1. Introduction

Recently, broadband parametric interactions in quadratic nonlinear media have been extensively studied because of their applications in ultra-fast optical pulses. Broadband second-harmonic generation (SHG), for example, has been proposed in poled optical fibers by using the concept of group-velocity matching (GVM) [1], and realized in a periodically poled lithium niobate (PPLN) crystal employing type-I interaction [2]. The fundamental idea was to match the group-velocities between the fundamental and the second harmonic waves in the desired spectral regions by controlling the material dispersion (by MgO-doping in this case), while high conversion efficiency was achieved by quasi-phase-matching (QPM). Indeed, efficient SHG of ~100 fs pulses has been successfully demonstrated with the same PPLN device [3]. The method of utilizing the GVM concept has advantages over the other broadband methods employing aperiodic QPM gratings and non-collinear beam configuration [4, 5] due to its simplicity in device design and optical setup, respectively.

Broad phase-matching or QPM bandwidth in difference frequency generation (DFG) or optical parametric amplification (OPA) is essential for applications such as ultra-fast pulse amplification [6] and IR-spectroscopy [7]. Yanagawa et al. have obtained broadband DFG around 2 μm region in a PPLN crystal, aiming at IR-spectroscopic gas detection [7]. Tiihonen et al. reported ultra-broad parametric gain band in a periodically poled KTiOPO₄ crystal by choosing the pump wavelength in order to match the degeneracy point to the point of zerogroup velocity dispersion [8].

In this paper we report a broad optical parametric generation (OPG) gain band, and demonstrate collinear OPA of broadband signals at the communication band in a PPLN crystal with a uniform QPM period pumped by a 35 ps pulse at a fixed wavelength around 870 nm. The GVM idea in QPM SHG [2] can also be applied to broadband QPM DFG or OPA, where the QPM period and pump wavelength are chosen to match the group-velocities of the signal and the idler in the desired spectral region. A significant advantage in the case of OPA is that the largest nonlinear coefficient of LiNbO₃, d₃₃ can be utilized at the specific pump wavelength instead of much smaller d₃₂ in the type-I broadband SHG in the previous report [2].

2. Broadband QPM OPA design

The wavevector mismatch for DFG is given by Δk = k_p - k_s - k_i where k’s are wavevectors for the pump (p), signal (s) and the idler (i) waves, respectively. If we differentiate Δk with signal angular frequency ω_s for a fixed ω_p, we obtain

Here, v_g,i and v_g,s are the group velocities of the idler and the signal pulses, respectively. Group velocity matching (GVM) can be achieved in the spectral region where the wavevector mismatch (inversely proportional to the QPM period, Λ) takes an extremum, around which the coherence length is nearly constant over a wide signal (and idler) wavelength range. Thus, GVM and broadband QPM DFG are equivalent concepts, as in the case of QPM SHG [2].

LiNbO₃ is the most frequently used QPM nonlinear optical material due to its large nonlinear optical coefficient d₃₃, and to the well-characterized dispersion in the visible and near-IR. In particular, the temperature-dependent Sellmeier’s equation for the extraordinary wave in congruent lithium niobate has been accurately established in the spectral range between 400 and 5000 nm by Jundt [9]. We tried to bring the GVM band near the communication band, aiming at OPA of the pulsed lasers in this range. In order to predict the GVM regions based on Eq. (1), we calculated QPM period versus signal wavelength (λ_s) for a fixed pump wavelength (λ_p) for the DFG process ω_p - ω_s → ω_i using the Sellmeier’s equation in Ref. [9]. A representative result is shown in Fig. 1 for λ_p = 870 nm. The two maxima of Λ(λ) shown in the figure correspond to the GVM wavelengths for the signal and the idler, respectively as represented by the horizontal tangential line (a), where one can verify that the group-velocities of the two waves are equal as indicated in the figure. The local minimum around 1740 nm is the degeneracy point where the signal and the idler approach each other, also satisfying the condition of GVM in Eq. (1), as represented by horizontal tangential line (b). Furthermore, when the minimum merges the maxima by choosing proper pump wavelength and QPM period, we can obtain an extremely broad OPG band [8]. However, one should be careful in utilizing degeneracy in the design of OPA devices for ultra-fast pulses, because the broad signal spectrum may cross the degeneracy point, resulting in possible cross-talk between the amplified signal and the idler output. The curve of Λ(λ) in Fig. 1 can be shifted up or down with sample temperature tuning, and changes its shape drastically when the pump wavelength is changed. Thus, with a carefully designed QPM period for a desired range of OPG or OPA, GVM conditions can be achieved by choosing a proper pump wavelength and sample temperature.

