定义：用作反射镜的光学环路。

光纤光学中一种很简单的反射装置（反射镜）是制作一个光学环，利用一个2*2定向光纤耦合器，其中一边的两个端口连接在一起（如图1）。 

 图1：一个简单的光纤环反射镜。 
如果在其一端口输入光（例如，图1中上面的端口），光被分为两个相反方向的光在环中传播。当这两束光在耦合器中再次结合，它们会相互干涉。干涉效应决定了返回到入射端口和另一个端口出射的功率分配。干涉条件会受多模特性，偏振态变化和非线性效应的影响。 
光纤环反射镜也可以看做是一个Sagnac干涉仪。 

线性的光纤环反射镜 
最简单的情况是只采用单模光纤，并且在传播过程中偏振态不发生改变。（可以采用保偏光纤或者光纤偏振控制器。）并且，假设功率非常低，以至于非线性效应（尤其是克尔效应）可以忽略。另外，假设光纤中没有光强损耗，并且光纤耦合器的功率分离比为50:50（即，3-dB耦合器）。在这种情况下，干涉条件使所有输入的光重新返回到入射端口。这表明此时光纤环反射镜是一个很理想的反射器，工作在很大的波长范围内，并且在任意偏振态的情况。光纤环的长度对结果也没有影响。同样的，光纤环中的环境效应，例如温度改变，不会有影响，因为它不能影响偏振态。 
如果功率分离比偏离50:50，那么不能得到100%的反射率。图2给出了演示。但是，结果仍然与环的长度无关。 

   图2：线性的光纤环反射镜的功率反射率随光纤耦合器耦合比的变化曲线。 
由于光纤耦合器的耦合比与波长有关，因此该曲线可以转化为光纤环反射镜反射率随波长的变化。 
反射率与波长强相关的同时还会受到双折射的影响。如果光纤环采用很高双折射的光纤（例如，一个保偏光纤），并且偏振态由光纤偏振控制器仔细调整，那么得到的光谱透射方程会实现振荡。光谱周期反比于双折射（两偏振方向的折射率差）和光纤长度。由于透射凹陷位置与温度和应力有关，这种装置可用于光纤传感器中。其优势在于，当测量双折射随干涉的变化时，无需考虑环境因素对双折射光纤与普通光纤连接处的影响。也可以实现与温度无关的应力传感器，这时需要采用高双折射的光子晶体光纤，其双折射与温度几乎无关，至少当聚合物涂层去除后与温度几乎无关。 

非线性光纤环反射镜 

  图3：非线性放大环反射镜，包含一根有源光纤和一根更长的无源光纤。
光纤中传播超短脉冲时，非线性克尔效应非常强，因为峰值功率很高。但是，只要光纤环是对称的，并且耦合比为50:50，那么产生的非线性相移就不会影响光纤环的反射率。这是因为在两个方向传播的光的相移相等，因此附加相移不会影响干涉效应。 
在非对称结构中并非如此。例如，光纤环中包含一根稀土掺杂光纤，当输入合适的泵浦光时可以使光放大，还有一根长的无源光纤（如图3）。这种结构成为非线性放大环反射镜（NALM）。当光从左侧以较低功率进入耦合器后，其大部分光被反射到相同的入射端口。而入射具有很高峰值功率的超短脉冲时，环中会产生很大的非线性相位变化。在逆时针方向的相位变化更大，因为该光先经过放大后再在无源光纤中传播。而反方向的波则是在很长的距离上以较低的功率传播。因此，入射光随功率变化的部分进入输出端口时干涉受到影响。 
这一功率相关性仅仅来自于一段无源光纤中的强光学衰减，或者来自于非对称的耦合比。这种情况下得到非线性环反射镜（NOLM）。 

图4：放大光纤环反射镜时间域上量端口的输出功率曲线。 
其工作细节比较复杂，因为在脉冲时间曲线上非线性相移并不是一个常数，而是在峰值处最大，两侧较小。因此，只能采用数值模拟模型来得到总体性质。图4给出了一个例子，其中环包含1 m长的掺镱光纤和10 m无源光纤。入射脉冲为孤子型的，能量为0.1 nJ，长度为2 ps，很大一部分的输出功率进入上面的输出端口。放大器泵浦光为100 mW，975 nm的光，稳态脉冲列的重复速率为10 MHz。两根光纤都具有正常色散，反常色散区域存在孤子效应，这时非线性环反射镜的性质就有很大的不同。 

