Study of the frequency fluctuations of a semiconductor diode laser

Abstract

Frequency fluctuations of an inexpensive single-mode semiconductor diode laser, which operates in the 822 nm region, are investigated by direct measurement of the error signal. The linear slope of first derivative signal of a transition in the (2,1,1) vibration-rotation band of water vapour is used as a frequency discriminator. A balanced photodetector is used to reduce the intensity noise and to improve the S/N ratio. Frequency stability of the diode laser is investigated when the laser is under a free-running condition and is locked to the line center of the reference transition. An integrator is used to provide feedback voltage to the laser current driver. After frequency stabilization, a more than 60-fold improvement in long-term laser-frequency stability is attained over the performance provided by the free-running semiconductor diode laser. The frequency-noise power spectrum of the diode laser is extracted from the error signal for the Fourier-frequency range ∼100 Hz. The Allan variance curve for the laser system is obtained from the frequency-noise power spectrum of the error signal by using a suitable mathematical relation under certain approximations. The extracted values of the Allan variance are compared with the theoretical τ −1 model. The experimental setup is easy to implement in graduate laboratory classes.PACS Nos.: 42.55.Px, 42.62.Fi, 33.70.Jg Résumé : Nous étudions, en mesurant directement le signal d'erreur, les fluctuations en fréquence d'une diode laser à semiconducteur à mode unique de coût modique. La pente linéaire du premier signal dérivé d'une transition dans la bande vibration-rotation (2, 1, 1) de la vapeur d'eau est utilisée comme discrimateur de fréquence. Un photodétecteur balancé sert pour réduire l'intensité du bruit et améliorer le rapport (S/N). La stabilité en fréquence est analysée avec le laser opérant en condition libre et verrouillé sur le centre de la ligne de la transition de référence. Un intégrateur fournit le voltage de contre-réaction à l'alimentation du laser. Après stabilisation en fréquence, une amélioration par un facteur 60 est observée dans la stabilité à long terme du laser, comparé à son fonctionnement en mode libre. Le spectre de puissance de bruit en fréquence de la diode laser est extrait du signal d'erreur pour un domaine de fréquence de Fourier de ∼100 Hz. La courbe de variance d'Allan du laser est extraite du spectre de puissance de bruit en fréquence du signal d'erreur à l'aide d'une relation mathématique adaptée sous certaines approximations. Nous comparons les valeurs extraites de variance d'Allan avec les valeurs théoriques du modèle τ −1 . Le montage expérimental est facile à construire dans un cours de laboratoire pour étudiants de cycle supérieur.[Traduit par la Rédaction]

Tunable offset locking in a Ξ system: an experimental study on the rubidium atom

“…After closing the PI loop, the error signal is recorded for each of the discriminator. The recorded error signal is FFT analysed and the resultant data is used for the calculation of square root of Allan variance σ (2, τ ) using the equation [26][27][28]:…”

“…It is observed that at τ = 10 s, the EIT (TPA) locked probe laser attains a stability of σ ∼ 1.2 × 10 −12 (2.35 × 10 −12 ) whereas the pump laser shows σ ∼ 2.4 × 10 −12 . The above-mentioned method of measuring frequency stability under closed-loop condition does not consider the noise of the discriminator [28] because the error signal is weighted by the servo loop transfer function H ( f ). In effect, the values of σ (2, τ ) calculated earlier predicts the best case of frequency stability [28].…”

“…The above-mentioned method of measuring frequency stability under closed-loop condition does not consider the noise of the discriminator [28] because the error signal is weighted by the servo loop transfer function H ( f ). In effect, the values of σ (2, τ ) calculated earlier predicts the best case of frequency stability [28]. However, despite this limitation, the closed-loop method can effectively explore the relative frequency stability of the laser.…”

Coherent spectroscopy of a Λ atomic system and its prospective application to tunable frequency offset locking

“…The noise power of the pump laser is more than that of the probe within f = 100 HZ → 1 kHz, while the probe laser noise is more within f = 100 mHz → 30 Hz. The Allan variance σ 2 (2, τ ) is calculated from S ν ( f ) using the relation [13,14,28,29]…”