Abstract

Although the variable stripe length (VSL) method has been widely used to measure the optical gain in thin film active media, different nor totally rigorous criteria have yet been used to estimate two important characterization parameters, namely, threshold and saturation lengths, on which the method critically depends. Here we present a formalism which leads to analytical expressions to rigorously calculate these characteristic lengths from VSL data, providing a unique criterion for the estimation of the amplified spontaneous emission threshold and saturation points.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Costela, O. García, L. Cerdán, I. García-Moreno, and R. Sastre, “Amplified spontaneous emission and optical gain measurements from pyrromethene 567–doped polymer waveguides and quasi-waveguides,” Opt. Express 16, 7023–7036 (2008).
    [CrossRef] [PubMed]
  2. A. Costela, O. García, L. Cerdán, I. García-Moreno, and R. Sastre, “Amplified spontaneous emission and optical gain measurements from pyrromethene 567–doped polymer waveguides and quasi-waveguides: erratum,” Opt. Express 16, 7587–7587 (2008).
    [CrossRef]
  3. L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzò, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440–444 (2000).
    [CrossRef] [PubMed]
  4. J. Mickevičius, G. Tamulaitis, M. S. Shur, Q. Fareed, J. P. Zhang, and R. Gaska, “Saturated gain in GaN epilayers studied by variable stripe length technique,” J. Appl. Phys. 99, 103513 (2006).
    [CrossRef]
  5. M. Vehse, J. Meinertz, O. Lange, P. Michler, J. Gutowski, S. Bader, A. Lell, and V. Härle, “Analysis of gain saturation behavior in GaN based quantum well lasers,” Phys. Status Solidi C 0, 43–47 (2002).
    [CrossRef]
  6. J. Valenta, I. Pelant, and J. Linnros, “Waveguiding effects in the measurement of optical gain in a layer of Si nanocrystals,” Appl. Phys. Lett. 81, 1396–1398 (2002).
    [CrossRef]
  7. L. Dal Negro, P. Bettotti, M. Cazzanelli, D. Pacifici, and L. Pavesi, “Applicability conditions and experimental analysis of the variable stripe length method for gain measurements,” Opt. Commun. 229, 337–348 (2004).
    [CrossRef]
  8. C. Lange, M. Schwalm, S. Chatterjee, W. W. Rühle, N. C. Gerhardt, S. R. Johnson, J.-B. Wang, and Y.-H. Zhang, “The variable stripe-length method revisited: Improved analysis,” Appl. Phys. Lett. 91, 191107 (2007).
    [CrossRef]
  9. M. D. McGehee, R. Gupta, S. Veenstra, E. K. Miller, M. A. Díaz-García, and A. J. Heeger, “Amplified spontaneous emission from photopumped films of a conjugated polymer,” Phys. Rev. B 58, 7035–7039 (1998).
    [CrossRef]
  10. K. Yamashita, T. Kuro, K. Oe, and H. Yanagi, “Low threshold amplified spontaneous emission from near-infrared dye-doped polymeric waveguide,” Appl. Phys. Lett. 88, 241110 (2006).
    [CrossRef]
  11. H. Azuma, T. Kobayashi, Y. Shim, N. Mamedov, and H. Naito, “Amplified spontaneous emission in α-phase and α-phase polyfluorene waveguides,” Org. Electron. 8, 184–188 (2007).
    [CrossRef]
  12. W. HolzerA. Penzkofer, T. Schmitt, A. Hartmann, C. Bader, H. Tillmann, D. Raabe, R. Stockmann, and H.-H. Hörnhold, “Amplified spontaneous emission in neat films of arylene-vinylene polymers,” Opt. Quantum Electron. 33, 121–150 (2001).
    [CrossRef]
  13. F. Lahoz, C. J. Oton, N. Capuj, M. Ferrer-González, S. Cheylan, and D. Navarro-Urrios, “Reduction of the amplified spontaneous emission threshold in semiconducting polymer waveguides on porous silica,” Opt. Express 17, 16766–16775 (2009).
    [CrossRef] [PubMed]
  14. L. Cerdán, A. Costela, I. García-Moreno, O. García, and R. Sastre, “Waveguides and quasi-waveguides based on pyrromethene 597-doped poly(methyl methacrylate),” Appl. Phys. B 97, 73–83 (2009).
    [CrossRef]
  15. T. Kobayashi, M. Flämmich, G. Jordan, R. D’Arcy, M. Rüther, W. J. Blau, Y. Suzuki, and T. Kaino, “Blue-green small-signal gain and saturation in a luminescent polymer gain medium,” Appl. Phys. Lett. 89, 131119 (2006).
    [CrossRef]
  16. Equation is implicit in IASE(L) and, hence, it cannot be fitted to an IASE(L) versus L plot as is done with Eq. . Fortunately Eq. is explicit in L and, consequently, g, Ω, and s=1/Is can be calculated by means of a least squares fit of Eq. to a L versus IASE(L) plot. When saturation is not evident (low pump intensity or short L) and the data dispersion is significant, the fit may render negative values of s (and so incorrect g and Ω values). In that case s=1/Is is fixed to zero, which is equivalent to saying that there is no gain saturation. Alternatively, Eq. can be fitted to the usual IASE(L) versus L plot. These two last fits will lead to slightly different g and Ω values since the former minimizes the sum of squared residuals in L, while the last minimizes the ones in IASE(L). Nevertheless, both fits are statistically significant.
  17. G. I. Peters and L. Allen, “Amplified spontaneous emission I. The threshold condition,” J. Phys. A 4, 238–243 (1971).
    [CrossRef]
  18. L. Cerdán, A. Costela, I. García-Moreno, O. García, R. Sastre, M. Calle, D. Muñoz, and J. de Abajo, “High-gain long-lived amplified spontaneous emission from dye-doped fluorinated polyimide planar waveguides,” Macromol. Chem. Phys. 210, 1624–1631 (2009).
    [CrossRef]

