L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063824 (2010).
[Crossref]
L. Ge, R. J. Tandy, A. D. Stone, and H. E. Türeci, “Quantitative verification of ab initio self-consistent laser theory,” Opt. Express 16, 16895 (2008).
[Crossref]
[PubMed]
H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646 (2008).
[Crossref]
[PubMed]
H. E. Türeci, A. D. Stone, and L. Ge, “Theory of the spatial structure of nonlinear lasing modes,” Phys. Rev. A 76, 013813 (2007).
[Crossref]
H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043822 (2006).
[Crossref]
H. Cao, “Review on the latest developments in random lasers with coherent feedback,” J. Phys. A 38, 10497–10535 (2005).
[Crossref]
X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Phys. Rev. B 69, 104202 (2004).
[Crossref]
B. Bidégaray, “Time discretizations for Maxwell-Bloch equations,” Numer. Meth. Partial Differential Equations 19, 284–300 (2003).
[Crossref]
X. Jiang and C. M. Soukoulis, “Time dependent theory for random lasers,” Phys. Rev. Lett. 85, 70 (2000).
[Crossref]
[PubMed]
O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref]
[PubMed]
A. S. Nagra and R. A. York, “FDTD analysis of wave propagation in nonlinear absorbing and gain media,” IEEE Trans. Antennas Propag. 46, 334–340 (1998).
[Crossref]
C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]
[PubMed]
H. Fu and H. Haken, “Multifrequency operations in a short-cavity standing-wave laser,” Phys. Rev. A 43, 2446–2454 (1991).
[Crossref]
[PubMed]
K. S. Yee, “Numerical solution of the initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans Antennas Propag. 14, 302–307 (1966).
[Crossref]
W. E. Lamb, “Theory of an optical maser,” Phys. Rev. 134, A1429 (1964).
[Crossref]
B. Bidégaray, “Time discretizations for Maxwell-Bloch equations,” Numer. Meth. Partial Differential Equations 19, 284–300 (2003).
[Crossref]
R. W. Boyd, Nonlinear Optics (Academic Press, 2008).
H. Cao, “Review on the latest developments in random lasers with coherent feedback,” J. Phys. A 38, 10497–10535 (2005).
[Crossref]
X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Phys. Rev. B 69, 104202 (2004).
[Crossref]
C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]
[PubMed]
C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]
[PubMed]
S. Chua, Y. D. Chong, A. D. Stone, M Soljac̆ić, and J. Bravo-Abad, “Low-threshold lasing action in photonic crystal slabs enabled by Fano resonances,” Opt. Express 19, 1539 (2011).
[Crossref]
[PubMed]
L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063824 (2010).
[Crossref]
H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043822 (2006).
[Crossref]
O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref]
[PubMed]
C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]
[PubMed]
X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Phys. Rev. B 69, 104202 (2004).
[Crossref]
H. Fu and H. Haken, “Multifrequency operations in a short-cavity standing-wave laser,” Phys. Rev. A 43, 2446–2454 (1991).
[Crossref]
[PubMed]
L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063824 (2010).
[Crossref]
H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646 (2008).
[Crossref]
[PubMed]
L. Ge, R. J. Tandy, A. D. Stone, and H. E. Türeci, “Quantitative verification of ab initio self-consistent laser theory,” Opt. Express 16, 16895 (2008).
[Crossref]
[PubMed]
H. E. Türeci, A. D. Stone, and L. Ge, “Theory of the spatial structure of nonlinear lasing modes,” Phys. Rev. A 76, 013813 (2007).
[Crossref]
C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]
[PubMed]
H. Fu and H. Haken, “Multifrequency operations in a short-cavity standing-wave laser,” Phys. Rev. A 43, 2446–2454 (1991).
[Crossref]
[PubMed]
H. Haken, Light: Laser Dynamics (North-Holland Phys. Publishing, 1985), Vol. 2.
X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Phys. Rev. B 69, 104202 (2004).
[Crossref]
X. Jiang and C. M. Soukoulis, “Time dependent theory for random lasers,” Phys. Rev. Lett. 85, 70 (2000).
[Crossref]
[PubMed]
X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Phys. Rev. B 69, 104202 (2004).
[Crossref]
Y. I. Khanin, Principles of Laser Dynamics (Elsevier, 1995).
O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref]
[PubMed]
W. E. Lamb, “Theory of an optical maser,” Phys. Rev. 134, A1429 (1964).
[Crossref]
O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref]
[PubMed]
Ge Li, Yale PhD thesis, 2010.
A. S. Nagra and R. A. York, “FDTD analysis of wave propagation in nonlinear absorbing and gain media,” IEEE Trans. Antennas Propag. 46, 334–340 (1998).
[Crossref]
C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]
[PubMed]
C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]
[PubMed]
O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref]
[PubMed]
O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref]
[PubMed]
H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646 (2008).
[Crossref]
[PubMed]
O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref]
[PubMed]
A. E. Siegman, Lasers (University Science Books, 1986).
C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]
[PubMed]
X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Phys. Rev. B 69, 104202 (2004).
