Effects of gain medium parameters on the sensitivity of semiconductor ring laser gyroscope
Introduction
Optical gyroscopes are inertial rotation sensors working mostly on the Sagnac effect to sense the angular velocity [1]. Novel optical gyroscopes based on rotation induced evolution of far-field emission patterns [2] and transmission response of coupled resonators have been proposed, but majority of optical gyroscopes still rely on Sagnac interferometer for inertial rotation sensing [3], [4], [5], [6]. Sagnac effect states that two light waves traveling different optical paths inside the same closed cavity, accumulate different phase shifts [7]. When the non-degeneracy in path length is brought about by rotating the cavity externally, the difference in phase accumulated by counter-traveling waves is proportional to the velocity of rotation. Thus, the angle of rotation, its rate and direction can be estimated by measuring the phase difference between the waves through interferometry. This technique is used in Interferometric Fiber Optic Gyros (IFOG) which are passive devices because the light waves counter-traveling inside the cavity are generated by a source which is external to the cavity [8].
Apart from phase shifts, inertial rotation also splits resonance frequencies of the ring resonator. Thus, on rotation, resonance frequency in the clockwise (CW) direction is different from that in the counter-clockwise (CCW) direction, with the difference proportional to the inertial rotation velocity [9]. Measurement of this frequency difference is inherently more sensitive than measuring the phase difference. In Resonant Fiber Optic Gyros (RFOG), the resonance frequency difference is measured by exciting the resonator from an external light source. Generally, acousto-optic modulators or tunable laser sources are required for accurate measurement of rotation rates by RFOG [10].
However, if the counter-traveling waves are generated by a laser source present inside the ring resonator itself, the rotation induced resonance frequency difference can be measured by simple interferometric techniques [11]. Thus, interference of the CW and CCW waves results in a beat signal whose frequency is equal to the resonance frequency difference. Such gyroscopes are called active ring resonator gyros or Ring Laser Gyros (RLG) [12]. In all the RLGs, the presence of light source or gain medium inside the closed cavity influences the dynamics of the device [13]. Because of the phase amplitude coupling, magnitude and linearity of the rotation induced Sagnac beat frequency depends upon various gain medium parameters like gain coefficient, linewidth, self and cross saturation coefficients, internal quantum efficiency etc. These parameters also affect the gyro performance metrics such as quantum limit, angle random walk and bias stability.
In Semiconductor RLG (SRLG), the gain medium is highly non-linear as compared to the gaseous gain medium of He-Ne RLG because of strong interaction between charge carriers and optical signal [14], [15], [16]. It has also been shown that the dynamics of semiconductor lasers subjected to optical feedback is affected by the phase-amplitude coupling, which further complicates the dependency of gyro performance on the gain medium parameters [17], [18]. Thus, an analysis of SRLG performance considering the effect of gain medium parameters is important to increase its sensitivity by parameter optimization. The inherent description of Sagnac effect quantifies the beat frequency in terms of only passive cavity parameters as the amplitude and phase rate equations are de-coupled from each other. Including the gain medium dynamics in the calculation of Sagnac beat frequency is essential to study the effects of amplitude-phase coupling on the gyro output, as reported by us in [19].
In this paper, we model the bulk fiber-optic SRLG by the rate equations of electric field inside the cavity, with an aim to incorporate the phase and amplitude affecting parameters in the same equation. An experimental SRLG setup is also tested by manually rotating the optical table. The close agreement between theoretical and experimental beat signal output confirms the feasibility of the proposed model. The gain medium parameters such as gain coefficient, linewidth, internal quantum efficiency etc. are then varied to analyze their effect on the output sensitivity. Solutions to optimize these parameters and improve the bulk-optic SRLG performance is also discussed. A similar analysis for the on-chip integrated SRLG was also performed by us and reported elsewhere [20].
Section snippets
Experimental results
The basic configuration of bulk fiber optic SRLG consisting of a semiconductor optical amplifier (SOA) as the gain medium and an external optical fiber as the ring cavity is shown in Fig. 1(a). The gain medium used is an InP buried heterostructure (BH) type linear SOA, which is a low confinement factor device. The typical wafer structure used to fabricate the gain medium is a multiple quantum well (MQW) Aluminium quaternary i.e. . Here, the strained QWs and barriers are
Theoretical analysis
The semiconductor ring laser gyro of the above experimental setup can be modeled by using coupled-cavity rate equations [21]. This approach consists of using the rate equations to model the electric field in both the gain medium (active) cavity and the external fiber ring (passive) cavity, and a coupling coefficient to effectively couple the fields between them. The effect of external rotation can be modeled by varying the external cavity resonance frequency. Thus, both the CW and CCW modes
Effect of gain medium parameters
Since the gain medium is inside the ring resonator in a RLG, it plays an important role in the dynamics of RLG and the gain medium parameters have considerable impact on the output of the gyro. In this section, we will analyze the output of gyro by varying several gain medium parameters and finding their effects on the quality and linearity of the beat signal. Such an analysis helps in finding out the critical parameters and optimizing them to obtain the best gyro performance.
Conclusion
The importance of the active semiconductor gain medium parameters in the output characteristics of gyro is shown by calculating the beat signal from the rate equations. Several parameters of the gain medium such as gain coefficient, linewidth, group velocity, injection current and internal quantum efficiency are varied and their effects on the gyro output are analyzed. From the results obtained, the parameters can be optimized for a particular gyro application by taking care of the resulting
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