OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 15 — Jul. 20, 2009
  • pp: 12345–12350
« Show journal navigation

Warm target recoil ion momentum spectroscopy for fragmentation of molecular hydrogen by ultrashort laser pulses

Jia Liu, Jian Wu, Achim Czasch, and Heping Zeng  »View Author Affiliations


Optics Express, Vol. 17, Issue 15, pp. 12345-12350 (2009)
http://dx.doi.org/10.1364/OE.17.012345


View Full Text Article

Acrobat PDF (471 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We demonstrate warm target recoil ion momentum spectroscopy for the fragmentation dynamics of the warm hydrogen molecules at room temperature. The thermal movement effect of the warm molecule is removed by using a correction algorithm in the momentum space. Based on the reconstructed three-dimensional momentum vectors as well as the kinetic energy release spectra, different vibrational states of the H+2 ground state are clearly visible and the internuclear separation for charge resonance enhanced ionization of the second electron is identified. The results show adequate accordance with the former experiments using other techniques.

© 2009 Optical Society of America

1. Introduction

The Coltrims (Cold target recoil ion momentum spectroscopy), with a distinct multi-hits imaging ability and high momentum resolution, is widely used in the research of momentum imaging of electron and ion dynamics in strong laser fields [1

1. R. Dörner, V. Mergel, O. Jagutzki, L. Spielberger, J. Ullrich, R. Moshammer, and H. Schmidt-Böcking, “Cold Target Recoil Ion Momentum Spectroscopy: a ‘momentum microscope’ to view atomic collision dynamics,” Phys. Rep. 330, 95–192 (2000). [CrossRef]

3

3. Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-Ion Momentum Distributions for Single and Double Ionization of Helium in Strong Laser Fields,” Phys. Rev. Lett. , 84, 443–446 (2000). [CrossRef] [PubMed]

]. In general, ultracold target gas (~several mK) from supersonic jet expansion is used to rule out the thermal effects and obtain an optimal momentum resolution, which is actually difficult to handle. Here, we demonstrate the 3D momentum spectroscopy applicable on a room-temperature gas. We call this Wartrims (Warm target recoil ion momentum spectroscopy) as an allusion to Coltrims. It is shown that measurements of reactions where all fragments are charged do not necessarily need a supersonic gas jet system if a well-suited correction algorithm is applied on the data on an event-by-event basis. In this paper, as an example, we focus on the fragmentation dynamics of the molecular H2 exposed to intense near-IR femtosecond laser pulses. Different fragmentation channels produce distinct features in the kinetic energy release spectrum [4

4. S. Alnaser, T. Osipov, E. P. Benis, A. Wech, B. Shan, C.L. Cocke, X.M. Tong, and C. D. Lin, “Rescattering Double Ionization of D2 and H2 by Intense Laser Pulses,” P hys. Rev. Lett. 91, 163002 (2003). [CrossRef]

6

6. Ben-Itzhak, P. Q. Wang, A. M. Sayler, K. D. Carnes, M. Leonard, B. D. Esry, A. S. Alnaser, B. Ulrich, X. M. Tong, I. V. Litvinyuk, C. M. Maharjan, P. Ranitovic, T. Osipov, S. Ghimire, Z. Chang, and C. L. Cocke, “Elusive enhanced ionization structure for H+2 in intense ultrashort laser pulses,” Phys. Rev. A 78, 063419 (2008). [CrossRef]

], and different vibrational states are thus clearly visible. The results show an adequate accordance with the former experiments using cold targets.

2. Experimental setup

A schematic of the experimental setup is shown in Fig. 1(a). The femtosecond laser pulses from an amplified Ti:Sapphire laser system (800 nm, 40 fs, 1 kHz) were focused into an ultrahigh vacuum chamber (background pressure ~10-10 Torr) by a f=25 cm lens. Rather than using a supersonic gas jet for Coltrims, the room-temperature target gas was introduced into the chamber through a variable leak valve. The photon-ionization-induced ions were detected by the multichannel plate at the end of the time-of-flight spectrometer. The position information was then extracted by the time difference of the signals at the ends of the delay line detector. The complete 3D momentum vectors of the fragments were eventually obtained by combining the time-of-flight spectra and position information.

