dB highextinction autoconfigured Mach–Zehnder interferometer
0.8cm
Introduction
Photonics technology has been advancing strongly recently, especially with platforms like silicon photonics [1], with many potential applications in classical interconnects, communications and sensing [2], where it offers solutions to increasing problems of interconnect density and energy inside machines [3, 4], complements the processing abilities of electronics [5], and offers novel possibilities like modedivision multiplexing [2] at long distances. Also, photonics is considered a promising physical implementation for quantum information technologies including quantum communication [6, 7], metrology [8, 9], and computation [10, 11, 12]. This is owing to the photon’s properties of long coherence time and ease of manipulation [13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. A vast array of key components in integrated quantum photonics (IQP) have been reported in recent years including integrated photon sources [17, 18, 16], linear optical circuits [15, 14], and waveguide photon detectors [19, 20]. Many such uses of photonic technology, including sensing, mode conversion, IQP, and linear optical circuits generally, require quite precise interference of beams, for example in MachZehnder interferometers (MZIs). A key difficulty is, however, that it is difficult to fabricate such components very precisely; a particular problem that limits performance, such as extinction ratios, is beamsplitter splitting ratio imperfections. Fortunately, the technique demonstrated in this paper compensates for such imperfections, making photonics devices tolerant to these faults.
The MZI, typically consisting of one phaseshifter with two outer beamsplitters, is one of the most crucial components in integrated photonics [23, 24]. It is used in several fields from metrology and wavelength multiplexing, through to quantum photonics [14, 15, 16, 17] and quantum communications [22, 21]. As the integration density of photonic components increases, highperformance MZIs will become an extremely valuable resource because any operation error of a single MZI will propagate along the circuit and accumulate exponentially. This is especially true for faulttolerant linear optical quantum computing[25, 26, 27]. The quality of a highperformance MZI is typically quantitatively described by its extinction ratio. The extinction ratio, in the presence of indistinguishable photons, is a measure of how well one can distinguish between orthogonal computational basis states, and it is fundamentally determined by the splitting ratios of the beamsplitters used in the MZIs themselves [14, 15]. Because of fabrication imperfections, integrated beamsplitters usually have different splitting ratios to the desired ones—sometimes quite far away from 50:50 [23, 24, 28]. A possible solution is presented by the combined use of active components together with automated optimisation techniques [29, 30]. In this way, it is possible to compensate for fabrication imperfections in order to achieve highvisibility interference in MZIs.
Here we present the first experimental demonstration of a nearperfect MZI on a silicon photonic chip by implementing the adaptive selfoptimized approach proposed in Ref.[30]. This method consists of using two additional MZIs acting as reconfigurable variable beamsplitters (VBS) and finding their optimal configuration, thereby circumventing the requirements for perfect fabricated beamsplitters. This progressive approach allows automatic optimisation of the splitting ratios of two VBS to 50:50—without any prior calibration—and results in a highextinction ratio MZI. Using a silicon photonic device, we measured dB extinction in the interferometric fringes, corresponding to an increase of dB with respect to the nonoptimized case. This work represents the new state of the art in the achievable extinction for interference, and a new approach for the realization of ultrahigh fidelity operations for future faulttolerant linear optical quantum computing [27].
Selfoptimized Approach
Figure 1 shows the schematic of the MZI consisting of 7 components each with their own parameter: 3 thermooptical phaseshifters (, and ) with phases that we scan over, and 4 passive beamsplitters with fixed splitting ratios that are not of direct interest, as long as they fall within a range of 85:15  15:85 [30]. The phaseshifters are resistive heating elements and they induce a local change in the refractive index of the waveguide core by temperature variation. This allows us to optimize and control the MZI by applying electrical voltage onto each phaseshifter. To achieve an optimized MZI, we want to find the voltage settings for the outer phaseshifters, and , that construct the VBS to be beamsplitters of 50:50 splitting ratio. Once this has been determined, the and can be set to the constant phase value and the central varied as a usual phaseshifter in a MZI.
To find the optimum voltage settings for and we use an algorithm that enables us to set both and to 50:50 reflectivity, without precalibrating any component and only by simply minimizing or maximizing optical power in one output port [30]. Considering the optical power output at port , and rephrasing the reflectivities (i.e. splitting ratios) in their offset from the ideal 50:50 case (),
(1) 
where is the fabricated reflectivity of each VBS, is the phase of , and is the normalized measured optical power at port 3. The maximum and minimum power respectively correspond to and , with the cosine of therefore giving a sign change in the last term of Eq. (1). It is at these settings of the phase that we determine the optimal voltages for and . The problem of configuring the VBS is thus reduced to a twodimensional optimisation problem over the two VBS’ reflectivities, and . The convergence point of the algorithm [30] is exactly located at the point where both reflectivities are 0.5 — that is and are zero.
We use the algorithm of [30], though we have to extend it here because we do not have reliable prior knowledge of exactly what range of phase shifter voltages corresponds to monotonic increase or decrease of the splitting ratios of and ; for each such beamsplitter, that monotonic range will only occur over a specific range of size somewhere in a total range of phase shifts. So, we end up exploring the whole range for both beamsplitters to minimize or maximize power. We do this for the first pass of the algorithm; with subsequent passes we adapt the scan range to a smaller one centred on previously obtained voltage values. We start with all voltages set to zero. Hence our extended algorithm becomes:

Scan over the voltage range of to obtain the voltage for the minimum power at output port , .

Scan and over their voltage ranges in both equal and opposite directions to find minimum power: , where means up, and means down.

Scan over the voltage range of to obtain the voltage for the maximum power at output port , .

Scan and over their voltage ranges in all 4 directions to find the maximum optical power: .

Repeat steps 1–4 until there are no further statistically significant and measurable changes in settings.
During the algorithm’s operation all voltages are kept at their previously obtained values apart from the voltages modified in the current step.
Figure 2 (a) depicts a typical calculated optical power response for a VBS MZI when it is subject to variation in the phaseshifter voltages, and . The region plots were obtained by evaluating Eq. 1 for both the maximum and minimum power cases and equating them to the maximum (minimum) normalized power of 1 (0). The lines shown are contours for optical powers within a specified range of values. This threshold value is 0.995 for the maximum case, and 0.003 for the minimum case.
Experimental Results
The MZI device was fabricated on a standard SilicononInsulator wafer using 248 nm photolithography technology. The beamsplitters use a multimode interference (MMI) structure and thermooptical phaseshifters were formed using TiN resistive heaters. The asfabricated MMIs possess various splitting ratios that deviate from the ideal 50:50. The chip was mounted on a thermoelectrically controlled copper plate for stable temperature maintenance. Waste heat was dumped to a large copper heat sink. Each phaseshifter has a separate signal pin and mutually referenced ground pin, and was controlled by an individual voltage driver. Thermal crosstalk was negligible, and the device remained in a steady thermal state throughout.
Laser light at nm wavelength from a Tunics T100SHP laser was coupled to the chip (in at port and out at ) using grating couplers and a singlemode fiber array mounted on a piezocontrolled 6axis translation stage. The grating coupler here also works as an onchip transverseelectric (TE) polarizer [31], ensuring that all MZI components only interact with the TEpolarized light and thereby avoiding visibility degradation from an impure polarization state meeting in the MMIs. Before (after) light enters (leaves) the chip, it passes through a densewavelengthdivision multiplexer (DWDM) filter to reduce the amplified spontaneous emission noise from the laser and background signal from flat spectrum scattered light across the slab mode of the chip. Light is detected by a highsensitivity Thorlabs S155C InGaAs powermeter with a dynamic range of dB. All resistive heaters are controlled by a 12bit inhouse digitaltoanalog converter (DAC) electrical driver, which enables us to optimize and and scan with high accuracy [32].
The algorithm for finding the 50:50 VBS configuration was run on the device. The demonstration’s results shown in Fig 2(b) indicate a rapid convergence, caused by finding the region of the global extrema in the algorithm’s first pass. This was achieved using the smallest voltage resolution available from the voltage driver ( mV). This was limited by noise reducing the effective number of bits to 11 over a V range. Here, both were optimized as close to 50:50 allowable by both the algorithm and the equipment used. The subsequent MZI fringe measurement is a means of determining whether the beamsplitters are optimized or not. Throughout the experiment, light was injected in to port , and the optical power was measured only at port . This was important for demonstrating the capabilities of the algorithm, and that it only requires a single optical signal output to inform the voltage settings for subsequent steps.
Figs 2 (c) and (d) are the 2D fits of experimental data over the voltage space of the phaseshifters for the maximum and minimum optical power cases. These confirm the theoretical plot shown in Fig 2 (a). The fits are obtained by considering a cubic term in the phasevoltage relationship of the phaseshifters, which has also been considered in characterisation of other integrated photonic devices [14]. The cubic term encapsulates all nonOhmic behaviour of the phaseshifters, including the change in their resistance when subject to higher temperatures.
With the use of the selfoptimized and we then implement the MZI. The MZI yielded an ultrahigh extinction ratio of dB (Fig. 3). For comparison, a fringe for a single MZI on the same chip with two fixed MMI beamsplitters was also obtained with a dB extinction ratio, which corresponds to beamsplitters with a 48.4:51.6 splitting ratio. This illustrates the significant improvement offered — dB in this case — by compensating for fabrication imperfections. Moreover, this demonstration here is a dB increase from the previous reported result using an active device consisting of only one VBS [28].
The measured extinction ratio of 60.5 dB is at the limit of our temperature stability and our voltage drivers’ resolution, and we are investigating ways to improve our measurement further. The sinusoidal nature of the phase control relationship works against us for achieving 50:50 splitting ratio VBS because this is at the point where the rate of change of splitting ratio with respect to voltage is the greatest. Improved voltage stability is required to overcome this. We are also investigating an improved resolution voltage driver, as it is in the deepest region of the fringe that a small change in the applied voltage can induce a sharp change in the optical power. There is thus plenty of scope for further enhancing the performance of our MZI.
Conclusion
We have experimentally demonstrated a onepartinamillion dB highextinction ratio MZI (in spite of imperfect fabrication of beamsplitters) using a selfadjustment approach and without calibrating any components (Fig 3). The result has many potential applications in several fields, from the realisation of highquality photonics for telecommunication, to the development of quantum photonic technologies.The paper containing the original proposal of the beamsplitter 50:50 setup algorithm [30] also presents a further algorithm for optimising a larger optical circuit. The optimized VBS MZI such as ours can be cast as a functional building block which is repeated across a triangular array to form a Reck circuit for universal linear optics [33]. By virtue of the VBS MZI’s improved extinction, one can access proportionately more of the total state space. Calibration of complex manymode Reck schemes with highextinction VBS MZIs is easier and more accurate. It is also likely to be quicker because of the reduced propagation of errors in measurements. These reasons illustrate how using the VBS MZI increases the maximum size of any meaningful and useful Reck scheme.
The realization of nearperfect beamsplitters and MZIs is essential to reduce the cumulative error in quantum operations, thus resulting in a significant reduction of overhead resources for faulttolerant linear optical quantum computing [25, 26, 27]. This is because the number of errorcorrecting qubits scales inversely with the operation errors which are associated with the performance of beamsplitters [27]. Generally, this selfadjustable interferometric architecture offers potential to become a buildingblock component yielding the largescale integration of linearoptical circuits for quantum information processing.
* callum.wilkes@bristol.ac.uk
jeremy.obrien@bristol.ac.uk
Acknowledgements
This work was supported by the Engineering and Physical Sciences Research Council (EPSRC), a Marie Curie ITN in Photonic Integrated Compound Quantum Encoding (PICQUE), a Multidisciplinary University Research Initiative grant (Air Force Office of Scientific Research, FA99501210024), the U.S. Army Research Office (ARO) grant W911NF1410133, and the Centre for Nanoscience and Quantum Information (NSQI). M.G.T acknowledges fellowship support from the Engineering and Physical Sciences Research Council (EPSRC, UK). J.L.O‘B. acknowledges a Royal Society Wolfson Merit Award and a Royal Academy of Engineering Chair in Emerging Technologies.
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