Open Access
Add to BibSonomyAbstract
The characteristics of pulse trapping by use of ultrashort soliton pulses in optical fibers across the zero-dispersion wavelength are analyzed both experimentally and numerically. The spectrogram of pulse trapping is observed by use of the cross-correlation frequency-resolved optical gating technique, and the phenomenon of pulse trapping is confirmed directly. The pulse trapping is numerically analyzed by use of the coupled strict nonlinear Schrödinger equations, and the numerical results are in good agreement with the experimental ones. It is clarified that the pulse trapping results from the sequential cross-phase modulation by the Raman-shifted soliton pulse.
©2002 Optical Society of America
1. Introduction
With optical fibers and ultrashort pulses, nonlinear optical effects can be obtained effectively. We have demonstrated the generation of widely wavelength-tunable femtosecond soliton pulses and supercontinua, using several kinds of polarization-maintaining fibers [1–3]. For such wideband light generation, the dispersion characteristic of the fiber is one of the important factors. With photonic crystal fibers, anomalous dispersion can be obtained over a wide wavelength region [4]. The generation of wavelength-tunable soliton pulses and supercontinua has also been demonstrated by use of photonic crystal fibers, tapered fibers, and microstructure fibers [5–9]. These light sources are useful for ultrafast optoelectronics, spectroscopy, optical coherent tomography, and so on.
When the optical pulses collide in the optical fibers, the interaction phenomena between the pulses occur through the nonlinear effects in the optical fibers [10]. More than ten years ago, Islam et al. discovered the phenomenon of soliton trapping in birefringent optical fibers [11]. In this phenomenon, the orthogonally polarized fundamental soliton pulses trap one another and copropagate along the fiber. The wavelengths of the two soliton pulses are shifted toward the shorter and the longer wavelength sides as a result of cross-phase modulation (XPM), and the group-velocity mismatch from birefringence is compensated by the chromatic dispersion. The phenomenon of soliton trapping has been investigated in the low power regime, in which the effect of intrapulse Raman scattering is negligible.
Very recently, we discovered the novel phenomenon of trapped pulse generation by use of ultrashort soliton pulses [12]. This is the phenomenon in which the orthogonally polarized trapped pulse is generated by the ultrashort soliton pulse in birefringent fibers. The trapped pulse that is polarized along the fast axis experiences Raman gain from the soliton pulse that is polarized along the slow axis. The trapped pulse and the soliton pulse temporally overlap and copropagate along the fiber.
The soliton trapping and trapped pulse generation that are mentioned above are trapping phenomena between orthogonally polarized optical pulses in the anomalous-dispersion region. Recently, we discovered in experiments the phenomenon of pulse trapping by femtosecond soliton pulses across the zero-dispersion wavelength [13]. The optical pulse in the normal-dispersion region is trapped by an ultrashort soliton pulse in the anomalous-dispersion region. The wavelength of the trapped pulse is shifted to satisfy the group-velocity matching, and the soliton pulse and the trapped pulse copropagate along the fiber. It is expected that the phenomenon of pulse trapping is useful for wavelength control and optical switching of optical pulses in the normal-dispersion region.
In 1988 the coupling between the bright and the dark solitons across the zero-dispersion wavelength was discovered numerically by two groups [14,15]. However, this phenomenon is observed only when the effect of Raman scattering is ignored. When the effect of Raman scattering is active, the dark soliton cannot be sustained during pulse propagation [16]. Thus a large wavelength shift does not occur for this soliton coupling phenomenon.
In Ref. 13 we noted the experimental discovery of pulse trapping across the zero-dispersion wavelength. The mechanism and the precise behavior of the pulse trapping, however, have not yet been clarified.
In this paper we investigate the characteristics of pulse trapping by use of an ultrashort soliton pulse across the zero-dispersion wavelength both experimentally and numerically. The spectrogram of pulse trapping is directly observed by use of the cross-correlation frequency-resolved optical gating (X-FROG) technique [12,17,18]. In the numerical analysis, the coupled nonlinear Schrödinger equations are used and the behavior and physical mechanism of pulse trapping are investigated.
