1. Introduction

Photonic node systems using grouped wavelengths, or a waveband, are attractive for future high capacity networks [1]. In these systems, to prevent signal-blocking induced by optical-traffic collisions, wavelength conversion or waveband conversion will be very important. For this purpose, several wavelength-conversion or waveband-conversion methods have been proposed so far, which use cross-gain or cross-phase modulation in semiconductor amplifiers [2], four-wave mixing (FWM) in highly nonlinear optical fibers [3,4], FWM in semiconductor amplifiers [5,6], difference-frequency generation (DFG) in quasi-phase-matched (QPM) ferroelectric (typically LiNbO₃) devices [7], and DFG in QPM semiconductor devices [8]. Of these methods, DFG with QPM LiNbO₃ devices will be useful for waveband conversion because it has a wide conversion bandwidth, low optical losses, and no modulation-format dependence.

In addition, the tunability of a destination waveband will be important for flexible control in averting the signal-blocking. To obtain the wavelength-tunable output, several methods have been proposed so far [9–13]. Since the principle of these devices is based on all-optical waveband conversion, if they are introduced in optical networks, very high speed waveband conversion will be realized.

Among those devices, Asobe et al. have developed a multiperiod-QPM LiNbO₃ device containing a multiperiod-periodically-poled structure using cascaded DFG [12, 13]. The principle of this device stems from a super-structure grating of a refractive index [14, 15]. But the multiperiod-QPM LiNbO₃ has a super-structure grating of χ⁽²⁾ and produces multiple QPM peaks in the phase-matching curve. Using these multiple QPM peaks, we can shift a SHG wavelength generated from a pump wavelength from one SHG wavelength to another, and DFG between this SHG wavelength and the signal waveband gives rise to a shift of the destination (idler) waveband.

However, this device has a drawback that it generates crosstalk between wavebands, which originates from the following two types. The first type is caused by sum-frequency generation (SFG) between signal waveband and pump wavelength, phase-matched on ripples between QPM peaks in the phase-matching curve. Fortunately, this type can be suppressed if direct second-harmonic pumping is employed [16, 17]. Also, this type can be avoided by setting the signal and pump wavelengths so that their SFG wavelength is out of the range where there are the ripples.

The second type is caused by SFG between the signal and idler wavebands and subsequent DFG between the SFG wavelength and the signal waveband. The generation mechanism of this type is illustrated in Fig. 1.

 

Fig. 1 Generation mechanism for the second type of crosstalk between wavebands via cascaded difference-frequency generation (cascaded DFG). Step 1: Sum-frequency generation (SFG) occurs between the signal ❍ and idler ● lights, which is phase-matched on a ripple ❍ + ● between main quasi-phase-matched (QPM) peaks in the phase-matching curve. Step 2: DFG between the newly generated SFG light ❍ + ● and the signal light ❍ results in crosstalk on the idler light ●.

Download Full Size | PDF

Its detail is as follows: First, the idler frequency ω_i,n(= 2πc/λ_2,n) is generated from the signal frequency ω_s,n(= 2πc/λ_1,n) and the pump frequency ω_p(= 2πc/λ₀) via cascaded DFG:

Second, if the signal frequency ω_s,n and the idler frequency ω_i,n′ (e.g., the next idler frequency to ω_i,n) are phase-matched via SFG on the ripple frequency ω_ripple between QPM peaks at the left side in Fig. 1, then the equation

Finally, owing to the phase-matching on the ripple frequency ω_ripple, crosstalk is generated on ω_i,n′ via DFG:

We have already shown that the crosstalk size of this type can be reduced if we use an apodized multiperiod-QPM device [18]. In this paper, using this device, we measure its signal-power dependence of the idler power, the crosstalk power, and their ratio in detail, and we show that its power dependence well fits a theory and that the improved waveband-conversion characteristic is maintained even for reduced signal power.

This paper is organized as follows: Section 2 describes the detailed design of the apodized multiperiod-QPM device. Section 3 describes the method for fabricating the designed device, and provides waveband-conversion experiments with the fabricated device and measured properties of power dependences. Section 4 summarizes the obtained results.

2. Device design

To yield multiple QPM peaks, special phase modulation ϕ(z) is applied to the periodicity of the periodically-poled structure of an ordinary QPM device that has a constant period Λ₀ [19, 20], where z is the direction along the device.

