Solution of polarization eigenvalue problems taking depolarization into account

The shape of the transmission band of an active interferometer, a resonator with amplification and absorption cells excited by an external signal, is studied. Upon tuning the external signal frequency, the narrow saturated absorption resonances can be observed in the transmission band of the interferometer. It is shown that, by varying the gain, the resonance absorption amplitude can be compensated for one order of smallness in pressure. The effect of amplitude and frequency noises of the external signal on the results obtained is studied.     

Optical transfer functions of Kerr nonlinear cavities and interferometers

We present the optical transfer functions for third-order nonlinear cavities that involve an optical carrier frequency and its modulation sideband fields. Our approach is based on linearized transformations and provides a convenient tool to calculate squeezed light sources as well as complex interferometer topologies, containing subsystems that involve intensity dependent phase shifts, i.e., optical Kerr media. As the result we present the noise spectral density of a Michelson interferometer with Kerr nonlinear arm cavities and resonant sideband extraction and find that quantum noise can be squeezed by arbitrary amounts even outside the cavity linewidth. Such a system might apply for future gravitational wave detectors or simply for a continuous wave source of squeezed states.     

Influence of fluctuations of the weight coefficients on the characteristics of adaptive antenna arrays

We analyze theoretically the influence of the weight-coefficient fluctuations on the characteristics of adaptive antenna arrays (AAAs) with gradient adjustment algorithms under the assumption that the useful and noise signals have different correlation times. We obtain expressions for the correlation function and the spectral power density of the AAA output signal, find the average radiation pattern (RP), and derive an expression for the correlation matrix of the weight-coefficient fluctuations. It is shown that the weight-coefficient fluctuations bring about distortions of the useful signal and decrease its output power compared with the case of no fluctuations. In the frequency spectrum, this “overcompensation” phenomenon results in the depression of the output signal spectrum of the antenna array in the frequency band where high-power noise exists. As an example, we calculate the spectral power density of the output signal for an AAA with single linear constraints and plot the fluctuation RP and the variance of the weight-coefficient fluctuations versus the noise arrival angle. N. I. Lobachevsky State University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 1, pp. 83–92, September 2000.     

Noise spectrum of the 140-GHz gyrotron designed for controlled thermonuclear fusion installations

A method for measurement of gyrotron amplitude noise using the Mach-Zehnder interferometer as a rejection filter, the measurement facility, and results of testing a 140-GHz industrial high-power gyrotron are discussed. The method improved the sensitivity by two orders of magnitude over that of the direct detection method. The experimental relative power spectral density in a frequency range of 50–250 MHz from the line center is 7 × 10⁻²⁰–5 × 10⁻¹⁹ 1/Hz.     

Frequency chain towards the Ca intercombination line based on laser diodes: First step

Stable, narrow linewidth operation of red and 1.3 µm free-running laser diodes with external gratings in non-Littrow geometry is demonstrated. The resonance of the saturated fluorescence of an atomic beam with a contrast of 25% and a linewidth of 400 ± 50 kHz of the Ca intercombination line 4¹ S ₀–4³ P ₁ ( = 657 nm) is shown. A high-power (110 mW) single-mode external cavity laser diode at 1.3 µm is used for second-harmonic generation in a KTP crystal. The beat signal (signal to noise ratio about 25 dB) of 10 nW second-harmonic radiation at 1.3 µm and the radiation of a laser diode in the visible spectrum, as a step to realize a frequency chain, is observed.     

Long-external-cavity distributed Bragg reflector laser with subkilohertz intrinsic linewidth

We report on a simple, compact, and robust 780 nm distributed Bragg reflector laser with subkilohertz intrinsic linewidth. An external cavity with optical path length of 3.6 m, implemented with an optical fiber, reduces the laser frequency noise by several orders of magnitude. At frequencies above 100 kHz the frequency noise spectral density is reduced by over 33 dB, resulting in an intrinsic Lorentzian linewidth of 300 Hz. The remaining low-frequency noise is easily removed by stabilization to an external reference cavity. We further characterize the influence of feedback power and current variation on the intrinsic linewidth. The system is suitable for experiments requiring a tunable laser with narrow linewidth and low high-frequency noise, such as coherent optical communication, optical clocks, and cavity QED experiments.     

