis. (Figure extracted from Ref. [18]) with a linewidth so narrow as to be efficiently coupled to a high-finesse optical cavity, whose resonance mode linewidth can be as low as only few khz. Those accuracy and narrow-linewidth properties were also transferred to a power-boosted version [20] of the DFG source described above, based on intracavity non-linear generation in an active Ti:Sa laser cavity. This source was able to deliver up to 30 mw power around 4.5 µm and that relatively high power was used to perform SCAR spectroscopy at higher pressures, where the saturation intensity is much higher (scaling with squared pressure). This combination of high power and narrow linewidth in the same mid-ir source has allowed both the first absolute frequency measurement of the ν 3 ro-vibrational band of radiocarbon dioxide in a highly-enriched sample [45] and the first absolute concentration measurement of this species well below natural abundance ( 1 ppt) with an optical technique [46, 47]. The measured concentration values of radiocarbon were also independently validated by the well assessed and more sensitive accelerator mass spectrometry (AMS) technique [48]. A parallel research line has also used the DFG sources described above as references for phase/frequency characterization and stabilization of QCLs, thus improving the knowledge and performance of these emerging current-driven semiconductor-based mid-ir sources (see Refs. [49, 50] for a recent review). A first crucial step towards metrological QCLs was their reference to a visible/near-ir OFCS. This was possible by up-converting radiation from a DFB QCL around 4.4 µm in a PPLN crystal by mixing it with radiation at 1064 nm from a Nd:YAG laser [51]. A similar up-conversion scheme for locking a QCL at 4.3 µm to a near-ir OFCS was later on implemented by mixing QCL radiation with part of the OFCS emission spectrum around 1560 nm [52]. By using the OFCS-referenced setup of Ref. [51], it was possible to get absolute frequency measurements of sub-doppler CO 2 ro-vibrational transitions with a khz level precision [53].

10 294 M. Bellini et al. Fig Lamb-dip detection on the Doppler profile of the A (2) 1 R(4) transition at cm 1, obtained by means of a 3-mW DFG beam used in a simple pump-and-probe scheme. By phase-locking the DFG pumping lasers to the near-ir OFCS, absolute frequency measurement of the observed line is possible. The line is a Lorentzian fit to the experimental points Different concepts for transferring the frequency stability of OFCS-referenced DFG radiation to QCLs were demonstrated starting with In a first setup, control of a mid-ir QCL was directly obtained by optical injection of OFCS-referenced DFG radiation [54]. In a second scheme, ultra-narrow PPLN-generated differencefrequency radiation was used to test the sub-kilohertz linewidth of a QCL frequency locked to a molecular sub-doppler line [55]. This class of setups gave rise to a new scenario for high-precision mid-ir molecular spectroscopy, both for the measurement of line parameters [56] and for absolute frequency measurements with an overall uncertainty down to [57]. In a very recent setup, OFCS-referenced radiation generated by a difference-frequency non-linear process in a PPLN crystal was used for achieving a stability of the center frequency of a phase-locked QCL at a level of , providing at the same time full frequency tunability for spectroscopic applications [58]. 3-µm Experiment The method described above can be readily applied to different spectral windows by proper choice of the DFG pumping sources and the nonlinear crystal. In this regard, a more powerful and tunable DFG apparatus can produce absolute frequency measurements on several molecular species and in much simpler configurations. For this purpose, a DFG source operating from 2.9 and 3.5 µm with a maximum output power of 5 mw has been realized and used for sub-doppler molecular spectroscopy with no need of enhancement optical cavities [19]. Indeed, by a simple pump-and-probe scheme, saturation Lamb-dips have been observed for a number of ro-vibrational transitions belonging to the CH 4 ν 3 fundamental band. An example is shown in Fig for the A (2) 1 R(4) line at cm 1, recorded in a 50-cm-long cell filled with pure gas at a pressure of 40 µbar. Then, the above comb-referencing scheme is able to provide the absolute frequency of the observed