3. Software cooling

Different ionization/dissociation channels are identified on the basis of their characteristic momentum distributions, and the rule of momentum conservation is applied to identify the true coincident channels, such as H2→H++H+ for H2. Similar to the Coltrims, here, the z-axis velocities of the ionic fragments are calculated based on the arriving time difference between the forward and backward ions, and the x-axis and y-axis velocities are deduced form the spatial distributions of the fragments on the detector. The obtained momentum vectors are then used to calculate the kinetic energy release and angular distributions of the ions. However, in our case with room temperature gas, before the molecule is destroyed it has a certain velocity. Usually the thermal velocity is several hundred meters per second, corresponding to a kinetic energy of ~40 meV. Once the molecule is fragmented, the two ions fly away back to back from each other and land on the detector. Since each particle is measured independently from the other, it is possible to calculate the velocity of their center of mass, which can be subtracted from the two measured velocities. We then can obtain the momentum vectors as if the target gas is frozen. We call this technique as software cooling.

Fig. 1. (a) Schematic of the experimental apparatus. (b) Potential energy curves for H2 and H+ 2.

We take the Coulomb explosion of H2 with an initial thermal velocity vector of vthermo=(1133.0, 1133.0, 1133.0) m/s as an example, the corresponding molecular kinetic energy and momentum vector are 40 meV and 0.944 a.u., respectively. Supposing that the kinetic energy each ion gains is 3.0 eV, and the molecule is oriented along the z-axis, the velocity of each H+ fragments gain is 24063.2 m/s. Equation 1 shows the velocity vectors of the fragments

v1=(1133.0,1133.0,24063.2+1133.0)m/sv2=(1133.0,1133.0,24063.2+1133.0)m/s.
(1)

This net kinetic energy gain of 3.0 eV can then be extracted from the measured signals by applying the software cooling conditions as

v1'=v1(v1+v2)2=(v1v2)2=(0,0,24063.2)m/sv2'=v2(v1+v2)2=(v2v1)2=(0,0,24063.2)m/s,
(2)

which account for the real momenta or kinetic energy gain of the ionic fragments from the Coulomb explosion process. As shown in Eq. 2, the thermal effect of the warm target gas is removed, making our Wartrims a powerful tool for momentum analysis.

4. Results and discussions

H2 has relatively simple ionization and breakup (H2+ 2, H++H+, H+ 2, H++H) channels as compared to other molecules. Figure 1(b) shows the potential energy curves of H2 and H+ 2. By single ionization of H2, the molecule (initially in the ground state) is excited to the 1sσg electronic state of molecular ion H+ 2. The wave packets will propagate along this new potential curve, and the decrease of the energy gap between the ground 1sσg and the excited 2pσu states leads to subsequent breakup processes. Bond softening dissociation [7

7. P. H. Bucksbaum, A. Zavriyev, H. G. Muller, and D. W. Schumacher, “Softening of the H+2 molecular bond in intense laser fields,” Phys. Rev. Lett. 64, 1883–1886 (1990). [CrossRef] [PubMed]

] (if more than the minimum number of photons are absorbed, it turns to the above-threshold dissociation) and charge resonance enhanced ionization [8

8. T. Seideman, M. Y. Ivanov, and P. B. Corkum, “Role of Electron Localization in Intense-Field Molecular Ionization,” Phys. Rev. Lett. 75, 2819–2822 (1995). [CrossRef] [PubMed]

] are considered as the two main fragmentation channels. The charge resonance enhanced ionization results in an enhancement of the ionization rate at a critical internuclear distance Rc due to the barrier suppression at the specific internuclear separation [9

9. T. Zuo and A. D. Bandrauk, “Charge-resonance-enhanced ionization of diatomic molecular ions by intense lasers,” Phys. Rev. A 52, R2511–R2514 (1995). [CrossRef] [PubMed]