Frequency noise of free-running 4.6 μm distributed feedback quantum cascade lasers near room temperature

The frequency noise properties of commercial distributed feedback quantum cascade lasers emitting in the 4.6 μm range and operated in cw mode near room temperature (277 K) are presented. The measured frequency noise power spectral density reveals a flicker noise dropping down to the very low level of <100 Hz(2)/Hz at 10 MHz Fourier frequency and is globally a factor of 100 lower than data recently reported for a similar laser operated at cryogenic temperature. This makes our laser a good candidate for the realization of a mid-IR ultranarrow linewidth reference.     

Rare-earth-doped materials for applications in quantum information storage and signal processing

Realization of practical quantum memory and optical signal processing systems critically depends on suitable materials that offer specific combinations of properties. Solid-state materials such as rare-earth ions doped into dielectric crystals are one of the most promising candidates for several quantum information storage protocols, including quantum storage of single photons. This article provides an overview of rare-earth-doped material properties and summarizes some of the most promising materials studied in our laboratory and by other groups for applications in quantum information storage and for ultra-wide bandwidth signal processing. Understanding and controlling spectral diffusion in these materials, which ultimately limits the achievable performance of any quantum memory system, is also briefly reviewed. Applications in quantum information impose stringent requirements on laser phase and frequency stability, and employing a narrow spectral hole in the inhomogeneous absorption profile in these materials as a frequency reference can dramatically improve laser stability. We review our work on laser frequency and phase stabilization and report our recent results on using a narrow spectral hole as a passive dynamic spectral filter for laser phase noise suppression, which can dramatically narrow the laser linewidth with or without the requirement of active feedback.     

全频域下窄线宽激光器光谱线宽的分析

窄线宽激光器的线宽表征方式通常采用延时自外差法测量技术。该技术是通过延时光纤差拍产生一个与待测激光线宽相关的洛伦兹频谱,因此该频谱只具有单一的线宽表现形式。为了能够观察到激光器的线宽和频率噪声在其傅里叶频率分布下的完整特性,报道了一种基于β算法计算窄线宽激光器线宽的方法。该方法是结合频率噪声中的白噪声和1/f噪声分别诱导不同激光线型的理论,从而确定激光线宽。首先,对β算法的基本原理进行了详细的分析说明。通过基于维纳-辛钦定理,分析了窄线宽激光器不同频率范围内的频率噪声和激光线宽的依赖关系。阐明了在截止频率趋于0和无穷大的两个范围条件时,激光频谱特性从高斯线型向洛伦兹线型演变。同时推导出使两种线型转换的截止频率表达式,并将其转换为频率噪声函数,该函数定义为β分子线。此时频率噪声分量中高斯线型的总和即为激光线宽计算公式;其次,对窄线宽激光器的频率噪声和激光线型进行数值仿真。将通过OEwaves公司的OE4000互相关零差相位/频率噪声自动测试系统测得的频率噪声谱密度,带入β算法理论公式中。结果显示：1/f噪声导致激光呈现高斯线型,线宽随截止频率的增加而增大。而白噪声将导致洛伦兹线型,线宽不再随截止频率而改变。此外,在低频区域,频率噪声电平远大于其傅里叶频率,噪声调制系数较高,该部分噪声可以决定线宽大小。因此,高斯线型区域对应的频率噪声的积分,即为待测激光器的线宽;在高频区域,频率噪声电平与其傅里叶频率相差较小,频率波动较快,噪声对线宽影响可以忽略。并且频率带宽在截止频率范围内,计算的线宽误差较小。最后,实验上运用β算法对RIO公司的1 550 nm低噪声窄线宽激光器的频率噪声功率谱密度进行积分计算,成功获得了其不同傅里叶频率分布下对应的激光线宽值。其中β分子线将频率噪声中的白噪声和1/f噪声分隔两部分：当频率噪声谱密度大于β分子线时,激光即为高斯线型,线宽随频率积分带宽的增加而减少;而频率噪声谱密度小于β分子线时,激光呈现洛伦兹线型,线宽为定值不再改变。同时为了对β算法进行实验验证,搭建了延迟光纤为50 km、移频频率为60 MHz的延时自外差法测量系统。对注入电流为110 mA的RIO 1 550 nm低噪声窄线宽激光器的线宽进行实验测量,测量结果表明激光线宽为1.8 kHz,与上述β算法中2.8 kHz的频率带宽积分结果一致。充分证明了此算法的准确性。β算法可以对任意类型的窄线宽激光器进行线宽表征,对窄线宽激光器的研究具有重要意义。     

Measurements of the laser linewidth due to quantum phase and quantum amplitude noise above and below threshold. I

The natural linewidths and line shapes due to quantum phase and quantum amplitude noise have been investigated above, within and below the threshold region of laser operation using a Fourier spectroscopic technique. Outside the threshold region the linewidths of the laser spectrum were found to be inversely proportional to the laser power, and measurements confirm the “factor of two” difference in the linewidth equation. Within the threshold region the results are in agreement with calculations of Hempstead, Lax and Risken. A Mach-Zehnder interferometer with optical path differences up to 1500 meters was used for the measurements. The method of investigation combines a high spectral resolution with a good signal-to-noise ratio. The method is suited to linewidth measurements of a laser both above and below threshold and allows the technical and natural linewidths to be clearly distinguished.     

