1. Introduction

An optical isolator is a critical component in many optical systems as it avoids detrimental spurious reflections back to the laser that can seriously compromise the stability of the system by increasing laser noise, and in many cases causes loss of mode locking in a mode locked laser [1–4]. While integrated photonics is coming to fruition, amongst what is still missing is a reliable on-chip isolator that is broadband, mode and wavelength independent, has low insertion loss with high isolation, and is monolithically integrable within a small footprint without complicated fabrication process. Traditionally, in bulk and fibre based optical systems, isolators based on the magneto-optic effect are used which researchers are trying to implement in integrated photonics [5–9]. However, such isolators can have high insertion loss, and are not easy to implement for different polarizations, and are challenging to integrate on a CMOS platform especially together with the magnets.

There are other types of isolators that have been demonstrated recently that are being investigated to circumvent these problems such as, radio-frequency (RF) modulation [10–15], χ⁽²⁾ and χ⁽³⁾ optical nonlinearity based devices [16–25]. RF modulation based devices can suffer from lower isolation strength or narrow bandwidth and also require externally driven modulators, whereas the χ⁽²⁾ based devices require a pump laser and strong second order nonlinearity (not generally available in a CMOS compatible material), thus requiring complex integration processes with unconventional materials. On the other hand, isolators based on χ⁽³⁾ effects are interesting as they relax the fabrication and material requirement. However, the χ⁽³⁾ based isolators demonstrated so far, for example nonlinear resonators, tend to have narrow bandwidth [23–25], and may not be applicable for applications requiring ultrashort high power optical pulses.

In this work, we demonstrate a Kerr type Mach-Zehnder interferometer (MZI) isolator that overcomes most of these challenges and allow ease in fabrication, broadband operation, high power handling, low insertion loss, high isolation, polarization, wavelength, material and platform independence, and small footprint. This is possible because the device is based on nonlinear phase difference (differential phase shift) acquired between the two arms of the interferometer (explained later). Therefore, an isolator based on a nonlinear MZI can be versatile and can be made of any type of waveguide and material platform. Such an interferometer-based isolator can be used not only for integrated photonics, but such a method of isolation can equally be applied to fibre based optical systems where high power pulses are regularly used and high isolation with low insertion loss is critical. The device bandwidth is only limited by the power splitter bandwidth which can be extremely broadband >100 nm [26–28]. In this proof of principle study, we show up to 15 dB isolation and 0.4 dB of insertion loss at 1.55 µm with a single stage isolator, which can potentially be improved further with a multistage system where multiple nonlinear MZI isolators are concatenated together.

2. Device design

The device is based on optical nonlinear interference in an MZI. In this device, the input signal is split into two arms through a non-3 dB directional coupler (any other type of coupler can also be used). The unequal split of power from the coupler ensures one arm has higher power than the other, thus as the input power increases the Kerr induced nonlinear phase shift difference (differential phase shift) between the two arms increases. The transmission of the signal through the MZI is dependent on the differential phase shift which is a function of the input signal power (as shown in Fig. 1). When the differential phase shift reaches one π the transmission at the output through the interferometer (Through port) is at its maximum. However, when the signal is back reflected and goes back through the MZI, the transmission back to the input port is significantly weakend. That is due to the weak differential phase shift caused by the low power back reflected signal, and thus most of the power is transmitted to the other channel (drop port at the input side) and not the input through port thus achieving a high level of isolation (see Fig. 1).

 

Fig. 1. Isolator concept. a) MZI with input (In), through (Th) and drop port (Dr). Heaters are on top of the MZI arms. Optical images of the experimental setup and the two identical directional couplers at the input (DC_i) and the output (DC_o) are shown in the inset. b) The input power dependent transmission, in the forward direction, of the through and drop port, setup (a1). 0 to 1 corresponds to 0 to 100% in the vertical axis. Here, the split ratio of the identical directional couplers are 60:40 (60% to the upper arm). c) Isolation of the back reflected (Br) signal at the input port and signal strength at the drop port of the input, setup (a2). Here we see the isolation strength is reaching up to ∼15 dB for low power signal, and slowly reducing down with higher power (for example, 5 dB isolation for 1 kW back reflected signal power).

