The balanced homodyne detector (BHD) is widely used in quantum noise measurement, gravitational wave detection, high-sensitivity interferometric timing measurement, continuous-variable quantum key distribution, and quantum random number generation. Highly sensitive to the amplitude and phase of the incident light, the BHD can reliably extract quantum fluctuations, suppress the classical common-mode noise, and amplify quantum fluctuations to the macro level. However, the performance of the BHD is limited by the bandwidth, signal-to-noise ratio (SNR), and common-mode rejection ratio (CMRR) of the detector. The optimal design of the BHD has always been a research hotspot. The transimpedance circuit based on a direct current (DC) coupled circuit is not suitable for detecting quantum noise. The reason is that as the power of the incident light increases, the unbalanced DC increases rapidly, and the transimpedance amplifier is saturated, which significantly reduces the dynamic range of the BHD. The BHD based on an inductor-capacitor (L-C) coupled circuit generates higher electronic noise at an analyzing frequency in the kHz range. It is not suitable for low-frequency measurements due to the parasitic effect of the inductor and the low impedance of the inductor at an analyzing frequency in the kHz range. In this paper, the noise sources of the BHD are analyzed theoretically, and a resistor-capacitor (R-C) coupled transimpedance circuit is used to improve the performance of the BHD at an analyzing frequency in the kHz range. Furthermore, the transimpedance circuit is optimized to increase the bandwidth to 200 MHz. The CMRR of the BHD is improved by designing a self-subtraction photodetector scheme, a variable optical attenuator, and an adjustable reverse bias voltage. These designs allow the BHD to meet the low-frequency and high-frequency measurements with high SNR and CMRR in quantum noise measurement.

To enable the BHD to measure both low-frequency and high-frequency signals with high sensitivity, this paper adopts the BHD based on an R-C coupled transimpedance circuit. Two photodiodes are connected in series, and the balanced current signal in the two photodiodes is divided into a DC signal and an alternating current (AC) signal by the R-C coupled structure. The AC signal is converted into a voltage signal by a transimpedance amplifier (TIA) and is further used to measure the shot-noise power of the incident light. The DC signal is converted into a voltage signal by a load resistor and is then used to measure the balance between the two incident lights. To reduce the crosstalk between the DC circuit and the AC circuit, an isolation amplifier is added after the load resistor. An adjustable bias voltage (BV) circuit is used to adjust the junction capacitance of the photodiodes and further improve the CMRR. To compensate for the difference in the amplitude of the two photodiodes and thereby improve the CMRR of the BHD, the paper also utilizes a variable optical attenuator based on fiber bending, where variable attenuation is achieved by changing the radius of the bent fiber. The attenuation of the fiber is precisely adjusted to balance the photocurrent. In addition, an equivalent noise model is constructed. The electronic noise from the TIA circuit includes four parts, i.e., the noise introduced by the dark current in the photodiodes, the thermal noise in the feedback resistor, the noise generated by the input current noise in the TIA, and the noise produced by the input voltage noise. On the basis of theoretical analysis, reasonable DC load resistance and feedback capacitance, photodiodes with low dark current and low junction capacitance, and a TIA with low input noise are selected to reduce the electronic noise and improve the SNR of the BHD.

A BHD with an R-C coupled circuit structure is designed (Fig. 1). A test device is built to test the performance of the BHD. The AC output is connected with a spectrometer to measure the bandwidth and the SNR of the BHD. The DC output is connected with an oscilloscope to make sure that the power of the two incident lights is balanced (Fig. 3). When the incident optical power is 8, 4, 2, and 1 mW, respectively, the paper tests the shot-noise spectrum and the electronic noise spectrum of the BHD with different analyzing frequencies. The test results show that the 3-dB bandwidth of the BHD is 1 kHz-200 MHz. The resolution bandwidth (RBW) and the video bandwidth (VBW) of the spectrum analyzer are set to 10 Hz and 1 Hz, respectively, and the number of averaging times is set to 40. In this case, the SNR is 12 dB at the analyzing frequency of 5 kHz under an incident optical power of 8 mW. The SNR is 20 dB at the analyzing frequency of 100 MHz when the RBW is 200 kHz and the VBW is 100 Hz. Moreover, in the analyzing frequency range of 10 kHz-200 MHz, the shot-noise power decreases by about 3 dB when the incident optical power decreases by half, indicating that the AC output of the BHD has favorable linear gain characteristics in the range of 1 mW to 8 mW (Fig. 4). In addition, 5 kHz and 100 MHz sinusoidal signals are loaded into an electro-optical amplitude modulator to modulate the incident light and thereby test the CMRR. The results show that the CMRR is 70 dB at the analyzing frequency of 5 kHz and 66 dB at the analyzing frequency of 100 MHz (Fig. 5).

By analyzing the noise sources of the BHD, adopting the R-C coupled transimpedance circuit, and optimizing the TIA circuit, this paper implements a broadband balanced homodyne detector that works in the bandwidth range from 1 kHz to 200 MHz with low noise and high CMRR. In the case of an incident optical power of 8 mW@1550 nm, the shot-noise power is 12 dB higher than the electronic noise power and the CMRR reaches 70 dB at the analyzing frequency of 5 kHz, and the shot-noise power is 20 dB higher than the electronic noise power and the CMRR reaches 66 dB at the analyzing frequency of 100 MHz. Such a homodyne detector can serve as a high-performance detection tool in various applications, such as low-frequency gravitational wave detection, high-speed continuous-variable quantum key distribution, and high-speed quantum random number generation.