 

Fig. 1. QPM period (dotted line) and Group velocity dispersion (solid line) of congruent LiNbO₃ versus signal or idler wavelength for pump wavelength of 870 nm at 22 °C.

Download Full Size | PDF

 

Fig. 2. Calculated QPM DFG bands for the GVM case (a) in Fig. 1 (solid line, λ_p= 870 nm, Λ= 24 μm, T = 160 °C), and the GVM case (b) (dashed line, λ_p= 870 nm, Λ= 24 μm, T = 22 °C), and a non-GVM case (c) (dotted, λ_p= 1064 nm, Λ= 30 μm, T = 100 °C).

Download Full Size | PDF

We estimated QPM DFG intensities for the GVM cases in Fig. 1, assuming negligible pump depletion and line width, and plotted them in Fig. 2. For the GVM case (a), the DFG QPM signal band is estimated to be 1170 ~ 1305 nm. If we change the device temperature to 22 °C (the GVM case (b)), even broader QPM signal band (1604 ~ 1901 nm) is expected due to the near-degeneracy effect combined with near-GVM. A counter example of a conventional group-velocity mismatched case is also shown in the figure for comparison (curve c).

Since one usually needs a high intensity level in order to obtain a significant gain for OPA with the existing nonlinear materials, a pulsed pump is required. In the case of OPA, the temporal group walk-off between the pump (~ 870 nm) and the signal (idler) (1550 ~ 2050 nm) is about 2 ps/cm. If the pulse width of the pump is larger than the group walk-off plus signal (seed) pulse width, the above GVM concept is still valid. In our experiment the pulse widths of the interacting waves were about 35 ps, while the device length was 8 mm, approximately satisfying the pump pulse width requirement.

3. Experiment

We fabricated the PPLN samples by the standard electric poling method using a liquid electrode at room temperature [10] with 0.5-mm thick z-plate wafers of congruent LiNbO₃ crystal made by Yamaju Ceramics. Based on the predictions in the previous section, the QPM periods of the PPLN samples for our OPA experiment were chosen to be 23.5 and 24.0 mm. The quality of the PPLN samples was checked not only by measuring QPM SHG bandwidth [10], but also by diffraction measurements after etching [11]. The length of the PPLN sample was 8 mm along the crystalline x-axis, which is designated as the light propagation direction.

 

Fig. 3. Experimental setup. F1, F2 : Visible, UV cut filter, F3: 1500 nm pass filter, L: lens, M : mirror, H: half wave plate at 1064 nm, CCM: corner cube mirror, B: beam splitter, P: polarizer

Download Full Size | PDF

Figure 3 is a schematic diagram of our experimental setup. The pump light was obtained from a home-made OPG-OPA system employing two β-barium borate (BBO) crystals, which were pumped by the third-harmonic of a mode-locked Nd:YAG laser (YG801, Quantel). The first BBO crystal generates weak signal and idler selected by angle tuning, while the second one amplifies them with the collinear un-depleted 355 nm pump. The pulse width was ~35 ps with a 10 Hz repetition rate. The idler of the OPG-OPA system was tuned to 860~870 nm with a FWHM spectral width of ~ 4 nm, and used as the pump for the PPLN OPA experiment (PPLN-A in the figure). A broadband signal input for the OPA experiment was obtained from another PPLN (PPLN-S in the figure) with a period of 29.8 μm, pumped by the fundamental of the Nd:YAG laser. The input signal wavelength was varied by temperature tuning of PPLN-S, from 1516 nm (FWHM ~ 25 nm, at 21 °C) to 1580 nm (FWHM ~ 35 nm, at 170 °C). The signal and the pump beams were combined in a beam splitter, collinearly incident on the PPLN-A sample, and propagated along the x-axis. Beam diameters for the pump and the input signal were 230 μm and 220 μm, respectively. We also maximized the temporal overlap between the pump and the signal input pulses in the sample by adjusting the delay with a corner cube mirror (Fig. 3). The OPG gain spectrum was measured with the signal input blocked. Then, sending an input seed from PPLN-S within the gain band, the amplified signal output from the PPLN-A sample was spectrally analyzed by a calibrated monochromator / Ge-photodetector system. We also measured the signal output with increasing pump power. The experiments were repeated for various combinations of parameters such as QPM period, sample temperature, pumping wavelength, input seed wavelength and power.