], where a second electron is ionized and subsequently exploded into two H+ [10

10. S. Alnaser, X. M. Tong, T. Osipov, S. Voss, C. M. Maharjan, P. Ranitovic, B. Ulrich, B. Shan, Z. Chang, C. D. Lin, and C. L. Cocke, “Routes to Control of H2 Coulomb Explosion in Few-Cycle Laser Pulses,” Phys. Rev. Lett. 93, 183202 (2004). [CrossRef] [PubMed]

]. In different H2 experiments, the charge resonance enhanced ionization, which gives the largest ionization probability in the kinetic energy release of 2–4 eV, is observed and considered as the dominant channel of sequential ionization [11

11. G. N. Gibson, M. Li, C. Guo, and J. Neira, “Strong-Field Dissociation and Ionization of H+2 using Ultrashort Laser Pulses,” Phys. Rev. Lett. 79, 2022–2025 (1997). [CrossRef]

,12

12. Rudenko, B. Feuerstein, K. Zrost, V. L. B. de Jesus, T. Ergler, C. Dimopoulou, C. D. Schröter, R. Moshammer, and J. Ullrich, “Fragmentation dynamics of molecular hydrogen in strong ultrashort laser pulses,” J. Phys. B: At. Mol. Opt. Phys 38, 487–501 (2005). [CrossRef]

].

Fig. 2. (a) Time-of-flight spectra of H2 at different driving intensities, normalized by using the H+ 2 peaks. TOF: time-of-flight, BS: bond softening, ATD: above-threshold dissociation, CREI: charge resonance enhanced ionization. (b) The photoion-photoion coincidence spectrum.

In our experiments, the polarization of the laser field is parallel to the spectrometer axis (z-axis), leading to a maximum ionization probability of the diatomic molecules orientating along this direction [17

17. J. Wu, H. Zeng, and C. Guo, “Polarization effects on nonsequential double ionization of molecular fragments in strong laser fields,” Phys. Rev. A 75, 043402 (2007). [CrossRef]

,18

18. J. Wu, H. Zeng, and C. Guo, “Vertical and nonvertical transitions in triple-ionization-induced dissociation of diatomic molecules,” Phys. Rev. A 74, 065403 (2006). [CrossRef]

]. As shown in Fig. 3(a), a dumbbell-shaped momentum distribution along the z-axis is observed (i.e. Pz is much larger than Px and Py). The charge resonance enhanced ionization induced Coulomb explosion channel with fragmentation momentum of ~17 a.u. is clearly seen. Both momentum distributions of the Coulomb explosion induced H+ fragments for the cases with and without software cooling are shown in Fig. 3. As the software cooling is applied, the momentum distribution become slightly sharper and narrower by removing the thermal movement of the warm molecules. Here, the small difference between of the momentum distributions when the software cooling is applied or not is due to the broad momentum bandwidth of the dissociation channel that we studied as compared to the thermal effect. For dissociation channel with narrow momentum bandwidth, the software cooling influence will be much more visible, and is expected to be comparable to the Coltrims. The momentum resolution, depending on the position and timing resolution, can be improved by using tighter focusing condition or electrostatic lens to reduce the volume effect.

Fig. 3. The momentum distributions of the Coulomb explosion induced fragments H+ with and without software cooling.

Fig. 4. (a) Measured and fitted dissociation energy of the single-ionization-induced H+ fragmentation at a driving intensity of 7.5×1013 W/cm2. (b) The charge resonance enhanced ionization probability as a function of internuclear separation. The inset is the Edisso as well as the ECERI spectrum of H+.

5. Summary

Acknowledgement

This work was funded in part by National Natural Science Fund (Grants 10525416 and 10804032), National Key Project for Basic Research (Grant 2006CB806005), Projects from Shanghai Science and Technology Commission (Grant 08ZR1407100 and 09QA1402000), Program for Changjiang Scholars and Innovative Research Team in University, and Shanghai Educational Development Foundation (Grant 2008CG29). The authors thank the helpful discussions with O. Jagutzki.

References and links

1.

R. Dörner, V. Mergel, O. Jagutzki, L. Spielberger, J. Ullrich, R. Moshammer, and H. Schmidt-Böcking, “Cold Target Recoil Ion Momentum Spectroscopy: a ‘momentum microscope’ to view atomic collision dynamics,” Phys. Rep. 330, 95–192 (2000). [CrossRef]

2.

