We report on the design and demonstration of electro-optically tunable, multi-wavelength optical parametric generators (OPGs) based on aperiodically poled lithium niobate (APPLN) crystals. Two methods have been proposed to significantly enhance the electro-optic (EO) tunability of an APPLN OPG constructed by the aperiodic optical superlattice (AOS) technique. This is done by engineering the APPLN domain structure either in the crystal fabrication or in the crystal design process to increase the length or block-number difference of the two opposite-polarity domains used in the structure. Several orders of magnitude enhancement on the EO tuning rate of the APPLN OPGs constructed by the proposed techniques for simultaneous multiple signal wavelength generation over a conventional one has been demonstrated in a near infrared band (1500-1600 nm).
©2012 Optical Society of America
Optical parametric down conversion has been one of the most popular techniques in producing wavelength tunable light sources for versatile applications. Multi-wavelength operation of these light sources has further advanced a number of interesting applications such as multi-wavelength LIDAR, chemical sensing, terahertz wave generation, and biomedical measurements [1–4]. Several techniques have been used in an optical parametric generator/oscillator (OPG/OPO) to achieve the continuous tune of the output spectrum. To shift the parametric gain spectrum of an OPG/OPO, temperature control of the nonlinear crystal is usually used , while to tune over the parametric gain bandwidth, an etalon can be used in the OPO cavity . Moreover, the maturity of quasi-phase-matching (QPM) materials such as periodically poled lithium niobate (PPLN) has facilitated not only the construction of high-efficiency OPGs/OPOs but also the introduction of new wavelength-tuning mechanisms to these systems. For example, wide wavelength tuning of a PPLN OPO has been demonstrated by the translation of the PPLN crystal whose grating periodicity is engineered to vary either discretely (a multiple grating) or continuously (a fan-out grating) along the translation direction [6, 7]. However, spectral tuning methods employed in aforementioned systems have relied on a slow tuning mechanism using thermal or mechanical control, limiting the applicability of the systems. A fast, precise, and stable spectral tuning technique can be in great demand for light sources used in those aforementioned applications to largely increase the system scanning rate and resolving power (e.g., for the work in Ref , the detection limit might be effectively improved if a fast and fine wavelength scan can be done). Fast spectral tuning of an OPO has been demonstrated via the electro-optic (EO) control of the optical parametric gain medium (OPGM) . In particular, recent studies of the EO effects of PPLN [9, 10] have led to the development of several interesting OPG/OPO systems whose signal spectra can be either manipulated (via the access of the EO coefficient r51)  or continuously tuned (via the access of the EO coefficient r33) [12, 13]. However, these PPLN EO tuning systems can only either provide tuning among some specific spectral positions within the parametric gain bandwidth or work at one signal wavelength at a time. In this work, we have developed a technique that extends the concept of “asymmetric domain structure” design used in a PPLN EO tuning system [13, 14] to construct aperiodically poled lithium niobate (APPLN) OPG systems capable of performing multi-wavelength generation and tuning in a near infrared band (1500-1600 nm). This work, to the best of our knowledge, is the first demonstration of an electro-optically tunable, QPM multi-wavelength converter.
