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Abstract
Reconfigurability is an important requirement for implementing quantum photonic processing using waveguide circuits in which both high fidelity and the ability to change the optical transformation dynamically are necessary. This work aims to address the issue of scalability in reconfigurable waveguide circuits fabricated using the femtosecond laser direct-write (FLDW) technique. A set of reconfigurable waveguide Mach-Zehnder interferometers were designed and fabricated using a combination of femtosecond laser waveguide inscription and picosecond laser ablation. Thermal cross-talk between adjacent phase-shifters was managed by machining microchannels into the chip surface to isolate individual waveguides from the rest of the substrate. The tuning efficiency as defined by the dissipated power per unit of induced phase shift was improved by a factor of two in this way while maintaining a smaller device footprint than previous demonstrations of phase tuning in laser-written waveguides. The phase response of the waveguide interferometers to the heaters was thoroughly characterised and was well predicted by simulation. A characterization of the time-dependent response of the reconfigurable interferometers was also performed. A rise time measurement revealed that the circuit can be reconfigured within seconds. No long-term phase drifts away from a set point were observed over a period of more than 12 hours, and the short term phase stability was better than 6 mrad.
© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Developments in integrated, linear optical circuits have been a boon to quantum information processing using photonic qubits. Integrated optics allows complex waveguide circuits to be implemented on a chip scale, providing a scalable and stable platform for the design of quantum optical devices. The devices implemented thus far include waveguide circuits and arrays implementing quantum simulations [1–4], gates for linear-optical quantum computing [5–8] and interferometers capable of quantum-enhanced phase estimation [9]. The femtosecond laser direct-write (FLDW) technique has emerged as one versatile fabrication platform for quantum optical circuitry since the first demonstration of quantum interference in a laser-written beamsplitter [10]. This technique uses a tightly focussed femtosecond laser to produce a localized refractive index change within the bulk of a transparent material, resulting in an optical waveguide when the sample is translated with respect to the focus [11]. In this way, waveguides can be inscribed rapidly in three-dimensions, with minimal sample preparation and without the need for lithographic masks. These advantages make this technique well suited to niche applications in which short turn-around times and low cost are important. Its three-dimensional capability allows for the fabrication of waveguide configurations not possible using planar platforms. In non-classical optics, these include novel interferometers for quantum phase estimation [9,12] and circuits for spatial multiplexing of independent single photon sources [13]. In order for this technique to reach its full potential, the ability to reconfigure a laser-written circuit after fabrication must be introduced. This capability is necessary to correct errors in the fabrication process that result in the optical transformation implemented by the circuit deviating from the intended one [14,15]. In addition, novel protocols in both classical and non-classical optics have been put forward that require the functionality of a photonic circuit to be updated dynamically [2,16–19]. Phase-shifters based on the thermo-optic effect are a convenient choice in these applications by virtue of their low loss, simplicity and high phase stability [9, 19, 20].
Small-scale demonstrations of thermally reconfigurable circuits have recently been made using laser-written waveguides. A three-arm interferometer with a single phase shifter was implemented in [9]. A classical and quantum characterization was used to demonstrate the feasibility of quantum-enhanced phase measurements with such a device. This was followed by a two-arm device in which laser inscription was used both to fabricate the waveguide device itself as well as to pattern a metallic layer on the glass surface into resistors [20]. Vergyris et. al. then combined a reconfigurable interferometer with a pair of photon sources based on periodically-poled lithium niobate (PPLN) waveguides to produce a heralded two-photon state generator [21]. Although much progress has been made, these devices either required a large amount of dissipated heat to obtain the required phase shift, or present a device footprint that limits the prospects for the design of circuits incorporating multiple devices in a single chip.
A major obstacle to larger scale deployment of these components is the thermal cross-talk that occurs between different phase shifters when devices are placed in close proximity. When a voltage is applied to a thermo-optic phase shifter, a waveguide other than the targeted one can still experience a temperature change that depends on the separation between the heater and waveguide. If multiple phases need to be adjusted simultaneously, this will result in the circuit reaching a different configuration than expected. Additionally, since the induced phase in a particular waveguide scales linearly with the contribution of each individual heater, the dissipated heat required to reach a given circuit configuration can grow rapidly as phase shifters are added to the chip. For these reasons, taking steps to mitigate the cross-talk will be necessary if reconfigurable circuits based on this technology are to be scaled up.
