A novel scheme to eliminate the artificial background phase jitter is proposed for measuring the carrier-envelope phase drift of tunable infrared femtosecond pulses from an OPA laser. Different from previous methods, a reference spectral interference measurement is performed, which reveals the artificial phase jitter in the measurement process, in addition to the normal f-to-2f interference measurement between the incident laser pulses and it second harmonic. By analyzing the interference fringes, the accurate CEP fluctuation of the incident pulses is obtained.
© 2008 Optical Society of America
Carrier-envelope phase (CEP) is the relative phase between the envelope peak of a pulsed electric field and the closest peak of the carrier wave . CEP and its stabilization have been the critical parameters of ultrafast laser pulses in strong field interactions, such as above threshold ionization (ATI) and high harmonic generation (HHG) [2, 3]. For example, CEP stabilization is a necessary requirement for isolated attosecond pulses generation based on HHG in atoms subjected to intense few cycle laser pulses [4, 5]. Recently, CEP stabilized pulses in the near infrared (IR) wavelength region (1.5–3µm) were regarded as the optimum driving laser pulses for isolated attosecond pulse generation .
Several methods were put forward to measure the CEP drift or stability of few cycle laser pulses [5, 7–9]. The so-called f-to-2f spectral interference (SI) is a widely used technique for CEP stability measurement [7–10]. Concerning an amplified IR pulse, the typical measurement procedure includes three steps: first, the incident pulses are stretched to be octave-spanning in spectrum, such as being focused on a sapphire plate to generate white light continuum (WLC) that covers over one octave; then a piece of nonlinear crystal is used to frequency double the fundamental laser pulse; at last, the SI signals are generated between the fundamental laser pulse and its frequency doubled pulse. The SI signals can then be used to calculate the CEP fluctuation of the incident laser pulse. Single path collinear f-to-2f spectral interferometer is generally used for it is relatively compact and stable than typical two paths f-to-2f spectral interferometer. However, in single path f-to-2f spectral interferometer, the optical path difference for generating the SI signal is fixed for a certain incident laser wavelength. When the incident pulses are tuned widely in wavelength, the spectral range and period of the interference fringes change consequently. And it is difficult for a real spectrometer to measure and analyze the Fourier transform spectral interference accurately and sufficiently for too long or too short period. While with a two paths f-to-2f unit, the two-path SI signals can be optimized and identified easily by adjusting the optical path delay. However, the two-path method may cause other measurement noise which is brought in by the fluctuation of the optical length of the two paths. Based on above discussion, we designed a new two-path measurement which had the advantages of both methods. And as a SI method, it does not give the actual value of the CEP but is sensitive only to changes in the CEP.
2. Experiment and theoretical analysis
In this letter we demonstrate a novel two paths f-to-2f spectral interferometer for CEP stability measurement where the artificial background phase jitter is eliminated. A Mach-Zehnder interferometer based two paths f-2f spectral interferometer is used. Different from previous f-to-2f spectral interferometer, the generated white-light continuum (WLC) is divided into two paths; one of which passes a time-delay line and the other passes a β-barium borate (BBO) crystal. After recombination of the two beams with a beamsplitter, not only the interference signal between the fundamental pulses (FF) and its second harmonic (SH) is obtained, but also the interference signal of the fundamental pulses between the two paths is measured at the same time. The former SI contains the information of both real CEP drift of the incident laser pulses and the measurement noise, while the latter contains only the artificial phase jitter in the measurement process. By comparing the phase information inferred from these two groups of interference fringes, the accurate CEP shift of incident laser pulses can be obtained.
The experimental setup is shown in Fig. 1. The CEP stabilized pulses to be measured are produced by a home-made optical parametric amplification (OPA) system seeded and pumped by a commercially available 1kHz 50fs Ti:sapphire laser at 800nm based on the scheme of chirped pulse amplification (Spitfire 50, Spectra Physics), with a tunable output from 1.3µm to 2.3µm . A passive stabilization scheme for CEP is used in this OPA system. The incident laser pulse is attenuated to ~1µJ in energy, and then focused onto a 2-mm-thick sapphire plate to generate WLC by self-phase modulation process. The measurement for the 1.6µm laser pulses are shown in the following as an example. In this case, the WLC covers from 800nm to 2.1µm after the sapphire plate. After being collimated by a thin lens, the WLC is split to two beams. One passes a time-delay line (path 1), and the other is focused on a 3-mm-thick BBO crystal which serves as a SHG crystal (path 2). Therefore, the pulses in path 1 contain fundamental component only, and the pulses in path 2 contain two sets of spectra, fundamental and its second harmonic component after the BBO crystal (phase matched for SHG near 910 nm). While the fundamental and frequency doubled spectral parts in path 2 are orthogonally polarized. To solve this problem, a half-wave plate is inserted in path 1 to change the beam polarization in path 1 to generate the components both in the vertical and horizontal directions. When the beams from path 1 and path 2 are recombined by a beam splitter (BS 2), two groups of interference fringes are generated (shown in Fig. 2). Interference between the fundamental component from path 1 and the second harmonic component from path 2 generate a group of interference fringes around 910nm with the information of CEP jitter by tuning the BBO crystal and adjusting the delay line. That’s what one can obtain by using an ordinary f-to-2f interferometer . However, in the present case, another group of interference fringes around 1000nm due to the interference between the fundamental components from both two paths are also observed. Obviously, this set of interference fringes contain only the information of artificial phase jitter caused by the fluctuation of optical length difference between the two paths, the direction fluctuation of laser beam, and so on.
