## Abstract

We report the design and construction of a highly integrated two-dimensional (2D) aperiodic nonlinear photonic crystal (NPC) for working in a diode-pumped, dual-wavelength (1064 and 1342 nm) Nd:YVO_{4} laser to demonstrate a compact, high-peak-power intracavity sum-frequency generator (ISFG) radiating at orange 593.5 nm. The 2D aperiodic NPC was built in quasi-phase-matched LiNbO_{3} whose crystal domain was structured based on the aperiodic optical superlattice technique to best achieve its simultaneous performance of a dual-wavelength electro-optic Bragg Q-switch and a SFG in the Nd:YVO_{4} laser. When the NPC device was driven with a 350-V Q-switching voltage and a 1-kHz switching rate, we measured pulse energy of ~4.3 μJ (or peak power of ~531 W) at orange 593.5 nm from the constructed ISFG with 5.28-W diode power.

© 2014 Optical Society of America

## 1. Introduction

Intracavity nonlinear frequency up-conversion technique has been used in a near-infrared laser to implement efficient visible coherent light sources with the advantages of high nonlinear conversion efficiency due to the access of the intense laser intracavity power and of better system integration in contrast to an external cavity conversion scheme. Nd^{3+} lasers are no doubt one of the most important near-infrared (NIR) light sources providing several efficient lines around, e.g., 0.9, 1.06, and 1.3 μm. Frequency doubling of these lines to blue, green, and red have been demonstrated via the efficient second-harmonic generation (SHG) process: the green laser pointer gives an obvious example. To convert a Nd^{3+} laser to the yellow-orange (570-620 nm) spectral region, the nonlinear frequency sum of the 1.06 and 1.3 μm lines has been a widely used technique because of its relative simplicity in contrast to otherwise a technique based on the SHG of a Raman-shifted 1.06 μm line (where two nonlinear-optical (NLO) wavelength conversion processes are involved) [1]. A high-repetition-rate, pulsed yellow-orange laser has been in demand for many applications such as bio-medicine, astronomical imaging, display, and Lidar [2]. A sum frequency generator (SFG) intracavity pumped by a Q-switched, dual-wavelength (1.06 and 1.3 μm) Nd^{3+} laser can be an attractive scheme to build such light sources in terms of the system compactness and efficiency. A collinear three-mirror laser cavity with the use of single Q-switch and a nonlinear optical crystal has been a common configuration of constructing a robust intracavity SFG (ISFG) [3, 4]. Nevertheless, the laser Q-switches employed in these systems were usually based on an electro-optic (EO) Pockel’s cell or an acousto-optic (AO) Bragg cell whose performance is wavelength dependent according to the based birefringence-plate or Bragg conditions [5], implying the simultaneous optimization of the Q-switching performance (such as the hold-off capacity) of two laser lines with such a Q-switch (best performed at a specific wavelength) is problematic. Hold-off capacity of a Q-switch determines the energy and shape (temporal profile) of the generated laser pulses and therefore the SFG efficiency. Systems use two Q-switches working at respective laser lines could be an immediate solution to the optimization problem found with those single-Q-switch ISFG systems but were seldom reported [6], probably due to the increased system and operational complexity. It is thus desirable to develop an active Q-switch that can work simultaneously on the two Nd-laser lines to realize a highly integrated yet efficient yellow-orange source.

Nonlinear photonic crystals (NPC) have been realized in quasi-phase-matching (QPM) materials [7] whose crystal domain is structured via crystal poling (e.g., using the electric-field poling technique [8]) in which the domain polarity and therefore the quadratic nonlinear coefficient are spatially modulated. One-dimensional QPM NPCs have been widely used in performing high-efficiency nonlinear frequency mixing [8]. Two-dimensional (2D) NPCs were first studied by V. Berger in 1998 [9]. An important feature of a 2D QPM NPC is that it can provide a great number of in-plane (especially off-angle) reciprocal vectors, which facilitates the implementation of several interesting NLO technologies including the multiple non-collinear wavelength conversion [10], higher order harmonic generations [11], multiple/cascaded *χ*^{(2)} nonlinear frequency mixing [11], and the optical wavelength interchange [12]. However, all these 2D NPCs worked for single optical device functionality via the access of the NLO property of the material. In this work, we integrated for the first time dual optical device functionalities in a 2D *aperiodic* NPC via the access of the NLO and EO properties of the material to work in an all-solid-state laser to construct a compact, high peak-power orange light source.

