Abstract

We computationally investigate supercontinuum generation in an As2S3 solid core photonic crystal fiber (PCF) with a hexagonal cladding of air holes. With a goal of obtaining a supercontinuum output spectrum that can predict what might be seen in an experiment, we investigate the spectral and statistical behavior of a mid-infrared supercontinuum source using a large ensemble average of 106 realizations, in which the input pulse duration and energy vary. The output spectrum is sensitive to small changes (0.1%) in these pulse parameters. We show that the spectrum can be divided into three regions with distinct characteristics: a short-wavelength region with high correlation, a middle-wavelength region with minimal correlation, and a long-wavelength region where the behavior is dominated by a few rare large-bandwidth events. We show that statistically significant fluctuations exist in the experimentally expected output spectrum and that we can reproduce an excellent match to that spectrum with a converged shape and bandwidth using 5000 realizations.

© 2014 Optical Society of America

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References

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  1. H. Kano and H. O. Hamaguchi, “Vibrationally resonant imaging of a single living cell by supercontinuum-based multiplex coherent anti-Stokes Raman scattering microspectroscopy,” Opt. Express 13(4), 1322–1327 (2005).
    [Crossref] [PubMed]
  2. A. Schliesser, N. Picque, and T. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6(7), 440–449 (2012).
    [Crossref]
  3. C. S. Colley, J. C. Hebden, D. T. Delpy, A. D. Cambrey, R. A. Brown, E. A. Zibik, W. H. Ng, L. R. Wilson, and J. W. Cockburn, “Mid-infrared optical coherence tomography,” Rev. Sci. Instrum. 78(12), 123108 (2007).
    [Crossref]
  4. J. S. Sanghera, L. B. Shaw, and I. D. Aggarwal, “Chalcogenide glass-fiber-based mid-IR sources and applications,” IEEE J. of Sel. Topics Quantum Electron. 15, 114–119, (2009).
    [Crossref]
  5. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
    [Crossref] [PubMed]
  6. B. Wetzel, K. J. Blow, S. K. Turitsyn, G. Millot, L. Larger, and J. M. Dudley, “Random walks and random numbers from supercontinuum generation,” Opt. Express 20, 11143–11152 (2012).
    [Crossref] [PubMed]
  7. B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
    [Crossref] [PubMed]
  8. R. J. Weiblen, A. Docherty, J. Hu, and C. R. Menyuk, “Calculation of the expected bandwidth for a mid-infrared supercontinuum source based on As2S3 chalcogenide photonic crystal fibers,” Opt. Express 18, 26666–26674 (2010).
    [Crossref] [PubMed]
  9. U. Møller, S. T. Sørensen, C. Jakobsen, J. Johansen, P. M. Moselund, C. L. Thomsen, and O. Bang, “Power dependence of supercontinuum noise in uniform and tapered PCFs,” Opt. Express 20, 2851–2857 (2012).
    [Crossref] [PubMed]
  10. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
    [Crossref]
  11. R. J. Weiblen, J. Hu, C. R. Menyuk, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Maximizing the super-continuum bandwidth in As2S3 chalcogenide photonic crystal fibers,” Conference on Lasers and Electro-Optics OSA Technical Digest (CD) (Optical Society of America, 2010), paper CTuX7.
  12. J. Hu, C. R. Menyuk, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Maximizing the bandwidth of supercontinuum generation in As2Se3 chalcogenide fibers,” Opt. Express 18, 6722–6739 (2010).
    [Crossref] [PubMed]
  13. J. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,” Opt. Lett. 27, 1180–1182 (2002).
    [Crossref]

2012 (4)

A. Schliesser, N. Picque, and T. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6(7), 440–449 (2012).
[Crossref]

B. Wetzel, K. J. Blow, S. K. Turitsyn, G. Millot, L. Larger, and J. M. Dudley, “Random walks and random numbers from supercontinuum generation,” Opt. Express 20, 11143–11152 (2012).
[Crossref] [PubMed]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[Crossref] [PubMed]

U. Møller, S. T. Sørensen, C. Jakobsen, J. Johansen, P. M. Moselund, C. L. Thomsen, and O. Bang, “Power dependence of supercontinuum noise in uniform and tapered PCFs,” Opt. Express 20, 2851–2857 (2012).
[Crossref] [PubMed]

2010 (2)

