定义：
测量光的强度或者电场自相关函数的装置，通常可测量超短脉冲的长度。

光学自相干器具有很多用涂，尤其是测量皮秒或飞秒长度的超短脉冲的长度，这种情况下采用电子装置会太慢（例如，光电二极管）。 

自相关器测量脉冲长度的基本原理在后面会有描述。分束器使入射光束变成相同的两束。这两束光进入非线性介质并叠加一起，如果在时间上有重叠会发生非线性相互作用。 

强度自相关器 

图1：自相关器装置图。BS=分束器

如图1所示的强度自相关器中，分束器将入射脉冲分成两个脉冲，然后聚焦进入具有二阶非线性的晶体中。臂长差值以及两束脉冲之间的时间间隔可以采用可变延迟线来调节。（可以采用不同的延迟线，例如，采用旋转玻璃块或者安置在扩音器上的反射镜。）如果臂长差很小，两脉冲在非线性晶体中会相遇，发生和频产生过程，得到更短波长的输出光。如果相对时间延迟增大，晶体中两脉冲的交叠减小，非线性变弱。 

在测量脉冲长度时，混合积的功率记录为臂长差值的函数（可采用计算机控制，用电动平移台移动延迟线或者用扩音器移动角形反射器）。自相关信号与时间延迟之间的关系为： 

图2显示的为 sech2形状脉冲的自相关信号。水平轴是根据臂长差计算得到的时间延迟。 

图2：长度为150fs的 sech2形状脉冲的强度自相关函数图像。将延迟线移动15μm，对应的时间延迟为100fs。 

对于sech2形状的脉冲，其脉冲长度约等于自相关信号宽度的0.65倍，但是转化因子与脉冲形状有关。根据脉冲形状可以给出粗略的估计。将记录的自相关信号与理论得到的曲线对比可以进行合理性检查，但是并不是非常严格。需要注意的是，自相关总是关于中心对称的，几十脉冲形状是非对称的。（但是，非对准的自相关器可以得到非对称的自相关形状。） 

不采用快速的光电探测器也可以测量很短的脉冲长度：探测器只能测量平均功率（假设入射到自相关器的为普通的脉冲列），而不能得到脉冲的功率变化。
对于非常短的脉冲（例如，<20 fs），存在很多困难：分束器具有有限的带宽，并且其衬底和其它光学元件会引入反常色散。另外，如果波束角很大，几何弥散效应会使测量的脉冲长度偏大，并且群速度失配会限制相位匹配带宽。

在这时采用非常薄的非线性晶体，有时其厚度小于10 μm。 强度自相关测量的共线装置可以利用晶体的第二类相位匹配。这时两个相同的脉冲具有不同的偏振方向，而不是具有不同的传播方向。这样就可以避免几何弥散效应。 

强度自相关通常是无背景噪声的，因为当时间延迟很大时信号会消失。这与下面要描述的干涉型自相关器是不同的。 大多数情况下，需要测量不同脉冲在不同时间延迟的情况来得到自相关轨迹。但是，也可以采用单个脉冲测量得到整个自相关轨迹，前提是脉冲需要具有足够高的脉冲能量。

在单脉冲自相关器中，脉冲聚焦到非线性晶体中是利用的椭球棱镜，转化得到的信号由摄像机收集记录。晶体不同位置对应了不同的时间延迟。 

干涉型自相关器 

图3：干涉型自相关器的装置图。BS=分束器

干涉型自相关器（图3）的装置中包含了一个迈克尔逊干涉仪，其臂长差是可调的。两个叠加的脉冲在非线性晶体中共线传播（经过透镜或者曲面激光反射镜的聚焦后），并且偏振方向相同。 

通过记录倍频信号的平均功率可以得到干涉型自相关函数： 

这种自相关轨迹在半个波长范围内快速振荡。当经过分束器得到的两个脉冲经历理想的相消干涉后可以得到峰值信号（如图4），是单个脉冲情况下幅值的两倍，强度是该情况下的四倍，经过倍频过程后是强度的16倍。

