1. Introduction

A key issue in the evolution of optical communication networks is the availability of flexible photonic modules to manage a variety of operations - such as signal routing, switching and wavelength demultiplexing- in an integrated optics chip [1–3]. Liquid crystals, due to their large electro-optic response, mature and inexpensive technology, low dielectric constant and broadband transparency, are quite appealing for signal processing in optical systems [4–10]. Nematic liquid crystals (NLC), in particular, are constituted by elongated rod-like molecules which, aligned parallel to a specific direction in space as described by the director vector distribution [11]. Their large inherent birefringence and dipolar reaction are such that the application of an external electric field can alter the mean angular orientation of the director, sustaining an electro optic response orders of magnitude higher than conventional dielectrics, such as LiNbO₃. Albeit slow with respect to the latter, NLC hold great potentials for reconfigurable optical nodes, where speed is not an issue. However, only a few integrated optics solutions have been devised and even fewer demonstrated [12–16]. Integrated guided-wave geometries, in fact, tend to exhibit superior performance and flexibility in optical networks as compared to bulk configurations.

 

Fig. 1. Electro-optic mode-mixer: operation principle. The two propagating modes interact in phase for V=V_l (top) and out-of-phase for V=V_h (down) after a distance L.

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In this Paper, exploiting the electro-optical properties of nematic liquid crystals, we report the design and experimental demonstration of an integrated, low-power and broadband optical switch encompassing a single waveguide. The operating principle of the device stems from interference between two co-propagating co-polarized guided modes in an index-tunable channel (Fig. 1). At the input, a coherent superposition of two equal-power modes (e.g., mode “0” and mode “1”) is launched into the bi-modal waveguide of length L. The relative phase delay ΔΦ at the output (z=L) relies on the eigenvalue difference Δβ=β ₀-β ₁ between the propagating eigensolutions, i.e., ΔΦ=ΔβL. In the presence of an electro-optic response, therefore, the mode eigenvalues and their difference can be altered by an external bias V. For our purposes, two cases are the most relevant: (i) at a certain V=V_l the phase delay (or lag) ΔβL=2mπ, with m any integer, and the resulting intensity profile matches the input (Fig. 1-top); (ii) at an appropriate V=V_h, conversely, the phase delay is ΔβL=(2m+1)π: the two modes are in phase-opposition and the output intensity profile becomes symmetrically displaced with respect to case (i) (see Fig. 1-bottom). Hence, by switching the bias from V=V_l to V_h, the output peak shifts from one side to the other (Fig. 1) and the device, with a suitable Y-splitter at the end, can effectively operate as an optical switch or a 1×2 multiport router.

 

Fig. 2. Sketch of the electro-optic device: (a) top view, (b) side view. The angle between the major molecular axis (director) and the propagation direction z is θ.

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2. Device analysis

The switch, sketched in Fig. 2, consists of a thin film (i.e planar waveguide) of positive uniaxial nematic liquid crystals 5CB (Δε_RF=11.5, n_o=1.5158, n_e=1.6814 at λ=1.064µm) [19] sandwiched between two BK7 glass plates. The latter are coated with two transparent Indium-Tin-Oxide (ITO) electrodes which allow the definition of a channel via the application of a bias V. Under planar anchoring (with rubbed films of Teflon or Silica at the interfaces), in fact, the molecular reorientation taking place in the (x,z) principal plane (Fig. 2(b)) increases the director mean angle, thereby altering the “extraordinary” refractive index $n_e^2={\left(\frac{{\cos }^2\theta }{n_{\perp }^2}+\frac{{\sin }^2\theta }{n_{\parallel }^2}\right)}^{-1}$ experienced by a TM (transverse magnetic) eigenmode. In the latter expression n _‖ (n _⊥) refers to a field polarization parallel (normal) to the main molecular axis (or director). Since NLC encompass elastic as well as electromagnetic interactions, we derived a complete model by means of the Frank free-energy approach [11, 17, 18]. The governing equation for the mean director is obtained by minimizing the energy functional through the Euler-Lagrange equation:

being K the NLC elastic constant (for all deformations), [11] Δε_RF the birefringence and E_x the x-component of the applied (static or low-frequency) electric field. The potential distribution V(x,y) stems from Maxwell’s equations:

For the actual design, we resorted to a fully numerical procedure, with the aid of a 2-dimensional mode-solver and a BPM (Beam Propagation Method) written for TM-polarized light, i.e., with electric field belonging to the principal plane defined by the molecular director and the k-vector (parallel to z). To carry out the analysis, we used Eq. (1)–(2) to calculate the refractive index profile, obtained TM ₀₀ and TM ₀₁ guided-mode profiles with the mode-solver, and excited the channel with a balanced superposition of them, monitoring the emerging intensity and relative phase delay ΔΦ versus bias. Such procedure yields the results displayed in Fig. 3–4 for a cell-thickness h=6µm and top-electrode 6µm in width. The refractive index increases with bias (Fig. 3) and so does the phase-delay between TM ₀₀ and TM ₀₁ (Fig. 4 b), leading to switching (Figs. 4(a), (c), (d)). Note that this behavior can be qualitatively described by means of coupled mode theory, which neglects any perturbation in the mode profile s and assumes slowly-varying mode envelopes according to:

being a ₀₀ and a ₀₁ the TM₀₀ and TM₀₁ envelopes (in $W^{-\frac{1}{2}}$), respectively, and Q ₀₀ and Q ₀₁ the spatial overlap integrals:

with f _0i the TM _0i eigen-distribution (i=0,1) and Δn ²(x,y;V) the electro-optic perturbation. For small bias increments we can set Δn ²(x,y;V)=η(x,y)γ(V) and obtain:

Therefore, in z=L the phase-delay evolves with the bias (Fig. 4(b)), and switching is expected when ΔΦ(V_h)=ΔΦ(V_l)±(2m+1)π. Unfortunately, due to the large birefringence of NLC, it is not always possible to cast a priori a simple expression for γ(V). In addition, the appreciable variation in both TM ₀₀ and TM ₀₁ distributions for V_l <V <V_h justifies the use of a numerical approach rather than coupled mode theory. Based on simulations (Fig. 4), we expect optical switching as the bias V changes from V_l=0.98V to V_h=1.19V over a propagation distance L=160µm.

3. Experimental results and discussion

The experimental setup included a spatially filtered near-infrared (λ=1.064µm) Nd:YAG laser, a microscope and a high resolution CCD camera to collect the light scattered by the NLC out of the (y,z) plane. Typical results are displayed in Fig. 5 for a geometry corresponding to the one in the previous section. To excite a balanced superposition of TM ₀₀ and TM ₀₁ modes, a beam of power P=0.4mW was focused at the waveguide facet using a 10x microscope objective with carefully adjusted tilt and offset with respect to the channel axis. As visible in Fig. 5(a), for a bias V_l=0.98V, the propagating modes gain a relative phase ΔΦ=2π after 160µm and the output intensity peaks on the same side of the excitation. Switching is clearly observed in Fig. 5(b) for V=V_h=1.19V. Finally, Fig. 5(c) shows the transverse intensity profiles acquired in z=L for the two previous cases, underlining the substantial lateral shift obtained in just 0.16mm with a modulation ΔV=210mV.

 

Fig. 3. (a) Refractive index in the cell midpoint versus bias and (b) 2D map of refractive index for V=1V.

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Fig. 4. BPM analysis of the switch: (a) plot of the output intensity versus bias and (b) corresponding phase shift; (c) light evolution in the (y,z) plane for V=V_l=0.98V and (d) V=V_h=1.19V.

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Fig. 5. Typical experimental results: light propagation in the (y,z) plane for (a) V=V_l=0.98V and (b) V=V_h=1.19V. (c) Corresponding output intensity distributions.

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It is worthwhile to evaluate the relevant switching figures of this device, although in its first implementation. We calculated the transmission T and the corresponding crosstalk X between the two output ports [1]. To this extent, using a 3µm aperture, we estimated T=26% and X=-4.2dB. However, since in the actual configuration it is not possible to measure the power coupled into the waveguide, the transmission is just a rough and conservative indication of the overall performance. The observed propagation losses (of a few dB/cm) are essentially due to Rayleigh scattering, because the used wavelength is well within in the transparency spectral region of 5CB. [19] Such losses would be reduced by operating at optical wavelengths in the third communication window, [11] and crosstalk could be substantially lowered by employing an adiabatically tailored Y-junction at the output, yielding better spatial separation of the emerging beams in the two cases (i.e., V_l and V_h). Work is underway in these directions.

4. Conclusions

We have designed and demonstrated an integrated electro-optic switch with a single waveguide in nematic liquid crystals. A detailed model of the structure and our experimental results at 1064nm are in excellent agreement, and multiport routing was achieved for voltage modulations as low as 0.21V over a length of only 0.16mm.