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The ability to efficiently transmit and rapidly process huge amounts of data has become almost indispensable to our daily lives. It turned out that all-optical networks provide a very promising platform to deal with this task. Within such networks opto-optical switches, where light is directed by light, are a crucial building block for an effective operation. In this article, we present an experimental analysis of the routing and switching behaviour of light in two-dimensional evanescently coupled waveguide arrays of Y- and T-junction geometries directly inscribed into fused silica using ultrashort laser pulses. These systems have the fundamental advantage of supporting three-dimensional network topologies, thereby breaking the limitations on complexity associated with planar structures while maintaining a high dirigibility of the light. Our results show how such arrays can be used to control the flow of optical signals within integrated photonic circuits.
Information processing and networking schemes in all-optical circuits are expected to overcome the speed limitations associated with electronic systems1 and can fully exploit the long-distance transmission capabilities of photons. Fundamental to such architectures is the rapid switching and routing of light signals in the optical domain. Due to steadily growing data volumes, one of the primary scopes of today's developments is to build integrated high-capacity devices with improved miniaturization. A widely acknowledged approach is the use of silicon as the optical material, since it offers a range of beneficial nonlinear properties2 and waveguides with minute radii of curvature become feasible due to its high refractive index3,4. This allows for highly miniaturised devices, such as optical buffers5 and switches6,7, whereby the switching is actuated by optically induced refractive index changes and the switching speed is limited by free carrier generation. Other recent approaches employ silicon-organic hybrid waveguides for very fast signal processing8, slow light in coupled photonic crystal waveguides for all-optical switching on very short length scales9 or use quantum dots to impose phase shifts determined by control fields at the single-photon level10.
Regardless of their physical platform, such components have to be cascaded for more complex operations. In a planar, i.e., non-intersecting, network, rerouting from N inputs to N outputs requires N(N-1)/2 fundamental elements performing 2×2 switching, like a directional coupler11. Evidently, this O(N2)-scaling quickly becomes impractical as N increases. It is by now quite clear that the existing two-dimensional (2D) planar technologies can only support a limited number of input/output channels since the demands on fabrication tolerances become progressively more severe with the number of nodes. This planar bottleneck can be broken by introducing the third (out-of-plane) dimension into the routing paradigm which allows a convenient low-loss cross-connection of the nodes leading to an O(NlogN)-scaling12. In principle, a three-dimensional (3D) circuitry can be built from fundamental elements in which the light is routed within the plane perpendicular to the propagation axis of the waveguides. Ten years ago, such revolutionary elements were suggested in the form of two-dimensional (2D) junctions of evanescently coupled waveguide arrays13,14. To date, they could not be attempted experimentally in the optical domain due to a lack of appropriate materials and 3D waveguide fabrication technologies.
However, recent progress in the field of waveguide writing in glasses using ultrashort laser pulses15,16 has opened the gate for manufacturing arrays of waveguides with almost arbitrary arrangements in two transverse dimensions17,18. With this powerful and versatile technique we realised, for the first time, various all-optical routing and switching schemes in 2D waveguide arrays. We show that due to the interplay of linear and nonlinear light propagation, combined with polarisation as an additional degree of freedom, complex operations can be performed using simple settings.
In linear waveguide arrays (“photonic lattices”), light evanescently couples from one lattice site to the nearest neighbours, while propagating along the guides19. In particular, if the outermost waveguide is excited, the light forms a confined lobe that travels ballistically through the array20. In this work, such compact light distributions are used as signals. They can travel around sharp corners in the array, even perpendicularly to the initial transverse motion. As the light is propagating in the longitudinal direction, merely the small transverse momentum of light has to be changed to redirect the light signals. Hence, the light may pass corners without substantial losses, even for small refractive index contrasts. Such bends are described in the Supplementary Data & Discussion. We focus here on the presentation of two fundamental building blocks of 2D routing and switching schemes: the Y- and T-junction (see Fig. 1a), where low-power signals couple into separate output ports and can be steered along defined paths by a high-power gating beam. In order to fabricate such structures, we employ the femtosecond (fs) laser direct-writing approach (see Methods). In Fig. 1c, three microscope images of the front facet of our samples (length 10cm, waveguide separation 32µm) are shown, where the input positions of the low power signal and a high power gating beam are marked.