E. Gagnon, A.S. Sandhu, A. Paul, K. Hagen, A. Czasch, T. Jahnke, P. Ranitovic, C.L. Cocke, B. Walker, M.M. Murnane, and H.C. Kapteyn, “Time-resolved momentum imaging system for molecular dynamics studies using a tabletop ultrafast extreme-ultraviolet light source,” Rev. Sci. Instrum. 79, 063102 (2008). [CrossRef] [PubMed]

3.

Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-Ion Momentum Distributions for Single and Double Ionization of Helium in Strong Laser Fields,” Phys. Rev. Lett. , 84, 443–446 (2000). [CrossRef] [PubMed]

4.

S. Alnaser, T. Osipov, E. P. Benis, A. Wech, B. Shan, C.L. Cocke, X.M. Tong, and C. D. Lin, “Rescattering Double Ionization of D2 and H2 by Intense Laser Pulses,” P hys. Rev. Lett. 91, 163002 (2003). [CrossRef]

5.

B. D. Esry, A. M. Sayler, P. Q. Wang, K. D. Carnes, and I. Ben-Itzhak, “Above Threshold Coulomb Explosion of Molecules in Intense Laser Pulses,” Phys. Rev. Lett. 97, 013003 (2006). [CrossRef] [PubMed]

6.

Ben-Itzhak, P. Q. Wang, A. M. Sayler, K. D. Carnes, M. Leonard, B. D. Esry, A. S. Alnaser, B. Ulrich, X. M. Tong, I. V. Litvinyuk, C. M. Maharjan, P. Ranitovic, T. Osipov, S. Ghimire, Z. Chang, and C. L. Cocke, “Elusive enhanced ionization structure for H+2 in intense ultrashort laser pulses,” Phys. Rev. A 78, 063419 (2008). [CrossRef]

7.

P. H. Bucksbaum, A. Zavriyev, H. G. Muller, and D. W. Schumacher, “Softening of the H+2 molecular bond in intense laser fields,” Phys. Rev. Lett. 64, 1883–1886 (1990). [CrossRef] [PubMed]

8.

T. Seideman, M. Y. Ivanov, and P. B. Corkum, “Role of Electron Localization in Intense-Field Molecular Ionization,” Phys. Rev. Lett. 75, 2819–2822 (1995). [CrossRef] [PubMed]

9.

T. Zuo and A. D. Bandrauk, “Charge-resonance-enhanced ionization of diatomic molecular ions by intense lasers,” Phys. Rev. A 52, R2511–R2514 (1995). [CrossRef] [PubMed]

10.

S. Alnaser, X. M. Tong, T. Osipov, S. Voss, C. M. Maharjan, P. Ranitovic, B. Ulrich, B. Shan, Z. Chang, C. D. Lin, and C. L. Cocke, “Routes to Control of H2 Coulomb Explosion in Few-Cycle Laser Pulses,” Phys. Rev. Lett. 93, 183202 (2004). [CrossRef] [PubMed]

11.

G. N. Gibson, M. Li, C. Guo, and J. Neira, “Strong-Field Dissociation and Ionization of H+2 using Ultrashort Laser Pulses,” Phys. Rev. Lett. 79, 2022–2025 (1997). [CrossRef]

12.

Rudenko, B. Feuerstein, K. Zrost, V. L. B. de Jesus, T. Ergler, C. Dimopoulou, C. D. Schröter, R. Moshammer, and J. Ullrich, “Fragmentation dynamics of molecular hydrogen in strong ultrashort laser pulses,” J. Phys. B: At. Mol. Opt. Phys 38, 487–501 (2005). [CrossRef]

13.

Staudte, C. L. Cocke, M. H. Prior, A. Belkacem, C. Ray, H. W. Chong, T. E. Glover, R. W. Schoenlein, and U. Saalmann, “Observation of a nearly isotropic, high-energy Coulomb explosion group in the fragmentation of D2 by short laser pulses,” Phys. Rev. A 65, 020703 (2002). [CrossRef]

14.