2009

F. Lahoz, C. J. Oton, N. Capuj, M. Ferrer-González, S. Cheylan, and D. Navarro-Urrios, “Reduction of the amplified spontaneous emission threshold in semiconducting polymer waveguides on porous silica,” Opt. Express 17, 16766–16775 (2009).
[CrossRef] [PubMed]

L. Cerdán, A. Costela, I. García-Moreno, O. García, and R. Sastre, “Waveguides and quasi-waveguides based on pyrromethene 597-doped poly(methyl methacrylate),” Appl. Phys. B 97, 73–83 (2009).
[CrossRef]

L. Cerdán, A. Costela, I. García-Moreno, O. García, R. Sastre, M. Calle, D. Muñoz, and J. de Abajo, “High-gain long-lived amplified spontaneous emission from dye-doped fluorinated polyimide planar waveguides,” Macromol. Chem. Phys. 210, 1624–1631 (2009).
[CrossRef]

2008

2007

C. Lange, M. Schwalm, S. Chatterjee, W. W. Rühle, N. C. Gerhardt, S. R. Johnson, J.-B. Wang, and Y.-H. Zhang, “The variable stripe-length method revisited: Improved analysis,” Appl. Phys. Lett. 91, 191107 (2007).
[CrossRef]

H. Azuma, T. Kobayashi, Y. Shim, N. Mamedov, and H. Naito, “Amplified spontaneous emission in α-phase and α-phase polyfluorene waveguides,” Org. Electron. 8, 184–188 (2007).
[CrossRef]

2006

T. Kobayashi, M. Flämmich, G. Jordan, R. D’Arcy, M. Rüther, W. J. Blau, Y. Suzuki, and T. Kaino, “Blue-green small-signal gain and saturation in a luminescent polymer gain medium,” Appl. Phys. Lett. 89, 131119 (2006).
[CrossRef]

K. Yamashita, T. Kuro, K. Oe, and H. Yanagi, “Low threshold amplified spontaneous emission from near-infrared dye-doped polymeric waveguide,” Appl. Phys. Lett. 88, 241110 (2006).
[CrossRef]

J. Mickevičius, G. Tamulaitis, M. S. Shur, Q. Fareed, J. P. Zhang, and R. Gaska, “Saturated gain in GaN epilayers studied by variable stripe length technique,” J. Appl. Phys. 99, 103513 (2006).
[CrossRef]

2004

L. Dal Negro, P. Bettotti, M. Cazzanelli, D. Pacifici, and L. Pavesi, “Applicability conditions and experimental analysis of the variable stripe length method for gain measurements,” Opt. Commun. 229, 337–348 (2004).
[CrossRef]

2002

M. Vehse, J. Meinertz, O. Lange, P. Michler, J. Gutowski, S. Bader, A. Lell, and V. Härle, “Analysis of gain saturation behavior in GaN based quantum well lasers,” Phys. Status Solidi C 0, 43–47 (2002).
[CrossRef]

J. Valenta, I. Pelant, and J. Linnros, “Waveguiding effects in the measurement of optical gain in a layer of Si nanocrystals,” Appl. Phys. Lett. 81, 1396–1398 (2002).
[CrossRef]

2001

W. HolzerA. Penzkofer, T. Schmitt, A. Hartmann, C. Bader, H. Tillmann, D. Raabe, R. Stockmann, and H.-H. Hörnhold, “Amplified spontaneous emission in neat films of arylene-vinylene polymers,” Opt. Quantum Electron. 33, 121–150 (2001).
[CrossRef]

2000

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzò, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440–444 (2000).
[CrossRef] [PubMed]

1998

M. D. McGehee, R. Gupta, S. Veenstra, E. K. Miller, M. A. Díaz-García, and A. J. Heeger, “Amplified spontaneous emission from photopumped films of a conjugated polymer,” Phys. Rev. B 58, 7035–7039 (1998).
[CrossRef]

1971

G. I. Peters and L. Allen, “Amplified spontaneous emission I. The threshold condition,” J. Phys. A 4, 238–243 (1971).
[CrossRef]

Allen, L.

G. I. Peters and L. Allen, “Amplified spontaneous emission I. The threshold condition,” J. Phys. A 4, 238–243 (1971).
[CrossRef]

Azuma, H.

H. Azuma, T. Kobayashi, Y. Shim, N. Mamedov, and H. Naito, “Amplified spontaneous emission in α-phase and α-phase polyfluorene waveguides,” Org. Electron. 8, 184–188 (2007).
[CrossRef]

Bader, C.

W. HolzerA. Penzkofer, T. Schmitt, A. Hartmann, C. Bader, H. Tillmann, D. Raabe, R. Stockmann, and H.-H. Hörnhold, “Amplified spontaneous emission in neat films of arylene-vinylene polymers,” Opt. Quantum Electron. 33, 121–150 (2001).
[CrossRef]

Bader, S.

M. Vehse, J. Meinertz, O. Lange, P. Michler, J. Gutowski, S. Bader, A. Lell, and V. Härle, “Analysis of gain saturation behavior in GaN based quantum well lasers,” Phys. Status Solidi C 0, 43–47 (2002).
[CrossRef]

Bettotti, P.