11 11 Domain-Engineered Ferroelectric Crystals 295 Fig Layout of the optical table. A 3-µm frequency comb is created by difference-frequency generation in a PPLN crystal between a near-ir OFCS and a CW laser. A fast, 100-µm-diameter MCT detector is used to characterize the generated mid-ir comb transitions. However, one drawback of this approach is the impossibility of combreferencing for direct laser sources operating in the mid-ir, such as QCLs. In this section, we demonstrate a novel scheme, based on DFG, which directly realizes a mid-ir optical frequency comb. The nonlinear down-conversion process occurs in a PPLN crystal (with a period around 30 µm) between a near-ir OFCS and a CW tunable laser. The generated mid-ir frequency comb covers the region from 2.9 to 3.5 µm in 180-nm-wide spans with a 100-MHz mode spacing and keeps the same metrological performance as the original comb source. Such a scheme can be easily implemented in other spectral regions by use of suitable pumping sources and nonlinear crystals. The apparatus devised to create the 3-µm frequency comb, reported in a previous work [59],isshowninFig The DFG signal radiation comes from a near-ir OFCS based on an Er doped fiber laser which utilizes passive mode locking to provide ultra-short pulses ( 100 fs). The following spectral broadening through a nonlinear fiber makes the OFCS cover an octave from 1050 to 2100 nm. Its repetition rate (100 MHz) and carrier-envelope offset frequency are locked to a reference oscillator. The signal beam is then provided by feeding a fraction (25 mw) of the fs fiber laser system output (before the spectral broadening stage), covering the nm interval, to an external Er-doped fiber amplifier (EDFA). The power spectral distribution, resulting from the convolution with the EDFA gain curve, is measured by an optical spectrum analyzer. The amplified comb beam has an overall power of 0.7 W and spans from 1540 to 1580 nm with a 100 MHz spacing, corresponding to nearly N t = teeth (i.e. about 14 µw per tooth). The pump beam is generated by an ECDL emitting in the range nm and is amplified by an Yb-doped fiber amplifier which delivers up to 0.7 W,

12 296 M. Bellini et al. preserving the linewidth of the injecting source (less than 1 MHz). Afterwards, the two laser beams are combined onto a dichroic mirror and focused by a near-ir achromatic lens into a temperature-controlled, antireflection-coated PPLN crystal. The latter consists of an array of 9 channels, with different poling periods ranging from 29.6 to 30.6 µm. Once the wavelength of the pump source is fixed (1055 nm), the channel and temperature value (around 340 K) are properly chosen to satisfy the QPM condition with the center wavelength of the near-ir comb (1560 nm). The teeth on both sides are involved in as many DFG processes, with a conversion efficiency decreasing according to the well-known sinc 2 law [19]. The 3-µm comb is detected by filtering the DFG idler beam from the unconverted near-ir light and focusing it onto a liquid-n 2 -cooled, 150-MHz bandwidth HgCdTe (MCT) detector. In this way, a RF beat note at f r = 100 MHz is recorded by a spectrum analyzer, which is the sum of the beat signals between all pairs of consecutive teeth in the generated comb. The latter has a bandwidth of 180 nm (5 THz) centered near 3.3 µm and its measured overall power is about P = 5 µw. This value corresponds to a power of nearly P/N t = 100 pw per mode of the IR comb. Since the linewidth of the ECDL is around 1 MHz, the DFG comb lines are significantly wider than those of the near-ir OFCS. This can be partially overcome by locking the ECDL to a tooth of the near-ir comb (see Fig. 11.6), which also cancels out the carrier-envelope phase offset present in the original frequency comb. As discussed in the previous section, if the optical comb were used as a frequency ruler, its metrological performance would be transferred to a CW laser by phase-locking the latter to the closest comb tooth. In order to demonstrate that such a scheme is possible even in a hardly accessible spectral region, like the µm range, a CW DFG beam is simultaneously produced for characterization. This is accomplished by simultaneously seeding the Er-fiber amplifier with an ECDL emitting in the nm interval (having a linewidth lower than 500 khz). In this configuration, a CW 1.5-µm beam is also produced by the EDFA which gives rise to a second DFG process with the pump radiation thus producing a CW idler beam around 3 µm with a power between 1.5 and 3 mw, depending on the wavelength. As a consequence, two additional RF beat notes at f 1 = ν CW ν n and f 2 = ν n+1 ν CW are detected between the DFG CW radiation at ν CW and its two closest mid-ir comb teeth at ν n and ν n+1 respectively (see Fig. 11.7). The signal-to-noise ratio (SNR) for such beat notes can be measured as the 1.5-µm ECDL wavelength is tuned from 1540 to 1570 nm (ν CW from 3.22 to 3.35 µm). The SNR value reaches a maximum of 35 db at the center wavelength (1555 nm), while decreases almost symmetrically down to less than 20 db at the upper and lower edges. This configuration limits to about 130 nm the interval which is suitable for use in optical phase-locked systems. Actually, the 180-nm span can be fully exploited as higher beat notes are expected when only an external 3-µm mw-power source is used during normal operation (i.e. in absence of the simultaneous CW DFG beam coming from the same EDFA which subtracts power from the DFG comb). Moreover, SNR levels can be further improved selecting a smaller number of teeth by using an IR diffraction grating. Finally, by tuning the 1-µm laser wavelength, the center frequency of the DFG comb is tuned from 3.1 to 3.4 µm, without any need to adjust the QPM conditions. This is