Modulation on the phase function ϕ(z) in the second-order nonlinear coefficient d(z) is made so that ϕ(z) has a period of Λ_ph (≫ Λ₀) (i.e., ϕ(z) = ϕ(z + Λ_ph)) [12, 13]. This modulation creates new peaks at around Δβ = 2π/Λ₀ with a spacing of 2π/Λ_ph, or at Δβ = 2π/Λ₀ + 2πl/Λ_ph, where l takes integers.

To shift a waveband using those new peaks and to keep the power of the shifted waveband constant, the conversion efficiencies at those peaks have to be equalized. We can achieve this by optimizing the phase-modulation function ϕ(z) so that the trial function T can be minimized [21]: $T={\sum }_{l=1}^N{({\eta }_l-{\eta }_{0}N)}^2$, where N is the number of the peaks to be equalized, η₀ is the efficiency when N = 1, and η_l is the efficiency at the lth peak for N > 1. This optimization is carried out with the help of the numerical method called the downhill simplex method [22]. As an example, we calculated a phase-matching curve for N = 5 by this method, as illustrated by the red line in Fig. 2.

 

Fig. 2 Calculated phase-matching curve for the unapodized and apodized multiperiod-QPM devices.

Download Full Size | PDF

Using those peaks, if we shift the pump wavelength (or the SHG wavelength) corresponding to the peak at Δβ = 2π/Λ₀ to another peak at Δβ = 2π/Λ₀ + 2πl/Λ_ph, we can shift the idler waveband.

As seen at the red line in Fig. 2, there are ripples between 5 major peaks. Owing to these ripples, crosstalk on the idler waveband occurs. To decrease the size of the crosstalk by reducing that of the ripples, we redesigned the multiperiod-QPM structure with the following apodization technique. The apodization technique used for fiber Bragg gratings for a similar purpose is well known [23–26]. But, unlike a continuous change in the refractive index of apodized fiber Bragg gratings, we cannot change the χ⁽²⁾ value smoothly because the χ⁽²⁾ grating is composed of binary χ⁽²⁾ values, i.e., upward χ⁽²⁾ and downward χ⁽²⁾. For this reason, we adjust the duty ratio between a pair of the upward and downward χ⁽²⁾ segments to obtain a similar apodization effect, as depicted in Fig. 3 [18, 27].

 

Fig. 3 (a) Constant duty ratio in the unapodized QPM device, indicated by the dashed line. (b) Changed duty ratio in the apodized QPM device, indicated by the solid line.

Download Full Size | PDF

We tested several trial functions to control the duty ratio and to minimize the ripple size, and found that the hyperbolic-tangent-type function f (z) shown below provided a satisfactory ripple reduction:

In Eq. (5), the denominator tanh(a) in f (z) compensates for the reduction in peak conversion efficiency for a small a. For example, at the center of the device (i.e., at z = L/2), f (L/2) is 1/2, but without tanh(a), f (L/2) is tanh(a)/2. This becomes very small as a decreases to zero, resulting in a very low conversion efficiency. Thus the denominator tanh(a) in Eq. (5) is necessary. To show the compensation effect concretely, we illustrate the dependence of the peak conversion efficiency on a in Fig. 4, which is normalized by the peak conversion efficiency without apodization. Figure 4 indicates that as a approaches zero, the peak conversion efficiency converges to a finite value of −4.5 dB, not a zero value.

 

Fig. 4 Efficiency of a QPM peak as a function of the apodization parameter a, where the efficiency is normalized by that without apodization. The inset shows the magnified figure of the dotted ellipse at 0 ≤ a ≤ 1.8.

Download Full Size | PDF

Next, we depict the a-dependence of the ripple/peak ratio in Fig. 5. In this case, there is a minimum value for the ripple/peak ratio at a = 0.85, and this value is used for our device design. At the blue line in Fig. 2, we show a calculated phase-matching curve for an apodized device with a = 0.85. Although the power peaks become less than half, the ripples between the peaks are sufficiently decreased.

 

Fig. 5 Ripple/peak ratio as a function of the apodization parameter a. The inset shows the magnified figure of the dotted ellipse at 0 ≤ a ≤ 1.8.