当臂长差较大时，脉冲不会再非线性晶体中交叠，这时的强度仅仅是单脉冲情况的两倍。因此只要干涉仪经过合适的对准，得到的峰值信号总是背景信号的8倍。 

图4：长度为15 fs的sech2形状啁啾脉冲的干涉型自相关曲线。 

干涉型自相干效应对啁啾非常敏感，原理上可以从脉冲中获取更多的信息。但是，如果采用自相干信号的宽度得到的啁啾脉冲的长度偏小（如图5）。
一种改进的方法为干涉自相关修正光谱方法（MOSAIC）也是基于干涉自相关效应，采用后续的数值过程从而能够更容易分析啁啾。 

图5：长度为15 fs的sech2形状啁啾脉冲的干涉型自相关曲线。尽管脉冲长度与图4中的相同，这里的信号具有更小的宽度。 

对于较长的脉冲，干涉型自相关轨迹中的振荡可以通过平均消除掉。这时，峰值信号是背景信号的3倍（不是4倍，由于振荡是非正弦的）。

干涉型自相关器由于具有更加简单的装置比强度自相关器更加适用于测量很小的脉冲长度（几飞秒）。尤其是，可以避免我们以上提到的几何效应。但是，在小于10 fs时，其它的脉冲表征方法（例如，FROG或者SPIDER）更加精确。 

非线性晶体选择 
选取合适的非线性晶体和晶体厚度需要考虑很多因素，尤其是在飞秒情况下需要考虑群速度失配。薄的KDP晶体非常适合脉冲长度短至几个飞秒时。碘酸锂（LiIO3）也很常见，主要是因为它具有很宽的相位匹配带宽。 

基于双光子吸收的自相关器 
采用很大带隙的光电二极管可以制作非常小的、简单的自相关器，其中光电二极管中只有双光子吸收对光电流有贡献，由于光子能量小而不存在线性响应。这种双光子探测器有时可以实现很宽的光学测量带宽。

Definition: devices for measuring the intensity or field autocorrelation function of light, mostly used for determining the duration of ultrashort pulses

More general terms: optical metrology instruments, pulse characterization instruments

Optical autocorrelators are used for various purposes, in particular for the detailed analysis of light, in particular for the measurement of the duration of ultrashort pulses with picosecond or femtosecond durations, where an electronic apparatus (based on, e.g., a photodiode) would be too slow.

The basic principle of operation of an autocorrelator for a pulse duration measurement is to check the correlation of the temporal pulse trace with itself; it is explained in the following. A beam splitter creates two copies of the incoming pulses. These copies are superimposed in a nonlinear medium, where they interact on the basis of some nonlinearity, provided that they overlap temporarily.

This article does not treat devices with an interferometer but no nonlinear crystal, as can be used to measure the optical spectrum of a source; for such things, see the article on Fourier transform spectroscopy. In that context, one uses autocorrelations of optical amplitudes, rather than of powers.

Autocorrelators should not be confused with autocollimators, which have a completely different purpose.

Intensity Autocorrelators

Figure 1: Setup of an intensity autocorrelator. BS = beam splitter.

In an intensity autocorrelator as shown in Figure 1, a beam splitter splits an incoming pulse into two pulses, which are then focused and sent into a crystal with a χ(2) nonlinearity. The arm length difference and thus the relative timing of the pulses can be mechanically adjusted via the variable optical delay line. (Different kinds of delay lines are used, e.g. using rotating glass blocks or mirrors mounted on loudspeakers.) If the arm length difference is made small, so that the pulses meet in the nonlinear crystal, the process of sum frequency generation occurs, leading to an output with a shorter wavelength. If the relative time delay is increased, so that the overlap of the two pulses in the crystal is reduced, the mixing product becomes weaker. Obviously, that overlap is lost sooner if the pulses are rather short.

For measuring the pulse duration, the power of the mixing product is recorded as a function of the arm length difference. This can be done under computer control, using a motorized translation stage to move the delay line, or simply a loudspeaker moving a corner cube prism. The dependence of the autocorrelation signal on the temporal delay is given by

Figure 2 shows the autocorrelation signal for sech2-shaped pulses. The horizontal axis shows the time delay as calculated from the arm length difference.