It is known that a high power beam, launched into a single site of a waveguide array, results in the formation of a nonlinearly trapped state, called "discrete soliton"19,21,22,23,24,25. Due to the optical Kerr effect, the effective refractive index of the respective guide is dynamically changed, resulting in a transient lattice defect, which follows the field intensity essentially instantaneously24. Evidently, such defects can be used to deflect optical signals and route them along defined paths13,14,26,27,28. In the first part of our experimental survey we investigated all-optical routing of linear signals by discrete solitons at Y-junctions with an opening angle of 90°. The experimental results and the corresponding simulations are summarised in Fig. 2. In absence of the blocker, a weak signal (λ = 800nm, pulse duration ~300fs, pulse energy ~50nJ, see Methods) couples equally into both arms of the Y-junction, as shown in the central column. We blocked one of the branches by launching high power laser pulses (λ = 800nm, pulse duration ~300fs, pulse energy ~1µJ) into the waveguide adjacent to the junction. A pronounced spatial localisation of this gate pulse is visible in the first column, inducing the desired transient lattice defect, and thus effectively blocking that branch for the signal. The last column reveals how the path of the signal is altered by the presence of the blocker: The power transmitted into the blocked branch is reduced drastically and most of the signal light is steered into the remaining branch.
Beyond mere routing of signals, this scheme may also be used as a logic operator. To this end, we investigated optical switching on a waveguide T-junction. The results, obtained with similar parameters as for the Y-junction, are summarised in Fig. 3. In absence of the blocker, most of the light is found in the vertical branch, a state which could be associated with a digital ‘1' in this port and a ‘0' in the horizontal branch. The blocker effectively diverts the signal beam into the horizontal branch, into a direction perpendicular to the initial direction of transverse motion, which would then yield the reverse output configuration. Due to the basically instantaneous nature of the Kerr nonlinearity the switching speed is only limited by the rate at which the blocker pulse itself is switched.
The presented optical switching concept can be extended by polarisation selective routing. To demonstrate this feature of our proposed scheme, we rotated the ellipses of the waveguides by 90°, as shown in the right microscope image of Fig. 1c, and measured the output intensity distributions for both input polarisations (termed s- and p-polarisation). Due to the modal shape of the beams at different polarisations (Fig. 1b), the output patterns become strongly polarisation dependent, in contrast to our results presented in Figs. 2 and and3.3. In absence of the blocker the s-polarised signal couples into both output branches (Fig. 4a). In case of p-polarisation the light moves straight across the junction as the coupling in the perpendicular direction is weaker than in the forward one (Fig. 4c). If the first waveguide of the forward path is blocked, s-polarised light is mainly routed into the side branch (Fig. 4b), whereas a p-polarised signal is reflected back into the input port, due to the p-specific coupling conditions (Fig. 4d). Thereby, the device acts as an all-optically switched polarisation filter, separating polarisations on demand.
Our results demonstrate how discrete solitons can be used to effectively route and switch light signals at junctions of evanescently coupled waveguide arrays. Non-planar network topologies are supported by such routing and switching elements.
Note that the waveguide arrays investigated in this survey are merely weakly coupled due to their relatively large separation (32µm), which has been chosen for experimental convenience. To allow for circuits combining several elements on the same length, as depicted in Fig. 1a, one needs to reduce the waveguide separation, and thereby increase the coupling, which is well possible by one order of magnitude for directly written waveguides in fused silica29.