在脉冲峰值处，两传播方向上非线性相移的差值大于π，该值是将光耦合进上面的输出端口的理想值。但是，这会增大两侧的耦合。总体来说，这种情况接近于峰值耦合的情况。 

一般来说，脉冲畸变很大，尽管其类型和大小与色散和工作功率等细节密切相关。 
图5给出了上面端口输出能量与下面端口输入能量的比值随入射脉冲能量的变化曲线。它们的相干性受很多效应的影响：放大光纤中增益饱和增大，提高脉冲能量会由于色散和光纤非线性而增大脉冲畸变。 

图5：上端口输出功率的比例随入射脉冲能量的变化曲线。 

非线性环反射镜的应用包括： 
在锁模光纤激光器中，这种装置可作为饱和吸收器，触发和稳定模式锁定，即脉冲形成。一个常见的方案是8字形光纤激光器，其中非线性光纤环反射镜作为8字的一部分，另一部分为一个激光器谐振腔。参阅词条锁模光纤激光器中得到更多细节。 

在光纤通信中，光纤环反射镜可以用作非线性滤波器。例如，某一滤波器可以很好的透射孤子脉冲（无显著畸变），但是会强烈抑制低强度北京辐射，这称为孤子滤波器。在其它需要光信号处理的应用中也很重要。

Acronym: FLM, NOLM, NALM

Definition: fiber loops which act as reflectors

Alternative term: fiber loop reflectors

A simple way to realize a reflecting device in fiber optics is to make a fiber loop, using a two-by-two directional fiber coupler where the ports on one side are connected to each other with a piece of fiber (see Figure 1).

Figure 1: A simple fiber loop reflector.

If one feeds light into one input port (e.g., the upper one in Figure 1), the power is split so that two counterpropagating waves are formed in the loop. When these waves then again come together at the coupler, they interfere with each other. This interference determines the optical power sent back into the input port as well as the power leaving the other port. The interference conditions can in general be influenced by various aspects that as multimode behavior, polarization changes and nonlinear effects.

Strictly speaking, such a fiber loop should be called a fiber loop reflector, but the more often used term is a fiber loop mirror. (Note that reflectors are a wider category than mirrors.)

The fiber loop reflector can also be considered as a Sagnac interferometer, although the Sagnac effect is in many cases not utilized.

Linear Fiber Loop Mirrors

In the simplest case, one uses only single-mode fibers, and the polarization state remains unchanged during propagation. (One may use polarization-maintaining fiber or alternatively a properly adjusted fiber polarization controller to obtain that situation even when using a long loop.) Also, we assume that the optical powers are so low that nonlinear effects (particularly the Kerr effect) are negligibly weak. Further, we assume that no power losses occur in the fibers, and that the fiber coupler has 50:50 power splitting ratio (i.e., it is a 3-dB coupler). In that case, the interference conditions are such that all injected power goes back to the port into which it was injected. This means that the fiber loop mirror acts as a perfect reflector, working in a wide range of wavelengths, and for any input polarization state. The length of the fiber loop is not relevant in this case, except that of course it determines the group delay. Similarly, environmental effects on the fiber in the loop such as temperature changes have no effect as long as they cannot affect the polarization.

If the power splitting ratio deviates from 50:50, one obtains less than 100% reflectance. This is shown in Figure 2. Again, the results are not dependent on the loop length.

Figure 2: Reflectance of a linear fiber loop mirror as a function of the coupling ratio of the used fiber coupler.

As the coupling ratio of a fiber coupler usually exhibits a substantial wavelength dependence, this transforms into an overall wavelength-dependent reflectance of the fiber loop mirror.

A strong wavelength dependence can also be associated with birefringence. If a highly birefringent fiber (e.g. a polarization-maintaining fiber) is incorporated into the fiber loop, and the polarization evolution is properly adjusted with a fiber polarization controller, the spectral transmission function can exhibit pronounced oscillations. Their spectral period is inversely proportional to the birefringence (the index contrast between the polarization directions) and the length of that fiber. As the positions of the relatively sharply defined transmission dips react to temperature and strain, the configuration can be used as a fiber-optic sensor. An attraction is that whereas one measures changes of birefringence with interferometric accuracy, one is not particularly sensitive to environmental influences on the ordinary fiber connecting the birefringent fiber. One may also realize nearly temperature-independent optical strain sensors by using highly birefringent photonic crystal fibers, exhibiting a low temperature dependence of the birefringence, at least when the polymer coating is removed.

Linear fiber loops can also be used as rotation sensors based on the Sagnac effect: the relative phase delay becomes direction-dependent as a result of a rotation of the whole ring e.g. around an axis perpendicular to it. Such a device may be called a Sagnac loop.