Recent studies of the EO effects of a QPM crystal have led to the development of several efficient EO Q-switches including a periodically poled lithium niobate (PPLN) Bragg Q-switch [13]. In this work, we report the construction of a genuine dual-wavelength EO Q-switch implemented in a 2D domain engineered LiNbO_{3} crystal where in addition the functionality of a PPLN SFG is built in. Here the dual-wavelength EO Q-switch was constructed based on the EO QPM Bragg cell technique to allow for a temperature-insensitive operation [13] to facilitate its monolithic co-operation with an up-conversion QPM frequency mixer (i.e., the PPLN SFG here) which is usually characterized by a narrow temperature acceptance bandwidth (~4 °C-cm for a 1.06 and 1.3 μm pumped PPLN SFG). With this highly integrated 2D QPM device, we further demonstrated a compact, efficient pulsed ISFG radiating at orange 593.5 nm in a diode-pumped Nd:YVO_{4} laser.

## 2. Device design, fabrication, and characterization

The central idea of the design of a dual-wavelength EO Bragg cell is to make equal the diffraction efficiency of the device at the two wavelengths under the same operating conditions (incident angle, working voltage, and temperature, etc.) so that an equal hold-off capacity can be possibly achieved when it works as a Q-switch of two laser lines in a laser system. The diffraction efficiency of an EO QPM Bragg cell can be derived from the coupled-mode theory [5], given by

*L*is the coupling length,

*κ*is the coupling coefficient, Δ

*n*(

*E*) is the refractive index change of the crystal under an electric field (

_{z}*E*) along the crystallographic

_{z}*z*axis,

*G*is the Fourier coefficient associated to the accessed reciprocal vector

_{m}*K*provided by the EO QPM domain structure,

_{m}*λ*

_{0}is the wavelength in vacuum, and

*θ*

_{B}is the Bragg angle satisfying ${\theta}_{B}={\mathrm{sin}}^{-1}({\lambda}_{0}{K}_{m}/4\pi n)$ with

*n*being the refractive index. Accordingly, we calculated the conversion bandwidths (at half maximum) of a PPLN EO Bragg cell to be Δ

*λ*~ ± 67 and ± 107 nm-cm for design wavelengths of 1064 and 1342 nm, respectively, under the same Bragg angle of 0.7° (a larger bandwidth can be obtained by using an even smaller Bragg angle with, however, a penalty of lower laser diffraction loss or lower hold-off capacity at the low-Q state of the Q-switching operation). The use of single PPLN EO Bragg Q-switch to work simultaneously on the two Nd-laser lines (of wavelength difference 278 nm) with high efficiency is obviously not viable.

Figure 1 illustrates the dual-wavelength Bragg phase-matching schemes used in the present design. Unlike the usual setup configuration of a (single-wavelength) PPLN EO Bragg device in a laser system where the device is rotated about the *z* axis by an Bragg angle with respect to the laser axis [13], here no rotation of the crystal has been made (i.e., the *x* axis of the crystal is aligned with the laser axis) to enable the collinear oscillation of the two laser lines (see below). Two off-angle reciprocal vectors *K _{B1}* and

*K*are thus required to accomplish such dual-wavelength Bragg conversion schemes. It is a 2D aperiodic NPC (a 2D aperiodically poled lithium niobate (APPLN) here) that can provide such reciprocal vectors. Besides, in this design the 2D APPLN structure also provides another reciprocal vector

_{B2}*K*along the crystallographic

_{SFG}*x*axis to satisfy the QPM condition of the 1064 and 1342 nm pumped sum frequency generation process. In this work, we have developed an algorithm based on the aperiodic optical superlattice (AOS) technique with the aid of the simulated annealing (SA) optimization method [14, 15] to calculate an optimal 2D QPM domain structure for performing the multiple wave energy conversion processes (an important alternative design algorithm, built directly based on the quasi-crystal dual-grid model, has also been developed for constructing a 2D NPC [16, 17]). In calculating the 2D domain structure, we assume the crystal consists of an array of