Consider a PPLN OPG of grating period Λ (with an asymmetric duty cycle) working in the presence of an external electric field Ez along the crystallographic z axis, the QPM condition for waves interacting in this OPGM is now a function of the electric field due to the EO effect, given by12], n is the refractive index , λ is the wavelength, l+ and l- are the thicknesses of the two opposite-polarity unit domains constituting the QPM grating, and is the grating duty cycle. It is readily seen from Eq. (1) that output signal (idler) of a PPLN OPG can only be electro-optically tunable when an asymmetric-duty-cycle domain period (i.e., when or ≠0.5) is used and the tuning rate (the change of or the corresponding spectral shift per the applied electric field) is directly proportional to Δl. Besides a uniform grating structure as usually formed in a PPLN crystal, a non-uniform domain structure can also be engineered in a QPM crystal. According to the Fourier theory, a non-uniform grating structure can provide more than one reciprocal vector and therefore can allow the simultaneous performance of multiple wave-energy couplings in such a QPM crystal. APPLN is thus an interesting candidate for the realization of an electro-optically tunable, multi-wavelength light source. Several methods have been proposed to construct non-uniform gratings in QPM materials, such as the continuous phase modulation (CPM) , Fibonacci optical superlattice (FOS) , nonperiodic optical superlattice (NOS) , and aperiodic optical superlattice (AOS)  techniques. However, the freedom of spectral design is limited in the CPM method where only equally spaced phase-matching peaks can be produced with spacing determined by the modulation period and in the FOS method because of its low flexibility in domain structure optimization. Though the NOS method (optimized by genetic algorithm) has been shown to be superior in conversion efficiency and spectral fidelity over the AOS method , the nonlinearly increased computation time with the complexity of the design spectrum has largely limited its applicability. In this study, we chose the AOS technique to construct the APPLN devices because of its high freedom and working efficiency of the aperiodic domain structuring that facilitates the design of a multi-wavelength device with high efficiency and spectral fidelity. Since there exists no “duty cycle” in an aperiodic grating structure, the derivation of an equivalent domain-structure parameter dominating the EO tuning rate of an APPLN OPG is thus essential in this work for the device design.
2. Devices design and performance simulation
Assume an APPLN OPG constructed using the AOS technique consists of a sequence of N domain blocks with each a thickness of Δx and a domain polarity of either + 1 or −1 denoting the + z or −z crystal orientation, respectively, as schematically shown in Fig. 1 . The coordinate xj = jΔx labeled on the top of the scheme represents the position of the j-th block of the APPLN for j = 0, 1, 2…(N-1). Consider a set of waves (pump, signal, and idler) performing the opticalparametric interaction in such a domain structure of length L, the phase mismatch of the waves under the application of an Ez now becomesEq. (1) for an asymmetric-duty-cycle PPLN can now be obtained from Eq. (2) for an APPLN, given byEq. (3) the EO tuning rate of an APPLN OPG is proportional to () and therefore to ΔN = (N+-N-) or ΔL = (L+-L-) (i.e., the difference of the block numbers or lengths of the two opposite-polarity domains) for a given Ez. It is thus crucial to establish a methodology that the APPLN domain structure can be manipulated during its construction (either design or fabrication) process to allow for building the EO tunability in a multi-wavelength APPLN OPG. To address this purpose, the domain structures of conventional APPLN OPGs designed by the AOS technique with the aid of the simulated annealing (SA) optimization method  are first generated and investigated. The APPLN OPGs are designed to radiate at multiple signal wavelengths of equal parametric gain (or equivalently, equal conversion efficiency) when pumped at 1064 nm. Since the parametric gain of a QPM OPG is a function of the effective nonlinear coefficient deff accessed by the waves coupling in the nonlinear crystal as the gain coefficient , where d33 ( = 27 pm/V for PPLN) is the relevant nonlinear coefficient, Ip is the pump intensity, and Gm is the Fourier coefficient analyzed from the domain structure, it is thus possible to manipulate the relative parametric gains of the multiple conversion processes through the design of the domain structure. For a given domain structure like the schematic shown in Fig. 1, the Fourier coefficient Gm can be calculated accordingly as21] of the three waves interacting in the generated domain structure under the plane-wave approximation.
