Integrated Pound−Drever−Hall laser stabilization system in silicon

Low noise stable lasers have far-reaching applications in spectroscopy, communication, metrology and basic science. The Pound−Drever−Hall laser stabilization technique is widely used to stabilize different types of lasers in these areas. Here we report the demonstration of an integrated Pound−Drever−Hall system that can stabilize a low-cost laser to realize a compact inexpensive light source, which can ultimately impact many fields of science and engineering. We present an integrated architecture utilizing an electronically reconfigurable Mach−Zehnder interferometer as the frequency reference to reduce the frequency noise of semiconductor lasers by more than 25 dB and the relative Allan deviation by more than 12 times at 200 μs averaging time. Compared to the bench-top implementations, the integrated Pound−Drever−Hall system has significantly lower power consumption, less sensitivity to the environmental fluctuations and occupies an area of only 2.38 mm2. The photonic and electronic devices are integrated on a standard 180 nm complementary metal-oxide semiconductor silicon-on-insulator process.

to the laser, changing the phase and frequency of the laser electric field. The laser output electric field, Elaser, is phase modulated and the modulated signal, Emod, passes through the electronically reconfigurable Mach-Zehnder interferometer (MZI). The MZI output, Eout, is photo-detected. The photo-current, iPD(t), is amplified and converted to a voltage using a trans-impedance amplifier (TIA). The TIA output, VRF, is mixed with the oscillator output (which is also used to phase modulate the laser output electric field) and low-pass filtered. The filter output voltage is converted to the PDH read-out current, iout(t), using a voltage-to-current converter.     Figure 7| The schematics of the on-chip core electronic blocks. (a) The trans-impedance amplifier (TIA) and the high frequency amplifier. The TIA input current, Iin, is amplified and converted to a differential output voltage, Vout. (b) The DC offset compensation loop. The TIA output is amplified, low-pass filtered and injected back to the TIA input to compensate for the DC offset. The feedback loop can be disabled by setting the switch voltage, Vswitch, to zero. (c) Frequency mixer. The differential input radio frequency (RF) voltage, VRF+ -VRF-, is mixed with the differential local oscillator (LO) voltage, VLO+ -VLO-, to generate the differential intermediate frequency (IF) voltage, VIF+ -VIF-. (d) Voltage-to-current converter (VtoI). The VtoI converts its input voltage, Vi, to a current, Iout, which is injected to the laser. (e) Phase modulator driver. The input voltage, Vi, is converted to a current, Iout, driving the phase modulator. The gain and phase responses of the driver can be adjusted. (f) Oscillator channel select circuit. A 3x8 digital decoder is used to select one of the 7 frequency channels of the oscillator, 1 to 7 , using 3 control bits, 0 to 2 . (g) The voltage-controlled ring oscillator. The channel selection for the 3-stage RF ring oscillator is performed by adjusting the switchable capacitors, 1 to 7 , in the oscillator stages and the fine tuning is performed by adjusting the tuning voltage, Vtune. The differential output of the oscillator, Vout+ -Vout-, is buffered and routed to the modulator driver and the mixer.   Figure 1a where the PDH read-out signal is defined as the voltage-to-current converter (VtoI) output current, out ( ). Consider the case that the electric field of the laser output is written as where 0 and ω 0 are the laser power and frequency, respectively. Also, assume the electrical oscillator output voltage can be written as where 0 and are the oscillation amplitude and frequency, respectively. The phase modulator (PM) driver increases the level of the oscillator output to 0 and introduces a phase shift, , between its input and output. In this case, the modulator driver output is written as The modulation index can be defined as where is the current required to generate a radians optical phase shift across the optical phase modulator and in,mod represents the input impedance of the phase modulator. In this case, the electric field at the output of the phase modulator is written as The modulated signal passes through the electronically reconfigurable Mach-Zehnder interferometer (MZI). The MZI output is photo-detected and the photo-current is written as PM,driver ( ) = 0 sin( + ).
where , α, τ and are the photodiode responsivity, the total optical transmission, the delay difference between the two arms of the MZI and the relative phase between the two arms of the MZI, respectively. The photo-current can be simplified to where Using the Jacobi-Anger expansion 1 , the photo-current is written as where 2n−1 (. ) represent the Bessel functions of the first kind. The photo-current is converted to a voltage and amplified using a trans-impedance amplifier (TIA) and mixed with osc ( ). The mixer output is low-pass filtered (to remove higher order terms), amplified and converted to a current using a VtoI. In this case, the output current of the VtoI, the read-out signal, can be written as where OE is calculated as In Supplementary Equation (11), i = out PD = TIA Mixer VtoI represents the total electrical current gain which is defined as the ratio of the VtoI output current to the photo-current. Also, TIA , Mixer and VtoI are the TIA transimpedance gain, the mixer conversion gain and the VtoI trans-conductance gain, respectively. Note that since the onchip delay is much smaller than −1 , in the derivation of Supplementary Equation (11), it is assumed that 2 sin ( 2  ) ≈ .
Supplementary Figure 1b shows the simulated read-out signal and the simulated MZI transfer function. As shown, the read-out signal is asymmetric with respect to the frequency of the notch in the MZI frequency response, notch .
Therefore, the read-out signal indicates both the difference between the laser frequency and notch and whether the laser frequency is greater or less than notch . Thus, by injecting the read-out signal to the laser, the laser frequency can be locked to the frequency of the notch in the MZI.

