Modulation-free laser stabilization technique using integrated cavity-coupled Mach-Zehnder interferometer

Stable lasers play a significant role in precision optical systems where an electro-optic laser frequency stabilization system, such as the Pound-Drever-Hall technique, measures laser frequency and actively stabilizes it by comparing it to a frequency reference. Despite their excellent performance, there has been a trade-off between complexity, scalability, and noise measurement sensitivity. Here, we propose and experimentally demonstrate a modulation-free laser stabilization method using an integrated cavity-coupled Mach-Zehnder interferometer as a frequency noise discriminator. The proposed architecture maintains the sensitivity of the Pound-Drever-Hall architecture without the need for any modulation. This significantly simplifies the architecture and makes miniaturization into an integrated photonic platform easier. The implemented chip suppresses the frequency noise of a semiconductor laser by 4 orders-of-magnitude using an on-chip silicon microresonator with a quality factor of 2.5 × 106. The implemented passive photonic chip occupies an area of 0.456 mm2 and is integrated on AIM Photonics 100 nm silicon-on-insulator process.


I. Introduction
Precise laser frequency control is a crucial requirement in various applications, including optical communication [1,2], optical atomic clocks [3], microwave photonic [4], and sensing [5] which makes stable and narrow linewidth lasers indispensable part of precision optical experiments.Researchers have explored various methods to suppress unwanted laser frequency noise using optical feedback [6,7], electro-optic feedback [8,9], and electro-optic feed-forward [10] techniques.The Optical feedback method relies on the Rayleigh scattering [11] within the cavity and can be an effective and promising way to suppress the laser frequency noise.This mandates the co-design of laser system and optical signals with an ultra-high quality factor (Q-factor) cavity.Electro-optic techniques, on the other hand, leverage state-of-the-art and mature electronic devices and systems to control the laser frequency precisely.This will push some of the challenges from optical domain into the electrical one where control and manipulation of the signals and systems are comparatively more manageable and cost-effective.
A key building block in electro-optic laser stabilization techniques is an optical frequency noise discriminator.An OFND measures frequency fluctuations by comparing to a frequency reference and translates it into an electronic signal that can be processed in the electrical domain.Different OFND configurations have been explored such as "squash" locking technique [12,13], the PDH laser stabilization method [8], and the unbalanced MZI [9,14].The PDH loop stands out as the most well-known precision laser instrumentation technique among the extensively utilized OFNDs [15][16][17][18].Using the PDH technique, a sharp asymmetric error signal can be generated, which can then be utilized as a servo signal to stabilize the laser frequency.Despite excellent performance, the PDH scheme requires electro-optic phase modulator and relatively fast and complex electronics for modulation and demodulation which increases the power consumption and area for an integrated PDH chip [19,20].Alternatively, a passive-only unbalanced MZI can serve as an OFND where the two arms of the MZI are phase locked at the quadrature point [21].Although the unbalanced MZI has a simple architecture to implement on a chip, achieving high-frequency detection sensitivity comparable to the PDH method requires either a large optical delay line or a substantial electronic gain that comes at the cost of chip area of overall system power consumption.
Here, we propose and experimentally demonstrate a modulation-free laser stabilization technique using a cavity-coupled MZI on a silicon photonic chip as an OFND.The proposed frequency noise discrimination technique utilizes a high Q-factor cavity coupled to a MZI which breaks the trade-off between sensitivity, complexity, chip area, and power consumption.
With a careful design of the on-chip high Q-factor cavity coupled to an MZI, 4 orders of magnitude suppression in frequency noise of a commercially available distributed feedback (DFB) laser is achieved.On-chip thermal tuners are implemented for the potential trimming of fabricationinduced errors and also for facilitating the broadband operation of the OFND.The proposed architecture combines the advantages of a passive-only structure, which offers simplicity and less electronic power consumption for error signal processing, with the high sensitivity of the widely utilized PDH technique.The proof-of-concept integrated photonic chip is fabricated in AIM Photonic commercially available 180 nm silicon-on-insulator (SOI) process.The photonic chip occupies an area of 0.456 mm 2 and consumes only about 50 µW power for reverse biasing the balanced photo detector.The proposed architecture offers a promising solution for achieving sensitive, simple, and low power laser frequency stabilization systems and sets the stage for the development of low-cost, scalable, and stable integrated lasers.As mentioned earlier, the key part of this loop is an OFND that senses the frequency fluctuations of the incoming laser signal, compares it with an optical frequency reference (f ref ), and generates an electronic signal whose amplitude is proportional to the intensity of frequency fluctuations.This error signal is amplified in the electrical domain and fed back into the laser to stabilize its frequency.The details of the close-loop operation and the linearized block diagram of the control loop is discussed comprehensively in Supplementary Note 1.The OFND can mathematically be represented by an asymmetric transfer function where the small frequency perturbation around f ref is amplified by a gain (K F D ) and converted into an electronic error signal.The slope of the transfer function also indicates the sensitivity of the OFND in measuring frequency noise.

