Noise in interferometric optical systems: an optical Nyquisttheorem

The index of refraction of an optical medium at a temperature above absolute zero undergoes statistical fluctuations, which in turn introduce fluctuations in the phase of an optical signal propagating in the medium. The magnitude and spectral density of these phase fluctuations are calculated, and it is shown that they can be larger than the phase uncertainty due to quantum noise. Barring the onset of nonlinearities, these fluctuations and not quantum noise set the limit to the measurement of optical phase     

Cancellation of Vibration-Induced Phase Noise in Optical Fibers

Vibration causes mechanical distortions in optical fibers that induce phase fluctuations in the transmitted optical signal. Information encoded on the optical signal by modulation, such as in a radio-frequency (RF)-photonic link also degrades. A feed-forward correction technique is described that enables 20 dB or more cancellation of vibration-induced phase fluctuations in an optical fiber wound on a spool. The scheme is also applied to an optoelectronic oscillator (OEO). The OEO has emerged as an excellent low-noise source that rivals the best electronic RF oscillators over a broad range of offset frequencies. However, close-to-carrier spectral purity of an OEO is degraded mostly by the vibration-induced phase fluctuations in optical fibers when the temperature is held constant. Implementation of feed-forward phase correction in an OEO has shown improvement by almost an order of magnitude in the vibration sensitivity of the oscillator.      

Carrier-induced phase noise in angle-modulated optical-fiber systems

Phase noise in angle-modulated optical-fiber communication systems arising from optical power fluctuations is analyzed. The nonlinear refractive index of silica is the physical mechanism which converts power fluctuations into phase fluctuations. The effects of self-phase modulation (an optical wave acting on itself) and cross-phase modulation in wavelength-division multiplexed (WDM) systems (one optical wave modulating a channel at a different wavelength) have been calculated. The phase noise generated in single-channel systems is negligible for laser fluctuations less than 1-mW rms. In WDM systems containing as few as four channels the phase noise exceeds tolerable levels (0.15 rad) for power fluctuation of 1 mW in each channel.     

激光传输湍流大气的折射率起伏双尺度模型

运用Kolmogorov 1941串级湍流模型理论和近似①湍流大气中传输激光束的强度起伏可抽象为大尺度湍涡导致对小尺度湍涡产生强度起伏倍乘性再调制的双尺度过程;②分别由大尺度湍涡和小尺度湍涡产生的光闪烁相互统计独立;③在双尺度模型下,即使在湍流起伏饱和区,用于处理光闪烁的Rytov方法仍然适用.导出了包含湍流内外尺度因子的简化折射率起伏双尺度模型和湍流大气中传输平面波的闪烁孔径平滑因子.结果表明,有限湍流内、外尺度在0.5＜d＜3.5孔径区域增加了闪烁的孔径平滑作用.     

用于多波长激光器功率均衡的光纤光栅的理论研究

基于半导体光放大器的多波长激光器输出的激光普遍存在功率不均衡的问题 ,文中提出了一种采用光纤光栅梳状滤波器对其进行均衡的方法 ,并给出理论设计步骤及参数选取。结果表明 ,与自由振荡时相比 ,加入所设计的光纤光栅后 ,激光器可实现多路波长间隔稳定的激光输出 ,其功率获得了很好的均衡     

1/f noise in the extinction coefficient of an optical fibre

The extinction coefficient, used to express losses in optical fibres due to absorption and diffusion, fluctuates in time with a 1/f spectrum. The authors have measured fluctuations in the intensity of light propagating through optical fibres. Noise measurements as a function of fibre length show that the noise is not due to fluctuations in reflectivity at the ends. The relative noise in the intensity of the transmitted light is proportional to fibre length     

Noise of strongly-multimode laser diodes used in interferometricsystems

A unified model of the phase and partition noise of a multimode semiconductor injection laser is presented in the context of the assumption that all modes radiate the same average optical power. Noise is shown to be associated with two processes: phase fluctuations common to all modes, arising from carrier fluctuations, and partition and phase fluctuations describable in terms of a random walk of the optical field state on the surface of an abstract sphere. Both processes are driven by spontaneous emission. The model is solved analytically; results for the intensity noise level to be expected at the output of an unbalanced interferometer illuminated by a multimode diode laser are derived. These predictions are confirmed experimentally using a laser with nine modes at full width half maximum     

Noise power spectra of optical two-beam interferometers induced by the laser phase noise

Dynamic range of many optical signal processing and sensing devices incorporating two-beam interferometers (such as Mach-Zehnder and Michelson interferometers) can be limited by random phase fluctuations of the optical source emission field. This paper is concerned with the intensity fluctuations, originating from the laser source phase noise, at the output of a two-beam interferometer. Closed-form theoretical expressions are presented for the autocovariance function, variance, and noise power spectral density of the instantaneous output intensity which are valid for any optical biasing phase and any source coherence time. Application of the results in the noise performance evaluation of optical devices incorporating two-beam interferometers will also be shown.     