13 11 Domain-Engineered Ferroelectric Crystals 297 Fig Beat signals recorded by the RF spectrum analyzer at the center of the 3-µm comb span. The peak at f r = 100 MHz is the sum of the beat signals between all pairs of consecutive teeth in the generated comb, while the peaks at f 1 and f 2 correspond to the beat notes between the DFG CW radiation and its two closest comb teeth. Resolution and video bandwidth are 3 khz and the sweep time is about 1 s Fig SNR for the beat note at f r = 100 MHz as a function of the DFG wavelength, recorded by tuning the pump source from 1040 to 1070 nm. Each point represents a frequency comb with a span of about 150 nm. The asymmetric behavior with respect to the central wavelength is caused by the decrease in the optical power of the Yb fiber amplifier showninfig.11.8 where the peak signal of the beat note at 100 MHz is plotted as a function of the 1-µm wavelength, the upper limit being set by the laser tunability range. By also tuning the QPM conditions, higher conversion efficiencies and further extension of the span (from 2.9 to 3.5 µm) can be accomplished. Thus, such a generated comb might be strategic for future metrological applications of novel lasers under development [60] Future Perspectives We have presented two schemes for performing absolute frequency measurements in the mid-ir spectral region. OFCSs are used either to directly create a mid-ir frequency comb through a DFG process with a CW laser or to reference the DFG radiation to the Cs primary standard by phase-locking of the pumping sources. This opens

14 298 M. Bellini et al. new perspectives for absolute frequency measurements on ro-vibrational molecular transitions for determination of molecular constants and frequency grids with improved accuracy. As a direct spectroscopic source, the range of mid-ir combs applications is more and more widening, e.g. exploiting coherent coupling to highfinesse cavities to provide sensitive molecular detection [61]. The QCL is proving to be a key tool for mid-ir spectroscopy [62]. Hybrid sources combining telecomderived fiber technology with non-linear crystals and QCLs will possibly emerge as convenient and flexible tools for even the most demanding applications Structured Nonlinear Crystals for Quantum Optics Quantum mechanical phenomena, besides their importance for our understanding of the fundamental structure of Nature, have the potential of enormously improving the performances in a variety of emergent technologies. Since the theoretical beginnings, dating back to the eighties, the exploitation of quantum effects in the field of information processing has seen an explosive growth, both in the number of theoretical proposals and in the first experimental realizations [63].Thenewfieldof quantum information science has so far identified several important objectives, ranging from quantum computation [64], and cryptography [65], to quantum-enhanced metrology [66]. Quantum computation may result in computation faster than any computation possible with classical means. Quantum cryptography, and in particular, quantum key distribution, makes intrinsically secure sharing of cryptographic keys possible against any possible attack of an eavesdropper. Quantum metrology allows one to attain an unsurpassable precision in the measurement of a physical quantity by beating the standard limits due to shot noise. The practical realization of such applications is particularly well suited to optical systems, where the basic quantum states can be simply prepared, manipulated, and detected, and where some of the basic quantum operators are readily implemented. Photons are ideally suited for the transmission of quantum information and can be made relatively immune to decoherence, i.e., to the loss of their quantum character. In order to efficiently pursue such objectives, photonic technologies are asked to provide reliable sources of quantum light states, and high-efficiency photon counting detectors Quantum Light Sources Squeezed Light In general, squeezing refers to the reduction of quantum fluctuations in one observable below the standard quantum limit (the minimal noise level of the vacuum state, or shot-noise) at the expense of an increased uncertainty of the conjugate variable.

