1. Introduction

Quasi-phase-matching (QPM) materials, also named nonlinear photonic crystals (PCs) [1,2], have been extensively studied in nonlinear optics regime [1,3,4]. The wide operation range and large quadratic nonlinearity make them good candidates for all-optical signal processing [5–9]. As a typical QPM material, periodically poled lithium niobate (PPLN) has been successfully used in optical switches [10], wavelength shifters [11–14] and pulse shapers [14,15]. Recently, the nonreciprocal structures become hot topics [8,9,16]. PPLN with geometrical asymmetry is a promising nonreciprocal material, which has been designed as an optical diode alternative to standard magneto-optic Faraday rotator [9]. When the fundamental wave (FW) propagates in PPLN with a defect, the second-harmonic wave (SH) and FW would go through different degrees of disturbance owing to the introduced phase discontinuity (δφ) at the defect area. Both the FW and SH thus are sensitive to the defect’s parameters like its position and thickness. As long as the defect is not just at the middle of the PPLN, lights to opposite directions would see different structures then different FW and SH are obtained at the output ports. An extreme case is that one wave, e.g., the FW only may be detected at a single direction. The opposite FW is totally converted to SH. An optical diode thus is obtained for the FW. A unitary contrast $C=(T_{\lambda }^{+}-T_{\lambda }^{-})/(T_{\lambda }^{+}+T_{\lambda }^{-})$ defines the degree of optical isolation, where $T_{\lambda }^{+}$ and $T_{\lambda }^{-}$ are the FW transmission on forward and backward direction respectively. The contrast varies from −1 to 1 that is greatly affected by phase discontinuity δφ, the position of δφ, and the fundamental input power. C = 1 and −1 represent optical diodes with opposite passing directions, respectively, which could be realized by designing suitable PPLN parameters. However, for a given PPLN, the δφ and its location has been fixed. The contrast only can be tuned by the intensity of input power, which is not very convenient. In another word, the light power has limited range to realize the optical diode effect. It would be much desired to introduce an extra tuning approach, such as inducing electric field or acoustic wave, to adjust the isolation contrast. Thus C could be dynamically locked at ± 1 or be intentionally set to a specific value. An extreme case is that C could be adjusted from 1 to −1, meaning the diode’s forward direction is reversible. This unique bidirectional tunable optical diode might be useful for some photonic applications.

We have already studied the photon-phonon interaction in previous work [17], and found that the acoustic wave could affect the wave vector matching between FW and SH. Therefore the second harmonic generation (SHG) process could be controlled by adjusting the input acoustic wave’s intensity. Since the acoustic wave is an effective tuning approach in normal PPLN, it might also supply a way to adjust the asymmetric PPLN based optical diodes. In this paper, we designed a series of optical diodes with different defect positions and phase discontinuities. We found that the acoustic wave really could affect the FW’s isolation contrast effectively. As long as a suitable acoustic wave is employed, the isolation contrast could be tuned from −1 to 1, even if the initial contrast is around zero, which makes the fabrication and operation of an optical diode more convenient. The corresponding RF driving power is only around several hundred milliwatts. A promising acoustic wave tunable bidirectional optical diode is thus obtained.

2. Theory and simulation

The nonreciprocal PPLN is sketched in Fig. 1 . A defect is introduced in a PPLN of length L and period Λ₀. When a collinear acoustic wave travels in it along x-axis, a periodic index modulation is built up due to the elasto-optic effect, which could induce the acousto-optic (AO) polarization rotation [17]. The polarization rotation effect may happen for either FWs or SHs depending on the phonon’s frequency. Let’s assume the FW’s polarization is rotated. The input light wave is a Z-polarized FW (to make use of the largest nonlinear coefficient d₃₃ of LiNbO₃) as indicated in Fig. 1. A Z-polarized SH thus is generated though QPM (E_1z + E_1z → E_2z), which means the phase mismatch of SHG, Δβ₁ = k_2z - 2k_1z is compensated by a reciprocal vector (G1) of PPLN, i.e., G₁ = Δβ₁. On the other hand, the acoustic wave is able to rotate the FW’s polarization, so that the Y-polarized FW emerges after the acoustic wave is coupled in. As the Y-polarized and Z-polarized FWs normally have different wave vectors, they are not coupled because of the phase mismatch, i.e., Δβ₂ = k_1y - k_1z ≠ 0. When an longitudinal acoustic wave is introduced with its wave vector H = Δβ₂, the phase mismatch between Y- and Z- polarized FWs is compensated as well. Y-polarized FW (E_1z → E_1y) is generated through AO polarization rotation. As a consequence, both the light’s and acoustic wave’s frequencies should be well selected for efficient SHG and polarization rotation. In this case, the incident Z-polarized FW and the generated Y-polarized FW and Z-polarized SH are tightly coupled together due to phase matching. Although the polarization rotated Y-polarized FW and Z-polarized SH may also generate a few Y-polarized SH, it could be neglected in a general case. Therefore three-wave coupling equations could be deduced as follows. For simplicity, a plane-wave approximation is taken and the propagation loss is ignored.