*N*by

_{x}*N*crystal-domain blocks (as schematically shown in Fig. 2(a), where filled areas represent the domain inverted region), each with a dimension of

_{y}*a*(in

*x*axis) ×

*b*(in

*y*axis) and a domain polarity of either + 1 or −1 denoting the + z or −z crystal orientation of the block, respectively. The spatial frequency spectrum of the 2D domain structure can then be obtained from the Fourier analysis of the structure, where the corresponding Fourier coefficient of a reciprocal vector $K={K}_{x}\widehat{x}+{K}_{y}\widehat{y}$ provided by this structure is calculated by [10]:

*A*is the area of the 2D structure,

*s*= + 1 or −1 denotes the domain polarity, and

*p*and

*q*are integers indexing the (

*p*,

*q*)-th element of the

*N*by

_{x}*N*domain-block array (refer to Fig. 2(a)). The target of this design is to generate an optimum domain structure for the 2D QPM NPC to have equal diffraction efficiency for the two laser wavelengths when it works as a dual-wavelength EO Bragg cell and to have as high as possible nonlinear-optical frequency conversion efficiency under a designated Bragg diffraction efficiency when it works as a SFG. The calculation areas,

_{y}*L*(length, along the crystallographic

*x*axis) ×

*l*(width, along the crystallographic

_{w,λi}*y*axis), were 30 × 1.06 and 30 × 1.034 mm

^{2}for the

*λ*

_{1}= 1064 nm and

*λ*

_{2}= 1342 nm lasers, respectively. The structure widths for the two lasers are different because the width is related to the laser mode size in the device by

*l*= (

_{w,λi}*L*× tan(2

*θ*

_{B}) +

*D*), which is the beam size (

_{λi}*D*) of the incident wave plus the lateral shift of the diffracted beam after passing through the whole device length

_{λi}*L*( = 30 mm here) with a Bragg angle

*θ*

_{B}( = 0.7° here), as schematically illustrated in Fig. 2(b). The beam sizes of the 1064 and 1342 nm waves in the 2D APPLN device in the dual-wavelength laser system were 326 and 301 μm, respectively, estimated according to the experimental configuration (see below) with an presumed cavity length ratio of the two laser lines of 1.56 suggested by our previous study of a pulsed SFG (where two cascade Q-switches and a separate SFG were used) in single-Q-switch mode (where the two Q-switches were switched simultaneously) [6]. Note the cavity length ratio presumed here has been based on the cavity configuration of using a relatively thin and long (0.5-mm thick and few centimeters long) intracavity nonlinear crystal and might not be an optimum value for best balancing the gain competition between the two laser lines for having an optimized SFG efficiency [4]. An objective function (

*OF*) [14] has been employed in thecalculation to guide the SA algorithm to pursue the target efficiencies of the 2D APPLN device, given by

*η*

_{B}_{0}and

*η*

_{SFG}_{0}are the target diffraction and SFG efficiencies, respectively,

*η*(

_{B}*G*

_{B}_{1}) and

*η*(

_{B}*G*

_{B}_{2}) are the calculated diffraction efficiencies for the

*λ*

_{1}= 1064 nm and

*λ*

_{2}= 1342 nm waves under

*E*= 700 V/mm, respectively,

_{z}*η*(

_{SFG}*G*) is the calculated SFG efficiency,

_{SFG}*w*

_{1},

*w*

_{2}, and

*w*

_{2}are the weighting factors, and the operators max[…] and min[…] output the maximum and minimum values of the quantities enclosed in the square brackets, respectively. Figure 2(c) shows a part of the calculated APPLN domain structure in a 2D matrix barcode form (the black and white areas represent the negative and positive crystal domains, respectively).