A. The principle of operation
Figure 1(b) shows the proposed cavity-coupled MZI as an OFND that maintains a simple passive structure without any need for fast optical phase modulation.In this method, the incoming laser intensity is split equally into two MZI branches using a broadband Y-junction.The top branch of the MZI is coupled into an optical frequency reference (e.g. an optical resonator or a cavity).
The amplitude and phase of the electric field at the output of the cavity is affected by that of the frequency reference, T (ω).The bottom arm of the MZI is used to interfere with the frequency reference output electric field using a directional coupler.a balanced photodetector is used to photodetect the output of the MZI and by subtracting the currents, the error signal (i error ) is generated.In other words, the proposed architecture is a coherent detector that uses the input laser signal (bottom arm of the MZI) to down-convert the signal at the output of the cavity.In this way the sharp asymmetric phase transition in the transfer function of the cavity at frequency of f ref will translate in a sharp electrical error signal that can be used to lock the laser in a feedback loop.As discussed in Supplementary Note 2, the error signal can be written as where |T (ω)|, ψ(ω), ϕ, P 0 , and R are the amplitude and phase of the optical reference at the frequency of ω, phase difference between arms of the MZI controlled by a thermal phase shifter, intensity of the electric field at the input of the MZI, and the responsivity of the photodetectors, respectively.Figure 1(c) is the numerical analysis of the normalized error signal of the PDH, a conventional unbalanced MZI, and the proposed cavity-coupled MZI structure using Eq. ( 1).To ensure a fair comparison, assuming a fixed area to implement the OFND, a 1 mm circumference ring resonator is used as the frequency reference in both the PDH and the cavity-coupled MZI.The length mismatch between the arms of the unbalanced MZI is also set to 1 mm .The waveguide loss is assumed 0.2 dB/cm.The details of the numerical comparison is presented in Supplementary Note 3. As shown in Fig. 1(c), the error signal of the cavity-coupled MZI is significantly sharper than the conventional unbalanced MZI for a same given setting, and indeed is comparable to that of the PDH offering the same level of sensitivity but much simpler architecture.In order to achieve a high Q-factor microring cavity, it is necessary to minimize intra-cavity losses including silicon nanophotonic waveguides.The propagation loss is influenced by several factors, with interface scattering and bend radiation loss being the most significant in a state-of-the-art silicon photonic foundry process [23][24][25].The top-bottom surface roughness of a waveguide is well-controlled by the foundry and it is not a design parameter.However, careful design of waveguide width can significantly improve the propagation loss.Figure 3 illustrates the implemented microring resonator in silicon.Utilizing multi-mode waveguides can reduce TE-mode overlap with side-wall roughness and greatly enhances the waveguide transmission [23].Higher order mode excitation < -23 dB Taper Fig. 3. High Q-factor silicon microring resonator.In order to minimize the interface scattering loss due to waveguide edge roughness, a wide multi-mode waveguide is utilized.Moreover, to avoid excitation of higher order modes and Euler bend is used.As shown by the Finite-Difference Time-Domain simulation of the waveguide cross-sections (y-z and x-y planes), the fundamental TE-mode is well preserved inside the cavity.The higher order mode excitation is less than -23 dB.
if a tight bend is used [26], especially for a highly multi-mode waveguide.An Euler bend is employed to achieve a compact multi-mode bend with minimal excitation of higher-order modes and mode cross-talk.The ring resonator is designed to achieve critical coupling to maximize OFND sensitivity, however, the fabricated ring are slightly under-coupled due to the potential fabricationinduced errors.Supplementary Note 4 discusses OFND gain sensitivity to waveguide loss and ring coupling ratio.As illustrated in Fig. 3, the fundamental TE-mode remains preserved within the bent multi-mode waveguide.The implemented microring resonator has a circumference of about 950 µm which corresponds to a free spectral range (FSR) of about 83.5 GHz with a loaded Q-factor of about 2.5 million at the resonance wavelength of 1550.73 nm.multaneously using an oscilloscope .Figure 4(b) shows the response of the ring where the Q-factor is about 2.5 million.The measured extinction ratio is about 4.8 dB that suggests the fabricated microring is slightly under coupled, likely due to fabrication error in the coupling gap. Figure 4(c) shows the measured normalized asymmetric error signal that suggests OFND sensitivity of 1.3×10 −8 Hz −1 which agrees well with analytical models.Since the ring and MZI are optimized for 1550 nm, there was no need to utilize Heaters 1 and 2 during the measurement.