Experimental demonstration of a classical analog to quantum noise cancellation for use in gravitational wave detection

We present results that are a classical analog to quantum noise cancellation. It is possible to breach the standard quantum limit in an interferometer by the use of squeezing to correlate orthogonal quadratures of quantum noise, causing their effects on the resulting sensitivity to cancel. A laser beam incident on a Fabry-Perot cavity was imprinted with classical, correlated noise in the same quadratures that cause shot noise and radiation pressure noise. Couplings between these quadratures due to a movable mirror, sensitive to radiation pressure, cause the excess classical noise to cancel. This cancellation was shown to improve the signal to noise ratio of an injected signal by approximately a factor of 10.     

Frequency-stabilized Nd:YVO4 thin-disk laser

We have developed a Nd:YVO₄ thin-disk laser at 914 nm with single-frequency operation and active frequency stabilization to a low-finesse reference cavity. The spectral density of laser frequency noise is analysed by means of noise measurements at the error point of the frequency control loop. To address the 3¹S₀→3³P₁ magnesium intercombination line at 457 nm, we use an external frequency doubling stage based on periodically poled KTiOPO₄ for the generation of more than 150-mW output power at 457 nm. Optical beat signal measurements at 457 nm with a frequency-stable dye laser show a short-time line width of the thin-disk laser of less than 100 kHz. PACS 42.55.Xi; 42.60.Lh; 42.62.Fi; 42.65.Ky     

Natural line shape

The observable line shape of the spontaneous emission depends on the procedure of atom’s excitation. The spectrum of radiation emitted by a two-level atom excited from the ground state by a π pulse of the resonant pump field is calculated for the case when the Rabi frequency is much larger than the relaxation rate. It is shown that the central part of the spectral distribution has a standard Lorentzian form, whereas for detunings from the resonance that are larger than the Rabi frequency the spectral density falls off faster. The shape of the wings of the spectral line is sensitive to the form of the π pulse. The implications for the quantum Zeno effect theory and for the estimates of the duration of quantum jumps are discussed. The article is published in the original.     

High sensitivity HCN laser interferometer for plasma electron density measurements

This paper describes a high sensitivity 337 μm HCN laser interferometer for plasma electron density measurements. The plasma phase shift is transferred to a low frequency signal obtained by slightly shifting the frequency of the 337 μm radiation in the reference beam of the interferometer. The frequency shift is produced by diffracting the radiation of a cylindrical rotating blazed grating. A phase shift is deduced from the time variation of the zero crossings of the low frequency signal, giving a result which is independent of amplitude fluctuations. Using pyroelectric detectors, the interferometer has a time resolution of 100 μsec and a sensitivity of 10^-2 fringe.     

Generation of 10-GHz ultra-short pulses with low time jitter in an actively mode-locked fiber laser

We have experimentally achieved the 8.3-ps ultra-short pulse at 10 GHz repetition rate with the time jitter as low as 590 fs in an actively mode-locked fiber ring laser. The ring-cavity laser is mode-locked by a semiconductor optical amplifier based on cross-gain modulation. The external CW source is modulated with radio frequency signal by an amplitude modulator as the external optical pulses and, then, injected into the fiber ring cavity to achieve active mode locking. Further investigating the laser output characteristics, it indicates that the linewidth of employed CW source affects properties of the generated ultra-short pulse, such as phase noise and time jitter. Ultra-short pulse at high repetition rate with low time jitter can be generated by the optimization of CW laser source.     