M. R. Thompson, M. K. Thomas, P. F. Taday, J. H. Posthumus, A. J. Langley, L. J. Frasinski, and K. Codling, “One and two-color studies of the dissociative ionization and Coulomb explosion of H2 with intense Ti:sapphire laser pulses,” J. Phys. B: At. Mol. Opt. Phys 305755–5772 (1997). [CrossRef]

15.

L. J. Frasinski, K. Codling, and P. A. Hatherly, “Covariance Mapping: A Correlation Method Applied to Multiphoton Multiple Ionization,” Science 246, 1029–1031 (1989). [CrossRef] [PubMed]

16.

P. Hering and C. Comaggia, “Coulomb explosion of N2 and CO2 using linearly and circularly polarized femtosecond laser pulses,” Phys. Rev. A 59, 2836–2843 (1999). [CrossRef]

17.

J. Wu, H. Zeng, and C. Guo, “Polarization effects on nonsequential double ionization of molecular fragments in strong laser fields,” Phys. Rev. A 75, 043402 (2007). [CrossRef]

18.

J. Wu, H. Zeng, and C. Guo, “Vertical and nonvertical transitions in triple-ionization-induced dissociation of diatomic molecules,” Phys. Rev. A 74, 065403 (2006). [CrossRef]

19.

T. D. G. Walsh, F. A. Ilkov and S. L. Chin, “The dynamical behavior of H2 and D2 in a strong, femtosecond, titanium:sapphire laser field,” J Phys. B: At. Mol. Opt. Phys. 30, 2167–2175 (1997).

OCIS Codes
(020.4180) Atomic and molecular physics : Multiphoton processes
(020.2649) Atomic and molecular physics : Strong field laser physics

ToC Category:
Atomic and Molecular Physics

History
Original Manuscript: May 20, 2009
Revised Manuscript: June 25, 2009
Manuscript Accepted: June 25, 2009
Published: July 6, 2009

Citation
Jia Liu, Jian Wu, Achim Czasch, and Heping Zeng, "Warm target recoil ion momentum spectroscopy for fragmentation of molecular hydrogen by ultrashort laser pulses," Opt. Express 17, 12345-12350 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-15-12345