E. The closed-loop operation and laser frequency noise suppression
As mentioned previously, the asymmetric error signal can serve as the servo signal to precisely adjust and lock the laser frequency to the resonance frequency of the cavity.Figure 5 (a) shows the block diagram of the closed-loop measurement setup.As shown in Fig. 5(a), a DFB laser (AeroDiode 1550LD-2-0-0-1) with a free-running integral linewidth of 6.1 MHz is used.The laser output is directed into the chip by utilizing a 90%/10% coupler, which is then followed by a 0.5 mW.The generated error signal is amplified using a low noise TIA with a gain of 5 KΩ and total input-referred current noise of 3.4 pA/ √ Hz which is three orders of magnitude lower than the thermorefractive noise (TRN) of the microring.Part of the laser power is used in a fiberbased delayed self-heterodyne (DSH) interferometer and the output signal is digitized and sent to a computer for processing [27].the suppressed frequency noise is limited to the TRN of the silicon microring resonator [30,31].

III. Discussion
Ideally, a cavity that supports a larger mode volume and is made from a temperature insensitive material can enable a lower TRN limit, resulting in a more stable laser.Ultra-low loss silicon nitride and micro-fabricated mirrors [32] present themselves as promising technology platforms for fulfilling these requirements.However, this improvement comes at the cost of chip area, packaging complexity, and availability of the technology for large-scale and robust integrated photonic chip manufacturing.On the other hand, silicon photonic platforms are evolving rapidly and while silicon may not be the most suitable choice for achieving highly stable micro-cavities, it certainly serves as an excellent alternative in numerous applications where strict level of laser stability may not be required.The combination of robust large-scale silicon photonic manufacturing and the ability to monolithically integrate with mature CMOS electronics provides integrated silicon photonics with a significant advantage over other alternatives.It is important to note that the choice of technology depends on the specific application.Our proposed architecture can be implemented on a suitable technology platform to effectively meet the requirements of an application.
In conclusion, we have experimentally demonstrated the first modulation-free laser frequency noise stabilization using integrated cavity-coupled MZI.IV.Methods