[Crossref]
X. Jiang and C. M. Soukoulis, “Time dependent theory for random lasers,” Phys. Rev. Lett. 85, 70 (2000).
[Crossref]
[PubMed]
S. Chua, Y. D. Chong, A. D. Stone, M Soljac̆ić, and J. Bravo-Abad, “Low-threshold lasing action in photonic crystal slabs enabled by Fano resonances,” Opt. Express 19, 1539 (2011).
[Crossref]
[PubMed]
L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063824 (2010).
[Crossref]
H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646 (2008).
[Crossref]
[PubMed]
L. Ge, R. J. Tandy, A. D. Stone, and H. E. Türeci, “Quantitative verification of ab initio self-consistent laser theory,” Opt. Express 16, 16895 (2008).
[Crossref]
[PubMed]
H. E. Türeci, A. D. Stone, and L. Ge, “Theory of the spatial structure of nonlinear lasing modes,” Phys. Rev. A 76, 013813 (2007).
[Crossref]
H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043822 (2006).
[Crossref]
C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]
[PubMed]
L. Ge, R. J. Tandy, A. D. Stone, and H. E. Türeci, “Quantitative verification of ab initio self-consistent laser theory,” Opt. Express 16, 16895 (2008).
[Crossref]
[PubMed]
H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646 (2008).
[Crossref]
[PubMed]
H. E. Türeci, A. D. Stone, and L. Ge, “Theory of the spatial structure of nonlinear lasing modes,” Phys. Rev. A 76, 013813 (2007).
[Crossref]
H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043822 (2006).
[Crossref]
O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref]
[PubMed]
K. S. Yee, “Numerical solution of the initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans Antennas Propag. 14, 302–307 (1966).
[Crossref]
A. S. Nagra and R. A. York, “FDTD analysis of wave propagation in nonlinear absorbing and gain media,” IEEE Trans. Antennas Propag. 46, 334–340 (1998).
[Crossref]
X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Phys. Rev. B 69, 104202 (2004).
[Crossref]
K. S. Yee, “Numerical solution of the initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans Antennas Propag. 14, 302–307 (1966).
[Crossref]
A. S. Nagra and R. A. York, “FDTD analysis of wave propagation in nonlinear absorbing and gain media,” IEEE Trans. Antennas Propag. 46, 334–340 (1998).
[Crossref]
H. Cao, “Review on the latest developments in random lasers with coherent feedback,” J. Phys. A 38, 10497–10535 (2005).
[Crossref]
B. Bidégaray, “Time discretizations for Maxwell-Bloch equations,” Numer. Meth. Partial Differential Equations 19, 284–300 (2003).
[Crossref]
S. Chua, Y. D. Chong, A. D. Stone, M Soljac̆ić, and J. Bravo-Abad, “Low-threshold lasing action in photonic crystal slabs enabled by Fano resonances,” Opt. Express 19, 1539 (2011).
[Crossref]
[PubMed]
L. Ge, R. J. Tandy, A. D. Stone, and H. E. Türeci, “Quantitative verification of ab initio self-consistent laser theory,” Opt. Express 16, 16895 (2008).
[Crossref]
[PubMed]
W. E. Lamb, “Theory of an optical maser,” Phys. Rev. 134, A1429 (1964).
[Crossref]
H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043822 (2006).
[Crossref]
H. E. Türeci, A. D. Stone, and L. Ge, “Theory of the spatial structure of nonlinear lasing modes,” Phys. Rev. A 76, 013813 (2007).
[Crossref]
H. Fu and H. Haken, “Multifrequency operations in a short-cavity standing-wave laser,” Phys. Rev. A 43, 2446–2454 (1991).
[Crossref]
[PubMed]
L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063824 (2010).
[Crossref]
X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Phys. Rev. B 69, 104202 (2004).
[Crossref]
X. Jiang and C. M. Soukoulis, “Time dependent theory for random lasers,” Phys. Rev. Lett. 85, 70 (2000).
[Crossref]
[PubMed]
C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]
[PubMed]
O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref]
[PubMed]
H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646 (2008).
[Crossref]
[PubMed]
A. E. Siegman, Lasers (University Science Books, 1986).
H. Haken, Light: Laser Dynamics (North-Holland Phys. Publishing, 1985), Vol. 2.
Ge Li, Yale PhD thesis, 2010.
Y. I. Khanin, Principles of Laser Dynamics (Elsevier, 1995).
The equations are written for the TM case, the modifications for TE are straightforward.
The observation that coherent and incoherent pumping are nearly equivalent for most systems, is invalid when the coherent pumping is supplied at a similar frequency to the atomic lasing transition and thus interactions between the lasing field and pumping field must be taken into account.
For any 1D cavity which is uniformly pumped the TCF states for solving SALT can also be found using a transfer matrix method which does not require discretizing space. We use a more general TCF solver in the calculations presented here which does discretize space.
R. W. Boyd, Nonlinear Optics (Academic Press, 2008).