2009 (1)

J. S. Sanghera, L. B. Shaw, and I. D. Aggarwal, “Chalcogenide glass-fiber-based mid-IR sources and applications,” IEEE J. of Sel. Topics Quantum Electron. 15, 114–119, (2009).
[Crossref]

2007 (2)

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[Crossref] [PubMed]

C. S. Colley, J. C. Hebden, D. T. Delpy, A. D. Cambrey, R. A. Brown, E. A. Zibik, W. H. Ng, L. R. Wilson, and J. W. Cockburn, “Mid-infrared optical coherence tomography,” Rev. Sci. Instrum. 78(12), 123108 (2007).
[Crossref]

2006 (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[Crossref]

2005 (1)

2002 (1)

Aggarwal, I. D.

J. Hu, C. R. Menyuk, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Maximizing the bandwidth of supercontinuum generation in As2Se3 chalcogenide fibers,” Opt. Express 18, 6722–6739 (2010).
[Crossref] [PubMed]

J. S. Sanghera, L. B. Shaw, and I. D. Aggarwal, “Chalcogenide glass-fiber-based mid-IR sources and applications,” IEEE J. of Sel. Topics Quantum Electron. 15, 114–119, (2009).
[Crossref]

R. J. Weiblen, J. Hu, C. R. Menyuk, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Maximizing the super-continuum bandwidth in As2S3 chalcogenide photonic crystal fibers,” Conference on Lasers and Electro-Optics OSA Technical Digest (CD) (Optical Society of America, 2010), paper CTuX7.

Bang, O.

Blow, K. J.

Brown, R. A.

C. S. Colley, J. C. Hebden, D. T. Delpy, A. D. Cambrey, R. A. Brown, E. A. Zibik, W. H. Ng, L. R. Wilson, and J. W. Cockburn, “Mid-infrared optical coherence tomography,” Rev. Sci. Instrum. 78(12), 123108 (2007).
[Crossref]

Cambrey, A. D.

C. S. Colley, J. C. Hebden, D. T. Delpy, A. D. Cambrey, R. A. Brown, E. A. Zibik, W. H. Ng, L. R. Wilson, and J. W. Cockburn, “Mid-infrared optical coherence tomography,” Rev. Sci. Instrum. 78(12), 123108 (2007).
[Crossref]

Cockburn, J. W.

C. S. Colley, J. C. Hebden, D. T. Delpy, A. D. Cambrey, R. A. Brown, E. A. Zibik, W. H. Ng, L. R. Wilson, and J. W. Cockburn, “Mid-infrared optical coherence tomography,” Rev. Sci. Instrum. 78(12), 123108 (2007).
[Crossref]

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[Crossref]

J. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,” Opt. Lett. 27, 1180–1182 (2002).
[Crossref]

Colley, C. S.

C. S. Colley, J. C. Hebden, D. T. Delpy, A. D. Cambrey, R. A. Brown, E. A. Zibik, W. H. Ng, L. R. Wilson, and J. W. Cockburn, “Mid-infrared optical coherence tomography,” Rev. Sci. Instrum. 78(12), 123108 (2007).
[Crossref]

Delpy, D. T.

C. S. Colley, J. C. Hebden, D. T. Delpy, A. D. Cambrey, R. A. Brown, E. A. Zibik, W. H. Ng, L. R. Wilson, and J. W. Cockburn, “Mid-infrared optical coherence tomography,” Rev. Sci. Instrum. 78(12), 123108 (2007).
[Crossref]

Dias, F.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[Crossref] [PubMed]

Docherty, A.

Dudley, J.

Dudley, J. M.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[Crossref] [PubMed]

B. Wetzel, K. J. Blow, S. K. Turitsyn, G. Millot, L. Larger, and J. M. Dudley, “Random walks and random numbers from supercontinuum generation,” Opt. Express 20, 11143–11152 (2012).
[Crossref] [PubMed]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[Crossref]

Genty, G.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[Crossref] [PubMed]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[Crossref]

Hamaguchi, H. O.

Hänsch, T.

A. Schliesser, N. Picque, and T. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6(7), 440–449 (2012).
[Crossref]

Hebden, J. C.