基于单向传输的光纤时延波动测量

为了与现有光纤通信网络兼容,研究了一种基于单纤单向传输的光纤时延波动测量方法。基于色散温变效应和Sellmeier等式,建立了利用温度的准确测量和双波长光信号传输时延差波动反推单向时延波动的比例模型。令模型中的比例系数是单波长时延波动和双波长时延差波动的比,仿真研究了温度和波长差对比例系数的影响。搭建了75 km光纤单向时延波动测量实验平台,实验结果表明:实测比例系数?258.4接近于理论比例系数?277.3,对应单向传输时延波动误差为660 ps,实验结果验证了模型的正确性和基于单向传输的光纤时延波动测量的可能性。     

Demonstration of optical fiber probes for high bandwidth thermalmeasurements in turbomachinery

Interferometric temperature sensors comprising a zinc selenide film on the end of a single-mode optical fiber have been incorporated into rugged probes for measurement of gas temperature fluctuations in aerospace turbomachinery test rigs. Two-wavelength illumination provides signals in quadrature for determination of optical phase change of the signal reflected from the film which is exposed to the gas flow. We present ensemble-averaged results showing 15 K amplitude gas temperature fluctuations up to 70 kHz with a resolution of 1 K     

Effects of a turbulent atmosphere on the phase and frequency of optical waves

The main theme is a tutorial presentation of the major effects of atmospheric turbulence on the phase and frequency of electromagnetic waves in the optical spectrum. The emphasis is not on a comprehensive review, but rather on the tutorial aspect. Starting from fundamental principles, all significant results are derived by simple physical reasoning and are compared to existing ones in the literature. Unlike classical reviews, some of the more important results that pertain to coherent optics, in particular laser heterodyning, are derived and discussed. Finally, an attempt is made to compare optical phase fluctuations with fluctuations in other portions of the electromagnetic spectrum.     

Thermal noise in optical fibers and its influence on long-distancecoherent communication systems

The theory of phase noise caused by thermal fluctuations in an optical fiber is revised, accounting for both longitudinal and transverse phonons, and for the anisotropy of the elastooptic effect. A realistic optical mode field is accounted for. The theory is applied to calculations of bit error rates in DPSK coherent fiber-optic communication systems. Numerical results show that the thermal phase fluctuations are unimportant for transmission distances below 10000 km     

RF Amplitude and Phase-Noise Reduction of an Optical Link and an Opto-Electronic Oscillator

In this paper we examine the optical sources of noise that degrade high-performance microwave photonic links. In particular, we study the residual phase noise due to laser frequency fluctuations and the detector nonlinearity on microwave signals transmitted on an optical fiber, or generated in the opto-electronic oscillator (OEO). Based on experimental findings, we identify a significant reduction of the relative intensity noise of the laser if the received optical power saturates the photodiode. Furthermore, we suggest the use of a semiconductor optical amplifier in saturation as yet another means to reduce the phase noise induced by laser intensity fluctuations. We also identify the use of multiple photodetectors to reduce the influence of associated 1/f noise, which adds to the phase noise of a transmitted microwave signal, and is the ultimate limitation to the phase noise of the high-performance OEO. Reduction of noise that is due to optical interferences is also addressed.     

Performance of homodyne detection of binary PSK optical signals

This study evaluates the performance of an optical receiver for binary phase shift keyed (BPSK) signals in the presence of noise originating from the photodetectors and the phase fluctuations of the optical sources. Analysis of the homodyne detection process shows that the performance is degraded by two effects: One due to the phase error fluctuations of the recovered carrier and the other due to reduction of the energy per bit available for data recovery. The resulting power penalty can be minimized by dividing in an optimal way the received optical signal between the carrier recovery and the data recovery circuits of the receiver. The minimum penalty thus obtained depends on the 3-dB linewidth and on the transmission rate. For example, a penalty of 0.5 dB, relative to the quantum limit of 9 photon bit needed to achieve a BER of 10^-9, imposes a minimum transmission rate of about 180 Gbit/s when the optical source has a 3-dB linewidth of 20 MHz.     