Figure 3 shows the results of the 2D Fourier analysis of the calculated APPLN domain structure. Three predominant spatial frequencies at (*f _{x}*≡

*K*/2π,

_{x}*f*≡

_{y}*K*/2π)~(0.0006, 0.0495), ~(0.00048, 0.039), ~(0.1053, 0)

_{y}*μ*m

^{−1}are resolved, corresponding to the off-angle reciprocal vectors required for phase-matching the designated EO Bragg interactions of the 1064 and 1342 nm waves with LiNbO

_{3}and the on-axis reciprocal vector (along the crystallographic

*x*axis) required for quasi-phase-matching the designated 1064 and 1342 nm pumped sum-frequency-generation (593.5 nm) process in LiNbO

_{3}at 52.4°C, respectively. The associated Fourier coefficients are

*G*

_{B}_{1}~0.218,

*G*

_{B}_{2}~0.286, and

*G*~0.35 for the two Bragg interaction and sum-frequency-generation processes, respectively. The ratio of the obtained Fourier coefficients,

_{SFG}*G*

_{B}_{1}/

*G*

_{B}_{2}, is ~0.76, which is a value expected to make equal the coupling coefficient and therefore the diffraction efficiency of the two waves according to Eq. (1).

It is interesting to compare the efficiency of the present device with an alternative scheme cascading three PPLNs under the same total device length (say, a device cascading a 1-cm long 1064-nm PPLN EO Bragg cell, a 1-cm long 1342-nm PPLN EO Bragg cell, and a 1-cm long PPLN SFG). Though the Fourier coefficient associated to a PPLN structure is *G _{PPLN}* = 2/π (~0.637) which is higher than those obtained with the 2D APPLN device, the present devicestill outperforms the cascade PPLN device because it uses three times longer device length for all the conversion processes. Since the diffraction efficiency of a Bragg cell is a function of

*G*according to Eq. (1), the performance of the present 2D APPLN device can be analogous to or outperform (in working voltage) the cascade PPLN device when working as a dual-wavelength EO Bragg cell according to the calculation results revealing

_{m}L*G*

_{B}_{1}

*L*>~

*G*(

_{PPLN}*L*/3) and

*G*

_{B}_{2}

*L*>

*G*(

_{PPLN}*L*/3). On the other hand, the (single-pass) SFG efficiency is approximately proportional to (

*ΓL*)

^{2}and therefore proportional to (

*G*)

_{m}L^{2}, where

*Γ*is the nonlinear gain coefficient. Accordingly a remarkable (maximum) enhancement of the SFG efficiency by a factor of ~2.7 ((

*G*)

_{SFG}L^{2}/(

*G*/3)

_{PPLN}L^{2}, under non-depleted pump limit) can then be expected with the present 2D APPLN device over the cascade PPLN scheme. The above comparison shows the success and advantages of the design in this work using the AOS technique to integrate and optimize the multiple wave-energy conversion processes in a single QPM domain structure.

The calculated 2D QPM domain structure was then fabricated in a 30-mm long (along the crystallographic *x* axis), 3-mm wide (along the crystallographic *y* axis), and 0.5-mm thick LiNbO_{3} using the standard electric-field poling technique [8]. The two *z* surfaces of the poled crystal were sputtered with NiCr alloy to form surface electrodes for the *E _{z}* application. Both the end (

*x*) faces of this crystal were optically polished and had an anti-reflection (AR) coating for 1064, 1342, and 593.5-nm wavelengths. We first characterized the diffraction efficiency of the fabricated 2D aperiodic NPC when working as a dual-wavelength EO Bragg cell by a 1064 nm and a 1342 nm cw Nd:YVO

_{4}lasers. In this measurement, the output 1064 and 1342 nm laser beams have been collimated to sizes of ~326 and ~301 μm in the crystal, respectively, in accordance with the design. Figure 4 shows the measured zeroth-order transmittances of the 1064 and 1342-nm lasers traversing the 2D aperiodic NPC as a function of the applied voltage. It shows the two transmission curves are in reasonable agreement and reach the first minima (corresponding to the first maximum diffraction efficiency of the device, which is >~55%) at ~350 V as design.