4. Results and discussion

Figure 4 shows representative OPG spectra from PPLN-A with temperature tuning for an 8 μJ- pump at 869 nm without signal input. At 160 °C, the OPG spectrum had two peaks around 1206 nm (~ 18 nm FWHM) and 1300 nm (~ 100 nm FWHM) (spectrum A in the figure), while at 100 °C, the peak on the longer wavelength side had a 250 nm bandwidth around 1420 nm (spectrum B). The OPG spectrum at 22 °C had a peak at 1570 nm and a relatively flat band towards the longer wavelength range (spectrum C), which is expected to have ~ 400 nm bandwidth around 1738 nm due to the near-degeneracy effect. However, we could not measure the spectrum for longer wavelengths than 1680 nm due to the limited spectral response of our detection system.

Spectrum A is close to the GVM case (a) in Fig. 1. At a higher temperature than 160 °C the two peaks would have merged completely, while spectrum C belongs to the case (b). However, all the three spectra exhibited broad gain bands due to the near-GVM in the experimental conditions due to near-GVM provided by the present experimental conditions. Furthermore, all of the above OPG bands were broader than those of DFG predicted by the Sellmeier’s equation, which is explained by the broad spectral width (~ 4 nm) of our pump source.

 

Fig. 4. OPG spectra of PPLN with QPM period of 24 μm and pump at λ_p = 869 nm (A : 160°C, B: 100 °C, C: 22 °C).

Download Full Size | PDF

We performed OPA experiments within the OPG gain bands by launching seed signals obtained from PPLN-S in Fig. 3. Figure 5 shows a representative result of the amplification of the input signal. In this case we used the OPG spectrum C in Fig. 4 for our OPA experiment in order to take advantage of the flat band near the degeneracy point. At 170 °C PPLN-S generated a signal pulse centered at 1580 nm with a FWHM of 35 nm, which is entirely within the OPG gain band C. We also tuned the seed within the OPG band, obtaining similar amplification results (not shown here). The signal input energy was 8 nJ/pulse, while the pump energy was varied from 2 to 8 μJ/pulse. The signal output increased with pump intensity up to a certain point, maintaining the spectral shape, and then showed a saturation behavior. At high pump intensities, we also observed significant parametric fluorescence in the longer wavelength range over the input signal spectrum, acting as a white noise.

 

Fig. 5. (a) OPA by various pump energies for λ_p = 869 nm with 8 nJ seed pulse centered at 1580 nm, (b) OPA gain of signal versus pump intensity. Experimental result (symbols), and theoretical prediction (solid line).

Download Full Size | PDF

The parametric gain measured at the peak wavelength of the signal input spectrum is plotted in Fig. 5(b), compared with theoretical estimation. The measured gain for pump energy of 8 μJ/pulse was about 20 dB when the signal input energy was 8 nJ/pulse. For theoretical prediction, pump beam energy depletion effect was considered and the pump and the input seed waves were treated as Gaussian pulses. The discrepancy between the data and theoretical prediction is partially attributed to overestimation of the pump beam diameter. The tendency of saturation is obvious at strong pumping, which can be a consequence of energy transfer to parametric fluorescence, photorefractive energy loss, and multi-photon absorption.

5. Conclusion

We designed and experimentally demonstrated a broadband QPM optical parametric gain band with a PPLN crystal, and the subsequent optical parametric amplification of a broadband signal at the communication band, by choosing proper pump wavelengths and QPM periods for group-velocity matching between the signal and the idler. We also observed that degeneracy enlarged the bandwidth further, but with a red-shifted gain band.

Our broadband method with PPLN can be used to amplify the mode-locked pulses of the lasers emitting at the communication band (e.g. Er:fiber laser) with a lower pump power than the other nonlinear optical devices due to the large d₃₃ coefficient of LiNbO₃. Furthermore, material engineering such as MgO-doping can not only increase the optical damage threshold, but also control the dispersion of lithium niobate, giving more flexibility in designing broad QPM optical parametric bands.