Optoelectronic mixer

Chapter IV: Optical phased array receiver

4.4 Optoelectronic mixer

Figure 4.3: (a) Array pattern of an 8-by-8 array with𝑑/𝜆=1.3 and(𝜃

0=0, 𝜙

0 =0) (b) Array pattern of the designed OPA receiver for 𝜙 = 0 and (𝜃

0 = 0, 𝜙

0 = 0) (element spacing = 11.2𝜇𝑚). It is assumed that one side of the chip is blocked and light impinging on the aperture comes only from 0≤ 𝜃 ≤ 𝜋/2

of the array pattern and the antenna pattern, the grating lobes can be suppressed by engineering the element pattern,𝐺(𝜃 , 𝜙). Moreover, a physical spatial filter can be used to block the light impinging from the unwanted direction and limit the FOV.

Therefore, the FOV of the system is defined by the grating-lobe-free steering range or the aliasing free range which is the maximum angular range that can be received and reconstructed. In addition to the grating lobes, side lobes [72], which are other minor picks in 𝑃(𝜃 , 𝜙, 𝜃

0, 𝜙

0), can reduce the accuracy of the reconstruction.

The average side lobe level is inversly proportional to the number of elements and decreases as the array scales.

SNR of the signal.

Figure 4.4: (a) Block diagram of the optoelectronic mixer (b) simplified drawing of the integrated optoelectronic mixer.

In this work, to suppress the impact of the optical loss and detection noises an optoelectronic down-conversion mixer is designed as the first stage of the receiver chain. The mixer is input a reference light in addition to the received signal and down-converts the received signal to radio frequencies while preserving the signal information. The output signal is also amplified through the conversion and thus the received optical wavefront can be robustly processed in the electronic domain with stronger signal processing tools.

The designed optoelectronic mixer is shown in Fig. 4.4 which includes a 90-degree hybrid directional coupler[57], [125], a PiN diode phase shifter in the reference path, and two photodiodes forming a balanced photodiode [126], all of them integrated on the chip. The mixer is fed with the received signal and the reference signal at its two optical ports and generates a current at its electrical output port. The PiN phase shifter is a pin-diode and introduces optical phase shift through the carrier injection effect [127]. Passing a current through the PiN diode determines the phase shift provided by the phase shifter which is can be adjusted on a range more than 2𝜋and thus capable of adding an arbitrary phase to the reference signal. Figure 4.5(a) shows the cross section of the designed PiN diode phase shifter in which a p+ and an n+

region form the anode and cathode of the diode, respectively. The silicon waveguide

in between the two doped regions is the the intrinsic region of the PiN diode as well as an optical path for light. As shown in Fig. 4.5 the distance between the doped regions and the optical mode provides a safe margin to prevent optical loss. The phase shifter structure is 500 µm long and for 28 mA of injected current provides a 2𝜋 phase shift. Moreover, there is a 25 µm spacing between the adjacent mixers on the chip that results in a negligible thermal and electrical cross-talk between the phase shifters. The directional coupler is formed using a symmetric structure of closely spaced waveguides. An epitaxially grown germanium layer is used to form the two photodiodes with the size of each photodiode being 16 µm by 4 µm.

Figure 4.5: (a) Structure of the PiN diode phase shifter (b) Optical mode propagating inside the phase shifter (the doped regions do not interfere with the optical mode, avoiding optical insertion loss).

To understand the functionality of the mixer, the signal flow through the structure, Fig. 4.4, can be considered. The phase of the reference light which can be arbitrarily modified is adjusted to𝜙_𝑟 by the PiN phase shifter. The received light by the antenna and the adjusted reference signal, which are

𝐸_𝑖(𝑡) = 𝐴_𝑖cos(2𝜋 𝑓_𝑖𝑡+𝜙_𝑖), (4.9)

𝐸_𝑟(𝑡) = 𝐴_𝑟cos(2𝜋 𝑓_𝑟𝑡+𝜙_𝑟), (4.10) respectively, are then fed into the two input ports of the directional coupler using on-chip waveguides. Therefore, the 90-degree hybrid directional coupler evenly distributes the input optical power of each port between the two output ports and yields the sum of the two input signals. Moreover, the transferred signal to the through port of the directional coupler (for each input port) experiences a 90° phase shift [57]. Therefore, the two output waves of the directional coupler in the form of

a low-frequency envelope and an optical carrier at frequency (𝑓_𝑖+ 𝑓_𝑟)/2 are 𝐸1(𝑡) = 1

√ 2

𝐴²

𝑟+𝐴²

𝑖+2𝐴_𝑟𝐴_𝑖cos(2𝜋(𝑓_𝑖−𝑓_𝑟)𝑡+𝜙_𝑖−𝜙_𝑟−𝜋/2) ¹

2

cos(2𝜋 𝑓_𝑖+ 𝑓_𝑟

2

𝑡+𝜓(𝑡)). (4.11)