 

Fig. 1 Schematic diagram of a nonreciprocal PPLN. Λ₀ is the period of grating. A defect of length δL is introduced at x = L₁.

Download Full Size | PDF

Equations (1) are satisfied in the both uniform segments of PPLN in Fig. 1. In the domain of δL, a phase jump δφ between FWs and SH is brought in. We suppose δL is short enough to ignore any influences on amplitude changes or phase-matching for both SHG and polarization rotation. While the waves travel forward, the original Z-polarized FW, induced Y-polarized FW and Z-polarized SH are coupled together along the PPLN in the segment L₁ (< L/2). There are two competing processes: SHG and polarization rotation, which are governed by the coupling coefficients K₁ and K₂ and their ratio [17]. When the light waves pass through the defect, their relative phase is changed and the SHG process is not standard any more. Then the seeded SHG and polarization rotation is engaged in the second segment L-L₁-δL. In the backward case, the same approach is adopted, except that the waves travel along the second segment L-L₁-δL firstly and thus the affection induced by dephasing δφ is different. In both situations, K₂ could be easily controlled by tuning the intensity of acoustic wave (S) that makes contrast C changes within the range [-1, + 1] accordingly.

At room temperature, we set the pumping FW intensity 10 MW/cm² at 1550 nm [19], the length of PPLN L = 1 cm, d₃₃ = 25.2 pm/V, p₄₁ = −0.05 [20], Λ₀ = 18.98 μm to satisfy the QPM condition. In the case of L₁ = 4/10 L, δφ = 0.3π and π, the contrast and transmittance in both directions for Z-polarized FW is plotted in Fig. 2 . From Fig. 2 (a), When δφ = 0.3π, C ≈1 (red solid, the forward transmission $T_{\lambda }^{+}$ = 83.73% and the backward transmission $T_{\lambda }^{-}$ ≈0) represents an optical diode which only allows the forward transmission. While C ≈-1 (green dash, the forward transmission$T_{\lambda }^{+}$≈0 and the backward transmission $T_{\lambda }^{-}$ = 45.38%) represents the same diode but only allows the backward transmission. Thus, a bidirectional optical diode is achieved by tuning acoustic wave. In Fig. 2 (b), when δφ = π, the contrast C is equal to 0 without any acoustic wave (K₂ = 0) which is agreed with the result in reference 8. Similarly, the red solid (C ≈1, $T_{\lambda }^{+}$ = 31.17%, $T_{\lambda }^{-}$≈0) and green dash (C = 94.36%, $T_{\lambda }^{+}$ = 2.66%, $T_{\lambda }^{-}$ = 91.58%) represent two opposite isolation directions in an optical diode. It’s obvious that the optical isolation with contrast (C) could be tuned nearly from −1 to 1 by adjusting the ratio of |K₂/K₁|. As the input FW intensity is fixed, the required acoustic intensity can be calculated using $I_a=\rho v^3{\left|HD\right|}^2/2$ [18], where ρ = 4640 kg/m³, v = 6570 m/s. Assume a 0.5 mm² sample cross-section, the minimum required RF driving power could be calculated from |K₂/K₁|, which is also marked in Fig. 2 at its top x-axes. As shown in Fig. 2, the contrast varies from 1 to −1 several times only by tuning the driving power from 0 to 0.187 W. Actually, the actual RF power consumption should be a little higher if the impedance mismatch and acoustic wave’s propagation loss are taken into account. However, from Fig. 2, a driving power around several hundred millwatts should be enough for the operation of our tunable optical diode.

