Timing Noise Measurement of High-Repetition-Rate Optical Pulses

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1 564 Timing Noise Measurement of High-Repetition-Rate Optical Pulses Hidemi Tsuchida National Institute of Advanced Industrial Science and Technology Umezono, Tsukuba, JAPAN Tel: ; Fax: ; Abstract- Precise evaluation of timing noise in ultra-short optical pulses is an issue of practical importance for various applications such as optical time-division multiplexed communication systems, optical sampling measurement and optical frequency metrology. The author has developed time domain measurement techniques for evaluating timing noise of optical pulses with repetition frequency ranging from 15 Hz to 160 GHz. These techniques have enabled the evaluation of timing noise over 9 decades of Fourier frequency (2.5 mhz 18.6 MHz) with 300-dB dynamic range. This paper describes the principle of the techniques and the results of timing noise measurements for mode-locked solid-state and semiconductor lasers. Index Terms- mode-locked lasers, time domain measurement, timing noise, ultra-short optical pulses I. INTRODUCTION Recently, the performance and reliability of mode-locked lasers, which emit ultra-short optical pulses at high-repetition-rate, has been greatly improved and these lasers are widely used not only as research tools but also as light sources for industrial applications such as optical time-division multiplexed communication systems, optical sampling measurement, and optical frequency metrology. In addition to short pulse duration, these applications require extremely small pulse timing noise and precise synchronization with electronics. To meet these demands, various techniques have been developed for noise evaluation and stabilization. From 1997 the author has been engaged in the developments of timing noise measurement and stabilization techniques for high repetition rate optical pulses within the framework of the Femtosecond Technology Project supported by the Ministry of Economics, Trade and Industry (METI). This paper reviews achievements [1] [12] produced in the above project with an emphasis on the evaluation of 160-GHz mode-locked laser pulses. II. PRINCIPLES A. Conventional Technique Various techniques have been employed for timing noise evaluation depending on the pulse repetition frequency that ranges from several Hz to several hundred GHz. Auto- and cross-correlation measurements are typical techniques in the optical domain and are suitable for low-repetition-rate pulses. In the electrical domain, frequency counter or spectrum analysis is commonly employed after converting the pulse intensity into electrical signals. Singe sideband phase noise (SSB-PN) measurement has been a most commonly employed technique, which was suggested by von der Linde [13] in The technique is based on the spectral analysis of pulse intensity detected by a high-speed photodetector. Although this technique is relatively easy to implement, it accompanies inherent limitations shown below: 1) Due to the approximated relation used to calculate timing noise and to the limited resolution bandwidth of spectral analysis equipment, it is difficult to estimate the low-frequency noise close to the carrier.

2 565 2) The technique cannot discriminate amplitude and timing noise. The contribution from amplitude noise can be reduced by comparing the spectra between different harmonics, which becomes difficult for high-repetition-rate pulses beyond 10 GHz. 3) The highest pulse repetition frequency is limited by the response of photodetectors. B. Measures of Timing Noise The fundamental component of the pulse intensity detected by a photodetector is represented by V (t) = V 0 [1+ (t)]sin[2 f rep t + (t)], (1) where V 0 and f rep denote the nominal amplitude and repetition frequency, (t) and (t) represent the amplitude and phase noise, respectively. Timing noise J(t) can be related to (t) by J(t) = (t)/2 f rep. (2) Therefore, timing noise measurement of optical pulses is equivalent to phase noise evaluation of electrical signals. We can also use harmonics of the pulse intensity to increase the sensitivity. The conventional SSB-PN measurement utilizes the power spectrum of the sinusoidal signal give by (1) to infer the phase noise (t). The most fundamental measure of timing noise is phase noise power spectral density (PN-PSD) S (f) [rad 2 /Hz] or timing noise PSD S J (f) [s 2 /Hz]. As a more intuitive measure, root-mean-square (rms) timing jitter J is commonly used, which is calculated from S (f) by J = 1 2 f rep f h S ( f )df, (3) f l where f h and f l represent the upper and lower limits of integration, respectively. It should be noticed that the value of J depends on the integration range. For complete characterization, f h and f l should be fixed at the Nyquist frequency (f rep /2) and around 10 Hz, respectively [14]. When rms phase jitter is much smaller than 1 radian, the following relation relates SSB-PN L(f) to PN-PSD S (f): L( f ) S ( f )/2. (4) It is essentially impossible to apply the above relationship to Fourier frequency close to the carrier. C. Time Domain Demodulation (TDD) To overcome the limitations associated with SSB-PN measurement, the author developed TDD technique [1], [2]. Equation (1) can be decomposed into in- and quadrature-phase components. V (t) = V I (t) sin(2 f rep t) +V Q (t)cos(2 f rep t) V I (t) = V 0 [1+ (t)]cos (t) V Q (t) = V 0 [1+ (t)]sin (t) (5) If we detect these two components separately in a time domain, we can demodulate instantaneous amplitude and phase using following relations: (t) = V Q 2 (t)+v I 2 (t) /V 0 1, (6) (t) = tan 1 [V Q (t)/v I (t)] (7) A series of processing represented by Eqs. (5) (7) can be performed by the use of a signal analyzer with vector analysis function. Since the resolution bandwidth of the analysis is determined by the length of data, we can easily resolve timing noise close to the carrier by increasing the measurement time. Moreover, this technique is more accurate than the conventional one due to its ability to discriminate amplitude and phase noise.

