ctuj6 analysis of comb frequency offset variations via phase

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Analysis of Comb Frequency Offset Variations via Phase-Only Line-by-Line Pulse Shaping
J. Caraquitena, Z. Jiang, D.E. Leaird, and A.M. Weiner
School of Electrical and Computer Engineering, Purdue University, 465 Northwestern Ave., West Lafayette, IN 47907-2035, USA jcaraqui@purdue.edu, zjiang@purdue.edu , leaird@purdue.edu, amw@purdue.edu

Abstract: We investigate the effect of optical frequency comb shifts on time-domain and RFdomain signals generated using phase-only line-by-line pulse shaping. As an application, we estimate the comb frequency offset fluctuations of a harmonically mode-locked laser.
2007 Optical Society of America
OCIS codes: (320.5540) Pulse shaping; (120.3930) Metrological instrumentation; (070.6760) Talbot effect.

Spectral line-by-line pulse shaping permits individual control of the amplitudes and phases of the discrete spectral components of an optical frequency comb. Further, it has been shown that optical arbitrary waveform generation based on line-by-line control is sensitive to comb frequency offset fluctuations [1]. Recently, this observation has motivated the first quantitative investigation of the impact of optical frequency offsets on time-domain intensity waveforms generated via line-by-line pulse shaping [2]. The influence of frequency offset variations on generated waveforms was analyzed for several line-by-line passband filter functions accompanied, in some cases, with spectral phase control. In Ref. [2], the optical comb was generated by a phase-modulated CW laser and the effects of the frequency offsets were emulated by shifting the center wavelength of the CW laser. Here, we perform phase-only line-by-line pulse shaping on a harmonically mode-locked 9-GHz fiber laser in order to evaluate the frequency offset variations with high fidelity. We demonstrate, through simulations and experimental results, that the resultant time-domain waveforms and RF spectra change in a simple fashion with the optical comb shift and, as a result, frequency offsets can be simply derived from these measurements. Further, we show that noise in the measured time-domain waveforms provides direct information about comb frequency offset fluctuations of the mode-locked laser.
LCM shift (µm)
9 GHz

LCM shift (µm)

Phase (π) I(T/2)/I(0)





0 -20





0 0

50 100 150 200 250 300

Frequency (GHz)
Fig. 1. Ideal (dashed) and real (solid) phase transfer function. The optical frequency comb for different frequency offsets is also represented.

Frequency offset (%)

RF spectra contrast ratio (dB)

0 100 200 300 400 500 600

0 100 200 300 400 500 600 60 (b) 50 40 30 20 10 0 -10 0 50 100 150 200 250 300

Frequency offset (%)

Fig. 2. Measured (dots) and calculated (dashed curve) contrast rations in (a) timedomain and (b) RF-domain.

A home-built actively mode-locked Er-fiber laser producing ~3-ps pulses at 9 GHz repetition rate, and 1542 nm center wavelength is utilized as the pulse source for our experiments. Spectral line-by-line control is performed by using a carefully designed pulse shaper [1] which includes a liquid crystal modulator (LCM) array that allows us to independently manipulate both the amplitude and phase of individual spectral lines making up the mode-locked laser frequency comb. The resulting optical signal is characterized by using an optical spectrum analyzer and a 20-GHz photodiode followed by a sampling scope and RF spectrum analyzer. Intensity cross-correlation measurements are also performed. In the experiment, we program the LCM to obtain a phase mask consisting of a periodic two-phase sequence {0, π/2} so that the same phase-shift is applied to every other line over the whole optical frequency comb. Ideally, the resultant spectral filter is a scaled version of the spatial masking function [3], as shown in Fig. 1 (dashed curve). However, numerical simulations accounting for the finite (2.6 GHz) spectral resolution of our shaper show