Download Full Size | PDF

3. Device fabrication and experimental results

3.1. Device fabrication

On the basis of the above design, using the electrical poling technique, we fabricated an apodized multiperiod-QPM pattern on a Zn-doped LiNbO₃ wafer that is highly resistant to the photorefractive damage when it is fabricated to a waveguide [17]. We also fabricated an unapodized multiperiod-QPM pattern to check the improvement for comparison. We set the poling period Λ₀ at 18.1 μm and the phase-modulation period Λ_ph at 8.6 mm so that 5 QPM peaks with a 200-GHz spacing appeared in the phase-matching curve at around 1.57 μm. The total device length L was taken to be 43.1 mm. The minimum size of the fabricated domains was 2 μm, and the minimum QPM period was 10 μm. Because of this domain size limit, the pattern near both ends of the apodized device was not well made (See Fig. 6), which also caused a slight remaining ripple amplitude between the 5 QPM peaks, as will be shown in Sec. 3.2.1.

 

Fig. 6 Microscopic photograph near the end of the apodized multiperiod-QPM device. The inset depicts the magnified picture near its end, which shows that the domain size up to 2 μm is well made.

Download Full Size | PDF

Furthermore, we fabricated a device with a small-core waveguide from the above poled LiNbO₃ wafer so that it would have a high conversion efficiency. The high efficiency enables us to use a simple fiber-based pump system with moderate power for optical pumping. To fabricate the waveguide, we first bonded the poled LiNbO₃ wafer to a LiTaO₃ substrate with a smaller refractive index by the direct-wafer-bonding technique [28]. We then reduced the thickness of the LiNbO₃ layer by polishing [28]. Finally, we cut two deep trenches in the LiNbO₃/LiTaO₃ wafer carefully with a rpm-controlled diamond-blade dicing saw. In this way, we produced a high-mesa-shaped waveguide with a 6-μm-thick and 8-μm-wide LiNbO₃ core on top of the mesa, as illustrated in Fig. 7.

 

Fig. 7 Schematic diagram of the fabricated waveguide.

Download Full Size | PDF

3.2. Experimental results

3.2.1. The phase-matching curves

Here we show the experimentally obtained phase-matching curves for the unapodized and apodized devices at a temperature of 27°C in Figs. 8(a) and 8(b), respectively [18], which are necessary to explain the new results obtained in this paper. Those phase-matching curves were obtained by using the SHG light pumped at around 1.57 μm with an external-cavity tunable laser diode. Here, the phase-matching curve for SHG at the used wavelength region could well approximate that for SFG.

 

Fig. 8 Measured phase-matching curves for (a) unapodized and (b) apodized multiperiod-QPM devices.

Download Full Size | PDF

The difference of peak positions in wavelength between Figs. 8(a) and 8(b) is that the yield of the devices with fine line structures was very low and that it was difficult to obtain the unapodized and apodized devices whose peak positions were well matched.

As shown in Fig. 8(a), the experimental result for the unapodized device exhibited ripples between 5 major peaks. Note that the size of the ripples in Fig. 8(a) was rather larger than the calculated result at the red line in Fig. 2 and that this could be attributed to the nonuniformity of the core size in the waveguide.

By apodization, the ripple size was considerably reduced, as shown in Fig. 8(b). The experimental result in Fig. 8(b) still showed some residual ripples. This could be due to the pattern-forming size limit to the apodization as mentioned above and the nonuniformity of the waveguide. The ripple amplitude will be reduced if the poling technique and the waveguide uniformity are improved.

From the measured powers of the pump and SHG lights, the conversion efficiency was estimated to be about 155 %/W for the unapodized device and about 115 %/W for the apodized device, where each value was averaged over the 5 peaks. The efficiency for the apodized device was about 26% smaller than that for the unapodized device in this experiment. This efficiency reduction did not match the calculated results, which could be due to the nonuniformity of the waveguide fabricated by the mechanical cutting.

3.2.2. Waveband-conversion experiments

Next, we show the experimental results of waveband conversion with the following measurement setup.

