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A femtosecond pulse characterization technique is developed using frequency-resolved optical gating based on the two-photon absorption in an InP crystal. The technique provides direct visual monitoring of pulse frequency chirping in the time-spectral domain for femtosecond pulses with a pulse energy as low as 3.8 pJ. Pulse chirping and pedestal wings of 10-GHz optical fiber solitons are characterized experimentally for the first time by this technique.
©2000 Optical Society of America
1. Introduction
Characterization of weak ultrashort optical pulses propagated in optical fibers and photonic devices has growing importance in the cutting-edge optical time-division multiplexing technology. Pulse spectrogram measurement based on frequency-resolved optical gating (FROG) in the time-frequency domain has provided a method to characterize ultrashort optical pulses [1]. For optical pulses with a pulse energy as low as a few pJ, high-sensitivity FROG based on second-order optical nonlinearity such as sum-frequency generation (SFG) was used, and pulse distortion at wavelengths near zero chromatic dispersion in a 700-m optical fiber was characterized [2]. A disadvantage of SFG FROG is that the technique produces an unintuitive pulse spectrogram that is symmetric in time due to the frequency mixing between gate and probe pulses. Thus, important information about optical pulses such as frequency chirping cannot be directly obtained without a reference [1]. Direct visual monitoring of pulse chirping at first sight by an intuitive pulse spectrogram plays a significant role in systematic analysis of chromatic dispersion in optical fiber communication systems over a long distance, since pulse distortion changes from time to time in such complex networks.
The sign of pulse chirping is uniquely determined, and an intuitive pulse spectrogram that directly reveals the magnitude and the sign of the pulse chirp can be obtained by third-order nonlinearity (χ (3) FROG, in which polarization rotation due to the Kerr effect or transient grating by four wave mixing under nonresonant virtual photoexcitation in a transparent medium is used as a mechanism of frequency-independent optical gating. However, the minimum pulse energy for the conventional χ(3) FROG is typically orders of magnitude higher than that in the high-sensitivity SFG FROG [1] and is thus unsuitable for characterizing weak pulses in optical fibers. Alternatively, an intuitive pulse spectrogram can be produced in cross-correlation-type SFG FROG using Fourier-transform-limit gate pulses [3]. In this system, however, timing synchronization between the probe and gate pulses, which limits the measurement time resolution in the cross-correlation technique, becomes a serious issue after long-distance pulse propagation in optical fibers.
In this paper, we have developed a novel high-sensitivity intuitive pulse spectrogram measurement technique based on two-photon absorption (TPA) in a semiconductor. Unlike the conventional χ (3) FROG that utilizes a nonresonant real part of χ (3), TPA in a semiconductor leads to a much larger coefficient of the imaginary part of χ (3). The optical gating efficiency in TPA FROG can be optimized by selecting a semiconductor suitable to the spectral range of the optical pulses under test, since the TPA coefficient is inversely proportional to the wavelength detuning of the incident optical pulses scaled relative to the fundamental-absorption edge of the semiconductors [4]. At lightwave communication wavelengths of 1500 nm, TPA in an InP crystal of about 300-µm thickness provides an efficiency sufficient for pulse spectrogram measurement of femtosecond optical pulses with energies lower than 4 pJ. The TPA FROG technique has been applied to the pulse spectrogram measurement of soliton pulses in a link of dispersion-managed optical fibers.
2. Measurement apparatus
An apparatus for TPA autocorrelation and pulse spectrogram measurements is illustrated in Fig. 1. The linear-polarized optical pulses under test were split into cross-polarized probe and gate pulses with an energy separation ratio of 50:50 through a half-wave plate (HWP) and a polarization beam splitter (PBS). The probe pulses represented the pulses under test, while the gate pulses provided the function of an absorptive time window. A variable delay of the gate pulses was generated by a retro-reflector scanned at a rate of 10 Hz. The probe and gate pulses were chopped with dual acousto-optic modulators (AOMs) at incommensurate frequencies of f 1 and f 2 for low-noise background-free detection using a lock-in amplifier. f 1 and f 2 were 1020 and 850 kHz, respectively. A difference frequency of |f 1-f 2| was taken as a reference for the lock-in amplifier. The chopping and reference signals were phase-locked. The probe and gate pulses were recombined colinearly through a polarization beam coupler (PBC), and focused onto an antireflection-coated (AR) InP crystal of 300-µm thickness through an aspheric lens (L) with a spot diameter of 5 µm. The colinear geometry was relevant to maintaining the overlap of the probe and gate pulses in the TPA medium. The gate pulses from the AR InP were blocked by a polarizer (pol.). Either of TPA autocorrelation and spectrogram measurements was selected by holding up or down a flipping mirror (FM). The zero point of the gate delay time was set at the peak of a TPA autocorrelation trace. The photoreceivers were InGaAs photodiodes (PDs).