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To understand the response of the device clearly, it is instructive to find out the analytical expression for transmission at the through and drop port in the absence of waveguide dispersion. The transmission of the through and drop port can be derived to be, $Th = {e^{ - \alpha L}} - Dr$, and $Dr = {e^{ - \alpha L}}2t({1 - t} )[{1 + \cos (\Omega )} ]$, respectively (see supplementary for details). Here, α and L are the propagation loss and the length of the arms, t is the signal power split factor of the directional coupler (to the upper arm), and $\Omega $ = ΔФ_n + ΔΘ. The power dependent differential phase shift is given as, ΔФ_n= $\gamma L({2t - 1} )P$, where P is the signal power in the waveguide, and $\gamma \; $ is the nonlinear coefficient. The phase ΔΘ is the linear phase offset which accounts for fabrication tolerance or any other externally applied phase shift such as thermally induced by an integrated heater. The relations above for the through and drop port show that the signal transmission varies cosinusoidally with $\Omega $. The maximum (minimum) for the through (drop) port happens when $\Omega $ is an odd integer of π and the maximum (minimum) for the drop (through) port happens when $\Omega $ is an even integer of π (including zero). As mentioned above, the back reflected signal, which is in a practical scenario and in the worst case <10% of the power of the input signal, causes only a weak differential phase shift (almost zero) as the power is low, thus most of the back reflected signal is blocked from going into the input port and therefore allowing a high level of isolation (for ΔΘ =0). To extract the full response of the device in the presence of waveguide dispersion and a short pulse, we solve the nonlinear Schrödinger equation (NLSE) for the pulse propagation through the MZI [29–31]. The transmission and isolation responses are shown in Fig. 1(b) & (c). When the pulse enters the MZI the electric field of the signal in the arm having high power is ${E_h} = \sqrt{t} E$, (in this case the upper arm of the MZI), and in the low power arm it is ${E_l} = j \sqrt{1 - t} E$, where E is the input electric field. At the output, the field at the through port is given as, ${E_t} = \sqrt{t} {E_h} + j \sqrt{1 - t} {E_l}$, and at the drop port it is, ${E_d} = j \sqrt{1 - t} {E_h} + \sqrt{t} {E_l}$ [30].

We designed a normal dispersion waveguide with 800 nm height and 600 nm width having a group velocity dispersion of 1.15 ps²/m (with both arms having equal waveguide cross-section and 8.7 mm of length). The device was designed to be of normal dispersion because, a) normally a thick film is required for anomalous dispersion which might not be readily available, b) it imposes a linear chirp across the pulse making it longer in time which can be externally compressed so that a shorter pulse than the one at the input can be generated, and additionally a back reflected linearly chirped pulse will experience stronger isolation for a significantly higher power compared to a compressed pulse (from anomalous dispersion) owing to the low peak power of a chirped pulse (thus lower differential phase shift, see supplementary), and c), in normal dispersion, break-up of a pulse due to soliton fission, that can happen in an anomalous dispersion waveguide at high power, can be avoided [29,31]. The designed split ratio of the directional coupler was 60:40, i.e. 60% of the signal power couples to the upper arm. In the simulation we used a pulse repetition rate and width of 216 MHz and 150 fs, respectively. The simulated signal power versus transmission through the two output ports is shown in Fig. 1(b). As expected, with the increase in the pulse power the through port transmission increases until a π differential phase shift ($\Omega $) is reached which is in this case reached at 3 kW of signal power (for ΔΘ =0). At the maximum transmission the loss is ∼ 0.4 dB which is mainly due to the waveguide propagation loss and the pulse shaping effect of a nonlinear interferometer [30,32–34], which causes some power to be rejected in the drop port. The isolation strength for the back reflected signal can reach up to ∼15 dB for a transform limited input pulse, as shown in Fig. 1(c)., which gradually reduces as the power of the back reflected signal increases, for example 5 dB isolation for 1 kW of back reflected signal power, and eventually reaching down to 0 dB for the back reflected signal power of ∼3 kW (not shown).

