## Abstract

We have demonstrated broadening of the phase-matching bandwidth in a periodically poled Ti:LiNbO_{3} (Ti:PPLN) channel waveguide (Λ=16.6 µm) by using a temperature-gradient-control technique. With this technique, we have achieved a second-harmonic phase-matching bandwidth of more than 13 nm in a 74-mm-long Ti:PPLN waveguide, which has a 0.21-nm phase-matching bandwidth at a uniform temperature.

© 2003 Optical Society of America

Advances in electric field poling techniques [1] to fabricate periodically poled ferroelectric crystal have led to progress in various nonlinear applications such as efficient wavelength conversion [2], optical pulse compression [3,4], and all-optical signal processing [5]. Quasiphase-matched (QPM) devices that use this periodic modulation of polarization allow us to access a large nonlinear coefficient that cannot be used in the conventional birefringence phase-matching condition. Among the ferroelectric materials that can be periodically poled, LiNbO_{3} is particularly attractive for QPM devices because of its large nonlinear coefficient (*d*
_{33}), its easy integration, and low-loss waveguide [6].

In general, the phase-matching bandwidth and phase-matching center wavelength of a periodically poled Ti:LiNbO_{3} (Ti:PPLN) waveguide in QPM second-harmonic generation (SHG) experiments can be controlled by the periodicity of QPM gratings. The regular periodicity and duty cycle can increase second-harmonic (SH) conversion efficiency. But some applications, such as ultra-short-pulse compression [3,4], require not only a high conversion efficiency but also a broad phase-matching bandwidth. Broadening of the phase-matching bandwidth in QPM SHG can be achieved with a chirped or aperiodic grating [3,4,7]. However, it is difficult to obtain the same QPM grating as with a QPM mask pattern in a Ti:LiNbO_{3} waveguide because of unexpected fabrication faults. Thus even usual SH curves from a Ti:PPLN waveguide, which has regular periodicity, do not show an ideal sinc function. This distortion of the SH curve results from several factors including nonuniform periodicity of grating, inhomogeneity of refractive index along the waveguide, and so on. These errors in the fabrication process cause performance degradation of the Ti:PPLN waveguide device. The influence of nonuniform phase matching on QPM SHG has been theoretically investigated by several researchers [7,8,9,10].

Figure 1 shows the SH curve of the 74-mm-long Ti:PPLN waveguide at room temperature. The QPM period of the Ti:PPLN is 16.6 µm, and the waveguide loss is determined to be 0.14 dB/cm at a 1.53-µm wavelength. The cross-sectional area of the waveguide is defined by the near-field intensity distribution. The horizontal and vertical full-width at half-maximum (FWHM) are measured 5 and 4 µm, respectively, with a TM-polarization beam (1.53-µm wavelength). The shorter-wavelength side ripple of a phase-matching peak in Fig. 1 (scattering) is influenced by positive parabolic variation of the refractive index (negative parabolic variation of the refractive-index induces the longer-wavelength side ripple of a phase-matching peak). This positive parabolic variation of the refractive index in a Ti waveguide is frequently caused by differences in Ti stripe thickness during deposition (thick end and thin center). This kind of SH curve distortion can be corrected by a local gradient-temperature-control technique [11]. In this paper we demonstrate, for the first time to our knowledge, the broadening of SH QPM bandwidth by a temperature-gradient technique.

In the case of a lossless SHG process, the coupled-mode equation is given by the slowly varying envelope approximation,

where *A*
_{1} and *A*
_{3} are the field amplitudes [*A _{l}*=(

*n*/

_{l}*ω*)

_{l}^{1/2}

*E*, where

_{l}*l*=1,3] at λ

_{P}and λ

_{SH}(P → pump, SH → second harmonic), respectively; κ is a nonlinear coupling constant; and Δ

*k*is the SHG wave-vector mismatch.

The theoretical fitting curve (solid curve) for the SH curve in Fig. 1 was calculated from the above coupled-wave equations and from Sellmeir’s equation. Through the fitting we obtained the positive parabolic modulation of refractive-index difference (*n*
_{SH}-*n*
_{P}) as shown in the inset.

If the QPMdevice has a broad phase-matching bandwidth, it can be applied to the ultra-short-pulse amplification and pulse-compression experiments [3,4]. Generally, the chirped QPMgrating has been used to broaden SH bandwidth. But one of the simple ways to obtain a broad QPM-SH bandwidth with a Ti:PPLN is by use of the temperature-gradient technique along the waveguide. In this case we can control the phase-matching bandwidth even with a regular QPM-grating device that has a perfectly periodic QPM grating.