C. S. Colley, J. C. Hebden, D. T. Delpy, A. D. Cambrey, R. A. Brown, E. A. Zibik, W. H. Ng, L. R. Wilson, and J. W. Cockburn, “Mid-infrared optical coherence tomography,” Rev. Sci. Instrum. 78(12), 123108 (2007).
[Crossref]

Hu, J.

Jakobsen, C.

Jalali, B.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[Crossref] [PubMed]

Johansen, J.

Kano, H.

Koonath, P.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[Crossref] [PubMed]

Kudlinski, A.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[Crossref] [PubMed]

Lacourt, P. A.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[Crossref] [PubMed]

Larger, L.

B. Wetzel, K. J. Blow, S. K. Turitsyn, G. Millot, L. Larger, and J. M. Dudley, “Random walks and random numbers from supercontinuum generation,” Opt. Express 20, 11143–11152 (2012).
[Crossref] [PubMed]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[Crossref] [PubMed]

Menyuk, C. R.

Merolla, J. M.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[Crossref] [PubMed]

Millot, G.

Møller, U.

Moselund, P. M.

Mussot, A.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[Crossref] [PubMed]

Ng, W. H.

C. S. Colley, J. C. Hebden, D. T. Delpy, A. D. Cambrey, R. A. Brown, E. A. Zibik, W. H. Ng, L. R. Wilson, and J. W. Cockburn, “Mid-infrared optical coherence tomography,” Rev. Sci. Instrum. 78(12), 123108 (2007).
[Crossref]

Picque, N.

A. Schliesser, N. Picque, and T. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6(7), 440–449 (2012).
[Crossref]

Ropers, C.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[Crossref] [PubMed]

Sanghera, J. S.

J. Hu, C. R. Menyuk, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Maximizing the bandwidth of supercontinuum generation in As2Se3 chalcogenide fibers,” Opt. Express 18, 6722–6739 (2010).
[Crossref] [PubMed]

J. S. Sanghera, L. B. Shaw, and I. D. Aggarwal, “Chalcogenide glass-fiber-based mid-IR sources and applications,” IEEE J. of Sel. Topics Quantum Electron. 15, 114–119, (2009).
[Crossref]

R. J. Weiblen, J. Hu, C. R. Menyuk, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Maximizing the super-continuum bandwidth in As2S3 chalcogenide photonic crystal fibers,” Conference on Lasers and Electro-Optics OSA Technical Digest (CD) (Optical Society of America, 2010), paper CTuX7.

Schliesser, A.

A. Schliesser, N. Picque, and T. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6(7), 440–449 (2012).
[Crossref]

Shaw, L. B.

J. Hu, C. R. Menyuk, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Maximizing the bandwidth of supercontinuum generation in As2Se3 chalcogenide fibers,” Opt. Express 18, 6722–6739 (2010).
[Crossref] [PubMed]

J. S. Sanghera, L. B. Shaw, and I. D. Aggarwal, “Chalcogenide glass-fiber-based mid-IR sources and applications,” IEEE J. of Sel. Topics Quantum Electron. 15, 114–119, (2009).
[Crossref]

R. J. Weiblen, J. Hu, C. R. Menyuk, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Maximizing the super-continuum bandwidth in As2S3 chalcogenide photonic crystal fibers,” Conference on Lasers and Electro-Optics OSA Technical Digest (CD) (Optical Society of America, 2010), paper CTuX7.

Solli, D. R.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[Crossref] [PubMed]

Sørensen, S. T.

Stefani, A.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[Crossref] [PubMed]

Sylvestre, T.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[Crossref] [PubMed]

Thomsen, C. L.

Turitsyn, S. K.

Weiblen, R. J.

R. J. Weiblen, A. Docherty, J. Hu, and C. R. Menyuk, “Calculation of the expected bandwidth for a mid-infrared supercontinuum source based on As2S3 chalcogenide photonic crystal fibers,” Opt. Express 18, 26666–26674 (2010).
[Crossref] [PubMed]

R. J. Weiblen, J. Hu, C. R. Menyuk, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Maximizing the super-continuum bandwidth in As2S3 chalcogenide photonic crystal fibers,” Conference on Lasers and Electro-Optics OSA Technical Digest (CD) (Optical Society of America, 2010), paper CTuX7.

Wetzel, B.

B. Wetzel, K. J. Blow, S. K. Turitsyn, G. Millot, L. Larger, and J. M. Dudley, “Random walks and random numbers from supercontinuum generation,” Opt. Express 20, 11143–11152 (2012).
[Crossref] [PubMed]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[Crossref] [PubMed]

Wilson, L. R.

