定义：
一种灵敏的光探测方法，即使在信号功率很弱时也能达到量子极限。

外差探测（也称为相干探测）是一种探测方法，最早是从无线电波和微波领域发展起来的。其中，很弱的输入信号与一些非线性装置中的强的“本地振荡”的波混合在一起，混合光在被滤除掉原始信号和局域振荡频率后被探测到。混合光的频率为信号频率与本地振荡频率的和或者差值。 

图1：光外差探测示意图
光外差探测涉及到信号光和本地振荡波，混合之后的光为电子信号。它们不是利用非线性晶体混合，而是直接采用平方律光电探测器，通常为光二极管，来探测叠加的波。例如，采用图1所示的合束器（或者分束器），调整两束光使它们满足模式匹配。这代表它们的波前在到达探测器时具有相同的曲率，而且在整个探测区域的干涉条件是一致的。当然，这只有在两光束是空间相干的情况下能够满足。采用光纤的系统时，光纤耦合器会取代分束器，所有的光纤都是单模光纤，可能甚至是保偏光纤。 
光电流正比于总的光强，也就是正比于总电场振幅的平方。如果信号和本地振荡的功率和频率都是常数，光电流包含两个不同的频率分量： 

• 常数部分（频率为0）正比于本地振荡和信号功率的和。 
• 以频率差振荡（拍音）的部分的振幅正比于信号光电场振幅与本地振荡光电场振幅的乘积。 

可以隔离振荡部分并采用电子学方法进行处理。其电场功率正比于信号光电场振幅与本地振荡光电场振幅的乘积。 
如果本地振荡很强，弱输入信号产生的外差信号比直接探测强很多。从这个角度，外差探测相当于提供信号增益，尽管并不涉及任何光学放大过程。 

目录

• 噪声限制
• 外差探测空间单模特性
• 平衡探测
• 时间相干问题
• 零差探测
• 利用脉冲光束进行外差探测
• 外差探测的应用

噪声限制 
探测信号时存在不同的噪声： 

• 散粒噪声，其功率谱密度正比于平均光功率。 
• 光探测器存在附加噪声，例如由于暗电流存在产生的噪声。 
• 电子学设备也会存在附加噪声。 

有些情况下，本地振荡功率足够强，以至于散粒噪声的功率谱密度比任何其它噪声都大。这时信噪比主要受限于散粒噪声。可以由光电流的均方值的比值来计算： 

其中Ps和Plo分别是信号功率和本地振荡功率，ηq是光二极管的量子效率，ηm是两光束的交叠因子，B是探测带宽。这一结果等价于平均时间为1/B时产生的光电子数。 
进一步提高本地振荡功率不会提高信噪比，因为信号光功率和散粒噪声功率谱密度也会相应的提高。 
另外，合束器的透射率需要很高，从而保证几乎所有信号光都能进入探测器。本地振荡在探测器中很大的损耗可通过提高进入分束器中的本地振荡的功率来进行补偿。 
如果合束器的透射率很高，并且光束交叠很好（ηm ≈ 1），得到的信噪比是直接探测的两倍。实际上，外差探测在灵敏度上具有很大的优势，因为直接探测只有当信号功率非常高时才能达到散粒噪声极限，而外差探测在很低信号功率时就能达到量子极限。因此，外差探测尤其适用于微弱信号探测。当然还存在一种情形，探测器饱和条件限制了本地振荡功率，从而无法实现量子极限。 
一个重要的细节需要指出，当信号光频率不为0而是有限频率时，探测器噪声（例如1/f噪声）会比0频率附近的噪声弱很多。 
采用压缩振幅的本地振荡光束，采用外差探测甚至可以达到量子极限以下。 

外差探测空间单模特性 
只有当交叠因子ηm很大时才能检测到强外差信号。如果本地振荡光束是完美的高斯光束，可以将总的入射信号光看做很多模式的叠加，模式系统由本地振荡光束确定。只有处于最低阶模式的信号光对外差信号有贡献，因为所有的高阶模式的交叠因子都为0.对于任一高阶模式，光二极管处仍会发生干涉，但是在整个探测区域对功率进行积分导致本地振荡光强抵消，这里假设探测效率在整个光束区域都是一致的。 
外差探测的单模特性是很重要的一个性质。例如，在敏感测量时可以抑制杂散光的影响。但是，它也会降低探测效率，例如当需要探测散射到很大面积区域的光时。 
理论上，采用的本地振荡光束应包含不同的空间模式，并且每个模式的频率是不同的。这样可以同时独立的测量多个模式的信号。然而，外差信号对应的每一个信号的功率都正比于其对应模式的本地振荡功率，噪声水平由总的本地振荡功率决定。这也表明外差探测主要是单模探测技术。 