With this design algorithm, we have calculated three APPLN OPGs optimized for generating 2, 3, and 4 signal wavelengths, respectively, in a near infrared band when pumped at 1064 nm. These crystals are all 4-cm long. The generation of more signal wavelengths is possible with the present design algorithm; however, the design fidelity of the output spectrum is generally degraded with the increase of the number of the output spectral peaks due to the increased difficulty in optimizing the domain structure without the increase of the crystal length (or unit domain block numbers) . Figure 2 shows the calculated output signal spectra from these APPLN OPGs at a pump intensity of 92 MW/cm2 (in accordance with the pump laser intensity used in the experiment, see below) at 40°C under the nondepleted pump approximation (the same pump intensity and approximation has been used for all the calculation data presented in this work). The signal spectra were obtained based on the calculation of the signal intensities with Eq. (6) with the given domain structures for a spectral range of interest. In Fig. 2, the output multiple signals with almost equal spectral peak intensity are indeed obtained as design. Since the parametric gain is a function of the nonlinear coefficient and the pump intensity as aforementioned, the pump intensity has to be a design parameter (used in the coupled-mode equations) to pursue an equalized signal peak height for the multiple parametric conversion processes with even a small discrepancy in their effective nonlinear coefficients due to the exponentially nonlinear parametric gain. The vertical (relative intensity) scales of the calculated output signal spectra shown in Fig. 2 and the figures below (Figs. 3 , 4 , and 6) were all normalized to the peak value at 1520 nm emerged in the 3-signal spectrum shown in Fig. 2(b) to make them directly comparable. Table 1 summarizes the design parameters and the domain structure information of these APPLN crystals. Noticeably for all the three designs the block numbers for the two opposite-polarity domains are about the same (i.e., N+≈N- or L+≈L-). This has resembled to a PPLN device where the highest conversion efficiency occurs when a symmetric-duty-cycle domain (i.e., L+ = L-) is used to obtain the best compensation for the phase mismatch. In this situation, the phase error accumulated along the crystal due to the application of an Ez is also minimal (see Eq. (2)), implying a very limited EO tunability with an APPLN wavelength converter constructed using the standard AOS technique (see the last column of Table 1) according to Eq. (3). To demonstrate a remarkable EO tuning rate in APPLN OPGs, we have worked out two techniques to engineer the domain structure either in the crystal fabrication or in the crystal design process to increase ΔL or ΔN to reach a tuning rate comparable to that with a PPLN device (e.g., a 30%/70% asymmetric-duty-cycle (i.e., ΔL/L = 0.4) PPLN OPG working in a near infrared band possesses a theoretical tuning rate of ~0.55 nm/(kV/mm) as calculated from Eq. (1) with the crystal dispersion data ).
2.1 Technique I: ΔL enhancement method
The first technique is similar to that employed in fabricating an asymmetric-duty-cycle PPLN. In the electric-field poling of a ferroelectric material like LiNbO3, the domain inversion area can be controlled (though not precisely, see below) via the use of an appropriate poling electric field or electrode width. In this way, ΔL can be made increased at, however, the cost of the device conversion efficiency as the domain structure has deviated from its default (calculated) one optimized for wavelength conversion. The -coordinate labeled in the scheme in Fig. 1 indicates a domain structure where the default inverted areas (black areas) are uniformly over-poled by an amount of δx (gray areas) from each border of these areas. Figure 3(a) shows the calculated signal spectra of an APPLN OPG whose domain structure is with a ΔL/L = 0.4 domain over-poling (corresponding to δx/Δx = 59%), engineered from that APPLN OPG presented in Fig. 2(b) for 3 signal-wavelength generation (original ΔL/L = 0.00025, see Tab. 1), when operated at an external electric field of Ez = 0 and ± 4 kV/mm at 40°C. The obtained spectral shape (even with that at Ez = 0 kV/mm) obviously deviates from that presented in Fig. 2(b) due to the domain over-poling effect [9, 22]. Figure 3(b) plots the calculated EO spectral tuning curves of the signals from the domain over-poled, 3-signal-wavelength APPLN OPG (orange lines with solid circles). The signal tuning curves of the APPLN OPG in its original design (see Table 1) are also plotted (black lines with solid squares) for comparison. It clearly shows an obvious spectral shift has been obtained with the domain over-poled APPLN OPG at a spectral tuning rate of ~0.54 nm/(kV/mm) at 1550 nm (~0.45 and ~0.64 nm/(kV/mm) at 1520 and 1580 nm, respectively) which is significantly a factor of 432 enhancement over the standard-design one (see Table 1). Though the signal conversion efficiency of the domain over-poled device is decreased inevitably as expected, the pump intensity (~170 MW/cm2) demanded to regain the original signal efficiency (refer to Fig. 2(b)) is still well below the damage threshold of the LiNbO3 crystal (~300 MW/cm2 for a 10-ns pulsed laser at 1064 nm ). It is also found from Fig. 3(a) that the spectral peak heights of the signals vary with the Ez. This can be understood from the fact that the nonlinear coupling strength is domain-structure (i.e., the Fourier coefficient Gm as given in Eq. (4)) and crystal-dispersion dependent according to the QPM coupled-wave theory  and therefore, is a function of Ez as the EO effect modulates the domain refractive index of the APPLN crystal (due to its bipolar domain structure) and the effect is dispersive to the multiple parametric generation processes performed in the crystal. We refer to this APPLN EO tuning technique as “ΔL enhancement method” thereinafter.