## 3. ISFG system construction and output performance characterization

Figure 5 shows the schematic arrangement of a pulsed 593.5-nm ISFG system constructed in a dual-wavelength Nd:YVO_{4} laser using the fabricated 2D aperiodic NPC as simultaneously the Q-switch and SFG of the two laser lines. The inset shows a typical microscopic image of HF-etched + *z* surface of the 2D NPC, revealing the finest constituent domain size is 4.75 × 5 μm^{2}. The laser gain medium is an a-cut 0.3-at. % Nd:YVO_{4} crystal, having a 9 mm length and 3 × 3 mm^{2} clear aperture. The pump source is an 809-nm fiber-coupled diode laser. A collinear cavity scheme, comprising three high-reflection mirrors, designated M1, M2, and M3, has been constructed to achieve the dual-wavelength oscillation. The 1342-nm laser oscillates in a cavity formed by mirrors M1 and M2, while the 1064-nm laser builds up in mirrors M1 and M3. M1 is a 15-cm radius-of-curvature meniscus dielectric mirror having >99.8% reflectance at 1064 and 1342 nm and ~95% transmittance at 809 nm. M2 is a plane-plane dielectric mirror having ~99.8% reflectance at 1342 nm and ~97% and ~95% transmittances at 1064 and 593.5 nm, respectively. M3 is a plane-plane dielectric mirror having ~99.8% reflectance at 1064 nm and ~95% transmittance at 593.5 nm.

In operation, we drove the 2D APPLN EO Bragg Q-switch with a 350-V, 300-ns voltage-pulse train at 1 kHz. The system was optimized at the pump power of 5.28 W with the 1342-nm laser cavity length *L*_{2} (see Fig. 5) being fixed at 7.4 cm for matching the mode size with the design structure width *l _{w,λ2}* of the 2D aperiodic NPC (see Fig. 2(b)). We found maximum 593.5-nm generation was obtained when a cavity length of

*L*

_{1}= 11.3 cm for oscillating the 1064-nm line was used. The length ratio

*L*

_{1}/

*L*

_{2}is ~1.53, which is quite close to that presumed in design ( = 1.56). We found this slight difference between the design and experimental length ratios results in only <1% variation in the Fourier coefficient associated to the 1064-nm Bragg diffraction process and produces no observable influence on the dual-wavelength Q-switching operation of the present system. Figure 6(a) shows the measured output peak power and pulse width of the 593.5-nm ISFG as a function of the diode pump power. Figure 6(b) shows the measured traces of the two (overlapped) infrared laser pulses (depleted, black line) and the 593.5-nm SFG pulse (orange line) from the system pumped at 5.28 W. Orange output pulses of 8.1-ns width and ~4.3 μJ/pulse (~531 W peak power) was obtained at this pump power.

The implementation of the present 2D aperiodic NPC device in a thicker (> 1mm) QPM crystal such as a MgO:LiNbO_{3} [18] can allow for the further optimization of the cavity configuration of the constructed dual-wavelength laser system for a better ISFG efficiency (to address the issue of the cavity length ratio as aforementioned). The power scalability of the present system can also be increased when the photorefractive-resistant MgO:LiNbO_{3} is used.

## 4. Conclusion

We have first constructed a 2D *aperiodic* NPC integrating dual optical device functionalities of QPM LiNbO_{3} to work simultaneously a dual-wavelength EO Q-switch and a SFG in a diode-pumped Nd:YVO_{4} laser with which a compact, high peak-power orange light source was demonstrated. An optimal 2D QPM domain structure (30 mm in length and 1.06 mm in width) was calculated for the NPC based on the AOS technique to provide three in-plane reciprocal vectors to enable the simultaneous operation of the three QPM devices on it. Fourier analysis of the 2D QPM domain structure shows the device is with equal Bragg diffraction efficiency for the two laser wavelengths and can have superior effective nonlinear gain for SFG over a cascade PPLN device scheme. We measured peak power of 531 W, 593.5-nm laser pulses from the ISFG at 5.28-W diode pump.

## Acknowledgments

This work was supported by the Ministry of Science and Technology (MOST) of Taiwan under Contract Nos. 102-2221-E-008-099-MY2 and 103-2623-E-008-004-D. The authors also thank the Thin Film Technology Center (TFTC) at National Central University, Taiwan, for offering the service of the optical coatings.

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