15 11 Domain-Engineered Ferroelectric Crystals 299 The suppressed quantum noise of squeezed light can thus improve the sensitivity of optical measurements (e.g. by increasing the precision in the measurement of phase shifts in an interferometer) [67]. Other applications involve quantum information processing with continuous variables [68], where squeezed states are used to generate entanglement and perform quantum teleportation [69]. Most of the experimental realizations of squeezed light have involved the process of parametric amplification and deamplification of vacuum field fluctuations in a nonlinear crystal. Either narrowband CW cavity-enhanced OPOs [70] or single-pass pulsed schemes [71] have been frequently used to demonstrate squeezing. Since the possible use of such squeezed sources critically depends on the amount of noise suppression available, efforts have concentrated in improving the squeezing level by increasing the strength of the nonlinear interaction between the pump field and the crystal. The use of periodically-poled crystals and waveguides was demonstrated already in 1995 with short pump pulses [72, 73] and it proved an efficient way to improve the nonlinear interaction (by using the d 33 nonlinear coefficient) and the longitudinal (thanks to QPM) and transverse (thanks to the waveguide) mode matching between the pump and the generated fields. Both KTP at 830 nm [73] and LN at 1064 nm [72] achieved squeezing levels of the order of %. More recently, single-pass parametric amplification in periodically-poled KTP has resulted in squeezing of about 3 db[74]. Nowadays, parametric down-conversion in subthreshold optical parametric oscillators is often employed for the generation of CW squeezed light. Although squeezing at a level of 6 db has been observed with bulk nonlinear crystals in non-critical PM conditions [75], the advent of QPM periodically-poled materials has allowed a dramatic increase in the efficiency and in the range of available wavelengths. Efforts in this direction have brought to impressive results, with up to 9 db of noise suppression below the shot noise achieved in PPKTP at 860 nm (see Fig. 11.9) [76]. The recently demonstrated possibility of generating narrowband CW highly-squeezed light resonant with atomic transitions [77] will open new perspectives in the use of atomic media as a possible way to delay and store quantum information. Even more recently, the race to increase the sensitivity limit in Gravitational Wave (GW) detectors has seen the development of new squeezed light sources. For this particular application, Michelson interferometers are generally used to translate tiny position changes of the mirrors, hopefully caused by an incoming gravitational wave, into a detectable change in the interference pattern of light. The ultimate sensitivity limit of such an interferometer is determined by the quantum noise of light and can only be beaten by using nonclassical (squeezed) light sources. For example, injecting squeezed light instead of vacuum into the unused input of the interferometer beam splitter would directly decrease the photon shot noise on the detector and hence increase the output signal-to-noise ratio. Since all current GW interferometers operate at 1064 nm, most research on squeezed light sources has been focused on the generation of CW squeezed light at this wavelength. While a maximum squeezing value of 11.5 db was obtained from a bulk LN crystal [78], a record value of 12.7 db was achieved when using

16 300 M. Bellini et al. Fig Experimental noise levels for a quadrature-squeezed vacuum state of CW light generated with a sub-threshold optical parametric oscillator containing a periodically-poled KTP crystal. (i) Shot noise level; (ii) noise level for the squeezed quadrature; (iii) noise level at the antisqueezed quadrature; (iv) noise level as recorded while the phase is scanned. A squeezing level of 9.01 db is observed. Figure taken from Ref. [76] a PPKTP crystal [79]. However, squeezing was only obtained in the MHz regime and by making use of monolithic resonators, two characteristics that do not fit well the requirements of GW detectors. Therefore, new schemes have been developed to work in the optimal detection band (in a range between about 10 Hz and 10 khz) and with half-monolithic resonators. These new compact squeezing sources, making use of periodically-poled crystals for the generation of nonclassical light, have already demonstrated their effectiveness when used in conjunction with real GW detectors [80]. The direct detection of up to 12.3 db of squeezing at 5 MHz and at a wavelength of 1550 nm from a half-monolithic nonlinear resonator based on PPKTP was also recently reported [81]. Single and Entangled Photon Sources Many of the proposed schemes for quantum communication and cryptography involve light sources capable of emitting fully characterized individual photons on demand. Unfortunately, such sources do not currently exist and one has to sacrifice either the purity of the single-photon states or their deterministic production. Single emitters, like quantum dots [82], isolated fluorescence molecules [83], or nitrogen vacancy color centers in diamond [84], have proved capable of emitting indistinguishable single photons almost on demand after their pulsed optical excitation, but their use is not straightforward and there are problems related to their broad bandwidth and low out-coupling efficiency which do not allow a precise characterization of the output mode.