2. Experiment
To analyze the phenomenon of pulse trapping, we have generated the soliton pulse and the anti-Stokes pulse using two different fibers and have used them as the control pulse and the signal pulse, respectively [13]. Figure 1 shows the experimental setup. A passively mode-locked Er-doped fiber laser (IMRA femtolight) is used as the pump light source. It generates 110-fs sech2-like pulses stably at a repetition frequency of 48 MHz. The center wavelength of the output pulse is 1.56 μm, and the spectral width is ∼20 nm [18]. The average output power is 60 mW.
The output of the laser is divided into two components by beam splitter BS1. A large part of the laser output is coupled into a 10-m-long diameter reduced-type polarization-maintaining fiber (PMF). The mode field radius is 6 μm, and the second-order dispersion β2 is -15 ps2/km at a wavelength of 1.55 μm. In the PMF, a wavelength tunable soliton pulse results from the effect of the soliton self-frequency shift (SSFS) [1,19]. The output of this fiber is passed through a low-pass filter, and only the generated soliton pulse is selected. The temporal width is 110 fs at full width at half-maximum (FWHM), and the pedestal free transform limited sech2 pulses are obtained.
A small part of the laser output is coupled into a 10-m-long polarization-maintaining highly nonlinear dispersion shifted fiber 1 (PM-HN-DSF1) [20]. The mode field radius is 3.7 μm, the magnitude of nonlinearity γ= 20 W-1km-1, and the second- and third-order dispersions are β2= -2 ps2/km, β3=0.01 ps3/km at a wavelength of 1.55 μm. In this fiber a wavelength tunable soliton pulse and an anti-Stokes pulse are generated [2]. The output of the fiber is also passed through the high-pass filter, and only the anti-Stokes pulse is selected and used as the signal pulse. The anti-Stokes pulse is not the transform-limited one, and it has a few peaks [2,18]. The actual temporal width that is measured by the cross-correlation method is ∼ 2 ps. The temporal separation between the soliton pulse and signal pulse is varied by use of a corner mirror. Then the pulses are spatially overlapped at beam splitter BS2 and coupled again into PM-HN-DSF2. The parameters of the fiber are the same as those of PM-HN-DSF1. The polarization directions of the two pulses are adjusted to the same birefringent axis of the fiber.
The output pulses from PM-HN-DSF2 are observed by use of the optical spectrum analyzer (Anritsu MS9710B) and the X-FROG system. The bandwidth of the optical spectrum analyzer is 600-1750 nm. In the X-FROG system, the input pulses are divided into two optical components [12,17,18]. One of them is passed through the low pass filter, and only the soliton pulse is selected and used as the reference pulse. The reference pulse and the signal pulse are temporally overlapped at the 5-mm-thick BBO crystal, and the generated sum frequency signals are observed with monochromator and photo multiplier tube. The temporal difference between the signal pulse and reference pulse are varied using the corner mirror. In the X-FROG system, we can observe the spectrogram (temporal distribution of the spectral components) precisely with high sensitivity.
Fig. 1. Experimental setup of pulse trapping by ultrashort soliton pulse across the zero-dispersion wavelength.
When the group velocity of the soliton pulse is slower than that of the signal pulse and the soliton pulse is coupled into PM-HN-DSF2 slightly before the signal pulse, a collision between the soliton pulse and the signal pulse occurs during pulse propagation. In this case we have observed that the signal pulse is trapped by the soliton pulse and the two pulses copropagate along the fiber.
Figure 2 shows the observed optical spectra at the input and output of PM-HN-DSF2 when pulse trapping occurs. The length of PM-HN-DSF2 is 150 m. The measured delay time owing to chromatic dispersion in PM-HN-DSF2 is also shown in Fig. 2. At the input of PM-HN-DSF2, the ideal sech2-shaped soliton pulse at a wavelength of 1650 nm (anomalous-dispersion region) and the signal pulse at a wavelength of 1440 nm (normal-dispersion region) are coupled into the fiber. The power of the signal pulse is 50 μW in front of the input port of PM-HN-DSF2. The coupling coefficient into PM-HN-DSF2 is about 40 %.