Supplementary Note 3: Characterization of the integrated electronically reconfigurable Mach-Zehnder interferometer
The measurement setup for the integrated reconfigurable MZI is depicted in Supplementary Figure 4. The output of an Agilent 81642A tunable laser is amplified using an Erbium-doped fibre amplifier (EDFA) and coupled into the reconfigurable MZI test structure using an on-chip grating coupler. The output of the MZI test structure is photodetected, amplified and monitored using a HP 3478A digital voltmeter. By adjusting the current injected to the PIN current-controlled attenuator, the loss mismatch between the two arms of the MZI can be minimized resulting in more than 28 dB extinction ratio as shown in Fig. 3b. Once the loss mismatch between the two arms of the MZI is minimized, the relative phase between the two arms can be adjusted using the heaters placed between the waveguides of the delay line.

Supplementary Note 4: The frequency noise discriminator
Supplementary Figure 5a shows the schematic of the optical fibre based MZI with 8.5 cm length imbalance used as a frequency discriminator in Fig. 6a. A thermoelectric cooler (TEC) is placed under the 8.5 cm delay line to set the relative phase between the two arms of the MZI to 90 o . The MZI output is split into two branches using a 50/50 fusion coupler. The bottom branch is photo-detected, amplified and used to monitor the frequency noise of the laser using an Agilent 8563E spectrum analyser. The top branch is used to adjust the relative phase between the two arms of the fibre based MZI using a control unit. The output of the control unit is monitored on an oscilloscope to ensure accurate relative phase adjustment (Fig. 6a).
Supplementary Figure 5b shows the schematic of the control unit used to set the relative phase between the two arms of the off-chip optical fibre based MZI (the frequency discriminator). Supplementary Figure 5c shows the output PD,ac ( ) = √ ∑ 2n−1 ( ) sin((2 − 1) ) ∞ =1 .
13 voltage of the control unit which corresponds to the relative phase between the two arms of the frequency discriminator. When the phase control loop is closed, the phase difference between the two arms can be set to 90 o .

Supplementary Note 5: The CMOS chip details
The block diagram of the reported PDH chip is shown in Supplementary Figure 6 where all photonic and electronic devices and blocks are monolithically integrated on a CMOS chip except for the photodiode which is hybrid integrated

Supplementary Note 6: Characterization of the CMOS electronic blocks
All electronic blocks have been integrated on the GlobalFoundries GF7RFSOI process, a standard CMOS SOI technology, with no post-processing. The performance of the core electronic blocks (shown in Supplementary Figure   7) is summarized in Table 1. 14 Supplementary Note 7: The noise sources The key noise sources affecting the PDH stabilization performance are the relative intensity noise (RIN) of the laser, the photodiode shot noise and the noise of the electronic devices. The effect of each of these noise sources can be modelled as a current noise referred to the input of the TIA 3 . Since these noise sources are independent, the total noise contribution can be written as the sum of these three current noises.
In presence of laser intensity noise, Supplementary Equation (1) 15 The noise contribution of electronic devices can be modelled as a current noise referred to the output of the photodiode 3 . In this case, the total photo-current including the effect of all aforementioned noise sources is written as where noise,total = PD,shot + 8 RIN + n,electronics , represents the total input referred current noise and n,electronics represents the noise of the electronic devices. Since the total current noise is a small signal, the linearized PDH system in Supplementary Figure 8 can be used for noise analysis. Note that in this figure, the PDH chip gain (i.e. OE in Fig. 5) is written as the product of an optical frequency to current gain, ωi , and the electrical current gain, (diameter of about 32 mm) which is more than 4 times larger than the grating coupler area (in Fig. 2a) resulting in a relatively relaxed alignment tolerance. To hybrid integrate the photodiode with the CMOS chip, the photodiode was placed on top of the CMOS chip and was moved using a DC probe and aligned with the grating coupler using markers.
Once the photodiode was aligned with the grating coupler, a drop of Loctite Instant Mix epoxy was placed at the corner of the CMOS chip flowing and surrounding the photodiode chip. When the epoxy was cured, the photodiode pads were wire-bonded to the input pads of the CMOS chip as shown in Fig. 1c. Note that the photodiode can be backside-illuminated since its substrate is substantially transparent at 1550 nm. This process that we have developed previously 5 is reliable and repeatable. The measured average coupling loss is under 1.8 dB which is lower than the coupling loss between a grating coupler and an optical fibre in the GF7RFSOI process (Fig. 2b).