A. Photonic chip implementation
All photonic devices are monolithically integrated on AIM Photonics commercially available 180 nm SOI process.The laser is coupled into the chip vertically using a grating coupler.A Y-junction with excess loss of less than 0.5 dB is utilized at the input of the MZI to split the laser intensity equally.A high Q-factor microring resonator is coupled to the top arm of the MZI.The ring resonator is made with wide multi-mode waveguides and Euler bends to both reduce the interfacial scattering loss and avoid excitation of higher-order modes.Thermal phase shifters are integrated into the photonic chip for potential adjustment of phase or compensation for fabrication-induced errors.The two arms of the MZI are combined using an adiabatic broadband directional coupler.
A balanced photodetector is used to generate the error signal.The responsivity and dark current of the on-chip Germanium photodetector at 2.5 V reverse bias voltage are 1.16 A/W (at 1550 nm) and 40 nA, respectively.The photonic chip occupies area of 0.456 mm 2 .

B. The closed-loop operation in presence of noise sources
Different noise sources contribute to the ultimate frequency noise limit.The two main sources of noise are the TRN of the reference cavity and the total electronic noise that includes input referred noise of electronics and shot noise of balanced photodetector.The closed-loop operation and minimum achievable frequency noise in the presence of these noise sources are discussed in Supplementary Note 1.

C. Delayed self-heterodyne frequency noise measurement
A fiber-based delayed self-heterodyne setup is built for laser frequency noise measurement.The first null of the MZI is at 8.7 MHz, corresponding to a single-mode fiber length of about 23 m.An acousto-optic frequency shifter is used in the second arm of the MZI to up-convert the laser phase noise to 27 MHz which helps to mitigate electronic flicker noise for better measurement sensitivity.
The two arms of the MZI are cross-coupled and fed into two independent low noise TIAs.The outputs of the TIAs are digitized at 250 MS/s and recorded for a duration of 5 msec and sent to a computer for processing.

D. The OFND gain sensitivity analysis
The design of the high Q-factor microring resonator in the OFND directly impacts the frequency noise detection gain and laser frequency noise suppression.Supplementary Note 4 discusses the sensitivity of OFND gain to both the coupling ratio of the ring and the waveguide propagation loss. by According to Supplementary Equation ( 7), the TRN of the cavity can impose a limit on the achievable stability.Therefore, considering the specific requirements of an application, the ultimate achievable frequency noise can be engineered by a careful design and proper selection of the material platform to implement the frequency reference [1]. as The optical signal at the output of the MZI is photodetected using a balanced photodetector.The photocurrents i 1 and i 2 are calculated as where R is the responsivity of the photodetectors.Using Supplementary Equations ( 11) to ( 14), the error signal, i 1 (t) − i 2 (t), can be written as where ℑ(.) denotes the imaginary operator.Combining Supplementary Equations ( 9), (10), and (15), the error signal can be simplified to i error (ω) = RP 0 |T (ω)| × Sin(ψ(ω) − ϕ), where |T (ω)| and ψ(ω) are the amplitude and phase of the optical reference at the frequency of ω.
Please note that ω can be written as where ω 0 and δω n (t) are the nominal frequency and frequency noise of the laser.
Supplementary Figure 2(b) and 2(c) show the numerical simulation of the frequency reference response and the asymmetric error signal, respectively.For numerical analysis purposes, we assume that the frequency reference is a critically coupled ring resonator with an approximately 80 GHz free-spectral range (FSR) (equivalent to a 1 mm circumference) and a Q-factor of around 3.3 million, corresponding to a propagation loss of approximately 0.2 dB/cm.As shown in Supplementary Figure 2(c), the error signal exhibits an asymmetric response around the frequency reference that can be used as a servo signal to lock the laser.

Figure 1 (
Figure 1(a) shows the block diagram of an electro-optic laser frequency noise reduction loop.