The selectivity of thermo-optic tuning can be improved by including an additional step in the fabrication process to remove a section of material in order to thermally isolate the target volume of a heater from the rest of the substrate [22–24]. In this work, heat diffusion across a laser-written waveguide chip is managed by patterning the surface of the glass substrate in order to separate adjacent waveguides that are elevated toward resistive heaters deposited on the surface. A set of waveguide Mach-Zehnder interferometers are fabricated in a sample of bulk glass using a high repetition rate femtosecond laser. Surface channels are then inscribed into the substrate surface through a second picosecond laser machining step in order to provide an insulating gap between the interferometer arms. In this way, the tuning efficiency as defined by the dissipated power per unit of induced phase shift is improved by a factor of two while maintaining a smaller device footprint than previous demonstrations of phase tuning in laser-written waveguides. A series of classical measurements are performed to characterize the response of the laser-written interferometers to the phase shifters and quantify the thermal cross-talk, which is predicted well by numerical simulations.
2. Theory
A series of numerical simulations were performed to predict the effect of the resistive heaters and microchannels on the chip substrate. The model solves the two-dimensional heat equation within a cross-section of a 1.1 mm thick silica glass substrate with a 300 µm-wide heat source placed at the top see (Fig. 1 for illustration). The heat flux Q of the source is calculated as the amount of electrical power dissipated per unit area by a rectangular NiCr resistor:
where Vapp = 20 V is the voltage applied across the resistor, theater =45 nm is the thickness of the NiCr layer, Lheater = 12.5 mm is the length of the resistor and ρNiCr = 1.5 × 10−6 Ωm is the resistivity of 80/20 NiCr alloy [25]. The bottom of the simulation domain is held at a constant temperature of 20° C= 293 K to simulate the effect of a heat sink at the bottom of the chip. Insulating boundary conditions are enforced at the other edges due to the negligible thermal conductivity of the surrounding air compared with glass. The temperature distribution within the cross-section is calculated by solving the heat equation subject to these boundary conditions via the finite element method using Comsol. The software divides the simulation domain into a mesh of triangular domains of variable size. Calculations are performed with a uniform substrate as well as one with a 150 µm wide, 200 µm deep section removed to simulate the effect of an isolation channel (top of Figs. 1(a) and 1(b).
Fig. 1 Two-dimensional cross-sections (top) and one-dimensional cuts (bottom) along a horizontal line at a distance of 50 µm from the top surface of a silica glass substrate with a 300 µm-wide heat source placed at the top without (a) and with (b) a rectangular section removed from the top to separate adjacent volumes of material. Positions of waveguide interferometer arms in a proposed device design are indicated by blue circles.
The calculated temperature distributions are plotted in Fig. 1. It is evident from the plotted horizontal profiles (Fig. 1 bottom) that the isolation channel results in a lower temperature from x =0 to x =0.5 mm, a region that encompasses the right arm of a Mach-Zehnder interferometer with a typical inter-waveguide pitch of 254 µm. At a depth of 50 µm, the temperature difference between x = +127 µm and −127 µm corresponding to the absolute positions of two waveguide interferometer arms in the proposed device design (indicated by blue circles in Fig. 1), increases by a factor of almost 2.5 from 10.1°C to 24°C in response to a 20 V step when the channel is included compared to a uniform substrate.
The importance of reducing thermal cross-talk in this way becomes clearer as the size of a reconfigurable circuit is scaled up. The additive nature of the contributions of multiple heaters to the response of an individual interferometer means that the power required to reach a desired circuit configuration scales rapidly as the number of elements is increased. This could lead to several Watts being dissipated if phases within many elements are adjusted simultaneously, requiring active cooling of the chip base. In addition, despite the small coefficient of thermal expansion of silicate glasses, large temperature gradients can still cause warping of the chip that are significant enough to affect the coupling efficiency between the waveguides and fibres at the chip facets [9].