Planning of Transport Networks based on Photonic and Electronic Cross-Connection

This paper deals with the problem of dynamic allocation of bandwidth in a hierarchical transport platform comprised of both broadband (optical) and wideband (ATM) crossconnects. The crossconnect platforms will react to fluctuations of traffic on different time scales. The model developed in this paper will take advantage of both multi-service and multi-hour character of traffic profiles and includes off-line and on-line algorithms. The off-line model will generate the configuration of optical bearers and the routing of origin-destination paths in the network for each time interval. The on-line algorithms will adjust the capacity allocated to each path in accordance with the short-term fluctuations of demand to decrease blocking probability and maximize resource utilization. We formulate the problem of designing a minimum cost network for a multi-hour, multi-service traffic profile where the cost is a piecewise linear function of the maximum possible number of optical paths as well as a linear function of the number of ports and of the traffic flow through tandem nodes. The model is a large-scale mixed integer program. Further, we provide a second model to carry out the fine tuning necessary to cater for traffic fluctuations. The alternative versions of the second model are given, including a goal program that optimally matches the network capacity to the varying traffic requirements.     

A survey of clear-air propagation effects relevant to optical communications

The theory and observations of the optical propagation effects of the clear turbulent atmosphere are reviewed, with particular attention to those characteristics most important to the designer of an optical communication system. Among the phenomena considered are the variance, probability distribution, spatial covariance, aperture smoothing, and temporal power spectrum of intensity fluctuations, and similar quantities for phase fluctuations and angle of arrival.     

Analysis of optical phase noise in fiber-optic systems employing a laser source with arbitrary coherence time

Performance of many optical circuits and systems, such as signal processing and sensing devices, is influenced by random fluctuations of the optical source emission field. This paper outlines a formalism for the analysis of laser phase noise effects on a general linear time-invariant optical system. Theoretical expressions are presented for the autocovariance function of the instantaneous output intensity which are valid for any source coherence time as long as the source intensity fluctuations are assumed to be negligible. Applications of the results to some fiber-optic systems such as Mach-Zehnder and recirculating delay line devices also are demonstrated, both in the coherent and incoherent regimes. Although the analysis is not limited just to fiber-optical systems, our attention is focused on fiber optics.     

Effect of chlorine impurities on the long-wavelength absorption edge of CdTe single crystals

The optical absorption spectra of the nominally undoped and Cl-doped CdTe single crystals in the region of the fundamental long-wavelength absorption edge are studied at room temperature. The crystals are grown by the modified physical vapor transport method. It is shown that the exponential dependence of the absorption coefficient of the undoped and lightly doped samples can be described by the Urbach rule. In the heavily doped crystals, the absorption edge is due to optical transitions involving density-of-state tails formed by fluctuations of the dopant concentration. The typical energy range of fluctuations of the extrinsic potential profile and the concentrations of charged centers are calculated for the heavily doped material.     

Evaluation of phase fluctuations of orthogonal optical eigen modesguided in an axially vibrating birefringent single-mode fiber

An optical heterodyne correlation-processing system is devised to process the phase fluctuations of the orthogonal linearly polarized two-frequency components guided in a length of axially vibrating birefringent single-mode fiber. Two wideband phase demodulators make it possible to take out separately both of the phase fluctuations of the two-frequency components from two generated beat photocurrents. The processing system provides the spectrum, the correlation, and the transfer function, as well as the coherency for the mechanically induced phase fluctuations. The phase-fluctuation characteristics and the system linearity are evaluated in terms of the statistical functions and the parameters obtained     

大气信道下窄线宽激光器对相干通信系统性能影响研究

在空间下行相干激光通信系统中,激光器的线宽大小会影响通信系统的性能,而窄线宽激光器能有效降低激光器线宽引起的激光器相位噪声,目前已经成为相干激光通信系统的首选。光信号在大气信道传输时,大气湍流会引起光信号强度和相位的波动,从而进一步影响系统的通信性能。针对上述问题,基于四相移键控(Quadri Phase Shift Keying, QPSK)通信系统的工作原理,进一步考虑窄线宽激光器线宽和大气湍流引起的光信号强度和相位的波动,给出了空间下行QPSK通信系统误码率模型。并基于该模型,数值仿真分析了窄线宽激光器对空间下行相干激光通信系统性能的影响。结果表明：大气湍流不仅严重影响系统性能,也会弱化激光器线宽对系统性能的影响。而对于大气湍流影响而言,其引起的相位波动要大于光强波动的影响。此外,随着通信速率增大,激光器线宽对于系统性能影响也会随之降低。文中对于空间下行相干激光通信系统的优化设计和调试具有一定的实际参考意义。