Fig. 1 .
Fig. 1.The cavity-coupled MZI frequency discriminator.(a) The block diagram of an electro-optic laser frequency stabilization using an optical frequency noise discriminator (OFND).The OFND response is asymmetric around the frequency reference point,f ref , and hence small frequency fluctuations translate into electrical signal by the OFND gain.(b) The conceptual diagram of the proposed cavity-coupled MZI.T (ω) is the transfer function of a frequency reference (e.g.optical cavity) coupled into the top arm of the MZI.(c) Numerical analysis comparing the normalized error signal for the proposed cavity-coupled MZI, a conventional unbalanced MZI and the PDH architecture.∆f and ∆ν are the laser offset frequency compared to f ref and the free-spectral range of the cavity.

Fig. 2 .
Fig.2.The modulation-free laser stabilization scheme.(a) The proposed cavity-coupled MZI is used as an OFND in a feedback loop for laser frequency noise suppression.A high Q-factor Euler microring resonator is utilized as a frequency reference.Half of the on-chip laser intensity is injected to the microring resonator and coherently interfered with the bottom branch and converted to electrical signal using balanced Germanium photodetectors.A small portion of the ring resonator output is used to monitor its response.The generated error signal, i error , is then amplified, and fed into the PID controller.(b) The micro-photograph of the integrated photonic chip in AIM Photonics 180 nm silicon-on-insulator (SOI) process.The size of the photonic integrated circuit measures 0.95 mm × 0.48 mm.PID: proportional-integral-derivative, TIA: trans-impedance amplifier.

Figure 4 (Fig. 4 .
Figure 4(a) shows the schematic of the measurement setup to characterize the open-loop performance and the error signal.A tunable continues wave laser (TOPTICA CTL 1550) with a wavelength of 1550.7 nm is coupled into the chip via the on-chip grating coupler.To ensure linear operation and thermal stability of the high Q-factor microring resonator, laser power coupled to the grating coupler is set to 0.7 mW using a variable optical attenuator (VOA).The silicon chip temperature is stabilized at 27 o C. The laser frequency is continuously scanned within the range of 30 GHz.A calibrated fiber-based MZI with a FSR of 20 MHz is used for time-frequency translation.As shown in Fig. 4(a), a sniffer photodetector with 5% coupling ratio is utilized to monitor the resonance response.The resonance response of the ring and the error signal are measured si-

Fig. 5 .
Fig. 5.The closed-loop operation.(a) Measurement setup for closed-loop operation and laser locking experiment.The small portion of the laser output power is used in the delayed self-heterodyne (DSH) for frequency noise measurement.Heaters are off during this measurement.(b)The power spectral density of frequency noise of the AeroDiode DFB laser under free-running and closed-loop operation.The highlighted regions indicate frequency band which contribute to the laser linewidth.The frequency noise of the DFB laser is suppressed by 40 dB at low Fourier frequencies and is limited to the silicon microring thermorefractive noise (TRN).VOA: variable optical attenuator, TIA: trans-impedance amplifier, CW: continues wave, GC: grating coupler.

Figure 5 (
b) shows the frequency noise measurement results for the free-running and locked laser.As shown in Fig.5(b), the cavity-coupled MZI OFND can effectively suppress the frequency noise of the free-running DFB laser by 40 dB at low Fourier frequencies.The frequency noise reduction bandwidth is about 300 KHz which is mainly limited by the frequency modulation response of the laser[28] and the modulation bandwidth of the current driver (<1 MHz).The β-separation line indicates highlighted regions that contribute to the laser linewidth[29].As shown by the highlighted regions in Fig.5(b), the integral linewidth of the free-running laser is reduced from 6.1 MHz to 695 KHz under closed-loop condition.It is worth mentioning that The integrated cavity-coupled MZI consists of a high-Q Euler microring resonator with a loaded quality factor of about 2.5 million and extinction ratio of about 4.8 dB which suggests normalized OFND gain of 1.3×10 −8 Hz −1 .The cavity-coupled MZI is used to suppress the frequency noise of a commercially available DFB laser by 40 dB at 1 KHz offset frequency.This corresponds to the integral linewidth reduction of the free-running laser from 6.1 MHz to 695 KHz.The implemented chip occupies 0.456 mm 2 and is integrated on AIM Photonics 180 nm process.