3. Results

The device was fabricated in a silicon foundry (Ligentec) on a silicon nitride (SiN) platform and was fully cladded in silica. We launched light into the waveguide from a femtosecond laser (Onefive) through an aspheric lens (3-5 dB coupling loss) which was collected at the output using a lensed fibre with a 3 µm spot size (1-1.5 dB coupling loss). An image of the setup is shown in the inset of Fig. 1. The waveguide loss was measured with an identical waveguide on the same chip to be ∼ 0.2 dB/cm loss. Due to fabrication tolerances the two arms of the MZI may not be identical and have fabrication induced minute dimensional change which can cause an undesired phase difference between the two arms (as is the case with our device). In order to compensate for that, we employ integrated heaters (on both arms) that can induce a thermal phase shift to compensate for fabrication tolerance based random phase shifts. Heaters are implemented on both arms to have the freedom to move the peak of the transmission curve (through port) to higher or lower power depending on which arm is heated. The heaters were 1.5 µm wide and 1.7 µm above the waveguide. The signal power transmission of the through and drop port of the device is shown in Fig. 2. Since our device suffers from fabrication tolerances causing the transmission peak (through port) to be shifted to lower power, the upper arm (having higher optical power) was heated with 11 mA of current (from a DC source) so that the through port (drop port) transmissions is at the lowest (highest) for the low power signal (just like a device without fabrication uncertainty, Fig. 1(b)). The current was kept fixed at 11 mA to measure the optical transmission as a function of signal power, as shown in Fig. 2(a). In Fig. 2(b), the transmission as a function of signal power, when no heating was applied on the device, is shown. Since we had a limited amount of power extractable from the source and experienced a high input coupling loss (3-5 dB), we were not able to measure a full transmission curve as in the simulation (Fig. 1(b)) for the heated device (Fig. 2(a)) due to limited on-chip power. Nevertheless, a trend in transmission response similar to the simulation could be seen in the experiment if the two plots (Fig. 2(a) and Fig. 2(b)) were to be placed next to each other and seen as a whole, as is done in Fig. 2. Then one could observe that the transmission, for example, of the through port is gradually increasing from the minimum (in Fig. 2(a)) and reaching a maximum (in Fig. 2(b)) for high power, which is just like in the simulation (Fig. 1(b)). There is a slight discrepancy, however, in the position of the peak (which is shifted to lower power) due to the fabrication tolerance [30]. We have also included a top horizontal axis in Fig. 2 to facilitate the comparison between the simulation and the experiment with respect to the peak power.

 

Fig. 2. The measured transmission response vs coupled peak power of the signal in the forward direction (0 to 1 corresponds to 0 to 100% in the vertical axis). a) and b) The through and drop port transmission for the heated (with 11 mA) and unheated as fabricated device. The top horizontal axis is to help compare the simulation in Fig. 1b to the experiment presented here.

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To measure the isolation response of the device, we coupled light into the device from the backward direction, the transmission response for which is shown in Fig. 3. We achieve up to 15 dB isolation for power levels up to 300 W, which is roughly 10% of the signal power of maximum transmission. As mentioned earlier, the power up to which such an isolation is maintained will be even higher if the back reflected pulse remains linearly chirped since a linearly chirped pulse accumulates lower differential phase shift (due to low peak power) compared to an unchirped input pulse used in the experiment (see supplementary). The transmission from the forward direction is also plotted (Fig. 3(b)) which shows high transmission. The slight discrepancy between simulation and experiment is due to the fabrication uncertainties, such as in the coupling ratio of the directional couplers near the input and output port of the device and waveguide widths of the two arms. Next, we measured the spectrum of the pulse at the output of the device from both the through and drop port. The spectrum was measured for a coupled input peak power of > 1000 W which is near the peak of the transmission curve (through port) of the device on the rising slope when no heating is applied (see Fig. 2(b)). Both the through and drop port show a self-phase-modulation (SPM) induced spectral broadening that matches to simulations (Fig. 4(b)). The spectrum of the through port signal is twice as wide as that of the input signal which can be compressed with an on or off chip negative dispersion component to produce a pulse twice as short as the input pulse [35–40]. The simulated normalized temporal response at the output is shown in Fig. 4(b) (inset). Here, we see the through port signal is broadened in time due to the linear chirp from SPM and normal dispersion of the waveguide, whereas the drop port has a dip in the middle of the pulse. The dip happens, because the peak of the pulse in the drop port has relatively lower transmission than the wings of the pulse, that is because as the power increases the transmission reduces in the drop port (see Fig. 1(b)), so the edges of the pulse (having lower power) experience higher transmission through the drop port than the center of the pulse [30]. The reference signal was taken by launching a low power signal directly into a single mode fibre (Thorlab SMF 28) connected to an optical spectrum analyzer in order to avoid any nonlinear effect.