17 11 Domain-Engineered Ferroelectric Crystals 301 Fig Scheme of the process of spontaneous parametric down-conversion where a pump photon of frequency ω p is split into two lower-energy photons at frequencies ω s and ω i such that ω s + ω i = ω p. The detection of the idler photon can be used to herald the presence of the twin signal photon in a well-defined mode The historically most used source of single and entangled photons is however the process of spontaneous parametric down-conversion (SPDC) of light in χ (2) nonlinear crystals [85]. In such a process a photon of high energy (usually produced by frequency doubling a laser field and named pump) is split into two longer-wavelength photons (normally named signal and idler) whose energies sum up to that of the parent (see Fig ). Besides energy conservation, also momentum conservation must be obeyed in the process, so that the directions where the two photons are emitted are strictly related. As the emission only takes place in pairs, the detection of the idler photon can be used to herald the presence of the signal photon, which can then be used for applications. This kind of source is non deterministic, since one cannot precisely know when the single photon will be emitted but, once the idler photon is detected in a well defined spectral/spatial mode, also the emission mode of the signal single photon is exactly determined by the energy/momentum correlations imposed by conservation rules (or PM conditions) [86]. This enables the conditional production of single photons in tightly defined modes which highly facilitates their coupling to subsequent optical processing and detection units [87 90]. Besides conditionally generating single photons in well-defined modes, the correlations existing between the twin photons emitted in SPDC are of an intrinsic quantum nature and lead to entanglement in one or more degrees of freedom between the photon pairs. Entanglement is the essence of quantum physics and dictates that, although the individual properties of the two parties may be totally (quantummechanically) undetermined, their relative value is perfectly fixed in a nonlocal fashion. Entangled states of light are a critical resource for the realization of many quantum information protocols, such as teleportation, and for improving the security of quantum cryptographic schemes. Polarization entanglement has been deeply analyzed and is the most used kind entanglement for demonstrating quantum properties [91], however time/energy and time-bin kinds of entanglement are receiving increasing attention and will probably prove more immune to decoherence for longdistance quantum communication [92, 93]. An optimal quantum source obviously requires high efficiency in the conversion of the pump photons into down-converted photon pairs in order to obtain higher

18 302 M. Bellini et al. Fig Schematics to characterize the down-conversion and photon-pair production efficiency of a PPLN waveguide. TAC is a time to amplitude converter and SCA is a single-channel analyzer. S 1, S 2,andR c denote single count rates in the two detectors or coincidences. Figure taken from Ref. [94] signal-to-noise ratios and shorter measurement times. Conversion efficiency in bulk materials is limited by the choice of available crystals, so the engineering of the crystal structure may bring significant advantages. Periodic poling allows one to take advantage of crystals (like LN) with higher nonlinear susceptibilities, thus helping in significantly enhancing the conversion efficiency. Furthermore, the presence of a waveguiding structure in the material can also greatly enhance the emission in welldefined spatial modes which are much easier to collect and couple into single-mode fibers. The use of periodically-poled crystals in the generation of entangled photon pairs is rather recent but it has already shown its exceptional potential. Already in the first works of 2001, an increase in the efficiency of about four orders of magnitude compared with bulk crystals was demonstrated (see Fig ). A PPLN waveguide with a period of 12.1 µm was used in that case, for type-i down-conversion of CW light at 657 nm into degenerate photon pairs at 1315 nm which are suitable for long distance fiber communications. Both energy-time and time-bin entanglement of the emitted photon pairs were demonstrated [94, 95]. A simple separation of the photons of the entangled pair was later obtained by using non-degenerate down-conversion. In this case, CW pump photons at 712 nm were converted into pairs at 1.55 and 1.31 µm, the best wavelengths for fiber transmission [96]. However efficient single-photon detectors are not available at these wavelengths (see later) and efforts have also been devoted to the generation of entangled photon pairs closer to the visible region, around 800 nm. The use of a PPLN waveguide for the generation of a pump beam at 427 nm by SHG of the diode laser emission at 854 nm and then for its down-conversion back to 854 nm was reported in Efficient CW conversion (of the same order of that obtained with bulk crystals with a thousand time greater pump power) took place with a poling period of only 3.2 µm [97]. Ultrashort pump pulses were used in conjunction with PPKTP for type-i downconversion [98], while the production of 800 nm orthogonal-polarization photons (hence much more easily separable by a simple polarizing beamsplitter) was re-