3 566 D. Time Interval Analysis (TIA) Although TDD technique offers wide frequency range and high dynamic range, it is not suitable for low-repetition-rate pulses and for pulses with drifting repetition frequency. To overcome the difficulties the author developed TIA technique [3]. This technique is based on the measurement of time interval between two pulses and is equivalent to the evaluation of the period T = [ 1 d (t) ] 1, (8) 2 dt of the sinusoidal signal given by Eq. (1). The measurement equipment consists of an internal reference clock whose frequency is much higher than that of pulses to be measured, and two zero-dead-time counters. The first counter captures the rising edges of the input pulses and records them as time stamps. The second counter continuously monitors the number of the reference clocks between two successive time stamps. this method beyond 100 GHz due to the limited response time of photodetectors. In order to overcome this limitation, the author proposed and developed an OEHM [8] that is schematically shown in Fig. 1 (b). Optical pulse trains are input to an electro-optic intensity modulator that is driven by a sinusoidal signal from a local oscillator. As shown in Fig. 1 (c), this produces modulation sidebands around each longitudinal mode that constitutes the pulse. With a sufficiently deep modulation we can locate higher order modulation sidebands close to the adjacent longitudinal modes. This enables the detection of the beat signal between the sideband and adjacent longitudinal mode with a slow-speed photodetector. The operation is equivalent to a harmonic mixer that converts a signal at f rep into an IF signal at f IF, which is given by f IF = f rep nf m, (9) where n and f m represent the order of sideband and modulation frequency, respectively. If we capture every N-th edges of the pulses, N-times improvement in the sensitivity is possible at the expense of the bandwidth. The most distinct feature of TIA technique is that no synchronization is required between the input pulses and the equipment, which is effective for evaluating drifting and/or low-repetition rate pulses. By combining TIA and TDD techniques, we can realize wide bandwidth and high sensitivity at the same time. E. Optoelectronic Harmonic Mixer (OEHM) Both TDD and TIA techniques cannot handle directly high-frequency RF signals, because they sample or count signals in a time domain. Therefore, we need frequency down-conversion for high-repetition-rate pulses before time domain signal processing. As shown in Fig.1 (a), the simplest method is the use of a double-balanced mixer and a local oscillator to convert the pulse intensity into a low-frequency electrical signal. However, it is difficult to apply Fig. 1 Frequency down-conversion for timing noise measurement; (a) electrical double-balanced mixer, (b) optoelectronic harmonic mixer, (c) optical spectrum of the pulse train at the modulator output.

4 567 III. TIMING NOISE EVALUATION OF MODE-LOCKED LASERS This section presents results of timing noise measurements for optical pulses emitted by mode-locked solid-state and semiconductor lasers. feedback control of cavity length, pump power or external phase modulator, an extremely small timing jitter below 10 fs has been achieved. Fig. 3 Block diagram of the experimental setup for subharmonic injection locking of CPM laser Fig. 2 Timing noise of a passively mode-locked Cr:LiSAF laser. A. Mode-Locked Solid-State Laser Figure 2 shows the timing noise of a laser diode-pumped Cr:LiSAF laser that is passively mode-locked by the use of a semiconductor saturable absorber mirror and emits 100-MHz pulse trains with a duration of 80 fs [1], [3]. SSB-PN (0.2 Hz 1 MHz), TDD (50 mhz 1 MHz), and TIA (1.8 mhz 10 Hz) are used for evaluating PN-PSD. By comparing the results for SSB-PN and TDD, it can be seen that the former results do not show correct value below 100 Hz due to the limited resolution bandwidth of a spectrum analyzer. The observed peak at 3 Hz is considered to be caused by the mechanical resonance of optical mounts in the laser cavity. By combining the TDD and TIA techniques it has become possible to estimate PN-PSD from 1 mhz to 1 MHz with 240 db dynamic range. An increased timing noise at low frequency is caused by the thermal drift of the laser cavity and is characteristic of passively mode-locked lasers. Such low-frequency noise can be effectively reduced by optoelectronic phase-locked loop. By the use of a digital phase detector and negative Fig. 4 Time dependence of the pulse repetition frequency for the free-running (upper) and injection-locked (lower) CPM lasers. B. Mode-Locked Semiconductor Laser Figure 3 shows the block diagram of the experimental setup for stabilizing a colliding pulse mode-locked (CPM) semiconductor laser [15] operating at 160 GHz. The laser is passively mode-locked by applying a dc bias voltage to a saturable absorber located at the center of the cavity. In order to reduce timing noise as well as to realize synchronization with electrical signals, subharmonic pulses from a 40-GHz actively mode-locked (AML) semiconductor laser are