Figure 2(b) shows the optical spectra of output pulses from PM-HN-DSF2 when the power of soliton pulse is 1.4 mW in front of the input port of the fiber. During the propagation along PM-HN-DSF2, the wavelength of the soliton pulse is shifted toward the longer wavelength side due to the effect of SSFS. The spectral shape remains sech2. The residual component that is not converted into the wavelength-shifted soliton pulse is negligibly small. The conversion efficiency of the SSFS is as great as 99%. As shown in Fig. 2(b), when the pulse trapping occurs, most of the spectral component of signal pulse is shifted to ∼1360 nm. At this wavelength, the group velocity of the signal pulse is almost the same as that of the soliton pulse, and the condition of the group-velocity matching is satisfied. If the soliton pulse is not coupled into PM-HN-DSF2, the optical spectrum of the signal pulse returns to that of the fiber input.
Figure 2(c) shows the optical spectra when the power of the soliton pulse is 3.1 mW. In this case, the wavelength of the soliton pulse is shifted up to 1880 nm and that of the trapped pulse is shifted to 1275 nm. The large wavelength shift is observed for both pulses. The condition of group-velocity matching is also satisfied in this power condition.
Fig. 2. Variation of optical spectra of output pulses for pulse trapping. The dotted line represents the delay time in fiber owing to chromatic dispersion.
Fig. 3. Characteristics of wavelength shift of soliton and trapped pulse as a function of power of soliton pulse in front of PM-HN-DSF2.
Figure 3 shows the characteristics of wavelength shift of soliton and trapped pulse at the output of 150-m-long PM-HN-DSF2 as a function of the power of soliton pulse in front of the fiber. As the power of soliton pulse is increased, the wavelength of soliton pulse is shifted continuously toward the longer wavelength side as a result of SSFS. The wavelength of trapped pulse is shifted to the wavelength at which the group velocity has the same magnitude of that of soliton pulse. As a result, one can shift the wavelength of the trapped signal pulse continuously by varying the power of the soliton pulse. In this experiment, as the power of the soliton pulse is increased up to 4 mW, the wavelength of soliton pulse is shifted from 1.65 to 1.95 μm and that of trapped pulse is shifted from 1.45 to 1.25 μm. If the fiber input power is much increased, we can obtain much larger wavelength shift.
Figure 4 shows the observed spectrogram for initial process of pulse trapping in 10 m of PM-HN-DSF using X-FROG technique. The power of soliton pulse is 4 mW in front of the fiber. In the X-FROG measurement, the soliton pulse is selected using the LPF and used as the reference pulse. For the soliton pulse, a pedestal free almost transform limited sech2 pulse is clearly observed. The temporal width is about 100 fs. For the trapped pulse, the leading part of the trapped pulse overlaps with the trailing edge of the soliton pulse and suffers the blue shift due to the effect of XPM. From the result of X-FROG measurement, we confirm that the signal pulse at normal-dispersion region is trapped by the soliton pulse at anomalous-dispersion region.
3. Numerical analysis and discussion
Next, we numerically analyze the phenomenon of pulse trapping across the zero-dispersion wavelength. The two independent ultrashort pulse propagation and interaction are represented with the strict coupled nonlinear Schrödinger equations written as [9]
where A and B represent the amplitudes of the pulse envelopes for the soliton and signal pulse, respectively. The symbol z is the distance and T=t-β1 z, where t is the time and β1 is the first-order dispersion for the soliton pulse. The left hand sides represent the linear effects; the effects of the chromatic dispersions are included. In the pulse trapping, since the wavelengths of the soliton and signal pulse are different, the magnitudes of the chromatic dispersions and the initial group velocities are different for two pulses. The symbols β2A and β3A are the magnitudes of the second- and third-order dispersions for the soliton pulse. In the same way, β2B and β3B are the magnitudes of the second- and third-order dispersions for the signal pulse. The effect of the initial group-velocity difference is included as the parameter d. The right hand sides correspond to the nonlinear effects; self-phase modulation, XPM, self-steepening, and intrapulse Raman scattering are considered. The symbol γ is the magnitude of the nonlinear coefficient in the fibers, ω0A and ω0B are the center angular frequencies for the soliton and signal pulses, and T R is the coefficient for the Raman scattering.