In order to confirm the interference fringes are what we need, the time-delay line is adjusted for the first step. As a result, the periods of both groups of the interference fringes are changed follow the delay time which indicates that the interference fringes are originated from the interference between the pulses from two different paths. Secondly, a 2mm thick BK7 plate is inserted in the incident pulses before WLC generation. And one group of the fringes (SI between FF and SH with CEP jitter information) change their position, while the other (SI between FF and FF with only measurement error information) don’t. The two set of interference fringes what we need are both identified.
The temporal evolution of a linearly polarized electric field of a single pulse can be expressed in the form: E=A(t)cos[ω(t)t+φce]. This description includes three physical parameters: the amplitude A(t), the frequency of field oscillations ω(t) (ω(t)=ω0+β(t), where ω0 stands for the central wavelength and β(t) stands for a possible chirp, if the chirp is constant, β(t)=β), and φce is CEP. After being focused on the sapphire plate, the femtosecond pulse spectrum is broadened. Here, we take 1.6µm incident pulses as an example (ω0=2πc/λ, λ=1.6µm) again. After the sapphire plate, the spectrum is broadened from 800nm to 2.1µm. And ω1, ω2 are supposed as the central frequency of two components whose wavelengths are around 1000nm and 1820nm, respectively. As shown in Fig. 1, l1 is the optical length of path 1 (from BS1 to BS2 passing by the time-delay unit); l2+l3 is the optical length of path 2 (l2, from BS1 to BBO; l3, from BBO to BS2); t1=l1/c, t2=l2/c and t3=(l2+l3)/c.
Thus, on BS 2, the pulses of the fundamental components at 1000nm coming from path 1 and path 2 can be respectively expressed as: I1(ω)▫cos (ω1t1+φce) and I2(ω)∝ cos (ω1t3+φce). By using a spectrometer, the interference fringes of I1(ω) and I2(ω), which contain the information of measurement noise, are obtained and can be expressed as: I3(ω)∝ cos[ω1(t1-t3)]. Simultaneously, through path 1, the pulses of the fundamental component around 910 nm can be expressed as: I4(ω)∝ cos(2ω2t1+φce); through path 2, the pulses of the fundamental component around 1820 nm is: I5-FF(ω)∝ cos(ω2t2+φce) before the BBO crystal. And after frequency doubling in the BBO crystal, the pulses of the SH component around 910nm can be expressed as: I5-SH(ω)∝ cos(2ω2t3+2φce). Therefore, the interference fringes between the FF and SH components are also obtained: I6(ω)∝ cos[2ω2(t1-t3)-φce]. Analyzing I3(ω) and I6(ω)by the use of Fourier transform and a filtering technique, we get two relative phases from two groups of interference fringes at a certain time: φnoise=ω1(t1-t3) contains the information of measurement noise due to optical path jitter and φce&noise=2ω2(t1-t3) -φce contains information of both CEP and measurement noise. Finally, the accurate CEP without background noise (noise caused by the optical path jitter) is now available: φce&noise·2ω2/ω1-φcenoise. Besides, the interference patterns expressed by I3(ω) and I6(ω) follow one form: I (ω)∝ cos(ωt+φce)=cos(2πΔL/λ +φce), ΔL represents the optical path difference. If λ1 and λ2 are set as the wavelengths of two neighboring peaks of the fringes, there must be 2πΔL/λ1-2πΔL/λ2=2π and Δλ=λ1 2/ΔL (Δλ=λ2-λ1, λ1≈λ2). Therefore the period of the SI signal is ~λ1 2/ΔL, that’s to say, a change in λ1 will result in visible change to the period that may make the fringes too sparse or too dense for a spectrogram and hard to be analyzed. For this reason, an adjustable ΔL is needed to catch suitable signals for tunable wavelengths.