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that the effective phase filter is a smooth function (solid curve). We arbitrarily choose zero relative frequency offset when the optical comb is centered on the frequency filter, as shown in Fig. 1 (black solid comb). Under this condition, the resultant time-domain waveform is, according to the temporal Talbot effect [4,5], a doubled repetition-rate replica of the input pulse train. Note that when the comb is shifted (grey combs), the effective phaseshifts applied to the spectral lines change in such a way that the phase difference between adjacent lines is gradually decreased ultimately to a zero phase-difference for 50% optical frequency offset. By further increasing the offset, the phase-difference value increases, in absolute value, until approaching π/2 for 100% frequency offset. This behavior is periodically repeated for larger offsets. It is simple to demonstrate that, for all frequency offsets except 50%, 2X repetition-rate multiplication is still obtained; however, adjacent pulses have different relative amplitudes depending on each particular phase-difference value. In other words, the only effect of shifting the comb is a change in the ratio of I(T/2) to I(0) in the output multiplied train, where T=111.1 ps is the period of the input pulse train in our experiments. This suggests the contrast ratio I(T/2)/I(0) as a suitable parameter to evaluate the variations of frequency offset. In Fig. 2(a) we show the calculated value of the contrast ratio as a function of comb frequency offset (dashed curve). In this experiment, we utilize a mode-locked laser as a comb source. In order to emulate the effects of frequency offsets we instead shift the LCM. In this way, there is a well-known relationship between the LCM shift and the equivalent frequency offset according to the linear spatial dispersion of the pulse shaper which in our specific design is α=3.54e-13 cm(rad/s)-1. This method is valid if the mode locked laser is stable or, alternatively, has frequency offset fluctuations varying around an average value, which will be confirmed by our experimental results given below. Fig. 2(a) shows the contrast ratio as a function of LCM-shift obtained from the measured scope traces (averaged 20 times). The experimental data are in good agreement with simulation results for contrast ratios higher than ~0.25. For smaller ratios, there is some deviation between theory and experiment which is attributed to the limited bandwidth of the 20-GHz photodiode. This is confirmed by performing intensity crosscorrelation measurements for which the resultant contrast ratios are in very good agreement with simulation results for all contrast values. A different approach to analyze the comb shifts is to measure the RF spectra after O/E conversion of the time-domain waveforms and, then, compare the first and second harmonics. In this way, Fig. 2(b) shows the calculated and experimental ratio of RF spectrum between the second and first harmonics as a function of frequency offset. In general, the agreement between theory and experiment is very good. The discrepancy at high contrast ratios is attributed to offset fluctuation effects. So far, the reported experimental results are the result of averaged measurements. We have also analyzed the time-domain waveforms obtained from the sampling scope without averaging. Fig. 3 shows typical scope traces (overlap of 100 scans) together with the corresponding averaged waveforms for different frequency offsets. Note that for ~0% offset, shown in Fig. 3(a), very clear sampling scope traces are generated. In contrast, for ~50% and ~25% offsets, Figs. 3(b) and 3(c) respectively, the resultant sampling scope traces are noisy. Noise is mainly found in the regions between the original input pulses (at T/2 and odd Fig. 3. Sampling scope traces for (a) multiples). Much weaker fluctuations, if any, are observed at the time locations of 0%, (b) 50%, and (c) 25% offsets. the input pulses. The amount of noise being dependent on frequency offset is consistent with how the value of I(T/2)/I(0) changes as a function of the frequency offset, shown in Fig. 2(a). Further, by calculating the noise standard deviation at T/2 in Fig. 3(c) and considering the variation of contrast ratio with offset, we have estimated the comb frequency offset fluctuations of the mode locked laser to be ~5% or 450 MHz (obtained as twice the value of the standard deviation). These comb shifts could not be measured by using our optical spectrum analyzer due to the limited spectral resolution (0.01 nm or 1.25 GHz). The effect of frequency comb shifts on time-domain and RF-domain signals generated using grating-based lineby-line pulse shaping has been quantitatively analyzed. Specifically, a spectral line-by-line phase-only filter has been considered which allows us to easily evaluate the frequency offset variations from the resultant time-domain waveforms and RF spectra. Finally, we have estimated the comb frequency offset fluctuations of our harmonically mode locked laser by analyzing the noise in the time-domain waveforms measured with a sampling scope. References
1. 2. 3. 4. 5. Z. Jiang, D. S. Seo, D. E. Leaird, and A. M. Weiner, Opt. Lett. 30, 1557-1559 (2005). C.-B. Huang, Z. Jiang, D. E. Leaird, and A. M. Weiner, submitted to Optics Express. A. M. Weiner, Rev. Sci. Instr. 71, 1929-1960 (2000). J. Azaña and M. A. Muriel, J. Sel. Top. Quantum Electron. 7, 728-744 (2001). J. Caraquitena, Z. Jiang, D. E. Leaird, and A. M. Weiner, accepted for publication in Optics Letters.

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