3. Measurement results
3.1 TPA autocorrelation and TPA coefficient
TPA autocorrelation traces were taken with femtosecond pulses from an optical parametric oscillator (OPO) to investigate the TPA characteristics and obtain the TPA coefficient. The OPO pulses were generated at a repetition rate of 80 MHz in Fourier transform limit with a 180-fs duration, a 1500-nm peak wavelength and a 17-nm spectral bandwidth. The peak intensity of the TPA autocorrelation traces grows with increasing pulse energy as shown on the left of Fig. 2. The peak intensity is plotted as a function of pulse energy W pulse on the right of Fig. 2 and reveals a quadratic dependence on W pulse as compared with a fitting curve described below.
Fig. 2. Left: TPA autocorrelation traces with different incident pulse energies. Right: pulse energy dependence of the TPA peak intensity from the autocorrelation traces (red dots) and a theoretical curve in the weak absorption limit (blue curve).
Theoretical pulse energy dependence is derived under the condition that reflections from the front and back surfaces are negligible. The optical intensity I (d) transmitted through a TPA medium of a thickness d is generally written as [5]
Here, I 0, and β represent incident intensity and TPA coefficient, respectively. The incident intensity I 0 is substituted with 4W pulse/(πD2τ pulse) using a spot diameter D and a pulse duration τ pulse. In the low absorption limit for weak pulses, namely I 0 βd={4W pulse/(πD 2 τ pulse)}βd<<1, Eq. (1) is reduced to
where ΔI(d) corresponds to the TPA intensity. This indicates that the TPA intensity is proportional to the square of W pulse in this limit. The TPA coefficient is obtained by fitting with a theoretical curve in Eq. (2). The TPA coefficient for the AR InP is obtained as about 1×10-8 cm/W, using the values D=5 µm, τpulse=180 fs and d=300 µm. The value provides the lower limit of the TPA efficiency since variation in the beam diameter along the depth direction is not taken into account. A waveguide structure should be employed for an accurate measurement of the TPA efficiency. The TPA coefficient was experimentally obtained for other semiconductors. In an InGaAsP waveguide with a band-edge wavelength of 1150 nm for example, the TPA coefficient was obtained as 6×10-8 cm/W at 1500 nm [6]. This is qualitatively higher than that of the AR InP, because the band-edge wavelength in the InGaAsP waveguide is closer to the one-photon wavelength of 1500 nm. Thus, InGaAsP thin layers, when stacked in a semiconductor optical amplifier waveguide should serve as a high-efficiency TPA medium for a spectrogram measurement with a pulse energy below 1 pJ, since the insertion loss to the waveguide can be cancelled by the gain.
The upper bound of pulse energy is limited by the bandgap reduction due to carriers generated via the two-photon transition. Transient probe transmission characteristics were measured using OPO pulses with a 100-pJ gate pulse energy and a 1-pJ probe pulse energy. A trace for the probe transmission characteristics is presented as a function of probe delay time in Fig. 3. The trace provides a slowly decaying absorption tail after the instantaneous TPA correlation peak. The absorption tail is caused by an increase in the linear optical absorption due to bandgap reduction in the AR InP. The bandgap reduction is induced by carriers generated under two-photon excitation with the gate pulses only. This result indicates that the pulse trailing edge is distorted and the pulse spectrogram cannot be measured accurately on account of the bandgap reduction if the energy of an incident pulse reaches about 100 pJ. In the case of even higher input energy, there is another origin of pulse distortion, that is self-phase modulation (SPM) due to the ultrafast refractive index change induced by the TPA. Change in pulse spectrum by SPM is, however, negligible if the pulse energy is less than a few 100 pJ.
Fig. 3. TPA autocorrelation trace for transform-limit OPO pulses with gate and probe pulse energies of 100 and 1 pJ, respectively.
3.2 Measurement of chirped OPO pulses
The TPA pulse spectrogram in the low absorption limit is defined as
which is the magnitude square of the Fourier transform of the probe electric field E(t) multiplied by a time window of gate intensity |E(t-τ)|2, identical to the case of the polarization-gate FROG [1]. Here, ω and τ are the angular frequency and gate delay time, respectively. TPA pulse intensity spectrograms, which provided S TPA(λ, τ) with wavelength λ instead of ω, were obtained in the experiments. Frequency chirping is directly visualized in TPA pulse intensity spectrograms as demonstrated in Fig. 4 with the OPO pulses with a negative, zero and a positive group delay dispersion. Group delay dispersion of the OPO pulses was varied by transmitting the OPO pulses through a pulse shaper. The pulse shaper, which consisted of a diffraction grating and a lens, generated a group delay dispersion with a variable magnitude and variable sign according to the distance between grating and lens [7]. The TPA intensity in Fig. 4 changes from zero to its maximum as the color turns from red to purple. In each case of group delay dispersion, the pulse energy from the OPO was attenuated to a pulse energy of 3.8 pJ incident to the apparatus. Measurement sensitivity P AV P peak for the OPO pulses of zero dispersion leads to 6.3×10-3 W2 using an average power P AV=3.0×10-4 W and a peak power P peak=21 W with a pulse duration of 180 fs and a repetition rate of 80 MHz. The intensity and phase of the OPO pulses were obtained by a pulse retrieval algorithm (FROG 3.02, http://www.wco.com/~fsoft) for the polarization-gate FROG as presented in Fig. 5. The retrieved phase data reveal the negative or positive group delay dispersion produced at the pulse shaper. The phase of the zero-dispersion pulses seems to be limited by higher-order chromatic dispersion which can not be compensated at the pulse shaper.