3. Design and fabrication
The waveguide chip consists of a series of four laser-written Mach-Zehnder interferometers separated by a centre-to-centre distance of 1.016 mm. The layout of the chip is sketched in Fig. 2. The relative phase of the interferometer arms was adjusted using resistive heaters positioned above the waveguides on the sample surface and offset laterally by ~98 µm. This offset distance was set by a combination of the spacing between the interferometer arms, the trench width and the heater width. These were fabricated by patterning a metal film deposited onto the surface using an additional laser processing step.
Fig. 2 Sketch (not to scale) of the layout of the waveguide chip indicating the numbering convention for the laser-written interferometers, input ports and heaters.
The interferometers are constructed from cascaded waveguide couplers following the design depicted in Fig. 3. The interferometer arms are raised out of plane to within 50 µm of the sample surface to interact with thermo-optic heaters deposited on the surface (see Fig. 3). Both interferometer arms were placed at the same depth in order to characterize the heat diffusion along the x -axis. The length and pitch of each curve segment was selected such that their minimum radii of curvature was greater than ≈50 mm in order to minimize bend losses [26]. The waveguide inscription system uses a Ti:Sapphire oscillator (Femtolasers FEMTOSOURCE XL 500, 5.1 MHz repetition rate) focussed through a 100× oil immersion objective (Zeiss N-Achroplan NA=1.25). This produces waveguides residing within the cumulative heating regime of material modification. A feedrate of 1500 mm/min and laser pulse energy of 32.3 nJ were selected to yield single mode waveguides at 800 nm wavelength.
Fig. 3 Illustration of a 3D tunable Mach-Zehnder interferometer. The two arms are raised to within 50 µm of the surface to interact with Ni-Cr heaters. A channel is machined between the arms for thermal isolation.
The isolation channels were machined into the glass substrate following the waveguide inscription step using a picosecond laser machining system (3D Micromac MicroSTRUCT C) operating at 532 nm wavelength (Fig. 4). A raster was applied to a 150 µm × 12 mm area for 10 separate passes at a fluence of 4.8 J/cm2. The machining fluence was just above the ablation threshold of ~1–3 J/cm2 for silicate glasses at this pulse duration and wavelength [27], allowing for removal of material from a localized area with minimal damage or modification to the surrounding volume. This yielded an approximately 170 µm deep channel with sloped walls. The machining step was applied to interferometers A-C on the chip with the channel being omitted from interferometer D in order to compare the tuning selectivity of interferometers with and without the isolation channel.
Fig. 4 Four-step fabrication process of the reconfigurable photonic chip. The waveguide interferometers are fabricated first. Channels are machined using picosecond laser ablation in a second step to thermally isolate each waveguide arm (top left). Next, a 45 nm-thick layer of 80/20 Nickel-Chromium (NiCr) alloy is deposited in a wide strip across the whole chip (top right). A second laser ablation step is used to pattern the NiCr strip into eight 300 µm wide resistors and contact pads (bottom left).
The resistive heaters were fabricated by patterning a metal layer deposited onto the glass in another picosecond laser processing step. A 45 nm thick, 24 mm-long strip of 80/20 nickel-chromium (NiCr) alloy is first evaporatively coated across the top surface of the chip above the interferometer arms. A raster with a period of 5 µm was applied to the negative of the resistor pattern Fig. 2 using a fluence of 0.42 J/cm2. This is below the ablation threshold of Eagle 2000 glass, allowing the metal film to be removed from the desired areas while the glass substrate remained unaffected. The patterning step resulted in a set of eight 300 µm×12.5 mm resistors and contact pads with a total resistance ranging between 1500 and 2000 Ω.