可调谐半导体激光器的瞬时光谱测量方法研究

可调谐半导体激光器在调谐过程中的瞬时光谱特性,如瞬时的波长、调谐率、功率、线型和线宽等参数影响着以激光器为光源的光学测量和光相干通信系统的精度。然而,能够同时测量这些瞬变参数的技术至今未见报道。提出了一个基于时频分析的测量半导体激光器在调谐过程中瞬时光谱参数的方法,利用一个短时延外差测量系统,利用激光器瞬时光谱参数与差拍信号瞬时参数的关系,最终获得了半导体激光器在连续电流调谐过程中的瞬时光谱。测量系统采用了10 cm光程差的Mach-Zehnder干涉仪,调谐电流是幅度为20~120 mA、频率是1 kHz的锯齿波,差拍信号可视为直流信号、载波信号与噪声的叠加,按照短时延相干光测量原理,差拍信号中的直流分量幅度的大小反映了激光器输出光信号的功率;载波信号是一种多项式相位信号,由其频率可以推算激光器输出光谱的中心频率或波长;噪声信号则与激光器输出光谱的线型和线宽相关,通过对噪声信号进行时频分析,可以获知激光器在连续电流调谐过程中每一时刻或每个电流下的瞬时线型、线宽。采用了趋势局部均值分解方法对差拍信号进行了准确分离,并对分离信号分别进行处理,同时获知了半导体激光器在调谐过程中的瞬时输出光功率、光波长、调谐率及线型、线宽。在去掉弛豫部分后截取的整周期差拍信号对应的调谐电流60~115 mA变化范围内,半导体激光器(FRL15DDR0A31-18950, Furukawa)瞬时输出光功率变化范围是5.16~10.6 mW,瞬时光波长变化范围为1 579.2~1 579.6 nm;激光器的瞬时调谐率在0.004 8~0.011 5 nm·mA-1范围内单调变化;线宽是852.55~954.95 kHz,呈非线性随机分布。基于短时延、局部均值分解和时频分析方法的瞬时光谱参数测量系统可以准确得到各瞬时光谱参数,测量结果与激光器的静特性相符,且测量系统结构简单,使我们更深入地理解激光器的工作原理,具有广阔的应用前景。     

Heterodyne interferometer scheme using a double pass in an acousto-optic modulator

We introduce a heterodyne interferometer scheme utilizing the double-pass arrangement of the deflected beams of an acousto-optic modulator. To prove our new idea, the interferometer has been applied for measuring small amplitude vibrations. The output intermediate frequency signal from the interferometer is processed by using an I/Q demodulator. In theory, it can provide the quantum noise limited sensitivity, whereas, in our present Letter, the sensitivity of the phase measurement is limited by the resolution of the 16?bit A/D converter used for processing the I/Q signals. Details of our interferometer scheme are discussed.     

On the Similarity of the Statistical Characteristics of Spontaneous Radiation of a Quantum Amplifier at Different Gain Factors

The transformation laws governing the statistical properties of the quantum noise of an optical amplifier when its gain factor and spectral line profile are varied are considered. The correlation functions of quantum noise both at the amplifier output and after nonlinear transformation normalized to the correlation time of quantum noise at the amplifier output were found to be independent of the amplifier gain provided that it exceeds 10 for the Gaussian spectral line profile and 10³ for the Lorentzian profile. The spectral density of quantum noise transformed in a nonlinear system was shown to possess the same similarity property. It was found that the statistical characteristics possess a similarity property even in the case of variation of the spectral line profile from Gaussian to Lorentzian. It was concluded that such a characteristic of quantum noise of an optical amplifier as the correlation time bears virtually all information on the above-mentioned statistical properties at a reasonably large amplifier gain. The similarity property revealed has an important application. It allows finding the matching condition between the optical signal spectrum and the gain profile of the optical quantum amplifier to achieve the highest sensitivity of signal detection by the amplifier.     

Modulation transfer in Doppler broadened Λ system and its application to frequency offset locking

We investigate modulation transfer through pump induced atomic coherence in pump-probe spectroscopy of Doppler broadened medium of cesium atoms. The mechanism of modulation transfer is discussed for a three level Λ configuration under slow frequency modulation. Modulation transfer is demonstrated by performing frequency modulation spectroscopy (FMS) on a sub-natural linewidth (<2 MHz) electromagnetically induced transparency (EIT) signal. Here the pump laser is modulated by acousto-optic frequency modulation and the modulation is transferred to the probe laser through atomic coherence. Finally the probe laser is locked on the first derivative spectrum of EIT signal. Such atomic frequency offset locking system totally removes the necessity of direct modulation of laser frequency, so that the spectral resolution is limited only by the practical linewidth of the laser systems. Moreover it provides a novel way to eliminate the additional frequency and intensity noise associated with direct frequency dithering, which may limit the experimental resolution.