We would like to emphasise the close correspondence of the numerical results and the experimental data shown in Figs. 2 and and3.3. The only major difference between the two is the stronger localisation of the blocker beam in the simulations, which were carried out assuming continuous wave (cw) illumination (see Methods). On the other hand, the experiments are subjected to the spatio-temporal dynamics inherent to a pulsed excitation, whereby the low-power slopes of the pulse do not contribute to localisation30. Therefore, the lower switching contrast in the experiment can be attributed to the temporal dynamics of the gate pulse propagation. To improve the performance of the junctions beyond these proof-of-principle values (~10dB for the T-junction), one can use longer gate pulses, and thereby an increased interaction window. Then, switching contrasts of ~15dB, as obtained from the simulations, can be expected. A further enhancement is possible by shifting the blocker pulse between the first waveguides of the two output branches instead of merely chopping its amplitude.
It is also insightful to have a look at the reflection loss for the signal at the junctions. Comparing to the data found in simple bends (see Supplementary Data & Discussion, Fig. S1), one finds that considerably more light is reflected at the junctions (Figs. 2 and and3,3, central column). This arises from an additional topological defect caused by the branching of the array31. However, this defect is overcome when the blocker beam is present, as the lower branch effectively vanishes for the signal. Hence, the remaining branches are equivalent to a bent array and exhibit a similarly weak reflection.
However, when it comes to building larger networks out of cascades of such elementary junctions, even small reflection losses are crucial. For instance, at the gated T-junction about 6% of the power radiates back into the input port, whereas 17% is lost in the ungated case. Such reflection losses can be mitigated by a detuning of the pivotal waveguide, as it has been numerically32 and experimentally33 shown for bent arrays.
The propagation loss in the laser-written waveguides is in the order of 0.4dB/cm, amounting to a global loss of 60% over the sample length. However, for a networking device one would use stronger coupling29, meaning that more junctions can be accommodated on a given propagation length. Also note, that losses as low as 0.05dB/cm have been reported for fs-laser written waveguides after thermal treatment34.
It may be of interest to compare the presented laser-written waveguide array junctions with similar structures constituted by photonic crystal waveguides. For example, integrated Mach-Zehnder interferometers have been realised, with a thermal35 or all-optical36 control of the light propagation. Such structures can be much more miniaturised; due to their enormous refractive index contrast, the light is normally confined to the µm-range, whereas the transverse dimension of our splitter is ~100µm. Interestingly, the reflection loss at a Y-splitter is predicted to be similar to the loss occurring at our devices, if the splitters are engineered accordingly37. Even though propagation losses are much higher for photonic crystal waveguides (~8dB/cm38), the much smaller propagation lengths (some 10…100µm per device instead of 1…10cm) more than compensate for it.
On the other hand, these remarkable properties come usually at the expense of a narrow bandwidth, whereas devices relying on directional coupling in laser written waveguides have been demonstrated to operate for spectra spanning more than an octave39. Moreover, all photonic crystal waveguides reported so far were entirely planar. Networks constructed out of them will thereby suffer from the aforementioned disadvantageous scaling properties11. Finally, the nonlinear response time is not limited in fused silica24, at the cost of requiring relatively large energies for the gate pulse.
Therefore, photonic crystal devices will be superior when it is desired to realise highly miniaturised, low-loss, energy-efficient networks with a moderate number of elements for signals at a predetermined spectral range and where speed is not absolutely critical. For broadband applications as well as for very large networks, where the better scaling of 3D topologies becomes relevant12, or when the speed of operation is more important than energy-efficiency, the waveguide array devices presented in this manuscript may provide a very useful alternative.
Notably, such routing and switching schemes in waveguide arrays may allow for a variety of further all-optical devices for communication and information processing. In Fig. 5 two different examples are given. The left column shows an optically gatable wavelength splitter. The coupling strength between adjacent guides, and hence, the transverse velocity of signals, increases with wavelength29. We envision a Y-junction where the high-power pulse can swap sides via curved waveguide sections. In such a 3D-device the signal may be split into its spectral components depending on the input position of the blocker pulse. A further possibility is the realisation of a (classical) all-optical controlled-NOT (CNOT) gate (right column of Fig. 5). The high-power pulse controls the gate, by blocking the signal and preserving the target bit if sent into the centre of the structure (Fig. 5c) or flipping the bit if propagating in the decoupled waveguide (Fig. 5d). Alternatively, a nonlinear CNOT gate could be constructed where the target bit is set by the control beam's power.