L. Dal Negro, P. Bettotti, M. Cazzanelli, D. Pacifici, and L. Pavesi, “Applicability conditions and experimental analysis of the variable stripe length method for gain measurements,” Opt. Commun. 229, 337–348 (2004).
[CrossRef]

Blau, W. J.

T. Kobayashi, M. Flämmich, G. Jordan, R. D’Arcy, M. Rüther, W. J. Blau, Y. Suzuki, and T. Kaino, “Blue-green small-signal gain and saturation in a luminescent polymer gain medium,” Appl. Phys. Lett. 89, 131119 (2006).
[CrossRef]

Calle, M.

L. Cerdán, A. Costela, I. García-Moreno, O. García, R. Sastre, M. Calle, D. Muñoz, and J. de Abajo, “High-gain long-lived amplified spontaneous emission from dye-doped fluorinated polyimide planar waveguides,” Macromol. Chem. Phys. 210, 1624–1631 (2009).
[CrossRef]

Capuj, N.

Cazzanelli, M.

L. Dal Negro, P. Bettotti, M. Cazzanelli, D. Pacifici, and L. Pavesi, “Applicability conditions and experimental analysis of the variable stripe length method for gain measurements,” Opt. Commun. 229, 337–348 (2004).
[CrossRef]

Cerdán, L.

L. Cerdán, A. Costela, I. García-Moreno, O. García, and R. Sastre, “Waveguides and quasi-waveguides based on pyrromethene 597-doped poly(methyl methacrylate),” Appl. Phys. B 97, 73–83 (2009).
[CrossRef]

L. Cerdán, A. Costela, I. García-Moreno, O. García, R. Sastre, M. Calle, D. Muñoz, and J. de Abajo, “High-gain long-lived amplified spontaneous emission from dye-doped fluorinated polyimide planar waveguides,” Macromol. Chem. Phys. 210, 1624–1631 (2009).
[CrossRef]

A. Costela, O. García, L. Cerdán, I. García-Moreno, and R. Sastre, “Amplified spontaneous emission and optical gain measurements from pyrromethene 567–doped polymer waveguides and quasi-waveguides,” Opt. Express 16, 7023–7036 (2008).
[CrossRef] [PubMed]

A. Costela, O. García, L. Cerdán, I. García-Moreno, and R. Sastre, “Amplified spontaneous emission and optical gain measurements from pyrromethene 567–doped polymer waveguides and quasi-waveguides: erratum,” Opt. Express 16, 7587–7587 (2008).
[CrossRef]

Chatterjee, S.

C. Lange, M. Schwalm, S. Chatterjee, W. W. Rühle, N. C. Gerhardt, S. R. Johnson, J.-B. Wang, and Y.-H. Zhang, “The variable stripe-length method revisited: Improved analysis,” Appl. Phys. Lett. 91, 191107 (2007).
[CrossRef]

Cheylan, S.

Costela, A.

L. Cerdán, A. Costela, I. García-Moreno, O. García, and R. Sastre, “Waveguides and quasi-waveguides based on pyrromethene 597-doped poly(methyl methacrylate),” Appl. Phys. B 97, 73–83 (2009).
[CrossRef]

L. Cerdán, A. Costela, I. García-Moreno, O. García, R. Sastre, M. Calle, D. Muñoz, and J. de Abajo, “High-gain long-lived amplified spontaneous emission from dye-doped fluorinated polyimide planar waveguides,” Macromol. Chem. Phys. 210, 1624–1631 (2009).
[CrossRef]

A. Costela, O. García, L. Cerdán, I. García-Moreno, and R. Sastre, “Amplified spontaneous emission and optical gain measurements from pyrromethene 567–doped polymer waveguides and quasi-waveguides: erratum,” Opt. Express 16, 7587–7587 (2008).
[CrossRef]

A. Costela, O. García, L. Cerdán, I. García-Moreno, and R. Sastre, “Amplified spontaneous emission and optical gain measurements from pyrromethene 567–doped polymer waveguides and quasi-waveguides,” Opt. Express 16, 7023–7036 (2008).
[CrossRef] [PubMed]

D’Arcy, R.

T. Kobayashi, M. Flämmich, G. Jordan, R. D’Arcy, M. Rüther, W. J. Blau, Y. Suzuki, and T. Kaino, “Blue-green small-signal gain and saturation in a luminescent polymer gain medium,” Appl. Phys. Lett. 89, 131119 (2006).
[CrossRef]

Dal Negro, L.

L. Dal Negro, P. Bettotti, M. Cazzanelli, D. Pacifici, and L. Pavesi, “Applicability conditions and experimental analysis of the variable stripe length method for gain measurements,” Opt. Commun. 229, 337–348 (2004).
[CrossRef]

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzò, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440–444 (2000).
[CrossRef] [PubMed]

de Abajo, J.

L. Cerdán, A. Costela, I. García-Moreno, O. García, R. Sastre, M. Calle, D. Muñoz, and J. de Abajo, “High-gain long-lived amplified spontaneous emission from dye-doped fluorinated polyimide planar waveguides,” Macromol. Chem. Phys. 210, 1624–1631 (2009).
[CrossRef]

Díaz-García, M. A.

M. D. McGehee, R. Gupta, S. Veenstra, E. K. Miller, M. A. Díaz-García, and A. J. Heeger, “Amplified spontaneous emission from photopumped films of a conjugated polymer,” Phys. Rev. B 58, 7035–7039 (1998).
[CrossRef]

Fareed, Q.