平衡探测 

图2：平衡外差探测示意图。
图1所示的简易外差探测装置还存在一个问题就是本地振荡波中的附加噪声会直接影响到信号光。采用图2的平衡探测装置则可以避免。这时分束器的反射率为50%。采用一个简单的电子回路，可以得到两光电流的差值。这一差值在一阶近似下不会被本地振荡波中的噪声影响。 

时间相干问题 
如果本地振荡波与信号光是完全独立的，很难测量入射信号的相位，因为电子信号的相位也是独立于本地振荡的相位，本地振荡相位只在很短的相干时间内是稳定的。 
如果需要测量相位，这时本地振荡波和信号通常由同一个光源产生，因此二者的相对相位是比较稳定的，虽然光源的相位噪声可能不是很低。例如，可以采用声光调制器使本地振荡波频移得到信号光。这时外差探测可以很灵敏的测得信号光的任意相位变化。 
对电子信号进行带通滤波，可以对信号的一部分很窄光谱进行采样。探测带宽可以远低于光带通滤波器。例如，这在精密激光光谱学中很有用处。 

零差探测 
很多外差探测都是零差探测，其中本地振荡波频率等于信号频率。在零差测量中，两波由同一激光光源产生。由于外差信号的功率与信号和本地振荡的相位差有关，因此零差技术也是与相位有关的。 
一种改进的方法是平衡零差探测，其中两个光二极管在分束器后面，分束器的反射率为50%，于是可以测量光电流的和与差。如果切断信号端口，光电流差值处于本地振荡光束的散粒噪声水平，尽管该光束的实际噪声是不同的。实际噪声可以通过光电流的总和得到。光电流总和的噪声与直接采用一个光二极管探测本地振荡光束是相同的。零差探测可以提供信号差分，因此可以很方便的比较时间噪声与散粒噪声极限。如果采用压缩振幅的光，光电流总和的噪声要低于差值。在许多压缩光实验中，可以采用零差探测测量压缩度。 
无输入信号的情况可以测量真空噪声。尽管没有光子进入输入端口，电场仍然存在真空涨落。测量的本地振荡散粒噪声是由真空噪声产生的，而不是由本地振荡光束。可以解释上述理论的一个试试就是当信号光为压缩振幅光时可以降低噪声水平。这与之前普遍认为散粒噪声是探测过程的一个内禀性质，而不是光场的特性的观点是冲突的。 

利用脉冲光束进行外差探测 
外差探测也适用于脉冲信号，采用本地振荡光脉冲。也可以采用超短脉冲。因为外差探测器只有当本地振荡光存在才能非常灵敏（假设信号功率远小于本地振荡功率），即使不采用响应快的探测器仍可以得到很高的时间分辨率。这一技术称为外差（或零差）线性光学采样。 

外差探测的应用 
下面是外差探测的一些应用： 

• 应用于相干多普勒LIDAR测量（及相关激光雷达技术），其中需要探测反射到大气中的很微弱的光。也可以准确测量多普勒偏移得到风速。如果信号光和本地振荡光束来自同一激光光源，那么可以分辨非常小的多普勒偏移。 
• 光谱学应用。例如太阳辐射线测量和腔衰荡光谱学。 
• 采用自外差技术可以测量激光器的线宽，其中经过频移的激光光束与自身经过时间延迟后的光叠加后进入光探测器。 
• 光纤通信中，外差和零差探测的相位灵敏度可以用于解调相位编码的信号，采用频移键控技术（FSK）（参阅相干通信）。它也是某些电子色散补偿技术的基础。

Definition: a sensitive method of photodetection, reaching the standard quantum limit even for weak signal powers

Alternative term: coherent detection

Heterodyne detection (also called coherent detection) is a detection method which was originally developed in the field of radio waves and microwaves. There, a weak input signal is mixed with some strong “local oscillator” wave in some nonlinear device such as a rectifier, and the resulting mixing product is then detected, often after filtering out the original signal and the local oscillator frequency. The frequency of the mixing product is the sum or the difference of the frequencies of the signal and the local oscillator.

Figure 1: Setup for optical heterodyne detection.