In conclusion, we experimentally studied 2D all-optical routing and switching schemes in fs laser-written waveguide arrays. The investigated structures can be combined to complex non-planar photonic networks in which discrete solitons direct light signals along specific paths. The presented approach suggests a new concept of building purely optical devices which may be used for a rapid routing and processing of data in form of optical pulses. The instantaneous nature of the Kerr nonlinearity sets no fundamental limits to the achievable speed of operation.
We used the femtosecond (fs) laser direct-writing technique to fabricate our devices. Femtosecond laser pulses from a Ti:Sapphire laser system (Coherent Mira/RegA; wavelength λ = 800nm, pulse length 170fs, pulse energy ~300nJ, repetition rate 100kHz) are focused into a transparent bulk material. Since the required energy densities for the underlying nonlinear absorption process are only reached in the focal spot of the writing objective (NA = 0.35), the resulting modifications are confined to a small volume. In case of fused silica as host material, illumination with fs pulses yields a localised refractive index increase in the order of 10−3. Consequently, an elongated waveguide following an arbitrary trajectory can be created by moving the sample with respect to the beam (velocity 1.5mm/s). Since the guides are written sequentially, extended arrangements with intricate geometries can be realised (see Fig. 1b). In addition, our proposed scheme makes use of the stress-induced birefringence of the waveguides, which causes light with different polarisation (termed s- and p-polarisation) to exhibit slightly different mode shapes.
To perform all-optical routing and switching in the experiment, two pulses from a Ti:Sapphire laser system (Spectra Physics Spitfire; λ = 800nm, pulse duration ~300fs) were simultaneously launched through a microscope objective (NA = 0.075) into the array-junctions. A Mach-Zehnder interferometer with adjustable path-length and combinations of half-wave plates and polarisers was used to overlap the pulses temporally and to select input sites, pulse energies and polarisations for both pulses individually (For more details see Supplementary Methods and Supplementary Fig. S2). The output intensity profile at the end facet of the sample was imaged onto a CCD. The beams were orthogonally polarised, such that the contributions of the two pulses could be measured separately by positioning an additional polariser behind the sample.
The paraxial Helmholtz equation including a Kerr nonlinearity governing the propagation of two orthogonally polarised modal field amplitudes A(x,y,z) and B(x,y,z), assuming material birefringence, |B||A| and slow variation in z-direction, is given by:
where is the vacuum wavenumber, βΑ(Β) denotes the propagation constant of the respective waveguide mode and nA(B)(x,y) the transverse refractive index profiles. The terms on the right hand side account for diffraction, the contribution of the trapping index profile and the Kerr nonlinearity, respectively. Thereby, the parameters of self- and cross-phase modulation are given by and for fused silica, with an intensity dependent refractive index We employed a Fourier-split-step algorithm40 to simulate the propagation of light through various waveguide arrays. The mode profiles of the fs laser-written waveguides were measured for both polarisations to obtain the corresponding index profiles by inverting the scalar linear Helmholtz equation41, neglecting form birefringence of the waveguides. Note that this approximation does not affect the simulation of the light propagation, as the correct modal profiles are recovered from these two index distributions again. The waveguides are found to have a maximum index of 1.2 × 10−3 above the bulk material for a p-polarised field and 9.8 × 10−4 for s-polarisation (Fig. 1b). Several of these profiles were concatenated to model Y- and T-junctions of waveguide arrays. Movies of the switching operations are presented in Supplementary Videos 1-4.
R.K., M.H., F.D., T.P., S.N. and A.S. devised the experimental setup and performed the measurements. R.K., M.H. and A.S. analysed the results and prepared the figures. F.D. fabricated the samples. R.K., F.D., D.C. and A.S. engaged in modelling and numerical simulations. All authors co-wrote the paper.
Supplementary Online Information
The authors acknowledge support by the Deutsche Forschungsgemeinschaft (Research Unit 532 and Leibniz program) and the German Academy of Science Leopoldina (grant LPDS 2009-13).