We report the design and experimental demonstration of electro-optically active TM-guided to TE-radiation mode converters in annealed proton-exchanged (APE) periodically poled lithium niobate (PPLN) channel waveguides in telecom S-C-L bands (1495-1640 nm). A maximum mode conversion efficiency of >95%/cm was obtained at 1520 nm from a 24-μm-period APE PPLN waveguide under an electro-optic (EO) field of ~6.3 V/μm at 35°C. This efficiency has been enhanced by a factor of >4.6 over a waveguide built in the single-domain (unpoled) LiNbO3; it is also to the best of our knowledge the most efficient guided-to-radiation (GTR) mode converter ever reported based on LiNbO3 on-axis waveguides. A conversion bandwidth of ~250 nm was also observed from this EO GTR mode converter.
© 2010 OSA
Waveguide mode coupling techniques have been used to develop various passive and active optical devices  that are of particular interest to the field of integrated optics and to the applications such as the optical information processing and communications. Among them, guided-to-guided (GTG) mode coupling is a more common mechanism used to perform a waveguide mode conversion process in contrast to another coupling scheme based on guided-to-radiation (GTR) mode interaction because of its much higher efficiency [2, 3]. The performance of GTG mode conversions, however, is restricted in waveguides supporting both interacting modes and requires a more careful control of the waveguide fabrication errors to achieve the phase matching between the two modes . GTR mode coupling has been first achieved with the combination of a waveguide and a prism or a grating structure . However, such a scheme operates passively and has limited applications, such as used in input/output couplers. An active operation of the coupling process is thus essential in extending its applications to such as optical integrated circuits. Electro-optic (EO) control of GTR mode conversion was first studied by Marcuse in LiNbO3 (and LiTaO3) based on the electro-optically induced off-diagonal dielectric perturbation mechanism . With this EO effect in, say, LiNbO3 waveguides, the coupling of a TM waveguide mode to a TE radiation mode is readily attainable due to the automatic phase matching of the process where a continuum of radiation modes is involved per the birefringence of LiNbO3 (a negative uniaxial crystal). Because of the leaky nature of radiation modes, such a mode coupling process can be used to construct an active direct amplitude modulator in just single waveguide. Unfortunately, the characterized modulation efficiency from such a simple modulator was usually very low mainly due to the inefficient field overlap between the guided mode and the phase-matched radiation mode escaping to the substrate . Though several schemes have been proposed to drastically increase the efficiency in LiNbO3, most of them relied on the use of an unconventional off-axis wave propagation scheme where passive mode conversion has existed . A more direct and common approach to enhance the field-overlap and therefore the coupling efficiency can be to produce a reciprocal vector via the periodic modulation of the off-diagonal dielectric tensor element of the material to compensate the phase mismatch of the two modes having efficient field overlap. Such an approach has been demonstrated via EO modulating where periodic electrodes were applied along the waveguide axial direction coincident with the crystalline x or y axis (on-axis waveguide scheme) . Generally a finger-type or interdigital electrode configuration has to be used to attain the periodic sign modulation of the relevant EO coefficient of the crystal .
Quasi-phase-matching (QPM) technique is known to create a spatially modulated domain-lattice structure in a nonlinear medium to provide a reciprocal vector to compensate for the wave-vector mismatch of a wave-energy coupling process in it and has been widely used in nonlinear frequency conversions . Recently, an EO effect accessing the off-diagonal dielectric tensor element of a QPM material has been studied and exploited to implement efficient polarization-mode converters (PMCs) . In particular, Chen has demonstrated an efficient TE↔TM GTG mode converter in Ti-diffused periodically poled lithium niobate (PPLN) waveguides based on this EO mechanism . In this work, we report the first demonstration of an efficient EO TM-guided to TE-radiation mode converter in a QPM-material (PPLN) waveguide. Such a scheme (referred to as PPLN EO GTR PMC thereinafter) allows the use of simple uniform electrodes as the sign of the EO coefficients of a QPM crystal is spatially modulated with its periodic domain inversion structure; it also allows to implement an efficient GTR mode converter with less dependence on the birefringence of the employed waveguide/material as the QPM grating structure can be tailored to satisfy the required phase-matching condition for efficient mode-field overlap in the waveguide. Moreover, the application of such an EO effect in a bulk PPLN wavelength converter has led to the demonstration of several unique photonics devices [10, 11]. Since high-quality optical waveguides have been developed to build in PPLN to work as single-pass, highly efficient optical frequency mixers (OFM) , the further integration of the present PPLN EO GTR PMC with a PPLN waveguide OFM could be an interesting direction of future development for various devices potential for, e.g., optical communications of high data transmission capacity.