Optical heterodyne detection involves optical signal and local oscillator waves, whereas the mixing product is an electrical signal. The mixing product is not obtained by mixing the signal and local oscillator wave in a nonlinear crystal, but rather simply by detecting the linearly superimposed waves with a square-law photodetector, typically a photodiode. For example, one uses a beam combiner (or beam splitter) as in Figure 1 and aligns the two beams such that they are mode-matched. This means not only that their intensity profiles overlap, but also that their wavefronts have the same curvature on the detector, so that the interference conditions are uniform over the full detector area. Of course, this is possible only if the two beams are spatially coherent. In a fiber-optic setup, a fiber coupler would be used instead of the beam splitter, and all fibers would be single-mode fibers, possibly of polarization-maintaining type; the mode matching is then guaranteed without a special alignment.

The resulting photocurrent is proportional to the total optical intensity, thus to the square of the total electric field amplitude. If the signal and local oscillator powers and frequencies are constant, the photocurrent has two different frequency components:

• The constant (zero-frequency) part is proportional to the sum of local oscillator and signal power.
• The part oscillating with the difference frequency (the beat note) has an amplitude proportional to the product of the electric field amplitudes (not the optical powers) of signal and local oscillator.

The oscillating part can then be isolated and processed further with electronic means. Its electric power is proportional to the product of the optical powers of signal and local oscillator.

With a strong local oscillator, the heterodyne signal resulting from a weak input signal can be much more powerful than for direct detection. In that sense, heterodyne detection provides a signal gain, although there is no optical amplification involved.

Noise Limitations

The noise in the detected signal has different contributions:

• There is shot noise, the power spectral density (PSD) of which is proportional to the optical average power.
• The photodetector may add some noise, for example due to some dark current.
• Additional noise can be added by the electronics.

In many cases, the local oscillator power is made so high that the corresponding shot noise PSD exceeds that of any other noise. The possible signal-to-noise ratio is then fundamentally limited by shot noise. It can be calculated from the ratio of mean squared photocurrent contributions:

where P_s and P_lo are the optical signal power and local oscillator, respectively, at the photodiode, η_q is the photodiode's quantum efficiency, η_m is the overlap factor for the two beams (basically the square of an amplitude overlap integral), and B is the detection bandwidth. This result equals the number of photoelectrons generated on average within a time 1 / B.

Further increases of local oscillator power would not increase the signal-to-noise ratio, as the signal power and the shot noise PSD are equally increased.

It is also apparent that the beam combiner (see Figure 1) should have a high transmittance, so that most of the signal power is sent to the detector. The resulting high loss of local oscillator power at the detector can be compensated by increasing the local oscillator power incident on the beam combiner.

If the beam combiner's transmission is high and the beam overlap is good (η_m ≈ 1), the obtained signal-to-noise ratio is twice that for direct detection. In practice, heterodyne detection can offer a much greater advantage in terms of sensitivity, because direct detection reaches the shot noise limit only for rather high signal powers, whereas with heterodyne detection the standard quantum limit can be reached for much lower signal powers. Therefore, heterodyne detection is particularly suitable for very weak signals. Note, however, that there are cases where the standard quantum limit can not be reached because detector saturation limits the local oscillator power [14].

An important detail is that the measured signal is not at zero frequency, but rather at some finite difference frequency, where the detector noise (e.g., 1 / f noise) can be much weaker than around zero frequency.

Using an amplitude-squeezed local oscillator beam, it is even possible to beat the standard quantum limit with heterodyne detection [15].

Spatial Single-mode Nature of Heterodyne Detection

A strong heterodyne signal is obtained only if the beam overlap factor η_m is high. If the local oscillator beam is a perfect Gaussian beam, one may consider the total incident input signal light as a superposition of modes, using the mode system which is defined by the local oscillator beam. We see then that only the signal light in the lowest-order mode (the Gaussian) contributes to the heterodyne signal, because the overlap factors are zero for all higher-order modes. For any such higher-order mode, interference still occurs on the photodiode, but the local oscillations of intensity cancel out by integrating the power over the full detector area, provided that the detection efficiency is uniform over the full beam area.

The single-mode nature of heterodyne detection is a crucial aspect. It can be very helpful, for example by suppressing influences of stray light in sensitive measurements. On the other hand, it would greatly reduce the detection efficiency, for example when light scattered on a large area needs to be detected.

In principle, one could use a local oscillator beam consisting of different spatial modes, ideally each one being associated with a separate optical frequency. That would allow to simultaneously and independently measure signals in multiple modes. However, the power of each signal component in the heterodyne signal would then be proportional to the local oscillator power in the corresponding mode, whereas the noise level would be determined by the total local oscillator power. This shows again that heterodyne detection is essentially a single-mode detection technique.