19 11 Domain-Engineered Ferroelectric Crystals 303 ported by means of type-ii SPDC in a PPKTP waveguide (with a 8.7 µm period) [99]. In the latter case, the use of a much weaker d 24 nonlinear element (compared to the usual d 33 ) was compensated by the long interaction allowed by the limited cross section of the waveguide, and resulted in the high-fidelity conditional production of fiber-coupled single photons. A 2-mm-long PPKTP crystal has also been recently used for type-ii collinear SPDC to achieve the heralded production of single photons at very high rates (up to about 100 khz) from a mode-locked laser system working at a repetition rate of 76 MHz [100]. The high efficiency of this scheme was the base for the heralded generation of arbitrary quantum states, containing up to two photons, achieved by the same group in Calgary [101]. The use of ultrashort pulses at about 800 nm from a Ti:sapphire laser in combination with a periodically-poled structure (and possibly waveguiding) in LN, both for frequency doubling and for subsequent SPDC, would greatly benefit of its higher nonlinear coefficient but is currently hard to realize. The main problem is due to the limitations in the realization of small scale periods (about 2.6 µm for operation at room temperature) with the available technology. One interesting new approach to the generation of entangled photon pairs in structured crystals has been recently discussed. It is based on the parametric downconversion generation of signal and idler photons in counter-propagating directions, when a periodic and waveguiding structure are transversely pumped [102, 103]. Not only the two counterpropagating guided signal and idler modes give the advantage of practical and efficient collection for applications in quantum optics, but also their frequency correlations can be fully controlled [104]. For example, there are particular quantum applications (like entanglement-enhanced clock synchronization [105]) that explicitly require strict frequency correlation between the two photons, as opposed to the usual frequency anticorrelation. The first experimental demonstrations of this process have been obtained with a semiconductor source at room temperature that combines the versatility of frequency state engineering with the potential of full optoelectronic integration [106, 107]. Also worth noting are recent results that bring together into the same crystal with zones of different structuring, the two steps of frequency up-conversion for pump generation and frequency down-conversion for the production of the entangled photon pairs (see Fig )[108]. It is foreseeable that the use of highly-efficient structured crystals and of appropriate waveguiding structures will gradually permit the transition towards compact diode-laser-based systems which will finally bring to completely integrated systems for quantum information processing on a chip Single-Photon Detectors The ability to detect photons with high efficiency and to distinguish the number of photons in an incident quantum state is of very high importance in quantum informa-

20 304 M. Bellini et al. Fig (a) Cascaded second order nonlinear process for the generation of photon pairs on the sidebands of the pump frequency. (b) Scheme of the experimental setup. Figure taken from Ref. [108] tion science. Detection efficiencies approaching unity are required for a loopholefree test of the violation of Bell s inequality (that would definitely prove the nonlocal character of Nature), and for the realization of a scalable linear-optics quantum computer. Distinguishing the number of photons in a state would allow to reliably produce many-photon entangled states and many other exotic states of light. Unfortunately, photon number resolution has only been obtained with superconducting bolometric detectors so far [109]. Apart from the inconvenience of working at cryogenic temperatures, these devices still suffer from low detection efficiency and low counting rates. If one relaxes the requirement of photon number resolution, visible photons can be conveniently detected with silicon avalanche photodiodes (APDs), which exhibit good quantum efficiency (50 70 %), a low number of dark events and a high counting rate. The situation in the infrared however is much worse. Here, InGaAs avalanche photodiodes are available but their efficiency is much lower and their high rate of dark counts can only be eliminated by working in a time-gated configuration. Since IR wavelengths are the most interesting for the transport of quantum information via the existing telecom fiber network, due to the low absorption and dispersion associated to the 1.31 and 1.55 µm regions, an efficient way to detect IR photons is highly desirable. Periodically-poled crystals have been recently shown to conveniently up-convert the frequency of IR photons to the visible, where single photon detection by standard silicon APDs is more efficient. If a strong pump is available, a weak IR input signal can be up-converted with near unity efficiency. Quantum frequency conversion was first proposed by Prem Kumar in 1990, who showed theoretically that the properties of a quantum state of light are unchanged upon frequency conversion in a χ (2) material [110]. The first experimental demonstration followed in 1992, where Kumar s group was able to upconvert a squeezed state from 1064 nm to 532 nm, and it was proposed that this approach can provide a