C. S. Colley, J. C. Hebden, D. T. Delpy, A. D. Cambrey, R. A. Brown, E. A. Zibik, W. H. Ng, L. R. Wilson, and J. W. Cockburn, “Mid-infrared optical coherence tomography,” Rev. Sci. Instrum. 78(12), 123108 (2007).
[Crossref]

Zibik, E. A.

C. S. Colley, J. C. Hebden, D. T. Delpy, A. D. Cambrey, R. A. Brown, E. A. Zibik, W. H. Ng, L. R. Wilson, and J. W. Cockburn, “Mid-infrared optical coherence tomography,” Rev. Sci. Instrum. 78(12), 123108 (2007).
[Crossref]

IEEE J. of Sel. Topics Quantum Electron. (1)

J. S. Sanghera, L. B. Shaw, and I. D. Aggarwal, “Chalcogenide glass-fiber-based mid-IR sources and applications,” IEEE J. of Sel. Topics Quantum Electron. 15, 114–119, (2009).
[Crossref]

Nat. Photonics (1)

A. Schliesser, N. Picque, and T. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6(7), 440–449 (2012).
[Crossref]

Nature (1)

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[Crossref] [PubMed]

Opt. Express (5)

Opt. Lett. (1)

Rev. Mod. Phys. (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[Crossref]

Rev. Sci. Instrum. (1)

C. S. Colley, J. C. Hebden, D. T. Delpy, A. D. Cambrey, R. A. Brown, E. A. Zibik, W. H. Ng, L. R. Wilson, and J. W. Cockburn, “Mid-infrared optical coherence tomography,” Rev. Sci. Instrum. 78(12), 123108 (2007).
[Crossref]

Sci. Rep. (1)

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[Crossref] [PubMed]

Other (1)

R. J. Weiblen, J. Hu, C. R. Menyuk, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Maximizing the super-continuum bandwidth in As2S3 chalcogenide photonic crystal fibers,” Conference on Lasers and Electro-Optics OSA Technical Digest (CD) (Optical Society of America, 2010), paper CTuX7.

Supplementary Material (3)

» Media 1: MOV (252 KB)     
» Media 2: MOV (390 KB)     
» Media 3: MOV (335 KB)     

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Figures (10)

Fig. 1
Fig. 1

Uniform gridding scheme. Realizations of the same color are averaged (see Media 1).

Fig. 2
Fig. 2

Example supercontinuum spectrum showing three regions.

Fig. 3
Fig. 3

Average correlation coefficient for short and middle wavelength regions when (a) the peak power is varied and (b) when the pulse duration is varied.

Fig. 4
Fig. 4

Single-shot simulation output (blue) and full 106 ensemble average output (red).

Fig. 5
Fig. 5

Comparison of output spectra with different bandwidths: 2.5 μm (green) and 3.2 μm (blue).

Fig. 6
Fig. 6

Histogram of output bandwidths.

Fig. 7
Fig. 7

Spectrogram plots for (a) a single simulation (see Media 2) and (b) a 1000-simulation average (see Media 3).

Fig. 8
Fig. 8

Variance of the fluctuations in the (a) short and (b) middle wavelength region. Lines corresponding to N−5/6 and N−1 are also shown for comparison.

Fig. 9
Fig. 9

Ensemble average output for 5000 samples (red) and 106 samples (blue).

Fig. 10
Fig. 10

Average bandwidth versus number of samples in the ensemble average.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

A ( z , t ) z + a ( ω ) 2 A i IFT { [ β ( ω 0 + Ω ) β ( ω 0 ) Ω β 1 ( ω 0 ) ] A ˜ ( z , Ω ) } = i γ ( 1 + i ω 0 t ) [ A ( z , t ) t R ( t t ) | A ( z , t ) | 2 d t ] ,
ρ = λ = λ 1 λ n ( X λ X ¯ ) ( Y λ Y ¯ ) [ λ = λ 1 λ n ( X λ X ¯ ) 2 λ = λ 1 λ n ( Y λ Y ¯ ) 2 ] 1 / 2 ,
σ 2 = 1 n λ = λ 1 λ n [ ( X λ X λ ¯ ) μ ] 2 ,

Metrics