 

Fig. 2 The contrast is tuned by the intensity of acoustic wave. Here L₁ = 4/10 L. The dephasing is (a) 0.3π and (b) π. The red solid and green dashes represent the optical isolation with contrast C = 1 and −1 respectively.

Download Full Size | PDF

To further describe the operating principle of the tunable optical diode, the detailed evolution of the Z-polarized FW inside the sample is revealed in Fig. 3 , which corresponds to the cases of C = 1 at red solid and C = −1 at green dash in Fig. 2. Here the black solid and red dashed curves refer to forward and backward propagation, respectively. In comparison, the case when there is no acoustic wave is shown at the top part. The forward FW is converted to SH gradually when propagating in the sample, then the SH transfers back to FW due to cascaded nonlinearity. It reaches a peak then drop again, meaning some SH is regenerated. The final FW power left at the output surface is only 68.27% in a 1 cm-long PPLN with L₁ = 4/10 L, δφ = 0.3π. However, the backward FW is converted to SH more efficiently. Only 4.53% FW power is left finally, which means the asymmetric defect at L₁ affects the depletion of SH. In this case, the PPLN shows the unidirectional isolation to some extent (C = 87.55%). However, when a weak acoustic wave is coupled (|K₂/K₁| = 0.08, RF power = 1.2 mW), part of the Z-polarized FW is converted to Y-polarized FW, but the SHG process still dominates the three-wave coupling, so that the curves still look similar. Only the second peak of the forward FW is lowers but it exists at a farther position in the sample. The final Z-polarized FW power becomes even higher at 83.73%. When the light propagates backward, almost all Z-polarized FW is depleted, corresponding a perfect optical diode with C = 1. When the driving power is higher (|K₂/K₁| = 0.42, RF power = 33.6 mW) as shown in the bottom part of Fig. 3, the polarization rotation effect is much stronger, which affects the SHG severely. A backward optical diode with C = −1 is realized.

 

Fig. 3 Evolution of the normalized Z-polarized FW intensity versus propagation distance with L₁ = 4/10 L, δφ = 0.3π. Black solid and red dashed curves refer to forward and backward propagation of fundamental waves, respectively.

Download Full Size | PDF

Simulations have also been done at different L₁, δφ and input light power. The results indicate that in most of the above situations, the isolation contrast can be nearly tuned from −1 to 1 by only changing acoustic intensity. For instance, Fig. 4 shows the tunable range of contrast versus dephasing δφ with different lengths of L₁ at a lower input power of 2.5 MW/cm². Black dashes and red solids represent the achieved maximum and minimum values of the isolation contrast by tuning the intensity of acoustic wave, respectively. The blue dots show the contrast without any acoustic wave. In our calculation, |K₂/K₁| is tuned from 0 to 2, i.e., the RF power ranges from 0 to 0.76 W, but normally the required RF power is much lower. From Fig. 4, it is found that

 

Fig. 4 The tunable range of contrast $C=(T_{\lambda }^{+}-T_{\lambda }^{-})/(T_{\lambda }^{+}+T_{\lambda }^{-})$ versus different dephasing δφ with different lengths of L₁. Black dashes and red solids represent the maximum and minimum contrast by tuning the intensity of acoustic wave, respectively. The blue dots show the contrast without acoustic.

Download Full Size | PDF

 

Fig. 5 The tunable range of contrast versus different dephasing δφ at L₁ = 4.9/10. Black dashes and red solids represent the maximum and minimum contrast by tuning the intensity of acoustic wave, respectively. The blue dots show the contrast without acoustic wave.

Download Full Size | PDF

From the analyses above, the acoustic wave is really great helpful for the realization and tuning of a PPLN optical diode. Although the acoustic wave could be introduced externally, it also can be generated from PPLN itself when it acts as an acoustic suprlattice [17,21]. In this case, another well-designed PPLN section should be integrated. This kind of monolithic device might have potential applications in photonic integrated circuits (PIC).

3. Conclusion

In summary, we proposed a bidirectional tunable optical diode in an asymmetric PPLN through cascading SHG and AO interaction. The optical isolation contrast could be tuned from −1 to 1 by adjusting the intensity of an induced acoustic wave. The influence of dephasing, location of defect, input power and the intensity of acoustic wave were discussed. In comparison with previously reported PPLN diodes, the introduction of acoustic wave makes our diode more flexible and easier to control.