Balanced Detection

Figure 2: Setup for balanced optical heterodyne detection.

A remaining problem of heterodyne detection in the simple form as shown in Figure 1 is that excess noise of the local oscillator wave directly affects the signal. This is avoided with a balanced heterodyne setup [5, 10] as shown in Figure 2. Here, the beam splitter must have a reflectivity of precisely 50%. With a simple electronic circuit, one can obtain the difference of the two photocurrents. That difference is to first order not influenced by noise of the local oscillator.

Temporal Coherence Issues

If the laser delivering the local oscillator beam is totally independent of the signal, it is hardly possible to measure the phase of the input signal, because the phase of the electronic signal is also dependent on the local oscillator phase, which is stable only over the typically short coherence time.

If phase measurements are required, the local oscillator and signal waves are usually generated from a single source, so that the relative phase of the two beams is fairly stable even if the source does not exhibit particularly low phase noise. For example, a signal wave may be generated from a local oscillator wave by frequency-shifting part of it with an acousto-optic modulator. A heterodyne measurement can then very sensitively reveal any phase changes to that signal.

By bandpass-filtering the electronic signal, it is also possible to sample a very narrow spectral portion of the signal. That detection bandwidth can easily be far below what is possible with optical bandpass filters. This can be useful for precision laser spectroscopy, for example.

Homodyne Detection

A variant of heterodyne detection is homodyne detection, where the local oscillator frequency equals the signal frequency. For optical homodyne measurements, both waves are virtually always derived from the same laser source. The homodyne technique is phase-sensitive in the sense that the power of the heterodyne signal depends on the relative phase of signal and local oscillator, and may even totally vanish.

A useful modification is balanced homodyne detection, where two photodiodes (Figure 2) are used after a beam splitter with precisely 50% reflectivity, and the sum and difference of photocurrents are electronically obtained. If the signal port is blocked, the difference of photocurrents exhibits the shot noise level of the local oscillator beam, even if the actual noise level of that beam is different. The latter noise level can be obtained in addition by taking the sum of the photocurrents. That sum exhibits the same noise as for direct detection of the local oscillator beam with a single photodiode. The homodyne setup provides the difference signal in addition, which allows one to conveniently compare the actual noise with the shot noise limit. For amplitude-squeezed light, the sum of the photocurrents exhibits a lower noise than the difference. In many squeezed-light experiments, the degree of squeezing is measured with the homodyne technique.

A possible interpretation of the situation without signal input is that the setup then measures vacuum noise. This is because although no photons can enter the signal input port, there are still vacuum fluctuations of the electric field. The measured local oscillator shot noise is interpreted as being caused not by the local oscillator beam, but rather by the vacuum noise [9]. This interpretation is supported by the fact that amplitude-squeezed light at the signal input can reduce that noise level. These findings are in conflict with the earlier (and still widespread) idea that shot noise is intrinsic to the detection process rather than a property of the light field.

Heterodyne Measurements with Pulsed Beams

The heterodyne technique can also be applied to pulsed signals by using a pulsed local oscillator beam. It is even possible to use ultrashort pulses. As the heterodyne detector is essentially sensitive only while the local oscillator light is there (assuming a signal power well below the local oscillator power), it is possible to obtain a very high temporal resolution without requiring a very fast photodetector. This technique is called heterodyne (or homodyne) linear optical sampling [18, 19].

Applications of Heterodyne Detection

Some examples for the application of optical heterodyne detection are:

• Heterodyne detection is used for coherent Doppler LIDAR measurements (and related laser radar techniques), where very weak light scattered in the atmosphere needs to be detected. It is possible, for example, to accurately measure wind speeds based on the Doppler shift. By deriving the signal and local oscillator beams from the same laser source (see above), it is possible to resolve very small Doppler shifts.
• There are other applications in laser spectroscopy. Examples are solar radiometry [6] and cavity ring-down spectroscopy [17].
• The linewidth of a laser, for example, can be measured with the self-heterodyne technique, where a frequency-shifted copy of the laser beam is superimposed with a temporally delayed copy on a photodetector.
• In optical fiber communications, the phase sensitivity of heterodyne and homodyne detection allows one to demodulate phase-encoded signals [11, 13], based on techniques like frequency shift keying (FSK) (→ coherent communications). Also, it the basis for some forms of electronic dispersion compensation.
• Radio and microwave over fiber sometimes uses heterodyne detection.

Bibliography