Figure 9 shows the configuration of the devices used in our experimental setup. 100-GHz-spacing 4-channel signal light at around 1.54 μm was generated using DFB laser diodes (DFB LDs), an arrayed waveguide grating (AWG), and an Er-doped fiber amplifier (EDFA). The pump light at around 1.57 μm was generated using an external-cavity tunable laser diode (ECL) and an EDFA. The signal and pump lights were combined with a fiber coupler and injected into the waveguide through a fiber. The amount of ASE noise from the EDFA for the pump light was reduced with band pass filters (BPFs). No BPFs were used for the signal light with an EDFA because the quantity of ASE noise from it was considerably small compared to that for the pump light. The collimated output idler light was injected into an optical spectrum analyzer (OSA) to measure its wavelengths. SHG light generated from the pump light was monitored with a power meter (PM) to make sure good optical coupling between the fiber and the waveguide.

 

Fig. 9 Measurement setup. AWG: Arrayed waveguide grating, ECL: External cavity tunable laser diode, EDFA: Er-doped fiber amplifier, BPF: Band pass filter, PM: Power meter, OSA: Optical spectrum analyzer.

Download Full Size | PDF

Figures 10(a) and 10(b) are the obtained crosstalk characteristics for the unapodized and apodized devices, respectively [18]. The thin line in Fig. 10(a) shows the idler spectrum observed for the unapodized device when all 4 signal channels were turned on. Here, we used a pump wavelength of 1571.8 nm for the idler spectrum in Fig. 10(a). This wavelength corresponds to the rightmost QPM peak in Fig. 8(a). We also used a pump wavelength of 1567.8 nm for the idler spectrum in Fig. 10(b), which corresponds to the rightmost QPM peak in Fig. 8(b). In addition, a signal power of 12.1 dBm/channel and a pump power of 21.9 dBm were used. The fact that the rightmost QPM peaks in Figs. 8(a) and 8(b) have almost the efficiency, 120 %/W, can be used for a proper comparison in the crosstalk reduction between the unapodized and apodized devices, as explained later in this section.

 

Fig. 10 Idler spectrum produced with (a) unapodized and (b) apodized devices when a 100-GHz-spacing 4-channel signal light was input, as indicated by the thin line, and that when one of the 4 channels was turned off, as indicated by the thick line.

Download Full Size | PDF

To know the crosstalk power, we measured the idler spectrum when one of the 4 signal channels was turned off, as indicated by the thick line in Fig. 10(a) for the unapodized device. We then observed a crosstalk peak with a crosstalk/idler power ratio of −30 dB.

Figure 10(b) with the thin line shows the idler spectrum for the apodized device when all the 4 signal channels were turned on. The thick line in Fig. 10(b) represents the idler spectrum when one of the 4 channels was turned off. In this case, the crosstalk/idler power ratio was −38 dB, and an 8-dB reduction in the crosstalk was obtained.

This 8-dB reduction is consistent with a value obtained from a theory, which will be described in detail in the next section. Since the crosstalk is caused by DFG between the ripple and the signal, the crosstalk power is proportional to the ripple power. As seen in Fig. 5, there is a 10.5-dB reduction in the ripple/peak ratio from −14 dB at a → ∞ without apodization to −24.5 dB at a = 0.85 with apodization. Under the same peak power, the crosstalk power will therefore have a 10.5-dB reduction, which is close to the experimentally obtained 8-dB reduction.

Finally, to verify that the observed crosstalk spectrum was not caused by FWM in optical fibers, we checked the same idler waveband after removing the device and connecting only fibers, and found that there was no crosstalk spectrum.

3.2.3. Power dependence of idler power, crosstalk power, and their ratio on signal power

Using the fabricated unapodized and apodized devices, we examined the dependence of the idler power, the crosstalk power, and their ratio on the signal power to check if it does not contradict the theory of the used nonlinear optical effects and if the crosstalk-reduction feature is kept even for small signal power.

Before providing our experimental results, we first review the theoretical power dependence of the idler power, the crosstalk power, and their ratio on the signal power by denoting the signal, pump, and idler powers by P_s, P_p, and P_i, respectively.

In cascaded DFG, the pump light with a power of P_p is first converted to the SHG light with a power of P_SHG proportional to $P_{\text{p}}^2$ (i.e., $P_{\text{SHG}}\propto P_{\text{p}}^2$). The idler light with a power of P_i is then produced by DFG between the signal and SHG lights (i.e., P_i ∝ P_sP_SHG). Thus, by substituting $P_{\text{SHG}}\propto P_{\text{p}}^2$ for P_i ∝ P_sP_SHG, the idler power P_i becomes $P_{\text{i}}\propto P_{\text{s}}{P}_{\text{p}}^2$, which is proportional to P_s.