2. Device design and calculation
In this work, we implemented the EO GTR PMC in z-cut annealed proton-exchanged (APE)  PPLN waveguides along the crystallographic x-axis direction to demonstrate efficient coupling between the TM00 mode and TE radiation modes. In the presence of an external electric field Ey along the PPLN crystallographic y axis, the dielectric tensor of the crystal is periodically perturbed along the x (domain grating vector) direction, inducing the energy coupling between two polarization modes having an interaction coherence length of equal to the PPLN domain thickness . An analytical expression for describing such a coupling process in GTG scheme has been established based on coupled mode theory . However, the treatment for a GTR scheme would be more involved as the conversion process is now associated with a continuum of radiation modes. The coupled mode equations  describing an EO TM00-guided to TE-radiation mode conversion process in a PPLN waveguide can be expressed as:Eq. (1), and are the slowly varying field amplitude envelopes of the TM-guided and TE-radiation modes, respectively, k0 is the wave number in vacuum, nos is the ordinary refractive index of the substrate, i is the imaginary unit , Δβ is the wave-vector mismatch of the coupling process, defined by3]. Because of the convenience of the power collection of a guide wave, the conversion efficiency of such a GTR mode converter is typically determined as the fractional power loss of the guided mode in it at the application of the EO field, given by
Unfortunately, an analytical solution of the coupled mode equations given in Eq. (1) cannot be found due to the involvement of the integral over ρ; nevertheless, it can be readily concluded from Eqs. (1), (3), and (4) that the coupling coefficient κgr, and therefore the overlap integral ϑ (or termed as “transverse phase matching” ), is the crucial parameter that determines the efficiency of the device as the EO GTR mode conversion is an automatic longitudinal-phase-matching process. According to Eq. (2), the PPLN grating period Λ can thus be a useful degree of freedom to phase-match the coupling to a radiation mode having a proper transverse field distribution to maximize ϑ. To find an optimum PPLN grating period for the present EO GTR PMC, we studied the overlap integrals of the mode couplings in this device with the aid of the numerical finite-element method  for the mode fields calculation in a diffused waveguide. Figure 1 shows the calculated normalized overlap integral according to Eq. (4) as a function of the effective refractive index no,eff (≡βρ/k0) and the corresponding escaping angle θ of the radiation mode for the coupling between the TM00 and TE radiation modes in an APE LiNbO3 waveguide at λ 0 = 1520 nm, at 40°C. The red line represents the fitting curve of the data distribution. The dashed green line indicates the corresponding value of the effective refractive index of the TM00 guided mode, which is ne,eff~2.1489. It clearly shows the TM00 guided mode (automatically) phase-matches to a radiation mode escaping at a large angle (~14°), resulting in a much lower overlap integral value. The overlap integral distribution peaks around an effective refractive index of no,eff~2.2120, approaching to the ordinary refractive index of the substrate nos = 2.2123. The radiation mode with this effective index has an escaping angle of θ ~1.2°. The mode-field overlap efficiency and therefore the GTR mode conversion efficiency can thus be highly enhanced if the conversion process is conducted in a near-collinear scheme (where radiation modes have small transverse wave numbers ). The PPLN grating period demanded to satisfy the longitudinal phase matching of this near-collinear conversion scheme can be derived from Eq. (2) with Δβ = 0, given by
The choice of the APE technique  as the waveguide fabrication method in the present work has many folds. First, APE technique has been one of the most mature approaches to fabricate a stable, low-loss optical waveguide in LiNbO3; second, APE LiNbO3 waveguide fabrication is a relatively low-temperature process (<400°C), which is of particular benefit to the QPM waveguide fabrication in contrast with the use of another popular waveguide fabrication method based on titanium diffusion requiring a high processing temperature (>1000°C); and third, only the TM polarized waves can be guided in a z-cut APE LiNbO3 waveguide as only the extraordinary refractive index is increased by the proton exchange (in contrast with the Ti:LiNbO3 waveguides that can support both TM and TE polarization modes). This third feature of APE LiNbO3 waveguides might be important for the accomplishment of the TM-guided to TE-radiation mode conversion in near-collinear scheme without the possible cross couplings to the TE guided modes. Per the birefringence of a Ti:LiNbO3 waveguide at 1561 nm, at 39.5°C , the QPM grating periods (Eq. (6)) demanded for a Ti:PPLN EO GTG PMC and a (collinear) Ti:PPLN EO GTR PMC are around 21.5 and 21.6 μm, respectively. It thus requires a careful fabrication and operation control of the Ti:PPLN waveguide to perform as a pure/efficient GTR mode converter under such a tight phase-matching tolerance.
