We have demonstrated the bandwidth control of a Ti-diffused periodically poled LiNbO3 (Ti:PPLN) Sﬞolc filter by a temperature-gradient-control technique. Up to 2.8 nm of filtering bandwidth was achieved with a simple temperature-gradient-control technique in a 78-mm-long of Ti:PPLN waveguide, which has a 0.2 nm filtering bandwidth at an uniform temperature. We have also analyzed the experimental results with the theoretical calculation which is derived from the codirectional coupled mode equations.
© 2008 Optical Society of America
The advance of the electric field poling techniques to fabricate periodically poled ferroelectric materials open new renaissance of nonlinear optics based on a quasi-phase-matching (QPM) device. Among the various periodically poled ferroelectric materials, a periodically poled lithium niobate (PPLN) is particularly attractive for various QPM devices due to its large nonlinear coefficient and easy integration. The main application fields of QPM device based on PPLN are all-optical wavelength conversion [1, 2, 3], optical pulse compression , all-optical switching [5, 6], and all-optical logic gate [7, 8] because periodically reversed spontaneous polarization of lithium niobate gives high conversion efficiency. Actually, the PPLN devices modulate not only the nonlinear optical coefficients but also the electro-optical (EO) coefficients due to the periodically reversed microdomains. The former property has been well utilized in various nonlinear optics fields, during past 15 years after first electric field poling was succeed in LiNbO 3 at room temperature . However, the latter property is only studied in high-frequency electro-optic modulator fields for quasi-matching between the traveling velocity of the optical wave and the electrical wave velocity in a waveguide . Recently, a peculiar birefringent narrow band wavelength filter based on a PPLN was proposed by using the latter property . Such kind of the wavelength filter is named Sﬞolc filter . After first PPLN Sﬞolc filter was proposed , several researchers reported bulk PPLN Sﬞolc filters and waveguide-type Sﬞolc filters . Most of the researches were focused on filtering wavelength tuning by a temperature change [13, 14] or an ultra-violet (UV) illumination method [15, 16] and multi-channel wavelength filtering by a waveguide-mode selecting  or a local-temperature-gradient technique . However, up to now, no research on active bandwidth control of a PPLN Sﬞolc filter has been reported. In this paper, we demonstrate, for what we believe is the first time, the bandwidth control of the Ti:PPLN Sﬞolc filter which has a domain period of 16.6 µm by a temperature-gradient-control technique .
In the case of narrow band wavelength filtering in a Ti:PPLN Sﬞolc filter , the power exchange between the two polarization modes in a periodically reversed ferroelectric domain can be described by codirectional coupled mode equations ,
where A o(z) and A e(z) are the field amplitude of the ordinary- and extraordinary-wave modes, respectively, Δk is the wave-vector mismatch and κ is the coupling coefficient. This is given by
where ρ is the rocking angle, D is the duty cycle, n o and n e are the effective refractive indices of the ordinary and extra-ordinarywaves, respectively. When TE-polarization beam is launched into a Ti:PPLN Sﬞolc filter, the initial condition at z=0 is given by
where s is given by s 2=κ * κ+(Δk/2)2.
A 78-mm-long Ti:PPLN waveguide of 16.6 µ m QPM period was used to demonstrate the bandwidth control of a Ti:PPLN Sﬞolc filter. The waveguide loss at 1280 nm (TM-polarization) was determined by the Fabry-Perot method  to be 0.11 dB/cm. Detail information about the Ti:PPLN waveguide is listed in Table 1.
To perform the active bandwidth control of the Ti:PPLN Sﬞolc filter, we used the temperature-gradient-control technique  along the waveguide. In this way, we can control the filtering bandwidth even with a regular PPLN device that has a uniform periodic QPM gratings. Figure 1 shows the schematic of a bandwidth controllable Ti:PPLN Sﬞolc filter. To obtain the temperature gradient along the waveguide, two Peltier devices were used in a sample holder, one is for heating and the other is for cooling. Through this method, we achieved almost linear temperature gradient along the whole length of a sample . The polarization of input beam was adjusted to TE-polarization by a first polarizer and end-fire coupled into the z-cut Ti:PPLN waveguide. The transmitted optical signal through the Ti:PPLN waveguide was analyzed by a second polarizer which is aligned to a TM-polarization direction. The details of experimental setup is described in Ref .
Figure 2 shows the transmission spectrum of the 78-mm-long Ti:PPLN Sﬞolc filter at room temperature. The normalized transmittance shows about 50%. If we consider the waveguide coupling losses (~-3 dB) of input and output Ti:PPLN waveguide, the measured transmittance indicates almost 100%. Actually, the transmittance of a Ti:PPLN Sﬞolc is decided by two parameters. One is a rocking angle and the other is a length of device (numbers of microdomain). The former can be controlled by an external electric field [22, 23] along the Y-axis of the Ti:PPLN waveguide. However, the latter is a fixed value after a device was fabricated. The relation between the transmittance and the length of the device is well discussed in Ref . The measured full-width at half-maximum (FWHM) of the filter was about 0.2 nm, which is slightly broader than that of the predicted value in theoretical calculation (~0.19 nm). Each microdomain of a Ti:PPLN works as a half-wave plate which is alternately aligned at small angles of +θ (positive domains) and -θ (negative domains) with respect to the crystal’s z-axis. From the previous experimental results and theoretical calculations [13, 16, 17], we know that the minimum rocking angle of a Ti:PPLN is about 0.001 o. However, the exact rocking angle and the origin of such small tilting angle in a microdomain are not clear. Only one paper had reported the origin of the angle as photovoltaic effect in a PPLN . Further research on this issue is required for more understanding of Sﬞolc filtering function in a PPLN. In the case of a Ti:PPLN Sﬞolc filter, the period of the grating is determined by the dispersion of the material given a desired center wavelength and the bandwidth is determined by the number of microdomains. Unfortunately, these are the fixed parameters after a Ti:PPLN waveguide was fabricated. Therefore, for the active control of a Ti:PPLN Sﬞolc filter, most of the researchers used the temperature control method which can induce the refractive index change in a PPLN. In this way, they tuned the center wavelength of the filter[13, 14] and demonstrated a tunable single- and dual-wavelength filter .