2.2 Technique II: ΔN enhancement method
The domain control method used in the first technique is usually a troublesomely trial-and-error process (e.g., it has a high risk of domain merging in producing an over-poled domain structure, while it increases the lithographic difficulty in producing an under-poled domain structure when a narrowed poling-electrode width is used). To relieve this possible fabrication difficulty, we further developed another approach resorting to the direct modification of the design algorithm to calculate a domain structure optimal for a multi-wavelength OPG under the designation of target device EO tunability. This is done by modifying the objective function OF in Eq. (5) toEq. (7) adds a constraint to the algorithm to compose an optimal APPLN OPG with a domain structure whose domain-polarity block number difference ΔN has to be ~ΔN0. Since the EO tuning rate is directly proportional to ΔN according to Eq. (3), a certain EO tuning rate can thus be readily obtained with the calculated structure without further engineering. We refer to this technique as “ΔN enhancement method”. A 4-cm long, 3-signal-wavelength APPLN OPG has been designed by this method and an optimal domain structure with ΔN/N = 0.4 (ΔN = 3200) was obtained with w = 0.6, β = 1.0, γ = 0.02, and ΔN0 = 3763 for unit-domain thickness Δx = 5 μm. Figure 4(a) shows the calculated signal spectra of the constructed APPLN OPG when again operated at Ez = 0 and ± 4 kV/mm at 40°C. The obtained EO tuning rates of this multi-wavelength APPLN OPG (Fig. 4(b)), ~0.45, ~0.54, and ~0.64 nm/(kV/mm) at 1520, 1550 and 1580 nm, respectively, are the same as those with the device using the domain over-poled technique, as expected due to ΔN/N = ΔL/L having been used in respective designs. Nevertheless, it is interesting to note that the APPLN OPG designed by the ΔN enhancement method is characterized by better signal conversion efficiency but lower spectral-shape fidelity in the EO tuning. This can be explained with the Fourier spectra of the QPM domain structures (calculated with Eq. (4)) of the 3-signal-wavelength APPLN OPGs constructed by the two EO-tuning enhancement methods at Ez = 0 and ± 4 kV/mm at 40°C, as shown in Fig. 5 . It shows the Fourier coefficients of the 3-signal-wavelength APPLN OPG designed by the ΔN enhancement method are ~1.1 times higher than those designed by the ΔL enhancement method. A small discrepancy in the effective nonlinear coefficient can already result in a significant difference in the output signal intensity because of the exponentially nonlinear parametric gain, as observed in Ref . This superiority in efficiency found with the APPLN designed by the ΔN enhancement method can be attributable to its unique domain structuring methodology where the efficiency and tuning rate of the device are simultaneously pursued in the optimization process according to Eq. (7). Besides, it also shows from Fig. 5 the Fourier spectrum (note especially the peak values) of the ΔN-enhanced APPLN OPG is a more sensitive function of the EO effect than that of the ΔL-enhanced one, leading to a lower spectral-shape fidelity (effect is again amplified by the nonlinear parametric gain) with the ΔN-enhanced device for performing the EO tuning as observed (Fig. 4(a)).