J. Mickevičius, G. Tamulaitis, M. S. Shur, Q. Fareed, J. P. Zhang, and R. Gaska, “Saturated gain in GaN epilayers studied by variable stripe length technique,” J. Appl. Phys. 99, 103513 (2006).
[CrossRef]

Ferrer-González, M.

Flämmich, M.

T. Kobayashi, M. Flämmich, G. Jordan, R. D’Arcy, M. Rüther, W. J. Blau, Y. Suzuki, and T. Kaino, “Blue-green small-signal gain and saturation in a luminescent polymer gain medium,” Appl. Phys. Lett. 89, 131119 (2006).
[CrossRef]

Franzò, G.

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzò, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440–444 (2000).
[CrossRef] [PubMed]

García, O.

L. Cerdán, A. Costela, I. García-Moreno, O. García, and R. Sastre, “Waveguides and quasi-waveguides based on pyrromethene 597-doped poly(methyl methacrylate),” Appl. Phys. B 97, 73–83 (2009).
[CrossRef]

L. Cerdán, A. Costela, I. García-Moreno, O. García, R. Sastre, M. Calle, D. Muñoz, and J. de Abajo, “High-gain long-lived amplified spontaneous emission from dye-doped fluorinated polyimide planar waveguides,” Macromol. Chem. Phys. 210, 1624–1631 (2009).
[CrossRef]

A. Costela, O. García, L. Cerdán, I. García-Moreno, and R. Sastre, “Amplified spontaneous emission and optical gain measurements from pyrromethene 567–doped polymer waveguides and quasi-waveguides,” Opt. Express 16, 7023–7036 (2008).
[CrossRef] [PubMed]

A. Costela, O. García, L. Cerdán, I. García-Moreno, and R. Sastre, “Amplified spontaneous emission and optical gain measurements from pyrromethene 567–doped polymer waveguides and quasi-waveguides: erratum,” Opt. Express 16, 7587–7587 (2008).
[CrossRef]

García-Moreno, I.

L. Cerdán, A. Costela, I. García-Moreno, O. García, R. Sastre, M. Calle, D. Muñoz, and J. de Abajo, “High-gain long-lived amplified spontaneous emission from dye-doped fluorinated polyimide planar waveguides,” Macromol. Chem. Phys. 210, 1624–1631 (2009).
[CrossRef]

L. Cerdán, A. Costela, I. García-Moreno, O. García, and R. Sastre, “Waveguides and quasi-waveguides based on pyrromethene 597-doped poly(methyl methacrylate),” Appl. Phys. B 97, 73–83 (2009).
[CrossRef]

A. Costela, O. García, L. Cerdán, I. García-Moreno, and R. Sastre, “Amplified spontaneous emission and optical gain measurements from pyrromethene 567–doped polymer waveguides and quasi-waveguides: erratum,” Opt. Express 16, 7587–7587 (2008).
[CrossRef]

A. Costela, O. García, L. Cerdán, I. García-Moreno, and R. Sastre, “Amplified spontaneous emission and optical gain measurements from pyrromethene 567–doped polymer waveguides and quasi-waveguides,” Opt. Express 16, 7023–7036 (2008).
[CrossRef] [PubMed]

Gaska, R.

J. Mickevičius, G. Tamulaitis, M. S. Shur, Q. Fareed, J. P. Zhang, and R. Gaska, “Saturated gain in GaN epilayers studied by variable stripe length technique,” J. Appl. Phys. 99, 103513 (2006).
[CrossRef]

Gerhardt, N. C.

C. Lange, M. Schwalm, S. Chatterjee, W. W. Rühle, N. C. Gerhardt, S. R. Johnson, J.-B. Wang, and Y.-H. Zhang, “The variable stripe-length method revisited: Improved analysis,” Appl. Phys. Lett. 91, 191107 (2007).
[CrossRef]

Gupta, R.

M. D. McGehee, R. Gupta, S. Veenstra, E. K. Miller, M. A. Díaz-García, and A. J. Heeger, “Amplified spontaneous emission from photopumped films of a conjugated polymer,” Phys. Rev. B 58, 7035–7039 (1998).
[CrossRef]

Gutowski, J.

M. Vehse, J. Meinertz, O. Lange, P. Michler, J. Gutowski, S. Bader, A. Lell, and V. Härle, “Analysis of gain saturation behavior in GaN based quantum well lasers,” Phys. Status Solidi C 0, 43–47 (2002).
[CrossRef]

Härle, V.

M. Vehse, J. Meinertz, O. Lange, P. Michler, J. Gutowski, S. Bader, A. Lell, and V. Härle, “Analysis of gain saturation behavior in GaN based quantum well lasers,” Phys. Status Solidi C 0, 43–47 (2002).
[CrossRef]

Hartmann, A.

W. HolzerA. Penzkofer, T. Schmitt, A. Hartmann, C. Bader, H. Tillmann, D. Raabe, R. Stockmann, and H.-H. Hörnhold, “Amplified spontaneous emission in neat films of arylene-vinylene polymers,” Opt. Quantum Electron. 33, 121–150 (2001).
[CrossRef]

Heeger, A. J.

M. D. McGehee, R. Gupta, S. Veenstra, E. K. Miller, M. A. Díaz-García, and A. J. Heeger, “Amplified spontaneous emission from photopumped films of a conjugated polymer,” Phys. Rev. B 58, 7035–7039 (1998).
[CrossRef]

Holzer, W.