On the other hand, when SFG between the signal and idler lights on the ripples occurs, the SFG power P_SFG is proportional to P_sP_i (i.e., P_SFG ∝ P_sP_i). Since the crosstalk arises from DFG between this SFG light and the signal light, the crosstalk power P_XT is proportional to P_SFGP_s (i.e., P_XT ∝ P_SFGP_s).

By inserting P_SFG ∝ P_sP_i into P_XT ∝ P_SFGP_s, we obtain $P_{\text{XT}}\propto P_{\text{s}}^2{P}_{\text{i}}$. Furthermore, substituting $P_{\text{i}}\propto P_{\text{s}}{P}_{\text{p}}^2$ for $P_{\text{XT}}\propto P_{\text{s}}^2{P}_{\text{i}}$, we obtain $P_{\text{XT}}\propto P_{\text{s}}^3{P}_{\text{p}}^2$, which is proportional to $P_{\text{s}}^3$. Finally, by use of the relation $P_{\text{XT}}\propto P_{\text{s}}^2{P}_{\text{i}}$, we obtain the crosstalk/idler power ratio $P_{\text{XT}}/P_{\text{i}}\propto P_{\text{s}}^2$, which is proportional to $P_{\text{s}}^2$.

We then checked those signal-power dependences experimentally, as shown below. We give the measured idler power P_i and crosstalk power P_XT in Fig. 11(a) for a number of P_s values, where P_p has a constant power of 21.9 dBm. In Fig. 11(a), (i) squares ▪, (ii) open circles ❍, and (iii) closed circles ● show (i) the P_s-dependence of P_i, (ii) that of P_XT for the unapodized device, and (iii) that of P_XT for the apodized device that is referred to as P′_XT hereafter. Here, their log-log plotting clearly shows (i) P_i ∝ P_s, (ii) $P_{\text{XT}}\propto P_{\text{s}}^3$, and (iii) $P_{\text{XT}}^{\prime }\propto P_{\text{s}}^3$, which agree well with the theoretical expectation. Also, we observed that a 8-dBm reduction in the crosstalk power between the unapodized and apodized devices was kept for decreased signal power. Since crosstalk with a power of less than −50 dBm was obscured by optical background noise generated from LDs and EDFAs despite filters, only the crosstalk power higher than this value was plotted in Fig. 11(a).

 

Fig. 11 (a) Signal-power dependence of the idler power, indicated by squares ▪, the crosstalk power for the unapodized device, indicated by open circles ❍, and the crosstalk power for the apodized device, indicated by closed circles ●, and (b) that of the crosstalk/idler power ratio for the unapodized device, indicated by open circles ❍, and the apodized device, indicated by closed circles ●.

Download Full Size | PDF

Furthermore, to examine the experimental crosstalk/idler power ratio P_XT/P_i, we depict the log-log plotting of (i) P_XT/P_i with open circles ❍ for the unapodized device and (ii) P′_XT/P_i with closed circles ● for the apodized device in Fig. 11(b). This clearly indicates that (i) $P_{\text{XT}}/P_{\text{i}}\propto P_{\text{s}}^2$ and (ii) $P_{\text{XT}}^{\prime }/P_{\text{i}}\propto P_{\text{s}}^2$ hold, which well match the theoretical anticipation, and that a 8-dB reduction in the crosstalk/idler power ratio between those devices was retained even if the signal power was decreased.

4. Summary

This paper investigated the power dependence of an apodized multiperiod-QPM LiNbO₃ device for low-crosstalk waveband conversion that uses cascaded DFG. The crosstalk was caused by SFG between the signal and idler wavebands that is phase-matched on ripples between multiple QPM peaks and by subsequent DFG between the SFG wavelength and the signal waveband. A guiding principle for the apodization design on the device to reduce the ripple size was described in detail. Also, a detailed fabrication method for the apodized multiperiod-QPM LiNbO₃ waveguide was described. Finally, in the experiment of waveband conversion with 100-GHz-spacing 4 signal channels, we measured the signal-power dependence of the idler power, the crosstalk power, and their ratio, and found that it was in good agreement with the theoretical prediction and that a 8-dB reduction in the crosstalk was kept even if the signal power was reduced.