In our experiments, the active bandwidth control of a Ti:PPLN Sﬞolc filter was performed by temperature-gradient-technique using a specially designed sample holder (Fig. 1). The distribution of the temperature along the Ti:PPLN waveguide T(z) and wave-vector mismatch Δk can be described follows:
where T(0) and T(L) are the temperatures at the input and output positions of the Ti:PPLN waveguide, and Λ is the period of QPM grating. Actually, the temperature induces the change of QPM grating period (Λ) as well as the refractive indices (n o, n e). The influence of the temperature in eq. (8) can be expressed as follows:
where α is the coefficient of thermal expansion. In the case of a Ti:PPLN, the influence of the changes in refractive indices (first term in right hand side of eq. (9)) to the effective grating period is about two orders of magnitude bigger than that of the thermal expansion (second term in right hand side of eq. (9)) . Therefore, we neglected the thermal expansion effects in a Ti:PPLN Sﬞolc filter. The temperature gradient along the Ti:PPLN waveguide results in the broadening of bandwidth in the filter, such kind of broadening effect can also be achieved by a chirped QPM grating [19, 25]. However, the temperature gradient method allows the active bandwidth control which couldn’t be obtained in the chirped QPM grating method. Moreover, we can use the temperature gradient method not only in a uniform QPM grating but also in a chirped QPM grating sample for the active control of the filtering bandwidth. The transmission curves of the Ti:PPLN Sﬞolc filter for various temperature gradients are shown in Fig 3. Figure 3(a) and 3(b) show the experimental and the theoretical results, respectively. The theoretical curves of Fig. 3(b) show good agreement with experimental results of Fig. 3(a) except for a 5.47oC case. In the case of a steep slope temperature gradient, we observed large ripples in transmission spectrum. This is mainly caused by several factors including inhomogeneity of refractive index along the Ti waveguide, and so on [26, 27]. As increased of the temperature gradients, the bandwidth of transmitted signal was broadened as you can see in Fig. 3. When the spectrum was broadened, the transmittance spectrum oscillates within bandwidth and transmittance was decreased as a function of spectrum bandwidth. The ripple feature in Fig. 3 is created by the interference among phase-matching conditions [25, 28]. We can solve this problem using apodized QPM grating which has different duty ratio of inverted mircodomains at the beginning and end parts of QPM grating [28, 29].
The bandwidth of the Ti:PPLN Sﬞolc filter as a function of temperature gradients is shown in Fig. 4. The theoretical bandwidths are calculated by using eq. (6) and (8). Here we used the effective refractive indices (n o, n e) of a Ti:PPLN as a function of temperature. The values of refractive indices are decided by the dispersion equations of the refractive index changes according to Ti diffusion densities . The bandwidths of experimental results show more broad than those of theoretical calculation through the almost whole temperature gradient. These kinds of different bandwidths come from the different effective length between the ideal and real Ti:PPLN Sﬞolc filter. The short effective length in the Ti:PPLN waveguide is induced by the difficulties with the fabrication technology in making the same QPM grating in a Ti:LiNbO 3 as originally intended when the QPM mask pattern was designed and homogeneous waveguide [6, 27, 31]. At a temperature difference of 5.47 °C at both endfaces of the Ti:PPLN, we achieved about 2.8 nm broad bandwidth in the filter which has a 0.2 nm filtering bandwidth at a uniform temperature. However, in the case of broad transmittance bandwidth, one cannot avoid a trade-off between transmittance and bandwidth. The transmittance of the filter as a function of temperature gradients is shown in Fig. 5. The transmittance decrease dramatically as a function of temperature gradients. To increase the transmittance of broadened bandwidth, the rocking angle, θ control is needed by applying an external dc-field along the Y-axis of the Ti:PPLN Sﬞolc filter .
In conclusion, for the first time to our knowledge, we have demonstrated the bandwidth control of a transmission spectrum in a Ti:PPLN Sﬞolc filter that has regular QPM grating (Λ=16.6 µ m). Up to 2.8 nm of filtering bandwidth was achieved with a simple temperature-gradient-control technique in a 78-mm-long Ti:PPLN Sﬞolc filter, which has a 0.2 nm bandwidth at an uniform temperature. Further research is underway to increase of the transmittance even in a broaden bandwidth by applying the electric field along th Y-axis of a Ti:PPLN Sﬞolc filter. We believe this kind of bandwidth controllable Sﬞolc filter to be very useful for various optical experiments.
This work was supported by IITA of Korea through the ‘Leading edge R&D Program and MEST of Korea through ’APRI- Research Program of GIST’.
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