W. HolzerA. Penzkofer, T. Schmitt, A. Hartmann, C. Bader, H. Tillmann, D. Raabe, R. Stockmann, and H.-H. Hörnhold, “Amplified spontaneous emission in neat films of arylene-vinylene polymers,” Opt. Quantum Electron. 33, 121–150 (2001).
[CrossRef]

Hörnhold, H. -H.

W. HolzerA. Penzkofer, T. Schmitt, A. Hartmann, C. Bader, H. Tillmann, D. Raabe, R. Stockmann, and H.-H. Hörnhold, “Amplified spontaneous emission in neat films of arylene-vinylene polymers,” Opt. Quantum Electron. 33, 121–150 (2001).
[CrossRef]

Johnson, S. R.

C. Lange, M. Schwalm, S. Chatterjee, W. W. Rühle, N. C. Gerhardt, S. R. Johnson, J.-B. Wang, and Y.-H. Zhang, “The variable stripe-length method revisited: Improved analysis,” Appl. Phys. Lett. 91, 191107 (2007).
[CrossRef]

Jordan, G.

T. Kobayashi, M. Flämmich, G. Jordan, R. D’Arcy, M. Rüther, W. J. Blau, Y. Suzuki, and T. Kaino, “Blue-green small-signal gain and saturation in a luminescent polymer gain medium,” Appl. Phys. Lett. 89, 131119 (2006).
[CrossRef]

Kaino, T.

T. Kobayashi, M. Flämmich, G. Jordan, R. D’Arcy, M. Rüther, W. J. Blau, Y. Suzuki, and T. Kaino, “Blue-green small-signal gain and saturation in a luminescent polymer gain medium,” Appl. Phys. Lett. 89, 131119 (2006).
[CrossRef]

Kobayashi, T.

H. Azuma, T. Kobayashi, Y. Shim, N. Mamedov, and H. Naito, “Amplified spontaneous emission in α-phase and α-phase polyfluorene waveguides,” Org. Electron. 8, 184–188 (2007).
[CrossRef]

T. Kobayashi, M. Flämmich, G. Jordan, R. D’Arcy, M. Rüther, W. J. Blau, Y. Suzuki, and T. Kaino, “Blue-green small-signal gain and saturation in a luminescent polymer gain medium,” Appl. Phys. Lett. 89, 131119 (2006).
[CrossRef]

Kuro, T.

K. Yamashita, T. Kuro, K. Oe, and H. Yanagi, “Low threshold amplified spontaneous emission from near-infrared dye-doped polymeric waveguide,” Appl. Phys. Lett. 88, 241110 (2006).
[CrossRef]

Lahoz, F.

Lange, C.

C. Lange, M. Schwalm, S. Chatterjee, W. W. Rühle, N. C. Gerhardt, S. R. Johnson, J.-B. Wang, and Y.-H. Zhang, “The variable stripe-length method revisited: Improved analysis,” Appl. Phys. Lett. 91, 191107 (2007).
[CrossRef]

Lange, O.

M. Vehse, J. Meinertz, O. Lange, P. Michler, J. Gutowski, S. Bader, A. Lell, and V. Härle, “Analysis of gain saturation behavior in GaN based quantum well lasers,” Phys. Status Solidi C 0, 43–47 (2002).
[CrossRef]

Lell, A.

M. Vehse, J. Meinertz, O. Lange, P. Michler, J. Gutowski, S. Bader, A. Lell, and V. Härle, “Analysis of gain saturation behavior in GaN based quantum well lasers,” Phys. Status Solidi C 0, 43–47 (2002).
[CrossRef]

Linnros, J.

J. Valenta, I. Pelant, and J. Linnros, “Waveguiding effects in the measurement of optical gain in a layer of Si nanocrystals,” Appl. Phys. Lett. 81, 1396–1398 (2002).
[CrossRef]

Mamedov, N.

H. Azuma, T. Kobayashi, Y. Shim, N. Mamedov, and H. Naito, “Amplified spontaneous emission in α-phase and α-phase polyfluorene waveguides,” Org. Electron. 8, 184–188 (2007).
[CrossRef]

Mazzoleni, C.

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzò, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440–444 (2000).
[CrossRef] [PubMed]

McGehee, M. D.

M. D. McGehee, R. Gupta, S. Veenstra, E. K. Miller, M. A. Díaz-García, and A. J. Heeger, “Amplified spontaneous emission from photopumped films of a conjugated polymer,” Phys. Rev. B 58, 7035–7039 (1998).
[CrossRef]

Meinertz, J.

M. Vehse, J. Meinertz, O. Lange, P. Michler, J. Gutowski, S. Bader, A. Lell, and V. Härle, “Analysis of gain saturation behavior in GaN based quantum well lasers,” Phys. Status Solidi C 0, 43–47 (2002).
[CrossRef]

Michler, P.

M. Vehse, J. Meinertz, O. Lange, P. Michler, J. Gutowski, S. Bader, A. Lell, and V. Härle, “Analysis of gain saturation behavior in GaN based quantum well lasers,” Phys. Status Solidi C 0, 43–47 (2002).
[CrossRef]

Mickevicius, J.

J. Mickevičius, G. Tamulaitis, M. S. Shur, Q. Fareed, J. P. Zhang, and R. Gaska, “Saturated gain in GaN epilayers studied by variable stripe length technique,” J. Appl. Phys. 99, 103513 (2006).
[CrossRef]

Miller, E. K.