 

Fig. 3. Isolation data. a) Signal injection from the backward direction with isolation at the input port (red) and transmission at the drop port at the input side (blue), with the heated device (11 mA). b) Signal transmission from the forward direction to the through port showing insertion loss ∼ 0.4 dB for an unheated device (excluding the free-space to chip coupling loss). The top horizontal axis is to help compare the simulation of Fig. 1 b and c, to the experiment presented here.

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Fig. 4. Pulse spectrum of the signal at the output launched in the forward direction at a power level near the peak of transmission (>1 kW) with no heating of the device. a) Optical spectrum at the through and drop port along with the reference (Ref). b) Simulation of the pulse spectrum at the through and drop port (normalized time domain signal is shown in the inset).

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4. Discussion and conclusion

The device shown in this work is material and platform independent, versatile, and easy to fabricate. We showed up to 15 dB isolation with a single stage nonlinear MZI for up to 10% of the back reflected signal, while incurring only 0.4 dB of insertion loss (not including the free-space to chip coupling loss). This can potentially be improved with multi stage nonlinear MZIs (with managed pulse chirp), for example with 3 stages up to 45 dB isolation can be achieved while incurring only <1.5 dB of insertion loss (the insertion loss can be further reduced to below 0.1 dB (single stage), by using lower loss waveguides [41]). In this proof of principle study most of the parameters were not fully optimized, by optimizing the components such as couplers, thermal phase shifters, and waveguide dispersion - for a specific center wavelength and pulse width, further improvement in the isolation strength can be achieved with a single stage nonlinear MZI isolator. For example, by using a larger splitting ratio, that is close to 3 dB, for example ∼ 53:47, single stage maximum isolation can reach up to 25 dB, however in this case the peak transmission also gets shifted to higher power. With a smaller split ratio (to shift the transmission peak to a lower power) one can still obtain high isolation strength, and that is with the help of an external π phase shift on the low power arm of the MZI, in that case however, the drop port becomes the signal output port. For example, by employing 70:30 couplers that has the peak transmission at 2 kW, isolation strength up to >30 dB can be obtained with the single stage (not shown). This is because an externally applied π phase shift is imposed on the entire low power pulse (for which the nonlinear differential phase shift is already negligible), thus causing a stronger signal amplitude contrast between the two output ports of the interferometer [30], hence higher isolation.

The device shown in this work is versatile because many of its functionalities can be easily modified, for example, the transmission peak can be shifted to higher or lower power by applying external bias (heater). By employing anomalous dispersion waveguides (thick films of SiN) the power required for maximum transmission can be reduced, that is because the pulse gets shorter in time (i.e. higher peak power) in anomalous dispersion and thus the differential phase shift increases (however, that comes at a cost of the possibility of soliton fission based pulse splitting and the power range over which isolation is high is reduced). Moreover, the device is polarization and mode independent as it can easily be designed for TE, TM or both (waveguide with symmetric cross-section), and it can also be very broadband (>100 nm), only limited by the bandwidth of the coupler. In comparison, Kerr-effect based isolators shown so far, for example ring resonator based isolators, have a very limited operation bandwidth (<< 1 nm) [23–25], and therefore they may not be useful for applications where ultrashort high peak power low noise modelocked lasers are used that are sensitive to back reflections. We must note however, for long pulse operation one may need to employ a device with higher Kerr nonlinearity and must take into consideration the interaction between the forward and backward waves [42], moreover, since the device is based on Kerr effect, it does not have a linear output vs input response. An important aspect of an integrated isolator is the footprint, the device shown here has a size of 0.4 mm² (unoptimized) which can easily be reduced down to <0.1 mm² as the size is mainly dominated by the minimum permissible separation between the two arms. Furthermore, the nonlinear MZI based isolation approach demonstrated here is not only limited to integrated photonics, it can equally be applied to fiber based optical systems, where high power lasers are used quite extensively and for low noise operation of mode-locked lasers very high levels of isolation to back reflections is required while experiencing low insertion loss.