5 568 injected into the CPM laser. Pulse durations for the AML and CPM lasers are 3.6 and 1.9 ps, respectively. Timing noise of the free-running and injection-locked CPM lasers is evaluated using TIA and TDD techniques, respectively, combined with OEHM. Upper and lower traces in Fig. 4 show time dependences of the pulse repetition frequency deviation for the free-running and injection-locked CPM lasers, respectively [11]. During the period of 2 s rms frequency jitter amounts to 240 khz and 9.9 Hz, for the free-running and injection-locked lasers, respectively. with injection locking is closely related to the locking bandwidth, the excess noise will be reduced by increasing the injected power. IV. SUMMARY Table 1 summarizes the performance of timing noise measurement techniques developed by the author. By combining TDD, TIA and OEHM techniques, we can evaluate timing noise of optical pulses with a repetition frequency between 15 Hz and 160 GHz with a 300-dB dynamic range. Table 1 Performance of timing noise measurement Repetition Frequency Frequency Range Dynamic Range 15Hz 160GHz 2.5 mhz 18.6 MHz < 300 db ACKNOWLEDGMENT The author would like to thank Dr. Y. Ogawa of Oki Electric Company for providing mode-locked semiconductor lasers. Fig. 5 PN-PSD and rms timing jitter for the AML and CPM lasers. Figure 5 shows the timing noise of AML and CPM lasers, respectively [11]. At free-running operation, the CPM laser exhibits large timing noise at low frequency due to the thermal drift of the repetition frequency. The rms jitter amounts to 1.8 ns for 10 Hz 9.7 MHz bandwidth. It can be seen that injection locking by the AML laser drastically reduces the timing noise of the CPM laser and the amount of noise reduction is becoming larger for lower frequency. The value of PSD for the injection-locked CPM laser is almost 16 times that of the AML laser below 100 khz indicating that the CPM lasers is precisely synchronized with the AML laser. The rms jitter for the CPM laser is 342 fs for 10 Hz 18.6 MHz bandwidth. However, there is a larger difference between the AML and CPM lasers above 100 khz suggesting incomplete synchronization. Since the bandwidth of noise reduction obtained REFERENCES [1] H. Tsuchida, Wideband phase-noise measurement of mode-locked laser pulses by a demodulation technique, Opt. Lett., vol. 23, no. 4, pp , February [2] H. Tsuchida, Correlation between amplitude and phase noise in a mode-locked Cr:LiSAF laser, Opt. Lett., vol. 23, no. 21, pp , November [3] H. Tsuchida, Time interval analysis of laser pulse timing fluctuations, Opt. Lett., vol. 24, no. 20, pp , October [4] H. Tsuchida, Pulse timing stabilization of a mode-locked Cr:LiSAF laser, Opt. Lett., vol. 24, no. 22, pp , November [5] H. Tsuchida, Timing-jitter reduction of a mode-locked Cr:LiSAF laser by simultaneous control of cavity length and pump power, Opt. Lett., vol. 25, no. 20, pp , October [6] H. Tsuchida, Pulse timing stabilization of a mode-locked laser using an external phase modulator, Jpn. J. Appl. Phys. Part 1, vol. 41, no. 1, pp , January 2002.

6 569 [7] H. Tsuchida, Time-domain measurement of pulse-timing fluctuations in a mode-locked laser diode, IEEE Photon. Technol. Lett., vol. 14, no. 4, pp , April [8] H. Tsuchida, Timing jitter measurement of 78 GHz optical time-division multiplexed pulses by optoelectronic harmonic mixing, Opt. Lett., vol. 27, no. 22, pp , November [9] H. Tsuchida, Pulse timing-jitter reduction by incoherent addition, Opt. Lett., vol. 28, no. 6, pp , March [10] H. Tsuchida, Pulse timing noise reduction of a mode-locked laser diode by incoherent addition (invited paper), IEEE J. Sel. Top. Quantum Electron, vol. 9, no. 4, pp , July/August [11] H. Tsuchida, Timing noise measurement of 160-GHz optical pulses by optoelectronic harmonic mixing, IEICE Trans. Electron., vol. E87-C, no. 7, pp , July [12] H. Tsuchida, Timing noise measurement of 320 GHz optical pulses using an improved optoelectronic harmonic mixer, Opt. Lett., vol. 31, no. 5, pp , March [13] D. von der Linde, Characterization of the noise in continuously operating mode-locked lasers Appl. Phys. B, vol. 39, pp , [14] T. Yilmaz, C. M. Priest, and P. J. Delfyett, Jr., Complete characterization of external cavity semiconductor laser hybridly modelocked at 10 GHz, Electron. Lett., vol. 37, no. 22, pp , October [15] S. Arahira, Y. Katoh, D. Kunimatsu, and Y. Ogawa, Stabilization and timing jitter reduction of 160 GHz colliding-pulse mode-locked laser diode by subharmonic-frequency optical pulse injection, IEICE Trans. Electron., vol. E83-C, no. 6, pp , June 2000.

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