2.3 Comparison with PPLN EO device
It is interesting to compare the APPLN devices constructed above with a PPLN device designed by the asymmetric-domain-structure technique. To build a multi-wavelength OPG system in a PPLN, a cascade or segment grating structure is usually employed to accommodate multiple grating periods to respectively satisfy the QPM conditions of the multiple conversion processes. In design, we cascaded three PPLN OPGs of grating periods 29.65, 30.01, and 30.31 μm in a monolithic crystal at 40°C, phase-matching to 1064-nm pumped 1520, 1550, and 1580 nm optical parametric generation processes, respectively, in accordance with the signal spectral positions of those 3-signal-wavelength APPLN OPGs presented above at Ez = 0 kV/mm. The lengths of the three PPLN sections are 13.39, 13.32, and 13.29 mm (40 mm in total), used for pursuing an equalized parametric gain for the three OPGs. Figure 6 shows the calculated output spectra of the cascade PPLN OPG device with Ez tuned to 0 and ± 4 kV/mm, if again a ΔL/L = 0.4 domain over-poling (corresponding to a 30%/70% asymmetric domain duty cycle) has been engineered to the crystal. The zigzag-like spectral peaks are produced as the signals build up in a parametric gain superposed by the three cascade OPGs. When comparing the result with that obtained with the ΔL/L = 0.4 domain over-poled, 3-signal-wavelength APPLN OPG (Fig. 3), we found both devices exhibit similar spectral tuning rates as expected; nevertheless, the APPLN OPG has an obvious advantage of much higher spectral-peak efficiency (note the vertical (relative intensity) scales of the figures) with narrower spectral linewidth over the cascade PPLN OPGs.
3. Proof-of-principle demonstration and discussion
To demonstrate the feasibility of the techniques proposed above for realizing an electro-optically tunable, multi-wavelength light source, we fabricated the APPLN OPGs designed by the ΔL and ΔN enhancement methods for simultaneous two signal-wavelength generation in 40-mm long, 5-mm wide, and 0.5-mm thick z-cut LiNbO3 crystals by using the standard electric-field poling method (a widened poling electrode has been employed for the ΔL enhancement method) . The choice of a 2-signal-wavelength APPLN OPG to perform the proof-of-principle demonstration is due to its relatively high efficiency (in contrast to a 3 or higher number of spectral-peak generation) while the feasibility of the technique can be unambiguously presented. The APPLN crystal designed by the ΔL enhancement method was first fabricated. A ΔL/L = ~0.23 (though a ΔL/L = 0.4 was desirable) domain over-poling was estimated via the inspection of the HF-etched z surface of the fabricated crystal. The APPLN crystal designed by the ΔN enhancement method with ΔN/N = 0.23 as a design target in the developed SA algorithm (see Eq. (7)) was then fabricated for the performance comparison. Both of the end (x) faces of the crystals were optically polished without the application of a coating layer. The ± z surfaces of the crystals were sputtered with NiCr alloy as electrodes for the Ez application. The APPLN crystal to be characterized was mounted on a temperature controlled oven. The pump source is a linearly-polarized, actively Q-switched Nd:YAG laser producing 10-Hz, ~35-kW peak-power 1064-nm pulses of duration ~9 ns. The laser radiates at multiple longitudinal modes with a linewidth of <0.2 nm. The pump laser beam was collimated and size-reduced to a radius of ~110 μm in the crystal (leading to a pump intensity of ~92 MW/cm2). The characterized beam divergence was ~20 mrad. An optical spectrum analyzer with a spectral resolution of 0.5 nm was used to measure the output signal spectrum. Figure 7 shows the signal spectra of the two fabricated APPLN OPGs measured at Ez = 0 and ± 4 kV/mm (2 kV across the 0.5-mm thick crystal). The crystal temperature was controlled at 140°C during the measurement for the alleviation of the possible photorefractive damage. The phase-matched wavelengths are at 1582 and 1598 nm at Ez = 0 kV/mm. The dashed lines in Fig. 7 represent the theoretical fit, obtained based on the calculation procedure made with Eq. (6) with the domain structures generated with proper ΔL and ΔN values (deduced with the aid of the design algorithm revealed in section 2) that can lead to the best fit of the two measured spectra, respectively, at a pump intensity of 92 MW/cm2, again under the nondepleted, single-frequency pump approximation. For spectral comparison, the intensities of the fit and measured spectra were normalized to the peak values of the respective spectra at Ez = 0 kV/mm. The fit data are in reasonable agreement with the measurement results. Some discrepancy between the fit and measured spectra could be attributable to the crystal fabrication error, measurement error, as well as the approximation made in the calculation (plane-wave and single-frequency pump for the solving of the coupled-mode equations ). The effect of the crystal fabrication error on an APPLN wavelength converter has been discussed in Ref , while the effects of the Gaussian laser beam and crystal temperature uniformity on an APPLN device have also been investigated in Ref . The effect of the pump linewidth (<0.2 nm) on the output signal spectrum should be minor as it has been considerably narrower than the parametric gain bandwidth (the measured bandwidths of the signal spectral peaks are ~7 nm, see Fig. 7).