For the optical fiber, the PM-HN-DSF, which is used in the experiment, is assumed. For the soliton pulse and signal pulse, 100 and 200 fs transform limited sech2 pulses are assumed. The center wavelength of the soliton pulse is 1.65 μm and that of the signal pulse is 1.4 μm at fiber input. The peak powers are 175 W for soliton pulse and 1 W for signal pulse, respectively. The coupled nonlinear Schrödinger equations are calculated using the split step Fourier method. In this simulation, we assume that the center of the signal pulse is delayed from that of the soliton pulse temporally by 250 fs.
Figure 5(a) shows the numerical results of the temporal variation for pulse trapping. The propagation length is changed from 0 to 15 m. The horizontal axis represents T, which is the temporal axis moving with the group velocity of input soliton pulse. In the pulse propagation, the group velocity of the soliton pulse is monotonously decreased due to SSFS. It is observed that when the signal pulse overlaps with the soliton pulse, the signal pulse sees the high index wall induced by the soliton pulse and it cannot go ahead of the soliton pulse. In other words the signal pulse suffers the XPM by the soliton pulse and it is trapped and copropagates with the soliton pulse along the fiber. The leading part of the trapped pulse is almost always overlapped with the trailing edge of the soliton pulse and the temporal shape is complex. For the propagation length above 15 m, the signal pulse is always caught at the trailing edge of the soliton pulse. The temporal width is about 1.5 ps at -10 dB level when the fiber length is 10 m. These results are in agreement with the experimental ones in Fig. 4. When the fiber length is increased up to 150 m, the temporal width of the trapped pulse is 2.6 ps at -10 dB level. If the pulse trapping does not occur, the temporal width of the signal pulse is broadened to be 15 ps at -10 dB level due to the effect of normal dispersion when the fiber length is 150 m. Thus we can say that the pulse broadening is suppressed by the pulse trapping. Owing to the soliton effect the soliton pulse keeps the sech2 shape after a few meters propagation.
Figure 5(b) shows the variation of optical spectra for the pulse trapping when the propagation length is changed from 0 to 150 m. At the beginning of the pulse propagation, the signal pulse suffers the blue-shift due to XPM by the soliton pulse. In the pulse propagation, the wavelength of soliton pulse is red shifted due to SSFS. As the propagation length is increased, the magnitude of wavelength shift is increased monotonously and almost continuously for both pulses. In the results of numerical analysis, almost 100 % conversion efficiencies are obtained for SSFS and pulse trapping. The spectral shape of the soliton pulse is kept to be sech2 one when the fiber length is longer than 10 m. The spectral shape of the trapped pulse is constructed with a few peaks and the wavelength of the trapped pulse is shifted to satisfy the condition of group-velocity matching. The numerical results are well in agreement with the experimental ones.
Figure 5(c) shows the variation of spectrogram for soliton and trapped pulse. The propagation length is 0-15 m. The spectrogram is calculated from the numerical results under assumption of the polarization gate (PG)-FROG measurement [21]. In the spectrogram, we can see both the temporal and spectral variations of two pulses simultaneously. The observed spectrogram is almost the same as that of the X-FROG measurement used for the experiment. In the PG-FROG measurement, we can observe the actual wavelength of detected signals. The soliton pulse at fiber input is assumed to be the probe pulse. We can see that the signal pulse cannot go ahead of the soliton pulse and is trapped by the soliton pulse. The signal pulse suffers the blue shift due to XPM by the soliton pulse. For the propagation length above 15 m, the leading part of the trapped pulse is almost always overlapped with the trailing edge of the soliton pulse.
Fig. 5. ((a) 223KB, (b) 690KB, (c) 1.17MB) Variation of (a) temporal and (b) spectral waveforms, and (c) spectrogram of soliton and trapped pulse. The corresponding propagation length is (a)(c) 0-15 m and (b) 0-150 m. In order to clarify the behavior of pulse trapping, the signal pulse is enlarged. In (a) and (c), the horizontal axis represents the magnitude of T, which is the temporal axis moving with the initial group velocity of the soliton pulse at fiber input. In (a) and (b), the red and blue lines show the soliton and signal pulses, respectively.