4. Characterization
The tunable interferometers were characterized by injecting light from a 808 fibre-coupled laser diode into each input port and monitoring the intensity at each output port while varying the voltage applied to the heaters. The measured fringes for two of the interferometers are plotted in Fig. 5. As seen from Eq. (1), the heat flux is linearly related to the power dissipated by the heater. By extension, the temperature change and therefore the induced phase shift is also linearly related to the power. The phase response of the interferometers to the heaters can therefore be quantified by fitting the measured intensities I(Pj) to a function of the form:
where is the power dissipated when a voltage Vj is applied to heater j, Rj is the resistance of heater j and is the fringe visibility. The constant αi,j gives the phase imparted between the arms of interferometer i per unit of power dissipated by heater j. A value of αD,7 = 15.4 ± 0.6 rad/W was found for the interferometer without an isolation channel after a fit of the fringes measured while varying the voltage applied to the 7th heater. Meanwhile, values of αi,j between 29.9 and 34.8±0.1 rad/W were found for interferometers A - C, showing that the tuning efficiency of the thermo-optic heater is improved by a factor of two or more by the presence of the isolation channel, demonstrating the efficacy of this technique for reducing heat diffusion across the chip.Fig. 5 Measured interference fringes obtained from (a) interferometer D having no isolation channel and (b) interferometer C containing an isolation channel when launching into the left input port and monitoring the intensity at the left (black circles) and right (blue asterisks) output ports. Lines: best fits to a model following the form of Eq. (2)
The measured interference visibilities varied between 84 and 94%. The limited visibilities are attributed to two factors. The interaction length of the couplers was incremented between 3.40 and 3.55 mm around the value of ~ 3.40 mm that was found to give a reflectivity of ~50%. This, and the inherent fabrication tolerance of up to ±5%, resulted in the reflectivity of the couplers making up the MZIs varying around the ideal value, reducing the visibility. Also, it is possible that the propagation losses of the raised interferometer arms were slightly unbalanced, which can also reduce the interference visibility [28].
The effect of the phase shifters on neighboring interferometers within the chip footprint was quantified by collecting a series of fringes from interferometer C (refer to Fig. 2) while applying a voltage to each of the heaters along the full width of the chip. The relative phase induced in interferometer C by each of the heaters was determined by applying fits of the same form as Eq. (2) to the measured intensities. The measured phase calibration constants αC,j were compared with the results of another set of numerical simulations considering a cross-section of the chip with three 150 µm×200 µm channels. A specific heat capacity, thermal conductivity and density of C = 736.88 J/kg K, k = 0.891 W/m K and ρ = 2370 kg/m3, respectively, for the Corning Eagle2000 substrate were selected based on the data available from the manufacturer [29]. The lower thermal conductivity of this material relative to fused silica leads to a higher temperature change in the vicinity of the heat source than in fused silica. However, the different compositions of borosilicate glasses such as Eagle2000 typically lead to lower values of dn/dT than for pure fused silica. Schott BK7, a commonly used borosilicate glass, for example, has a thermo-optic coefficient of only ≈ 3 × 10−6 K−1 [30]. Since no value of dn/dT for Eagle2000 exists in the literature it was first estimated by varying its value until the phase constant predicted by the simulation matched the experimentally measured value of αD,7 = 15.4 rad/W for the simplest case of an interferometer with no isolation channel. This gave a value of dn/dT = 6 × 10−6 °C−1 which lies within the typical range of 3 × 10−6 °C−1 to 1 × 10−5 °C−1 for silicate glasses.
The resulting experimental and theoretical phase calibration constants αC,j are plotted as a function of the centre-to-centre spacing x between interferometer C and heater j in Fig. 6. The decay of αC,j with x quantifies the phase cross-talk between adjacent reconfigurable elements on a single chip and the effect of the ablated trenches can be seen by comparing the left (−x ) and right +x sides of Fig. 6. Note that |α| decays by a factor of ~3 between x = −0.791 and −1.241 mm, compared with a factor of ~1.4 between x = +0.791 and +1.241 mm, showing that the trenches mitigate the inter-device cross-talk in addition to enhancing the tuning efficiency of each individual interferometer. This cross-talk reduction can be further enhanced by machining additional trenches to separate each interferometer.
Fig. 6 Measured (blue points) and theoretical (dotted lines) phase calibration constants α as a function of the centre-to-centre distance between each heater and interferometer C along the x-axis. The two lines delimit a range of 15% centred around the theoretically determined constants.
5. Time dependent operation
The low brightness of current photon sources means that an experiment can span from several minutes to months [31, 32]. For this reason an extremely high degree of phase precision is required so that the circuit maintains its configuration for the full duration of a measurement. In addition, implementing quantum computation [14], simulation [2] and metrology [33] schemes often requires multiple reconfigurations of a circuit based on a preliminary characterization of the phase-response of the circuit to each heater [19]. Long term drifts in the phase can result in the circuit being set to an erroneous configuration at later steps of the experiment. Hence, a practical reconfigurable circuit needs to be resistant to both short and long-term phase drifts and fluctuations.
An experiment was performed to check the stability of the tunable chip against phase drifts from an initial set-point. The applied voltage to a single heater was set to a constant value corresponding to a total phase of π/2, where the interferometer output is most sensitive to small shifts in phase. The ratio of the intensities emerging from each output port of the interferometer was monitored over a period of 12 hours. The measured phase exhibited short term fluctuations around the set point with a standard deviation of ≈ 6.4 mrad, and no long term drifts were observed (Fig. 7(a). This result shows that the circuit is robust to changes in ambient conditions over the typical time scale of non-classical optics experiments, despite no dynamic correction of the circuit configuration. Furthermore, the short term phase fluctuation reduces to ≈ 3.1 mrad near a phase of π, where the sensitivity to phase shifts approaches zero. This suggests that the observed fluctuations are only partially attributable to changes in the temperature difference between the interferometer arms. The remaining 3-4 mrad is likely due to wavelength fluctuations of the classical laser source used in the experiment and different drifts in the coupling efficiencies between the waveguides and collection fibres at the device output ports. This measured phase stability is sufficient for this circuit to implement operations with a fidelity approaching 99.7%, which is comparable to figures reported in previous studies of laser-written and planar silica waveguide circuits [20, 34, 35].
Fig. 7 a) Phase determined from the ratio of intensities emerging from each output port of an interferometer as a function of time. Inset: distribution of phase fluctuations over the duration of the experiment. The phase remained within a standard deviation of less than 6 mrad of the set point with no offsets. b) Measured (solid black line) and simulated (blue dash-dotted line) response of a fabricated interferometer to an instantaneous step in the voltage applied to a heater. The measured 10–90% rise time is ≈0.4 s.
The response time of interferometer C was also measured by monitoring the output intensities in response to an instantaneous 1 V step in the driving voltage of the heater. A 10–90% rise time of ≈0.4 seconds was measured, which agrees well with the value of ≈ 0.47 s determined from a time-dependent simulation step added to the FEM study presented in Section 2. The presence of the trench increases the time necessary for the sample to reach a steady state temperature distribution in response to a change in the voltage applied to the heater. The measured rise time is longer than the rise time of 0.28 s determined from a time-dependent simulation for a device with no trench. However, despite the presence of the trenches the circuit is still completely settled to a new configuration within seconds, which is sufficient for applications in quantum optics where fast switching is typically not an important requirement.
6. Conclusions
This paper detailed the design, fabrication and characterization of a 3D reconfigurable waveguide circuit in glass. Waveguide Mach-Zehnder interferometers were inscribed into a glass substrate using femtosecond laser direct writing. Heaters were fabricated above the interferometer arms by patterning a layer of NiCr metal deposited onto the glass surface using a picosecond laser. An additional subtractive machining step was employed to thermally isolate waveguides from one another, improving the phase tuning efficiency by a factor of two. The heat diffusion across the glass chip was quantified by measuring the response of an interferometer to heaters placed at a range of distances, showing a reduction in inter-device cross-talk in addition to the increase in tuning efficiency of the individual interferometers. A characterization of the time-dependent response of the reconfigurable interferometers was also performed. A rise time measurement revealed that the circuit can be reconfigured within seconds. No long-term phase drifts away from a set point were observed over a period of more than 12 hours, and the short term phase stability was better than 6 mrad, sufficient to achieve a circuit configuration with a fidelity approaching 99.7%.
These results show the efficacy of our surface patterning technique for scaling up the number of reconfigurable devices that can be incorporated onto a single sample substrate. Additionally, the technique could be straightforwardly improved through a combination of machining additional channels between interferometers and by increasing the channel depth and by more thoroughly optimising the design of the heaters and waveguide devices. This work therefore represents an important step toward realising ever more complex reconfigurable networks fabricated using the ultrafast laser inscription technique
Funding
Australian Research Council (CE110001018)
Acknowledgments
This research was supported by the ARC Centre of Excellence for Ultrahigh bandwidth Devices for Optical Systems (project number CE110001018), and performed in part at the Optofab node of the Australian National Fabrication Facility; a company established under the National Collaborative Research Infrastructure Strategy to provide nano and microfabrication facilities for Australian researchers.
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