Figure 2: Intensity autocorrelation of a sech2-shaped pulse with a duration of 150 fs. A shift of the delay line by 15 μm corresponds to a change in the time delay by 100 fs.

For sech2-shaped pulses, the pulse duration is ≈ 0.65 times the width of the autocorrelation signal, but this conversion factor depends on the pulse shape. A rough evaluation is often based on some assumption concerning the pulse shape. Fitting the recorded autocorrelation with a theoretical curve for that assumed pulse shape provides a kind of sanity check, but not a strict one. In this context, note that the autocorrelation is e.g. always symmetric with respect to its center, even for asymmetric pulse shapes. However, asymmetric autocorrelation shapes can be obtained from misaligned autocorrelators.

A relatively slow photodetector is sufficient even for characterizing ultrashort pulses.

Note that very short pulse durations can be measured without requiring a fast photodetector: the detector only has to measure an average power (assuming that a regular pulse train is sent into the autocorrelator), rather than resolving the power variations of the pulses.

Difficulties can arise for very short pulses.

For very short pulse durations (e.g. < 20 fs), various difficulties arise: the beam splitter may have a limited bandwidth, and its substrate and the other optical elements introduce chromatic dispersion. Furthermore, a geometric smearing effect leads to a too long measured pulse duration, if the beam angles are too steep, and group velocity mismatch can restrict the phase-matching bandwidth. Very thin nonlinear crystals are used in that domain, sometimes with a thickness less than 10 μm.

A collinear setup for intensity autocorrelation measurements can exploit type II phase matching in the crystal. The two pulse copies then have different polarization directions, rather than different propagation directions. In that way, the mentioned geometric smearing effect is avoided.

The intensity autocorrelation is called background-free, since the signal vanishes for large time delays. This is different for interferometric autocorrelators, as discussed below.

Scanning vs. Single-shot Autocorrelators

In most cases, an autocorrelation trace requires many different pulses from a regular pulse trains, since at least one pulse is required for every time delay setting, and a range of those must be scanned. However, it is also possible to measure a whole autocorrelation trace with a single pulse, if this has a sufficiently high pulse energy. A single-shot autocorrelator can be realized such that the focusing into the nonlinear crystal is done with a cylindrical (rather than spherical) lens, and the converted signal is recorded with a camera. Different spatial positions in the crystal then correspond to different time delays.

Interferometric Autocorrelators

Figure 3: Setup of an interferometric autocorrelator. BS = beam splitter.

The setup of an interferometric autocorrelator (Figure 3) contains a Michelson interferometer with a variable arm length difference. The superimposed copies of the pulse are collinearly propagating into the nonlinear crystal (after focusing with a lens or curved laser mirror) and have the same polarization.

An interferometric autocorrelation is obtained by recording the average power of the frequency-doubled signal:

where the integration is over the temporal range corresponding to one pulse. This kind of autocorrelation trace exhibits a fast oscillation with a period of half the optical wavelength. The maximum signal (Figure 4) is obtained when the two pulses after the beam splitter undergo perfect constructive interference, leading to twice the amplitude compared with a single pulse, and thus four times the intensity, and after frequency doubling 16 times the intensity. For a large arm length difference, the pulses do not overlap in the nonlinear crystal, and the intensity is only twice that generated by a single pulse. Hence the peak signal is always eight times higher than the background, provided that the interferometer is properly aligned.

Figure 4: Interferometric autocorrelation of a sech2-shaped unchirped pulse with a duration of 15 fs.

The interferometric autocorrelation is sensitive to chirps and thus in principle makes it possible to extract more information on the pulses. However, the pulse duration of a chirped pulse is underestimated if one simply uses the width of the autocorrelation signal (see Figure 5). An improved method called modified-spectrum autointerferometric correlation (MOSAIC) [15] is based on an interferometric autocorrelation, which is numerically post-processed such that the resulting trace makes it much easier to diagnose a chirp.

Figure 5: Interferometric autocorrelation of a sech2-shaped chirped pulse with a duration of 15 fs. Even though the pulse duration is the same as in Figure 4, the signal has a smaller width.

For relatively long pulses, the many oscillations of the interferometric autocorrelation trace can be averaged out. In that case, the peak signal is three times the background (not four times, due to the non-sinusoidal oscillation).