When the soliton pulse is in the middle of the signal pulse temporally at the fiber input, the component of the signal pulse which is delayed from the center of the soliton pulse is trapped by the soliton pulse and the leading part is not trapped and propagates independently. For the wavelength dependence of the trapping efficiency, the magnitude of trapping efficiency is decreased as the magnitude of group-velocity mismatch is increased. These results are in agreement with the experimental ones in ref. 13.
In the numerical simulation, when the effect of Raman scattering is neglected, the wavelength of the soliton pulse is not changed along the pulse propagation. For the signal pulse, the wavelength of the signal pulse is slightly blue shifted by the XPM when the collision between the soliton pulse and signal pulse initially occurs. Then the two pulses are separated temporally and the wavelength of the signal pulse is not changed after the initial pulse collision.
From these results, the physical mechanism of the pulse trapping is explained as follows. We assume that the signal pulse is coupled into the fiber after the soliton pulse at the fiber input. When the collision between the soliton and signal pulse occurs, the signal pulse suffers the XPM and the wavelength is blue shifted. Since the wavelength of the signal pulse is in normal-dispersion region, the magnitude of the group velocity of the trapped pulse is decreased and the trapped pulse is delayed from the soliton pulse. Then the wavelength of the soliton pulse is red-shifted due to the SSFS and the group velocity of the soliton pulse is decreased. Thus the soliton pulse and signal pulse collide again and the signal pulse suffers the blue shift again due to XPM. In the propagation, the signal pulse and soliton pulse collide repeatedly and the signal pulse suffers the sequential blue shift when the pulse collision occurs. As mentioned above, the physical mechanism of pulse trapping is the sequential XPM by the Raman shifted soliton pulse. This phenomenon is not observed when the effect of Raman scattering is not active.
Lately, ultrawide-broadened super continuum generation is receiving considerable attention and several groups are investigating the physical mechanism of super continuum generation [3,5,6,22]. We have also demonstrated wavelength tunable anti-Stokes pulse generation using dispersion shifted fiber [2,18]. The behavior of the blue shift of both the shorter wavelength side of the super continuum and the anti-Stokes pulse in more than several meter long fiber are the same as that of pulse trapping [2,3,18,22]. We believe that such a blue shift is induced by pulse trapping by the soliton pulse.
4. Conclusion
In this paper we have analyzed the characteristics of pulse trapping by use of ultrashort soliton pulses in optical fibers across the zero-dispersion wavelength both experimentally and numerically. In the experiment the wavelengths of the soliton pulse and the trapped pulse are shifted continuously to satisfy the group-velocity matching as the fiber input power of the soliton pulse is changed. The pulse trapping between the soliton pulse and trapped pulse is directly observed with the X-FROG measurement. The characteristics of pulse trapping are also analyzed by the use of coupled nonlinear Schrödinger equations. The behavior of pulse trapping is clearly shown in the temporal and spectral domains. The pulse trapping is also represented in terms of the spectrogram, and the initial process of pulse trapping is represented precisely. The observed spectrogram for pulse trapping is almost in agreement with the numerical ones. Using the results of analysis, we have clarified that the physical mechanism of pulse trapping is due to the sequential XPM by the Raman-shifted soliton pulse. We believe that the blue shift of both the shorter wavelength components of SC and anti-Stokes pulses in long fibers are induced though the pulse trapping across the zero-dispersion wavelength.
Acknowledgement
We would like to thank Dr. M. Onishi, T. Okuno and M. Hirano in Sumitomo Electric Industries for providing us with the PM-HN-DSFs. A part of this work is supported by Grant-in Aid for Scientific Research on Priority Areas.