Fig. 4. TPA pulse intensity spectrograms for OPO pulses with a negative, zero and a positive group delay dispersion.
Fig. 5. Pulse intensity (red dots) and phase shift (blue dots) data retrieved from the TPA spectrograms for the OPO pulses in Fig. 4.
3.3 Characterization of 10-GHz soliton pulses
As an application of the TPA spectrogram technique, low-energy 10-GHz soliton pulses were characterized. Fiber nonlinearities and dispersion effects play a significant role in ultrashort pulse propagation in optical fibers. Understanding the details of the soliton pulses by spectrogram measurements is essential in the development of lightwave communication technologies. The source set-up for the 10-GHz soliton pulses is depicted in the inset of Fig. 6. The 1550-nm continuous wave (CW) light from an external cavity laser was transformed to 11-ps pulses at 10 GHz through a DC-biased InGaAsP quantum-well electroabsorption modulator (EAM) driven by an RF source. The pulses were amplified up to an average power of 260 mW through an Er-doped fiber amplifier (EDFA). The amplified pulses were compressed in a 2-km standard single-mode fiber (SMF) using the second-order soliton compression. The pulses were further compressed using the adiabatic soliton compression through a 630-m dispersion-decreasing fiber (DDF) [8]. At the DDF output, femtosecond soliton pulses were generated with a time duration of 280 fs and a pulse energy of about 12 pJ.
A time-integrated spectrum of the soliton pulses is presented on the left of Fig. 6. The spectrum seems to consist of a broad peak (about 10-nm band width) and an intense narrow peak near the center of the broad component. The broad peak has been considered from numerical simulation as the main soliton component, while the narrow peak as the pedestals. A TPA pulse intensity spectrogram of the soliton pulses is plotted to the right of Fig. 6. The spectrogram shows a short pulse component around the zero delay, a weak narrow spectral band near the center of the spectrum and weak fringes outside the shot pulse component. The short pulse component has a few 100-fs temporal width. The weak narrow spectral band and the fringes, on the other hand, decay slowly in time.
To analyze the characteristics of the soliton pulses, the intensity and phase of the soliton pulses were reconstructed by the FROG pulse retrieval algorithm as shown in Fig. 7 with a FROG error of 0.006. The retrieved pulse has a positive group delay dispersion. This indicates that the soliton pulses can be further compressed if the positive group delay dispersion is compensated. The retrieved pulse characteristics is compared with the theoretical characteristics from numerical simulation based on a nonlinear Schrödinger equation [8]. The theoretical soliton pulses have a duration of 250 fs and are limited by a positive group delay dispersion. These characteristics are qualitatively similar to those of the retrieved pulses. In the theoretical pulse shape, the pedestal wings appear on both sides of the main soliton pulse as plotted in a magnified scale in Fig. 7. These pedestal wings are visualized as the narrow spectral band and the fringes in the experimental spectrogram. Noise in the experimental spectrogram limits the FROG error and masks the pedestal components in the retrieved pulse shape. Further improvement of the sensitivity such as by using an InGaAsP waveguide is required to clarify the pedestal characteristics experimentally in pulse reconstruction.
Fig. 6. Time-integrated spectrum (left) and TPA pulse intensity spectrogram (right) of 10-GHz optical fiber soliton pulses. Inset: a set-up for the soliton pulse generation.
Fig. 7. The retrieved and theoretical intensity (red dots) and phase of the soliton pulses (blue dots). Inset: theoretical intensity of the pulses in a magnified scale.
4. Conclusion
A high-sensitivity spectrogram measurement technique based on optical gating by two-photon absorption in an InP crystal has been developed to characterize ultrashort optical pulses with energy as low as 3.8 pJ in the 1.5-µm wavelength range. The technique was applied for characterization of 10-GHz optical fiber solitons. Pulse chirping of the solitons and time-spectral distribution of pedestal parts were visualized for the first time.
5. Acknowledgements
The work in this paper was supported by the New Energy and Industrial Technology Development Organization (NEDO).
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