M. D. McGehee, R. Gupta, S. Veenstra, E. K. Miller, M. A. Díaz-García, and A. J. Heeger, “Amplified spontaneous emission from photopumped films of a conjugated polymer,” Phys. Rev. B 58, 7035–7039 (1998).
[CrossRef]

Muñoz, D.

L. Cerdán, A. Costela, I. García-Moreno, O. García, R. Sastre, M. Calle, D. Muñoz, and J. de Abajo, “High-gain long-lived amplified spontaneous emission from dye-doped fluorinated polyimide planar waveguides,” Macromol. Chem. Phys. 210, 1624–1631 (2009).
[CrossRef]

Naito, H.

H. Azuma, T. Kobayashi, Y. Shim, N. Mamedov, and H. Naito, “Amplified spontaneous emission in α-phase and α-phase polyfluorene waveguides,” Org. Electron. 8, 184–188 (2007).
[CrossRef]

Navarro-Urrios, D.

Oe, K.

K. Yamashita, T. Kuro, K. Oe, and H. Yanagi, “Low threshold amplified spontaneous emission from near-infrared dye-doped polymeric waveguide,” Appl. Phys. Lett. 88, 241110 (2006).
[CrossRef]

Oton, C. J.

Pacifici, D.

L. Dal Negro, P. Bettotti, M. Cazzanelli, D. Pacifici, and L. Pavesi, “Applicability conditions and experimental analysis of the variable stripe length method for gain measurements,” Opt. Commun. 229, 337–348 (2004).
[CrossRef]

Pavesi, L.

L. Dal Negro, P. Bettotti, M. Cazzanelli, D. Pacifici, and L. Pavesi, “Applicability conditions and experimental analysis of the variable stripe length method for gain measurements,” Opt. Commun. 229, 337–348 (2004).
[CrossRef]

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzò, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440–444 (2000).
[CrossRef] [PubMed]

Pelant, I.

J. Valenta, I. Pelant, and J. Linnros, “Waveguiding effects in the measurement of optical gain in a layer of Si nanocrystals,” Appl. Phys. Lett. 81, 1396–1398 (2002).
[CrossRef]

Penzkofer, A.

W. HolzerA. Penzkofer, T. Schmitt, A. Hartmann, C. Bader, H. Tillmann, D. Raabe, R. Stockmann, and H.-H. Hörnhold, “Amplified spontaneous emission in neat films of arylene-vinylene polymers,” Opt. Quantum Electron. 33, 121–150 (2001).
[CrossRef]

Peters, G. I.

G. I. Peters and L. Allen, “Amplified spontaneous emission I. The threshold condition,” J. Phys. A 4, 238–243 (1971).
[CrossRef]

Priolo, F.

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzò, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440–444 (2000).
[CrossRef] [PubMed]

Raabe, D.

W. HolzerA. Penzkofer, T. Schmitt, A. Hartmann, C. Bader, H. Tillmann, D. Raabe, R. Stockmann, and H.-H. Hörnhold, “Amplified spontaneous emission in neat films of arylene-vinylene polymers,” Opt. Quantum Electron. 33, 121–150 (2001).
[CrossRef]

Rühle, W. W.

C. Lange, M. Schwalm, S. Chatterjee, W. W. Rühle, N. C. Gerhardt, S. R. Johnson, J.-B. Wang, and Y.-H. Zhang, “The variable stripe-length method revisited: Improved analysis,” Appl. Phys. Lett. 91, 191107 (2007).
[CrossRef]

Rüther, M.

T. Kobayashi, M. Flämmich, G. Jordan, R. D’Arcy, M. Rüther, W. J. Blau, Y. Suzuki, and T. Kaino, “Blue-green small-signal gain and saturation in a luminescent polymer gain medium,” Appl. Phys. Lett. 89, 131119 (2006).
[CrossRef]

Sastre, R.

L. Cerdán, A. Costela, I. García-Moreno, O. García, and R. Sastre, “Waveguides and quasi-waveguides based on pyrromethene 597-doped poly(methyl methacrylate),” Appl. Phys. B 97, 73–83 (2009).
[CrossRef]

L. Cerdán, A. Costela, I. García-Moreno, O. García, R. Sastre, M. Calle, D. Muñoz, and J. de Abajo, “High-gain long-lived amplified spontaneous emission from dye-doped fluorinated polyimide planar waveguides,” Macromol. Chem. Phys. 210, 1624–1631 (2009).
[CrossRef]

A. Costela, O. García, L. Cerdán, I. García-Moreno, and R. Sastre, “Amplified spontaneous emission and optical gain measurements from pyrromethene 567–doped polymer waveguides and quasi-waveguides,” Opt. Express 16, 7023–7036 (2008).
[CrossRef] [PubMed]

A. Costela, O. García, L. Cerdán, I. García-Moreno, and R. Sastre, “Amplified spontaneous emission and optical gain measurements from pyrromethene 567–doped polymer waveguides and quasi-waveguides: erratum,” Opt. Express 16, 7587–7587 (2008).
[CrossRef]

Schmitt, T.

W. HolzerA. Penzkofer, T. Schmitt, A. Hartmann, C. Bader, H. Tillmann, D. Raabe, R. Stockmann, and H.-H. Hörnhold, “Amplified spontaneous emission in neat films of arylene-vinylene polymers,” Opt. Quantum Electron. 33, 121–150 (2001).
[CrossRef]

Schwalm, M.