References and links
1. N. Nishizawa and T. Goto, “Compact system of wavelength tunable femtosecond soliton pulse generation using optical fibers,” IEEE Photon. Technol. Lett. 11, 325–327 (1999). [CrossRef]
2. N. Nishizawa, R. Okamura, and T. Goto, “Widely wavelength tunable ultrashort soliton pulse and anti-Stokes pulse generation for wavelengths of 1.32-1.75 μm,” Jpn. J. Appl. Phys. 39, L409–L411 (2000). [CrossRef]
3. N. Nishizawa and T. Goto, “Widely broadened super continuum generation using highly nonlinear dispersion shifted fibers and femtosecond fiber laser,” Jpn. J. Appl. Phys. 40, L365–L367 (2001). [CrossRef]
4. J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photon. Technol. Lett. 12, 807–809 (2000). [CrossRef]
5. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000). [CrossRef]
6. T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation in tapered fibers,” Opt. Lett. 25, 1415–1417 (2000). [CrossRef]
7. X. Liu, C. Xu, W. H. Knox, J. K. Chanadalia, B. J. Eggleton, S. G. Kosinski, and R. S. Windeler, “Soliton self-frequency shift in atapered air-silica microstructure fiber,” Opt. Lett. 26, 358–360 (2001). [CrossRef]
8. J. H. V. Price, K. Furusawa, T. M. Monro, L. Lefort, and D. J. Richardson, “Tunable, femtosecond pulse source operating in the range 1.06-1.33 μm based on an Yb3+-doped holey fiber amplifier,” J. Opt. Soc. Am. B 26, 1286–1294(2002). [CrossRef]
9. N. Nishizawa, Y. Ito, and T. Goto, “0.78-0.90-μm wavelength-tunable femtosecond soliton pulse generation using photonic crystal fiber,” IEEE Photon. Technol. Lett. 14, 986–988 (2002). [CrossRef]
10. G. P. Agrawal, Nonlinear fiber optics, third ed. (Academic, San Diego, Calif.2001).
11. M. N. Islam, C. D. Poole, and J. P. Gordon, “Soliton trapping in birefringent optical fibers,” Opt. Lett. 14, 1011–1013 (1989). [CrossRef] [PubMed]
12. N. Nishizawa and T. Goto, “Trapped pulse generation by femtosecond soliton pulse in birefringent optical fibers,” Opt. Express 10, 256–261 (2002) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-5-256. [CrossRef] [PubMed]
13. N. Nishizawa and T. Goto, “Pulse trapping by ultrashort soliton pulses in optical fibers across zero-dispersion wavelength,” Opt. Lett. 27, 152–154 (2002). [CrossRef]
14. S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Optical solitary waves induced by cross-phase modulation,” Opt. Lett. 13, 871–873 (1988). [CrossRef] [PubMed]
15. V. V. Afanas’ev, E. M. Dianov, A. M. Prokhorov, and V. N. Serkin, “Nonlinear pairing of light and dark optical solitons,” JETP Lett. 48, 638–642 (1988).
16. V. V. Afanasjev, E. M. Dianov, and V. N. Serkin, “Nonlinear pairing of short bright and dark soliton pulses by phase cross modulation,” IEEE J. Quantum Electron. 25, 2656–2664 (1989). [CrossRef]
17. S. Linden, H. Giessen, and J. Kuhl, “XFROG-a new method for amplitude and phase characterization of weak ultrashort pulses,” Phys. Stat. Sol. (b) 206, 119–124(1998). [CrossRef]
18. N. Nishizawa and T. Goto, “Experimental analysis of ultrashort pulse propagation in optical fibers around zero-dispersion region using cross-correlated frequency resolved optical gating,” Opt. Express 8, 328–335 (2001) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-6-328. [CrossRef] [PubMed]
19. F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11, 659–661 (1986). [CrossRef] [PubMed]
20. T. Okuno, M. Onishi, T. Kashiwada, S. Ishikawa, and M. Nishimura, “Silica-based functional fibers with enhanced nonlinearity and their applications,” IEEE J. Select. Topics in Quantum Electron. 5, 1385–1391 (1999). [CrossRef]
21. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997). [CrossRef]
22. B. R. Washburn, S. E. Ralph, and R. S. Windeler, “Ultrashort pulse propagation in air-silica microstructure fiber,” Opt. Express 10, 575–580 (2002) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-13-575. [CrossRef] [PubMed]