Figure 2 shows the schematic setup for the SHG experiment. The wavelength and power of the extended-cavity laser (ECL, OSICS-1560, Nettest) were controlled with a personal computer. The polarization of the pump wave was adjusted to TM polarization (to obtain maximum nonlinear interaction with nonlinear coefficient *d*
_{33}) and fiber butt-coupled to the Ti:PPLN waveguide. Generated SH signal, guided by a 10× objective lens, was measured by the silicon detector. To obtain the gradient temperature, we used two Peltier devices in a sample holder, one for heating and another for cooling (see the inset in Fig. 2). The temperature distribution along the sample holder shows good linearity, such as the circle scattering in Fig. 3. The triangle scattering shows the temperature dependence of the SH phase-matching wavelength in the Ti:PPLN waveguide. A red shift of the SH phase-matching center wavelength obtained by an increase of temperature is measured at a rate of ~0.128 nm/K. In Fig. 3, we can achieve QPM-SH bandwidth greater than 10 nm by maintaining the temperature difference between both endfaces of the Ti:PPLN waveguides at only 40 °C.

The differences in temperature between both endfaces of the 74-mm-long Ti:PPLN waveguide result in the broadening of SH phase-matching bandwidth. The SH curves for various temperature gradients of the 74-mm-long Ti:PPLN waveguide are shown in Fig. 4. Figures 4(a) and 4(b) show the theoretical results, and Fig. 4(c) shows the experimental results. The coupled pump power was 1 mW, and all *x* axes of Fig. 4 denote wavelength. Figure 4(a) shows the intensity mapping for theoretical simulation. In the theoretical calculations, the following distributions of the temperature, *T*(*z*), and wave-vector mismatch, Δ*k* (*z*), are used:

where *T*(0) and *T*(*L*) are the temperatures at the input and output positions of light in the sample and Λ′ (*z*) is the effective QPM-grating period, which is calculated from the modulation of refractive-index difference as shown in the inset of Fig. 1. The influence of the temperature change in the QPM material can be described as follows:

$$\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}=2\pi \left[\frac{\frac{d{n}_{\mathrm{SH}}}{dT}-\frac{d{n}_{P}}{dT}}{{n}_{\mathrm{SH}}-{n}_{P}}+\alpha \right]\delta T,$$

where δ*T* and α are the differential of temperature and the coefficient of thermal expansion, respectively. In the case of PPLN, the influence of the thermal expansion [second term on the right-hand side of Eq. (5)] upon the effective grating period is less than 1 order of magnitude than that of the changes in refractive indices [first term on the right-hand side of Eq. (5)]. Therefore we neglected the thermal expansion of the grating period.

From Fig. 4(a) one can see that as the temperature gradient of the sample increases, the SH bandwidth broadens. Figures 4(b) and Fig. 4(c) show theoretical and experimental SH curves for three different temperature gradients, which are denoted in Fig. 4(a). The generated SH power oscillates rapidly within the bandwidth and has an apparent peak at the long-wavelength end of the band [see Figs. 4(b) and 4(c)]. The peak originated from the parabolic profile of the refractive index along the wave-propagating direction. The experimental results show good agreement with the theoretical results. At a temperature difference of 44 °C at both endfaces of the sample, we obtained a 13-nm broadening of the SH phase-matching bandwidth, which is enough to compress the SH signal down to ~100-fs duration in ultra-short-pulse compression experiments [3,4]. However, in the case of broadening SH phase-matching bandwidth, one cannot avoid a trade-off between conversion efficiency and bandwidth. If the conversion efficiency is degraded because of the temperature gradient (refractive-index gradient of the Ti waveguide), then the bandwidth increases. The behavior of SH conversion efficiency and phase-matching bandwidth for a different temperature gradient in the Ti:PPLN waveguide is shown in Fig. 5. The scattering indicates experimental data, and curves (solid curve → SH efficiency; dotted curve → SH bandwidth) show theoretical results from Sellmeir‘s equation and from the coupled-wave equations [Eqs. (1) and (2)]. In Fig. 5 SH efficiency is defined by SH power over pump power; here SH power is not an integration of SH power but is the peak power of the SH curve in the spectrum.

In conclusion, for the first time to our knowledge, we have demonstrated the broadening of a SH phase-matching bandwidth in a Ti:PPLN waveguide that has regular periodicity. The temperature gradient in regular PPLN produces the same effect as chirped PPLN.We achieved up to 13-nm SH phase-matching bandwidth in a 74-mm-long Ti:PPLN waveguide (which had 0.21-nm bandwidth at a uniform temperature) by using the simple temperature-gradient technique. We believe this technique to be very useful for experiments in ultra-short-pulse amplification and pulse compression.

## Acknowledgments

This research was supported by the Ministry of Science and Technology of Korea through the R&D Infrastructure Program (M10330000001-03G0900-00110) and the Strategic National R&D Program (M10330000001-03B3700-00110).

## References and links

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**11. **Y. L. Lee, Y. Noh, C. Jung, T. J. Yu, D.-K. Ko, and J. Lee are preparing a manuscript to be called “Reshaping of second harmonic curve in Ti:PPLN waveguide by a local gradient-temperature-control technique,”