Owing to its simpler setup, interferometric autocorrelators are more suitable than intensity autocorrelators for measuring very small (few-femtosecond) pulse durations. In particular, the above-mentioned geometric effect is avoided. However, other methods of pulse characterization (e.g. FROG or SPIDER) are more precise in the regime below 10 fs.

Choice of Nonlinear Crystal and Phase Matching

The choice of a suitable nonlinear crystal and the crystal thickness involves various considerations e.g. concerning phase matching. In the femtosecond regime, the group velocity mismatch is also particularly important, potentially limiting the temporal resolution. Thin KDP crystals are a good choice for pulse durations down to a few femtoseconds. Lithium iodate (LiIO3) is also often used due to its particularly wide phase-matching bandwidth.

It can be advantageous to use a crystal with type-II phase matching, because it is then easier to achieve a high dynamic range (see below).

Autocorrelators Based on Two-photon Absorption

Particularly compact and simple autocorrelators can be constructed using photodiodes with large band gap materials, where only two-photon absorption in the photodiode contributes to the photocurrent, whereas there is no linear response due to the too small photon energy. Such two-photon detectors sometimes allow for a very wide optical measurement bandwidth.

Autocorrelators with High Dynamic Range

In some cases, it is desirable to measure autocorrelations with a particularly high dynamic range, so that one can detect even rather weak pedestals of a pulse, or side peaks which may e.g. be caused by parasitic reflections. (Mode-locked fiber lasers have a particular tendency to produce such features.) For that purpose, special high dynamic range autocorrelators have been developed. One may, for example, use a background-free intensity autocorrelator based on a type-II phase-matched crystal, where there is no upconverted signal outside the region of temporal overlap. Also, one may use a setup where the two input beams to the nonlinear crystal are modulated with a two-frequency optical chopper. The autocorrelation signal then has frequency components at the sum and the difference of the two modulation frequencies, and can be processed with a lock-in amplifier [8].

Another possibility is to use a third-order autocorrelator, using sum frequency generation of the laser light with a frequency-doubled component [7, 18]. Such a device can also reveal asymmetric features, such as pedestals of different height before and after the pulse.

The detectors are often photomultipliers because of their particularly low noise equivalent power.

For sufficiently high pulse energies, the dynamic range achieved with such techniques can be 80 dB or even 100 dB, although oft not in combination with highest temporal resolution. (Longer nonlinear crystals provide stronger signals and thus a higher dynamic range, but also limit the temporal resolution by introducing a group velocity mismatch.) Some mode-locked lasers exhibit no pedestals even in that large range, while others have substantial pedestals which are then easily seen.

Limitations of the Autocorrelation Method; The Coherent Artifact

From a measured autocorrelation trace, one can well retrieve the pulse duration if the pulse shape is known, and also check whether the autocorrelation trace is consistent with a given pulse shape. However, one can not uniquely measure the pulse shape with an autocorrelation trace alone. The primary reason is that the autocorrelation trace is always symmetric, even for asymmetric pulse shapes. Further problems arise if pulse trains are subject to noise; autocorrelation traces can then be quite misleading.

Further, the frequently used intensity autocorrelation technique cannot provide information on the phase profile; the obtained autocorrelation traces depend only on the temporal variation of optical intensity or power.

For very short pulses, e.g. with durations below 10 fs, accurate autocorrelation measurements are difficult to perform. One challenge is the limited phase-matching bandwidth of the nonlinear crystal, even if that is made very thin. Frequency-resolved optical gating (FROG) and spectral phase interferometry (SPIDER) have found to be more accurate in that domain, while also providing valuable phase information.

For pulses exhibiting strongly distorted temporal shapes, as can occur e.g. for a not properly working mode-locked laser, one can obtain an autocorrelation trace which exhibits a narrow feature – called a coherent artifact on top of a much broader structure. In such situations, it is wrong just to take the coherent artifact as a measure for the pulse duration and ignore the broad background [2]. In fact, the autocorrelation trace then coveys little information on the actual pulse shape. More comprehensive pulse characterization can then be achieved with frequency-resolved optical gating.

Bibliography