From the measurement results in Fig. 7, average tuning rates of ~0.38 and ~0.49 nm/(kV/mm) were obtained with the two samples that were constructed by the ΔL and ΔN enhancement methods, respectively. The tuning rates correspond to domain over-poled factors of ΔL/L~0.2 for the ΔL-enhanced sample and ΔN/N~0.25 for the ΔN-enhanced sample according to the fit data. These derived factors from the measurement data give a more precise estimation of the degree of the domain over poling. The measured tuning rates have been >101 times higher than that with a conventional APPLN OPG designed for two-wavelength generation (refer to Table 1). In Fig. 7(b), apparent unevenness in the spectral peak height does be observed in the EO tuning of the ΔN-enhanced APPLN OPG. The measured signal peak powers from the ΔL- and ΔN-enhanced OPGs were around 3 kW and 4.6 kW, corresponding to conversion efficiencies of ~8.6% and ~13%, respectively. For comparison, we also characterized a 4-cm long PPLN OPG of grating period 30 μm (domain duty cycle approaches 50%) fabricated for another purpose and obtained a signal (1596 nm) conversion efficiency of ~41% when pumped at 1064 nm of intensity ~92 MW/cm2 at 140°C. Due to the nonlinear gain, the efficiency of the fabricated 2-signal-wavelength APPLN OPGs can reach the same efficiency level of the single-signal PPLN OPG if about twice the pump power is used according to our estimation. These measurement results manifest the ΔN-enhanced APPLN OPG is characterized by better signal conversion efficiency/EO spectral tuning rate (depending on the design algorithm setting) but by lower spectral-shape fidelity with EO tuning in comparison with the ΔL-enhanced APPLN OPG.
The advantage and applicability of the EO spectral tuning technique demonstrated in this work can be even amplified when it is implemented in a (cw) OPO system to take advantage of its high stability and excellent spectral property (whose spectral linewidth can be several orders of magnitude narrower than that with the present scheme in OPGs)  and in a waveguide device to largely reduce the operation voltage (lowering to a few volts is possible) and even to increase the spectral tuning rate . However, simultaneous operation (tuning) of multiple wavelengths in these systems requires a more sophisticated system design and the study for it is underway.
We have successfully realized a unique electro-optically tunable, multi-wavelength light source based on APPLN OPGs constructed by the AOS technique. The domain structures of the APPLN OPGs have been engineered to increase the difference of either the lengths or block numbers of the two opposite-polarity domains constituting the structure (the ΔL or ΔN enhancement method) to effectively enhance the EO tuning rate of the devices. Calculation results showed that an EO tuning rate of ~0.54 nm/(kV/mm) at 1550 nm (~0.45 and ~0.64 nm/(kV/mm) at 1520 and 1580 nm, respectively) can be obtained from 40-mm long, 3 signal-wavelength APPLN OPGs constructed using the ΔL and ΔN enhancement methods with ΔL/L = ΔN/N = 0.4 in a near infrared band (1500-1600 nm). The obtained EO tuning rate has been significantly enhanced by a factor of 432 (at 1550 nm) over that with a conventional APPLN OPG, though at the cost of signal conversion efficiency (that can be regained by the increase of the pump power). We have also successfully demonstrated EO spectral tunings with APPLN OPGs fabricated for simultaneous two signal-wavelength generation (1582 and 1598 nm), where tuning rates of ~0.38 and ~0.49 nm/(kV/mm) and signal conversion efficiencies of ~8.6% and ~13% were obtained from the devices with the ΔL (ΔL/L = ~0.2) and ΔN (ΔN/N = ~0.25) enhancement methods, respectively, when pumped by a ~35-kW peak-power 1064-nm laser.
This work was supported by the National Science Council (NSC) of Taiwan under Contract No. 101-2221-E-008-082. The authors thank the Thin Film Technology Center (TFTC) at National Central University, Taiwan, for the support of the measurement instruments.
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