We present a rotated polarization directional coupler (RPDC) on a photonic chip. We demonstrate a double-track approach to modify the distribution of the refractive index between adjacent tracks and form a single waveguide with an arbitrary birefringent optical axis. We construct a RPDC with the two axis-rotated waveguides coupled in a strong regime. The obtained extinction ratios on average are about 16 dB and 20 dB for the corresponding orthogonal polarizations. We perform reconstruction of the Stokes vector to test the projection performance of our RPDC, and observe the average fidelities up to 98.1% and 96.0% for the perfectly initialized states in 0° and 45° RPDCs, respectively.
© 2018 Optical Society of America
Polarization manipulation of photons is a crucial approach in optical information processing, quantum communication, and quantum computing. Especially in free space, there are many mature bulk optical devices for the preparation, control, and projection of polarized states in very high precision. However, the scalability, robustness, cost, and insertion loss have activated developing integrated polarization devices for large-scale applications [1–6].
Femtosecond laser direct writing [7–15], taking advantage of precise control of highly localized material modifications through nonlinear absorption processes, has been an emerging technique for controlling birefringence [16–21] and constructing on-chip polarization devices. Moreover, its single-step, mask-free, phase-stable, and cost-effective features have promised a powerful polarization-based technique for integrated photonics, such as polarization-dependent light attenuators , polarization-insensitive directional couplers [23–26] (analogous to bulk optical beam splitters), polarization directional couplers [27–29], birefringent retarders, wave plates [30–32], and integrated source . However, the orientation of these polarization devices is often fixed as horizontal or vertical with the standard configuration of femtosecond laser direct writing.
In this Letter, we present an on-chip rotated polarization directional coupler (RPDC) that can be constructed at arbitrary orientation by using a double-track approach. We adjust the relative radial and azimuthal positions of the adjacent tracks to artificially set the birefringent optical axis of a single-mode waveguide with a high transmittance. With the two axis-rotated waveguides, we can construct a RPDC along the same rotated axis, with which we are able to make the projection measurement on any pair on an orthogonal basis, rather than either horizontal or vertical.
As shown in Fig. 1, the waveguide (gray) is composed of two adjacent parallel tracks (dark red) with specific offsets (radial and azimuthal). Different from the method of defect tracks  written nearby, our track pairs are laid out quite close and a bit overlapped. Therefore, the two tracks here are able to transmit light simultaneously without energy dissipation into the defect track. An optimal radial separation can be found where the track pairs are able to guide light, behaving as a single-mode waveguide . Moreover, a precise change of relative position in the track pairs may induce the anisotropic and inhomogeneous distribution of the refractive index, generating an artificial rotation in the birefringent optical axis.
We employ a regenerative amplifier based on Yb:KGW lasing medium, with a pulse duration of 290 fs, a repetition rate of 1 MHz, and a central wavelength of 513 nm, to conduct the fabrication. A (0.70 NA) microscope objective is adopted to tightly focus the subsequent linearly polarized (along the writing direction) laser pulses into a depth of 170 μm underneath a commercially available fused silica substrate surface. We move the substrate and laser focal spot with three air-bearing translation stages, and the formed trajectory of the focal spot is the track. The writing speed in our experiment is about 1.268 mm/s with a resolution of 0.1 μm. We fix the writing laser at optimized pulse energy of 180 nJ and shape the beam by using a cylindrical lens  with a focal length of 70 cm.
The single-track is able to guide a single mode at 780 nm as well as the double-track waveguide. However, its birefringence is around the order of , leaving the adjacent track to tenfold stress the birefringence . Also, the single-track waveguide modes are generally larger compared to double-track waveguides, due to decreased index change at lower fluence .
Figure 2(a) shows the induced rotation of the birefringent optical axis () dependent on the azimuthal orientation angles () of the track pairs from 0° to 180° per 5° at a fixed optimized radial separation of 2 μm. We deduce the orientation of the birefringent optical axis of the waveguide by placing two crossed polarizers (Pol and ) before and after the chip [Fig. 2(e)] [31,32,38]. The minimum transmission reveals the orientation of the birefringent optical axis, and the maximum is always 45° away from the minimum. Although not linearly proportional, the fast and slow axes are confirmed as orthogonal and tunable in the plane marked in Fig. 2(b) by controlling the orientation angles (), behaving as a stable and controllable transmission of -polarized or the corresponding orthogonal polarized light through the chip. The end-view microscope images (corresponding to an average area of ) of waveguide cross sections composed of the track pairs can be found in Fig. 2(c), for the real pictures of changing applied writing parameters of control orientation () and radial separation. Moreover, we find that the near-field profiles of the guided modes [Fig. 2(d)] (corresponding to an average area of width) at 780 nm wavelength are preserved well with a comparably small influence induced by differential . We also observe a high average total transmission rate up to 60% through 19.64 mm waveguide propagation with a objective in free space, and over 50% transmission coupled into a single-mode fiber.