3. Device fabrication and performance characterization
We first fabricated five 1.7-cm long, 2-mm wide PPLN grating sections of periods Λ = 10, 24, 30, 50, and 72 μm along with a single-domain section in a monolithic LiNbO3 crystal of 0.5-mm thickness using the standard electric-field poling technique. The 24 μm is expected to be the 1st-order birefringence QPM grating period for the coupling between the 1520-nm TM00 mode and near-collinear TE radiation modes in an APE PPLN waveguide at around 40°C according to Eq. (6). The other domain sections were fabricated for the experimental comparisons. We then fabricated an array of APE channel waveguides, with a center-to-center spacing of 125 μm, in the made PPLN crystal (i.e., there are 16 waveguides in each 2-mm wide domain section). In our design, these waveguides can support single-mode (TM00) operation in a spectral range of interest, 1495-1640 nm. The design and fabrication of APE channel waveguides in LiNbO3 has been a well-established technique , we shall not detail it here. Mainly, these waveguides had a proton-exchanged (PE) width of 9-μm and were fabricated by immersing the crystal in the molten benzoic acid at 180°C for 6-hour proton exchanging, then followed by an annealing process in air at 350°C for 14 hours. The characterized waveguide depth is around 4.1 μm. To apply an electric field along the crystallographic y axis of PPLN over all the waveguides, we fabricated two interleaved comb-shaped electrodes with teeth aligned along the waveguide sides and spaced by 40 μm on the + z surface of the monolithic crystal. The effective electrode length is 1-cm long. Both end faces (x surfaces) of the crystal were optically polished, but without the application of an optical coating. Figure 2 shows a microscopic image of a portion of the + z surface of the accomplished APE PPLN EO waveguide device. The HF etched -z surface is also visible in the image, revealing the PPLN gratings with a domain duty cycle of ~45%.
The performance of the APE PPLN EO waveguide device as a GTR PMC was then characterized in an optical testbed with a fiber-coupled external cavity laser (ECL) tunable in a spectral range of 1495-1640 nm as the light source. The output of the ECL was polarization maintained and connected to an in-line polarizer whose input and output were coupled with single-mode, polarization-maintaining (PM) fibers to fix the polarization state of the laser beam along the optic axis (i.e., z axis) of the crystal to fully excite the TM mode in the waveguide using the butt-coupling scheme. The coupled laser power in the waveguide was around 1.1 mW with an estimated fiber-waveguide coupling efficiency of −2.2 dB (including −0.62 dB transmission efficiency of the uncoated facet). The crystal was installed in a temperature controlled oven followed by a polarization beam splitter at the output end as an analyzer. We first measured the propagation loss of the APE PPLN waveguides using the Fabry-Perot method  and found it to be around 0.3 dB/cm. Figure 3 shows the measured spectral transmittances (TEO; refer to Eq. (5)) of the TM mode from a 24-μm-period APE PPLN waveguide for various EO voltages (VEO) at 35°C. The inset shows the measured transmittance of the TM guided mode at 1520 nm as a function of the crystal temperature from the 24-μm-period PPLN waveguide at an EO voltage of 250 V, indicating a moderate dependence of the coupling efficiency on temperature in a PPLN EO GTR mode converter. According to Fig. 3, a maximum mode conversion efficiency ηc (≡1-TEO) of >95% was obtained at around 1520 nm with 250-V EO voltage. This efficiency has been remarkably enhanced by a factor of >10 over a prior work in a Cu-ion diffused LiTaO3 waveguide using a periodic-electrode structure under the same interaction length (1 cm) and EO field (~6.3 V/μm) . It is also to the best of our knowledge the most efficient GTR mode converter ever reported based on LiNbO3 on-axis waveguides. Besides, a broad conversion bandwidth of ~250 nm (at VEO = 250 V) was also estimated from Fig. 3, which is a signature of the GTR mode conversion, in contrast with a typical bandwidth of <3 nm obtained from a PPLN EO GTG mode converter with the same electrode length . Figure 4(a) plots the measured spectral transmittances of the TM mode from the APE PPLN EO waveguides of various grating periods including Λ→ ∞ (the period of the single-domain section) when operated at 250 V and 35°C. The experimental results with periods of 10 and 50 μm (not shown) are similar to those obtained with the single-domain one. Figure 4(b) plots the mode conversion efficiency ηc of the device as a function of the PPLN period from the data at 1520-nm wavelength. As expected, APE PPLN EO waveguides of a period satisfying the birefringence QPM condition (i.e., 24 μm; refer to Eq. (6)) for a near-collinear conversion scheme do show the best GTR mode conversion efficiency over others of different periods and attain an efficiency enhancement of more than 4.6 folds over the waveguides built in the single-domain section. An observable GTR mode conversion was also measured from the 72-μm-period PPLN EO waveguides (dotted red line) due to the 3rd-order (m = 3) QPM grating structure. The ripple-like spectral transmission curves and the occurrence of some data with transmittance >1 in Figs. 3 and 4 can be attributed to the slight mode-confinement change in waveguides caused by an unwanted EO effect (accessing the EO coefficient r 33) arising from the z component of the applied electric field (Ez; along waveguide depth direction) inevitably produced in a surface-electrode configuration . Figure 5 shows the far-field intensity profiles of the 1550-nm TM00 guided mode measured from an APE waveguide in the single-domain section with an EO voltage of 0 V (left) and 250 V (right). Since the EO mode conversion effect induced by Ey around this wavelength is negligible for waves in the single-domain section, the observable discrepancy between the two field-intensity distributions manifests the change of the mode confinement condition due to the presence of Ez.
We have designed, fabricated, and demonstrated an efficient TM-guided to TE-radiation mode converter based on APE PPLN EO waveguides at telecom S-C-L bands. An array of APE channel waveguides were fabricated in a monolithic, multiple grating-period PPLN crystal including a period of 24 μm phase-matching to the 1st-order birefringence QPM coupling between the 1520-nm TM00 mode and near-collinear TE radiation modes in the waveguide at 35°C. We achieved a mode conversion efficiency of >95%/cm with an estimated ~250 nm bandwidth from the 24-μm-period PPLN waveguide at an EO field of ~6.3 V/μm. The obtained efficiency enhancement has been more than 4.6 times over a single-domain (unpoled) LiNbO3 EO waveguide GTR PMC and ~2.4 times over a LiNbO3 off-axis waveguide GTR PMC  under the same device length and EO field.
This work was supported by the National Science Council (NSC) of Taiwan under grants 98-2221-E-008-013-MY3 and 99-2623-E-008-010-D and partially supported by the Technology Development Program for Academia (TDPA) under Project Code 97-EC-17-A-07-S1-011. The authors thank the Thin Film Technology Center (TFTC) at National Central University and the High-Energy Optics and Electronics (HOPE) Laboratory at National Tsing-Hua University, Taiwan, for providing the measurement instruments.
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