定义：
Q因子，在包括WDM在内光通信系统中，传统上大家都认为OSNR是衡量光路性能的重要指标，而目前高速传输系统（单信道10G及以上速率）非线性效应很强，对系统最终BER有着举足轻重的影响。在相同OSNR情况下，非线性效应的大小会引起系统BER的显著变化。也就是说10G及以上速率的高速系统仅依靠OSNR无法更准确地衡量系统的性能，因此Q因子（质量因子）被引出来衡量系统性能。

基本介绍

Q因子被定义为在接收机判决电平信号和噪声的比值（即在最佳判决点、判决电路的信噪比），较高的Q值意味有较好的BER。

关系
OSNR与Q值的关系

1、OSNR改善1dB等同于Q值提高1dB，OSNR劣化1dB等同于Q值降低1dB，
2、OSNR不变，调制速率每增加4倍，Q(dB)降低6dB。 从10G到40G，OSNR容限升高6dB。
3、系统的OSNR应该足够高，便于为系统性能波动提供足够的容限。对于10G系统，一般要保证Q~26dB，即可为传输代价提供～6dB的富余度，即OSNR容限～26dB

      Q Margin指对于给定的BER，Q因子超过所需值的部分。Margin可以理解容限、余量、富裕度。也是用来衡量系统指标的一个参数。比如、对于传统SDH系统，线路码型都是NRZ，而40GSDH系统用RZ码型的一个重要原因就是RZ码型在同等OSNR条件下更大的Q值富余度。

Definition: a measure of the damping of resonator modes

Formula symbol: Q

Units: (dimensionless number)

The Q factor (quality factor) of a resonator is a measure of the strength of the damping of its oscillations, or for the relative linewidth. The term was originally developed for electronic circuits, e.g. LC circuits, and for microwave cavities, also for mechanical resonators, but later also became common in the context of optical resonators.

There are actually two different common definitions of the Q factor of a resonator:

• Definition via energy storage: the Q factor is 2π times the ratio of the stored energy to the energy dissipated per oscillation cycle, or equivalently the ratio of the stored energy to the energy dissipated per radian of the oscillation. For a microwave or optical resonator, one oscillation cycle is understood as corresponding to the field oscillation period, not the round-trip period (which may be much longer).
• Definition via resonance bandwidth: the Q factor is the ratio of the resonance frequency ν₀ and the full width at half-maximum (FWHM) bandwidth δν of the resonance:

Both definitions are equivalent only in the limit of weakly damped oscillations, i.e. for high Q values. The term is mostly used in that regime.

Q Factor of an Optical Resonator

The Q factor of a resonator depends on the optical frequency ν₀, the fractional power loss l per round trip, and the round-trip time T_rt:

(assuming that l ≪ 1).

For a resonator consisting of two mirrors with air (or vacuum) in between, the Q factor rises as the resonator length is increased, because this decreases the energy loss per optical cycle. However, extremely high Q values (see below) are often achieved not by using very long resonators, but rather by strongly reducing the losses per round trip. For example, very high Q values are achieved with whispering gallery modes of tiny transparent spheres (see below).

Important Relations

The Q factor of a resonator is related to various other quantities:

• The Q factor equals 2π times the exponential decay time of the stored energy times the optical frequency.
• The Q factor equals 2π times the number of oscillation periods required for the stored energy to decay to 1/e (≈ 37%) of its initial value.
• The Q factor of an optical resonator equals the finesse times the optical frequency divided by the free spectral range.

Intrinsic and Loaded Q Factor

The Q factor of an optical resonator is limited by optical losses, part of which can result from useful coupling to the external world – for example, through an output coupler mirror used for injecting light and probing the resonances. One may define the intrinsic Q factor as the value which results without the mentioned coupling; this is higher than the loaded Q factor obtained with the coupling. The inverse loaded Q factor is the sum of the inverse intrinsic Q factor and in addition due to the coupling.

For some kind of optical resonators, the coupling can be easily removed – for example, if it happens through frustrated total internal reflection over a gap which can be arbitrarily increased in width. That is the case for some whispering gallery mode microdisks, for example.

High-Q Resonators

One possibility for achieving very high Q values is to use supermirrors with extremely low losses, suitable for ultra-high Q factors of the order of 10¹¹. Also, there are toroidal silica microcavities with dimensions of the order of 100 μm and Q factors well above 10⁸, and silica microspheres with whispering gallery resonator modes exhibiting Q factors around 10¹⁰.

High-Q optical resonators have various applications in fundamental research (e.g. in quantum optics) and also in telecommunications (e.g. as optical filters for separating WDM channels). Also, high-Q reference cavities are used in frequency metrology, e.g. for optical frequency standards. The Q factor then influences the precision with which the optical frequency of a laser can be stabilized to a cavity resonance.

The Q Factor of an Oscillator

Sometimes, the term Q factor is applied to lasers and other kinds oscillators rather than to resonators. This requires additional careful thoughts, partly because a Q factor can then be defined in different ways:

• Considering the round-trip power losses of a laser resonator, there is also the laser gain, which in continuous-wave operation just compensates the losses. Taking into account that gain, one would arrive at effectively zero round-trip losses and there is an infinitely large Q factor. To avoid that problem, one may take the Q factor of the “cold” resonator, i.e., without laser gain. Many laser resonators exhibit a rather low Q factor; that is the case, for example, for most laser diodes. However, that parameter is not very relevant.
• One also take the definition based on the emission linewidth to get the Q factor as the ratio of the mean optical frequency to the bandwidth. That value, calculated for example for a laser oscillator, can be far higher than the cold-cavity value of the laser resonator. Similarly, an optical frequency standard can be operated with a very small linewidth, far below the natural linewidth of the used optical transition.

Generally, it should be recommended to use the term Q factor only for (passive) resonators, not for oscillators.

Q switching

Although the term Q factor is not particularly common for laser resonators, it lead to the term Q switching, a method of pulse generation. When the Q factor of a laser resonator (based on its resonator losses only) is abruptly increased, an intense laser pulse (giant pulse) can generated. However, the magnitude of the Q factor during pulse generation is not particularly relevant for the obtained pulse properties; there is no need to maximize that value.

Bibliography