In order to achieve a polarization directional coupler, one needs to utilize the difference in coupling coefficients between the input light polarized parallel and perpendicular to the birefringent optical axis. It has been proved that the coupling constants for H- and V-polarized light vary from each other, caused not only by projection magnitude, but also due to anisotropy under different spatial dispositions of waveguide arms with fixed horizontal and vertical optical axes . Also, a link among the geometry of the waveguides, polarization of light, and coupling constants has been revealed . The wanted difference of evanescent coupling may become weak and complex if the two waveguides are kept in the same plane while their birefringent optical axes are rotated [Fig. 3(a)]. This enlightens us to form a 3D tilted coupler with feasible experimental modified configuration to produce a compact and balanced RPDC with rotated optical axes [Fig. 3(b)]. Once the birefringent optical axis is confirmed, the evanescent light coupling of the two waveguides should still be subjected to coupling mode theory , in which the field amplitude evolutions and in two waveguide arms follow the equation
The coupling ratio (field amplitudes) with the configuration shown in Fig. 3(b) can be calculated as3(b). In order to exclude potential additional birefringent stress that the second waveguide arm may cause to rotate the optical axis, we made polarization analysis of the 45° rotated birefringent optical axis of the parallel straight coupling region by two crossed polarizers, as is mentioned above. As shown in Fig. 3(c), the linearly input H-polarized light is measured as V-polarized output light, etc. The input D/A-polarized light traveling along the optical axis retains visibility as high as 98%–99%. Transmission power of the 45° RPDC is characterized by different coupling lengths, as shown in Fig. 3(d). We calculate the ratio with beam diameter definition of full-width, half max. From our experiment, the coupling lengths reaching the 0° and 45° RPDCs are equal, which well verifies the theory of our RPDC. The two waveguide arms are split adiabatically through an “S curve,” as shown in Fig. 4(a). It should be noticed that evanescent coupling may also occur during the bending region, and a phase term should be added in the argument of the sine function. Therefore, the parallel coupling length reaching a RPDC could be shortened from 28.5 mm to 23 mm. Experimentally, we observe average extinction ratios up to 16 dB and 20 dB [Fig. 3(e)] for the diagonal (D) and anti-diagonal (A) polarizations, respectively. Here we define extinction ratio as
To further test the quality of the fabricated RPDC, we perform reconstruction of the Stokes vector by using a simple linear tomography [42,43] technique, shown in Fig. 4(a). In our experiment, we initialize high-purity polarization states with a high-extinction polarizer and wave plates at the state preparation part. In the state measurement part, we set the quarter-wave plate (QWP) and half-wave plate (HWP) to map the states to horizontal/vertical bases. Unlike the standard bulk optical implementation, the projection measurements are carried out by a RPDC rather than a polarization beam splitter. The additional HWP rotates the frame to our RPDC. In this way, we follow the standard procedure to perform state tomography while our RPDC acts as a polarization beam splitter to make projection measurements. The density matrix for the polarization degrees of light can be related to the Stokes parameters by the formula
Ideally, the fidelities measured with a perfect RPDC should be 100%. Here, we observe the average fidelities up to 98.1% and 96.0% in 0° and 45° RPDCs, respectively, where we rigorously perform a maximum likelihood estimation to keep the density matrix physical. The detailed reconstructed density matrices are shown in Figs. 4(c) and 4(d) with error bars omitted, as they are too small to be visible. The projection performance of RPDCs with not much difference identifies the ability to make general polarization projections on a photonic chip.
In conclusion, a new double-track approach is presented here to realize waveguides with rotated birefringent optical axes and to construct an on-chip RPDC with the two axis-rotated waveguides coupled in a strong regime. We test the quality of the on-chip RPDC by performing reconstruction of the Stokes vector with perfectly initialized polarization states. The features of straightforward fabrication, straightforward polarization projection, and high transmittance make this on-chip RPDC a good candidate for large-scale polarization-based optical communication and quantum information processing.
National Key R&D Program of China (2017YFA0303700); National Natural Science Foundation of China (NSFC) (11374211, 11690033, 61734005); Science and Technology Commission of Shanghai Municipality (STCSM) (15QA1402200, 16JC1400405, 17JC1400403); Shanghai Municipal Education Commission (SMEC) (16SG09, 2017-01-07-00-02-E00049).
The authors thank Roberto Osellame and Jian-Wei Pan for helpful discussions. X.-M. J. acknowledges support from the National Young 1000 Talents Plan.
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