C. Lange, M. Schwalm, S. Chatterjee, W. W. Rühle, N. C. Gerhardt, S. R. Johnson, J.-B. Wang, and Y.-H. Zhang, “The variable stripe-length method revisited: Improved analysis,” Appl. Phys. Lett. 91, 191107 (2007).
[CrossRef]

Shim, Y.

H. Azuma, T. Kobayashi, Y. Shim, N. Mamedov, and H. Naito, “Amplified spontaneous emission in α-phase and α-phase polyfluorene waveguides,” Org. Electron. 8, 184–188 (2007).
[CrossRef]

Shur, M. S.

J. Mickevičius, G. Tamulaitis, M. S. Shur, Q. Fareed, J. P. Zhang, and R. Gaska, “Saturated gain in GaN epilayers studied by variable stripe length technique,” J. Appl. Phys. 99, 103513 (2006).
[CrossRef]

Stockmann, R.

W. HolzerA. Penzkofer, T. Schmitt, A. Hartmann, C. Bader, H. Tillmann, D. Raabe, R. Stockmann, and H.-H. Hörnhold, “Amplified spontaneous emission in neat films of arylene-vinylene polymers,” Opt. Quantum Electron. 33, 121–150 (2001).
[CrossRef]

Suzuki, Y.

T. Kobayashi, M. Flämmich, G. Jordan, R. D’Arcy, M. Rüther, W. J. Blau, Y. Suzuki, and T. Kaino, “Blue-green small-signal gain and saturation in a luminescent polymer gain medium,” Appl. Phys. Lett. 89, 131119 (2006).
[CrossRef]

Tamulaitis, G.

J. Mickevičius, G. Tamulaitis, M. S. Shur, Q. Fareed, J. P. Zhang, and R. Gaska, “Saturated gain in GaN epilayers studied by variable stripe length technique,” J. Appl. Phys. 99, 103513 (2006).
[CrossRef]

Tillmann, H.

W. HolzerA. Penzkofer, T. Schmitt, A. Hartmann, C. Bader, H. Tillmann, D. Raabe, R. Stockmann, and H.-H. Hörnhold, “Amplified spontaneous emission in neat films of arylene-vinylene polymers,” Opt. Quantum Electron. 33, 121–150 (2001).
[CrossRef]

Valenta, J.

J. Valenta, I. Pelant, and J. Linnros, “Waveguiding effects in the measurement of optical gain in a layer of Si nanocrystals,” Appl. Phys. Lett. 81, 1396–1398 (2002).
[CrossRef]

Veenstra, S.

M. D. McGehee, R. Gupta, S. Veenstra, E. K. Miller, M. A. Díaz-García, and A. J. Heeger, “Amplified spontaneous emission from photopumped films of a conjugated polymer,” Phys. Rev. B 58, 7035–7039 (1998).
[CrossRef]

Vehse, M.

M. Vehse, J. Meinertz, O. Lange, P. Michler, J. Gutowski, S. Bader, A. Lell, and V. Härle, “Analysis of gain saturation behavior in GaN based quantum well lasers,” Phys. Status Solidi C 0, 43–47 (2002).
[CrossRef]

Wang, J. -B.

C. Lange, M. Schwalm, S. Chatterjee, W. W. Rühle, N. C. Gerhardt, S. R. Johnson, J.-B. Wang, and Y.-H. Zhang, “The variable stripe-length method revisited: Improved analysis,” Appl. Phys. Lett. 91, 191107 (2007).
[CrossRef]

Yamashita, K.

K. Yamashita, T. Kuro, K. Oe, and H. Yanagi, “Low threshold amplified spontaneous emission from near-infrared dye-doped polymeric waveguide,” Appl. Phys. Lett. 88, 241110 (2006).
[CrossRef]

Yanagi, H.

K. Yamashita, T. Kuro, K. Oe, and H. Yanagi, “Low threshold amplified spontaneous emission from near-infrared dye-doped polymeric waveguide,” Appl. Phys. Lett. 88, 241110 (2006).
[CrossRef]

Zhang, J. P.

J. Mickevičius, G. Tamulaitis, M. S. Shur, Q. Fareed, J. P. Zhang, and R. Gaska, “Saturated gain in GaN epilayers studied by variable stripe length technique,” J. Appl. Phys. 99, 103513 (2006).
[CrossRef]

Zhang, Y. -H.

C. Lange, M. Schwalm, S. Chatterjee, W. W. Rühle, N. C. Gerhardt, S. R. Johnson, J.-B. Wang, and Y.-H. Zhang, “The variable stripe-length method revisited: Improved analysis,” Appl. Phys. Lett. 91, 191107 (2007).
[CrossRef]

Appl. Phys. B

L. Cerdán, A. Costela, I. García-Moreno, O. García, and R. Sastre, “Waveguides and quasi-waveguides based on pyrromethene 597-doped poly(methyl methacrylate),” Appl. Phys. B 97, 73–83 (2009).
[CrossRef]

Appl. Phys. Lett.