Nonlinear Fiber Loop Mirrors

Particularly for ultrashort pulses in fibers, the Kerr nonlinearity can have substantial effects, as the peak power can be high. However, as long as the fiber loop remains symmetric and the coupling ratio is 50:50, the occurring nonlinear phase shifts do not influence the fiber loop's reflectance. This is because these phase shifts are the same for light propagating in both directions, so that these additional phase shifts cannot affect the interference conditions.

Figure 3: A nonlinear amplifying loop mirror, containing an active fiber and a longer passive fiber.

This changes for an asymmetric design, as needed to realize a nonlinear loop mirror (NOLM). One way of obtaining an asymmetry is to introduce a rare-earth-doped fiber, which can amplify light when suitable pump light is injected, and a long passive fiber (see Figure 3). This configuration is called a nonlinear amplifying loop mirror (NALM). When light injected on the left side at a low power level, it will be mostly reflected back into the same port. In case of ultrashort pulses with a substantial peak power, however, we have substantial nonlinear phase changes in the loop. These are stronger for light propagating in counter-clockwise direction, since this is first amplified and then travels through the long passive fiber. Light in the opposite direction propagates with a lower power level for most of the length. As a result, the interference conditions are affected such that a power-dependent fraction of the input light reaches the upper output port.

Such a power dependence would also result from strong optical attenuation on one side of a long passive fiber only, or simply from having an asymmetric coupling ratio. In that case, one has a nonlinear loop mirror (NOLM) without amplification.

The operation details are complicated by the fact that the nonlinear phase shift is not constant over the temporal pulse profile, but rather strongest for the peak and weaker in the wings. Furthermore, chromatic dispersion can have substantial effects. Therefore, the overall behavior can be understood well only by using a numerical simulation model. Figure 4 shows the outputs in an example case, where the loop contains a 1 m long ytterbium-doped fiber and a 10 m long passive fiber. For soliton-shaped input pulses with 0.1 nJ energy and 2 ps duration, a substantial part of the output power goes into the upper output port. The amplifier is pumped with 100 mW at 975 nm, and the steady state for a pulse train with 10 MHz repetition rate has been calculated. Both fibers exhibit normal dispersion; in the anomalous dispersion regime, where soliton effects can occur, the characteristics of the nonlinear loop mirror are significantly different.

Figure 4: Output powers of the two ports of an amplifying fiber loop mirror in the time domain. The numerical simulation has been done with the software RP Fiber Power.

For the pulse peak, the difference in nonlinear phase shifts between the two propagation directions in the loop is larger than π, which would be the ideal value for coupling to the upper output port. However, this improves the coupling in the wings. Overall, this situation is close to the case with optimum coupling.

Generally, substantial pulse distortions must be expected, even though their type and magnitude can strongly depend on details like chromatic dispersion and operation power levels.

Figure 5 shows how the ratio of output energy in the upper port to input energy in the lower port varies with the input pulse energy. This dependence is influenced by various effects: increasing gain saturation in the amplifying fiber and increasing pulse distortions through chromatic dispersion and fiber nonlinearity for increasing pulse energies.

Figure 5: Fraction of output power in the upper output port as a function of the input pulse energy in the steady state of the active fiber for a fixed pulse repetition rate.

For the above described designs, the ratio of output energy to input energy is always very small for small input pulse energies, where the nonlinear effects are weak. That can be changed, however, by introducing a non-reciprocal phase shift. One way of achieving that is to use two Faraday rotators and a waveplate – possibly two fiber-coupled Faraday rotators and a piece of birefringent fiber to obtain an all-fiber solution. That way, one can e.g. achieve maximum transmission for small pulse energies, or medium transmission with a high slope.

There are various applications of nonlinear fiber loop mirrors:

• In a mode-locked fiber laser, such a device can act as an artificial saturable absorber which starts and stabilizes the mode locking, i.e., the pulse formation [6]. A well-known embodiment of this approach is the figure-eight fiber laser, where the nonlinear fiber loop mirror forms one part of the “eight” and the actual laser resonator the other one. A modified form is the figure-nine laser, having a linear resonator outside the nonlinear loop mirror, and using a non-reciprocal phase shift in the loop. The article on mode-locked fiber lasers contains more details on this.
• In optical fiber communications, nonlinear loop mirrors can be used as nonlinear filters. For example, a well designed filter may well transmit soliton pulses (without substantial distortions) while largely suppressing any low-intensity background radiation; it can then be called a soliton filter. The same can also be useful in other application areas where optical signal processing is required.

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