𝐸2(𝑡) = 1

√ 2

𝐴²

𝑟+𝐴²

𝑖+2𝐴_𝑟𝐴_𝑖cos(2𝜋(𝑓_𝑖−𝑓_𝑟)𝑡+𝜙_𝑖−𝜙_𝑟+𝜋/2) ¹

2

cos(2𝜋 𝑓_𝑖+ 𝑓_𝑟

2

𝑡+𝜓(𝑡)). (4.12) It can be seen that the two 90° phase shifts lead to 180° out of phase envelopes or beat components at the two output ports. Feeding these signals into the photodiodes generates photo-currents which are proportional to the optical power determined by the envelope of the optical signal squared, divided by two [126], [128]. Therefore, the total output current which is the combination of the two photo-currents is 𝐼_𝑜𝑢𝑡(𝑡) =(𝑅 𝐴_𝑟)𝐴_𝑖sin(2𝜋(𝑓_𝑖− 𝑓_𝑟)𝑡+𝜙_𝑖−𝜙_𝑟)=2𝑅

p

𝑃_𝑟𝑃_𝑖 sin(2𝜋(𝑓_𝑖−𝑓_𝑟)𝑡+𝜙_𝑖−𝜙_𝑟), (4.13) in which 𝑅 is the responsivity of the photodiode and (𝑓_𝑖 − 𝑓_𝑟), beat component frequency. The beat component frequency is adjusted to be a few Megahertz due to the convenient and quality of electronic processing at these frequencies. However, any frequency range that electronic components meet the bandwidth and accuracy requirements of the down-converted signal can be used. As equation (4.13) shows, both amplitude and phase of the received signal are preserved at the output current.

Moreover, the amplitude of the reference signal appears as a gain factor at the output and its phase provides an tuning parameter for adjusting the phase of the output current through the PiN phase shifter. In case of the phased array processing, the reference phase𝜙_𝑟 for the receiving element at (𝑛, 𝑚) can be adjusted toΔ𝜙(𝑛, 𝑚). In a standard 50Ωsystem, the amplitude gain factor corresponds to the power gain of 𝑃𝑒𝑙 𝑒 𝑐𝑡𝑟 𝑖 𝑐𝑎𝑙/𝑃_𝑖 =100𝑅²𝑃_𝑟. Heterodyne detection scheme used in the mixer topology provides an extra conversion gain of 𝑃_𝑟/𝑃_𝑖 compared to the direct detection with power gain of 𝑃𝑒𝑙 𝑒 𝑐𝑡𝑟 𝑖 𝑐𝑎𝑙/𝑃_𝑖 = 100𝑅2𝑃_𝑖. This gain factor can be used to amplify the signal in the optical domain by increasing the magnitude of the reference signal effectively at the first stage of the receiver chain.

In addition to providing a gain factor, the phase shift control of the mixer is embedded in the reference path leaving the received signal path undisturbed. Another advantage of this system is that amplitude control can be achieved by either controlling the reference signal amplitude or electronic amplification of 𝐼_𝑜𝑢𝑡(𝑡). Moreover, the

stray light and interferers that reach the photodiode produce near-DC components at the output that are distinguished from the beat frequency (𝑓_𝑖 − 𝑓_𝑟) and can be easily filtered electronically. Furthermore, the 1/𝑓 noise components of the post- processing electronic blocks can also be filtered without disturbing the spectral content near the beat frequency.

As discussed, the optoelectronic mixer provides the capability of tuning both the amplitude and phase of the output signal by adjusting the phase and amplitude of the reference signal as well as manipulation of the current in the electronic domain.

Due to the short wavelength of the optical signals, phase shift operation in the optical domain is especially desired due to the simpler and more accurate optical phase shifter implementations. On the other hand, amplitude adjustment using a variable gain amplifier in the electronic domain is much more efficient. Moreover, since both amplitude and phase of the received signal are preserved at the output current, further more complicated signal detection processing techniques can be performed in the electrical domain to improve the sensitivity and accuracy of the receiver system.

To improve the SNR of the detected signal, the conversion gain of the optoelectronic mixer, 𝑅 𝐴_𝑟, can be increased by increasing the reference signal level. This leads to a stronger output mixed component while the shot noise associated with the photodiode dark current and the electronic noise sources later in the chain remaining the same. The output current of a single photodiode is

𝐼_{𝑡 𝑜𝑡} = 𝐼_𝑜𝑢𝑡 2

+𝐼_{𝐷 𝑎𝑟 𝑘} + 𝑅 𝑃_{𝑟 𝑒 𝑓} 2

+ 𝑅 𝑃_𝑅𝑥 2

, (4.14)

in which 𝑃_{𝑟 𝑒 𝑓} and 𝑃_𝑅𝑥 are the reference and received signal powers, respectively, and𝐼_{𝐷 𝑎𝑟 𝑘} is the dark current flowing through the photodiode due to its bias voltage.

Therefore, the SNR of the detected signal after passing through the receiver chain is

𝑆 𝑁 𝑅=

𝑃_{𝑠𝑖𝑔𝑛𝑎𝑙} 𝑃_{𝑛𝑜𝑖 𝑠𝑒}

= (2𝑅2𝑃_{𝑟 𝑒 𝑓}𝑃_𝑅𝑥) (4𝑒 𝐼_{𝑡 𝑜𝑡} +𝐼2𝑛,𝑇 𝐼 𝐴)𝐵𝑊

𝑅 𝑃_𝑅𝑥 𝑒 𝐵𝑊

1

1+ ^{2𝐼𝐷 𝑎𝑟 𝑘+𝐼2𝑛,𝑇 𝐼 𝐴/2𝑒}

𝑅 𝑃𝑟 𝑒 𝑓

, (4.15)

where BW the signal bandwidth,𝐼2𝑛,𝑇 𝐼 𝐴the current noise power spectral density of the electronic circuitry referred to the input of the transimpedance amplifier (TIA), and 𝑒 is the charge of an electron. While increasing 𝑃_{𝑟 𝑒 𝑓} improves the SNR, the SNR of the system has an upper limited of

𝑆 𝑁 𝑅 𝑅 𝑃_𝑅𝑥 𝑒 𝐵𝑊

. (4.16)

As the SNR approaches this limit, little improvement is achieved through increasing 𝑃_{𝑟 𝑒 𝑓} and the SNR depends mainly on the received signal power. In this situation, the receiver system operates in the shot noise limited regime and the detected signal is robust against the detrimental noise sources in different receiver blocks.