T. Kobayashi, M. Flämmich, G. Jordan, R. D’Arcy, M. Rüther, W. J. Blau, Y. Suzuki, and T. Kaino, “Blue-green small-signal gain and saturation in a luminescent polymer gain medium,” Appl. Phys. Lett. 89, 131119 (2006).
[CrossRef]

K. Yamashita, T. Kuro, K. Oe, and H. Yanagi, “Low threshold amplified spontaneous emission from near-infrared dye-doped polymeric waveguide,” Appl. Phys. Lett. 88, 241110 (2006).
[CrossRef]

J. Valenta, I. Pelant, and J. Linnros, “Waveguiding effects in the measurement of optical gain in a layer of Si nanocrystals,” Appl. Phys. Lett. 81, 1396–1398 (2002).
[CrossRef]

C. Lange, M. Schwalm, S. Chatterjee, W. W. Rühle, N. C. Gerhardt, S. R. Johnson, J.-B. Wang, and Y.-H. Zhang, “The variable stripe-length method revisited: Improved analysis,” Appl. Phys. Lett. 91, 191107 (2007).
[CrossRef]

J. Appl. Phys.

J. Mickevičius, G. Tamulaitis, M. S. Shur, Q. Fareed, J. P. Zhang, and R. Gaska, “Saturated gain in GaN epilayers studied by variable stripe length technique,” J. Appl. Phys. 99, 103513 (2006).
[CrossRef]

J. Phys. A

G. I. Peters and L. Allen, “Amplified spontaneous emission I. The threshold condition,” J. Phys. A 4, 238–243 (1971).
[CrossRef]

Macromol. Chem. Phys.

L. Cerdán, A. Costela, I. García-Moreno, O. García, R. Sastre, M. Calle, D. Muñoz, and J. de Abajo, “High-gain long-lived amplified spontaneous emission from dye-doped fluorinated polyimide planar waveguides,” Macromol. Chem. Phys. 210, 1624–1631 (2009).
[CrossRef]

Nature

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzò, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440–444 (2000).
[CrossRef] [PubMed]

Opt. Commun.

L. Dal Negro, P. Bettotti, M. Cazzanelli, D. Pacifici, and L. Pavesi, “Applicability conditions and experimental analysis of the variable stripe length method for gain measurements,” Opt. Commun. 229, 337–348 (2004).
[CrossRef]

Opt. Express

Opt. Quantum Electron.

W. HolzerA. Penzkofer, T. Schmitt, A. Hartmann, C. Bader, H. Tillmann, D. Raabe, R. Stockmann, and H.-H. Hörnhold, “Amplified spontaneous emission in neat films of arylene-vinylene polymers,” Opt. Quantum Electron. 33, 121–150 (2001).
[CrossRef]

Org. Electron.

H. Azuma, T. Kobayashi, Y. Shim, N. Mamedov, and H. Naito, “Amplified spontaneous emission in α-phase and α-phase polyfluorene waveguides,” Org. Electron. 8, 184–188 (2007).
[CrossRef]

Phys. Rev. B

M. D. McGehee, R. Gupta, S. Veenstra, E. K. Miller, M. A. Díaz-García, and A. J. Heeger, “Amplified spontaneous emission from photopumped films of a conjugated polymer,” Phys. Rev. B 58, 7035–7039 (1998).
[CrossRef]

Phys. Status Solidi C

M. Vehse, J. Meinertz, O. Lange, P. Michler, J. Gutowski, S. Bader, A. Lell, and V. Härle, “Analysis of gain saturation behavior in GaN based quantum well lasers,” Phys. Status Solidi C 0, 43–47 (2002).
[CrossRef]

Other

Equation is implicit in IASE(L) and, hence, it cannot be fitted to an IASE(L) versus L plot as is done with Eq. . Fortunately Eq. is explicit in L and, consequently, g, Ω, and s=1/Is can be calculated by means of a least squares fit of Eq. to a L versus IASE(L) plot. When saturation is not evident (low pump intensity or short L) and the data dispersion is significant, the fit may render negative values of s (and so incorrect g and Ω values). In that case s=1/Is is fixed to zero, which is equivalent to saying that there is no gain saturation. Alternatively, Eq. can be fitted to the usual IASE(L) versus L plot. These two last fits will lead to slightly different g and Ω values since the former minimizes the sum of squared residuals in L, while the last minimizes the ones in IASE(L). Nevertheless, both fits are statistically significant.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Dependence of ASE intensity ( I ASE ) on stripe length ( L ) as described by Eq. (2). I F and I ASE S-S are representations of Eqs. (4, 3), respectively. The corresponding lengths L t h and L sat are indicated in the graph with hollow points. Inset: Sketch of the VSL method.

Fig. 2
Fig. 2

Variation with pump intensity of (a) g, (b) L t h , and (c) L sat and g L sat . Points in (a) correspond to a fluorinated polyimide (6F-6F) waveguide doped with laser dye Pyrromethene 597 [18]. Points in (b) and (c) are calculated using Eqs. (8, 9), respectively. The hollow point in plot (b) is the value of I t h obtained from the input-output trace and corresponds to an excitation stripe L t h = 2   mm . Dashed lines are vertical asymptotes. Dotted lines in (b) are a guide to the eye.

Equations (9)

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

d I ( λ ) d z = Ω ( λ ) + γ ( λ ) I ( λ ) 1 + I ( λ ) / I s ( λ ) α ( λ ) I ( λ ) ,
L = I ASE ( L ) / I s g + Ω / I s + g ( g + Ω / I s ) 2 ln | Ω + ( g + Ω / I s ) I ASE ( L ) Ω | ,
I ASE S-S ( L ) = Ω g ( e g L 1 ) .
I F ( L ) Ω L .
L t h = 8 π Δ ν τ n λ 2 φ ,
I ASE S-S ( L t h ) = 2 I F ( L t h ) .
I ASE ( L sat ) = I s .
g L t h 1.256 ,
g L sat 1 + ln ( g I s Ω ) ,

Metrics