In the experiment, the exposure time of the spectrometer is set to be 1 ms, so that the relative CEP of single laser pulse can be measured. The interference fringes between the two fundamental components from different paths are shown in Fig. 3(a). These fringes containing the information of the measurement noise can be expressed by I3(ω), as mentioned earlier. And Fig. 3(b) shows the interference fringes between FF and SH, which contain the information of both CEP and measurement noise, expressed by I6(ω). In the two figures, the left panels show a single-shot interference pattern, while the right panels show the sequence of these interferograms during 3500 seconds. The fluctuation of the noise phase (φnoise) and the mixing phase (φce&noise) are revealed intuitively from the right panels of Figs. 3(a) and 3(b). The phase fluctuations of φce&noise, φnoise and φce are respectively shown by curves in Fig. 4. Among the curves, Fig. 4(a) shows how the mixing phase (φce&noise) changes during 3500 seconds, and that is what we obtained through previous methods. Evidently, its stability is much worse than the exact CE phase (φce) which is shown in Fig. 4(c). That’s because the measurement noise caused by the jitter of optical length and the amplitude disturbs the interference fringes. The fluctuation of noise phase (φnoise) shown in Fig. 4(b) caused by the environmental factors and the direction fluctuation of laser beam, takes a similar trend to that shown in Fig. 4(a). Besides, it is shown that, the measurement noise is strong enough for the CEP stability of the incident pulses in the measurement with duration of about 1 hour. And the CEP fluctuation of φce&noise from Fig. 4(a) and φnoise from Fig. 4(b) are 0.476rad (rms) and 0.332rad (rms), respectively. Following the above analysis, the CE phase (φce) without the measurement noise can be calculated by φce&noise and φnoise. And its fluctuation curve shown in Fig. 4(c) is almost flat. Finally, the CEP fluctuation of the 1.6µm incident pulses is 0.223rad (rms) over 3500 seconds.
Theoretically, the ideal output pulses from an OPA by means of difference frequency generation (DFG) process should be CEP stabilized. But there always be some disturbance which causes CEP fluctuation during the generation and the propagation of the laser pulses. By using this CEP stability measurement method, we demonstrate that our home-made infrared tunable OPA laser without any active CEP stabilization element can output tunable and CEP stabilized pulses in a relatively long period. As an example, the CEP fluctuation is 0.223rad (rms) over a 3500s for the 1.6µm incident pulses. The measurement error due to the influence of optical path jitter, the direction fluctuation of laser beam, and other environmental variation which finally translate into optical path jitter is eliminated. In addition, from Fig. 4(c), the CEP fluctuation curve is almost flat, but there is also fluctuation resulted from minor random noise. Then the pure CEP fluctuation is attributed to the CEP stabilized pulses themselves from the OPA laser. The real CEP fluctuation of the OPA output pulses still sensitively depends on many environmental conditions, such as temperature fluctuation and mechanical vibration. Under the good condition (peace night), we have measured the CEP fluctuation of the OPA output pulses is <0.1rad (rms) in shorter term. Therefore, we estimate the uncertainty of our measurement is <0.1rad. Besides, this method can’t eliminate the measurement noise caused by the intensity fluctuation of the input laser beam.
Moreover, from I3(ω) and I6(ω), the periods of the interference fringes (~λ1 2/ΔL) are adjusted to the spectrometer by changing the time delay line (ΔL) which makes it convenient to measure the CEP fluctuation of the tunable laser pulses. If the wavelength of the input laser changes, adjusting the time-delay line and crystal angle will make the fringes suitable for the spectrometer. That shows its distinct advantage to the previous single path method.
In summary, a new two-path interferometer for the CEP drift measurement of infrared tunable laser pulse was demonstrated. The scheme eliminates the CEP fluctuation measurement error due to artificial background phase jitter by measuring two groups of interference fringes at the same time. The interference fringes between FF and SH components which contain the information of both real CEP jitter of laser pulses and the environmental noise. And the interference fringes of fundamental pulses from both paths represent the noise information which can be used to correct the CEP drift measurement. Finally, we obtained the accurate CEP drift as 0.223 rad over 3500s for the 1.6µm laser pulses from an OPA laser.
This work is supported by the National Basic Research Program of China (Grant No.2006CB806000), National Natural Science Foundation (Grant Nos. 10734080, 10523003), the Knowledge Innovation Program of Chinese Academy of Sciences (Grant No.KGCX-YW-417), and Shanghai Commission of Science and Technology (Grant Nos. 06DZ22015 and 07JC14055).
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