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. R. Dörner, V. Mergel, O. Jagutzki, L. Spielberger, J. Ullrich, R. Moshammer, H. Schmidt-Böcking, "Cold Target Recoil Ion Momentum Spectroscopy: a ‘momentum microscope’ to view atomic collision dynamics," Phys. Rep. 330, 95-192 (2000). [CrossRef]
  2. E. Gagnon, A.S. Sandhu, A. Paul, K. Hagen, A. Czasch, T. Jahnke, P. Ranitovic, C.L. Cocke, B. Walker, M.M. Murnane,and H.C. Kapteyn, "Time-resolved momentum imaging system for molecular dynamics studies using a tabletop ultrafast extreme-ultraviolet light source," Rev. Sci. Instrum. 79, 063102 (2008). [CrossRef] [PubMed]
  3. Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, "Recoil-Ion Momentum Distributions for Single and Double Ionization of Helium in Strong Laser Fields," Phys. Rev. Lett.,  84, 443-446 (2000). [CrossRef] [PubMed]
  4. S. Alnaser, T. Osipov, E. P. Benis, A. Wech, B. Shan, C.L. Cocke, X.M. Tong and C. D. Lin, "Rescattering Double Ionization of D2 and H2 by Intense Laser Pulses," P hys. Rev. Lett. 91, 163002 (2003). [CrossRef]
  5. B. D. Esry, A. M. Sayler, P. Q. Wang, K. D. Carnes, and I. Ben-Itzhak, "Above Threshold Coulomb Explosion of Molecules in Intense Laser Pulses," Phys. Rev. Lett. 97,013003 (2006). [CrossRef] [PubMed]
  6. Ben-Itzhak, P. Q. Wang, A. M. Sayler, K. D. Carnes, M. Leonard, B. D. Esry, A. S. Alnaser, B. Ulrich, X. M. Tong, I. V. Litvinyuk, C. M. Maharjan, P. Ranitovic, T. Osipov, S. Ghimire, Z. Chang, and C. L. Cocke, "Elusive enhanced ionization structure for H2+ in intense ultrashort laser pulses," Phys. Rev. A 78, 063419 (2008). [CrossRef]
  7. P. H. Bucksbaum, A. Zavriyev, H. G. Muller, and D. W. Schumacher, "Softening of the H2+ molecular bond in intense laser fields," Phys. Rev. Lett. 64, 1883-1886 (1990). [CrossRef] [PubMed]
  8. T. Seideman, M. Y. Ivanov, and P. B. Corkum, "Role of Electron Localization in Intense-Field Molecular Ionization, " Phys. Rev. Lett. 75, 2819-2822 (1995). [CrossRef] [PubMed]
  9. T. Zuo and A. D. Bandrauk, "Charge-resonance-enhanced ionization of diatomic molecular ions by intense lasers," Phys. Rev. A 52, R2511-R2514 (1995). [CrossRef] [PubMed]
  10. S. Alnaser, X. M. Tong, T. Osipov, S. Voss, C. M. Maharjan, P. Ranitovic, B. Ulrich, B. Shan, Z. Chang, C. D. Lin, and C. L. Cocke, "Routes to Control of H2 Coulomb Explosion in Few-Cycle Laser Pulses," Phys. Rev. Lett. 93, 183202 (2004). [CrossRef] [PubMed]
  11. G. N. Gibson, M. Li, C. Guo, and J. Neira, "Strong-Field Dissociation and Ionization of H2+ using Ultrashort Laser Pulses," Phys. Rev. Lett. 79, 2022-2025 (1997). [CrossRef]
  12. Rudenko, B. Feuerstein, K. Zrost, V. L. B. de Jesus, T. Ergler, C. Dimopoulou, C. D. Schröter, R. Moshammer and J. Ullrich, "Fragmentation dynamics of molecular hydrogen in strong ultrashort laser pulses," J. Phys. B: At. Mol. Opt. Phys 38, 487-501 (2005). [CrossRef]
  13. Staudte, C. L.  Cocke, M. H. Prior, A. Belkacem, C. Ray, H. W. Chong, T. E. Glover, R. W. Schoenlein, and U. Saalmann, "Observation of a nearly isotropic, high-energy Coulomb explosion group in the fragmentation of D2 by short laser pulses," Phys. Rev. A 65, 020703 (2002). [CrossRef]
  14. M. R. Thompson, M. K. Thomas, P. F. Taday, J. H. Posthumus, A. J. Langley, L. J. Frasinski and K. Codling, "One and two-color studies of the dissociative ionization and Coulomb explosion of H2 with intense Ti:sapphire laser pulses," J. Phys. B: At. Mol. Opt. Phys 305755-5772 (1997). [CrossRef]
  15. L. J. Frasinski, K. Codling, and P. A. Hatherly, "Covariance Mapping: A Correlation Method Applied to Multiphoton Multiple Ionization," Science 246, 1029-1031 (1989). [CrossRef] [PubMed]
  16. P. Hering and C. Comaggia, "Coulomb explosion of N2 and CO2 using linearly and circularly polarized femtosecond laser pulses," Phys. Rev. A 59, 2836-2843 (1999). [CrossRef]
  17. J. Wu, H. Zeng, and C. Guo, "Polarization effects on nonsequential double ionization of molecular fragments in strong laser fields," Phys. Rev. A 75, 043402 (2007). [CrossRef]
  18. J. Wu, H. Zeng, and C. Guo, "Vertical and nonvertical transitions in triple-ionization-induced dissociation of diatomic molecules," Phys. Rev. A 74, 065403 (2006). [CrossRef]
  19. T. D. G. Walsh, F. A. Ilkov and S. L. Chin, "The dynamical behavior of H2 and D2 in a strong, femtosecond, titanium:sapphire laser field," J Phys.B: At. Mol. Opt. Phys. 30, 2167-2175 (1997).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1. Fig. 2. Fig. 3.
 
Fig. 4.
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited