Saturable absorber

Saturable absorption is a property of materials where the absorption of light decreases with increasing light intensity. Most materials show some saturable absorption, but often only at very high optical intensities (close to the optical damage). SESAMs,[1][2][3] .[4][5][6] dyes , carbon nanotubes and graphene are useful for saturable absorption,[7] which was highlighted in Nature Asia Materials [8] and nanowerk.[9]

At sufficiently high incident light intensity, atoms in the ground state of a saturable absorber material become excited into an upper energy state at such a rate that there is insufficient time for them to decay back to the ground state before the ground state becomes depleted, and the absorption subsequently saturates.

Saturable absorbers are useful in laser cavities. The key parameters for a saturable absorber are its wavelength range (where it absorbs), its dynamic response (how fast it recovers), and its saturation intensity and fluence (at what intensity or pulse energy it saturates). They are commonly used for passive Q-switching.

For the atomic layer graphene, one atom thick crystal can be seen with the naked eye because it absorbs approximately 2.3% of white light, which is π times fine-structure constant. Graphene's unique electronic properties produce an unexpectedly high opacity for an atomic monolayer, with a startlingly simple value: it absorbs πα ≈ 2.3% of white light, where α is the fine-structure constant.[10] Since the photonic response of graphene is universal and wavelength independent, graphene based saturable absorber could be regarded as a fullband optical element ranging from UV to IR, mid-IR and even to THZ. Graphene based saturable absorber is truly the first universal saturable absorber.[11]

Contents

Phenomenology of saturable absorption

Within the simple model of saturated absorption, the relaxation rate of excitations does not depend on the intensity Then, for the continuous-wave operation, the absorption rate (or simply absorption) A is determined by intensity I:

(1)~~ ~~ A= \frac{\alpha}{1+I/I_0}

where α is linear absorption, and I0 is saturation intensity. These parameters are related with the concentration N of the active centers in the medium, the effective cross-sections σ and the lifetime τ of the excitations.[12][13][14] [15]

Relation with Wright Omega function

Wright Omega function

In the simplest geometry, when the rays of the absorbing light are parallel, the intensity can be described with the Bouguer law,

(2)~~ ~~ \frac{\mathrm{d} I}{\mathrm{d}z}=-AI

where z is coordinate in the direction of propagation. Substitution of (1) into (2) gives the equation

(3)~~ ~~ \frac{\mathrm{d}I}{\mathrm{d}z}=-\frac{\alpha~ I}{1+I/I_0}

With the dimensionless variables u = I / I0, t = αz, equation (3) can be rewritten as

(4)~~ ~~ \frac{\mathrm{d}u}{\mathrm{d}t}=\frac{-u}{1+u}

The solution can be expressed in terms of the Wright Omega function ω:

(5)~~ ~~ u = \omega(-t)

Relation with Lambert W function

The solution can be expressed also through the related Lambert W function. Let u=V\big(-\mathrm{e}^t\big). Then

(6)~~ ~~ -\mathrm{e}^t V'\big(-\mathrm{e}^t\big)= - \frac{V\big(-\mathrm{e}^t\big)}{1+V\big(-\mathrm{e}^t\big)}

With new independent variable p = − et, Equation (6) leads to the equation

(7)~~ ~~ V'(p)=\frac{V(p)}{p\cdot (1+V(p))}

The formal solution can be written

(8)~~ ~~ V(p)=W(p-p_0)

where p0 is constant, but the equation V(p0) = 0 may correspond to the non-physical value of intensity (intensity zero) or to the unusual branch of the Lambert W function.

Saturation fluence

For pulsed operation, in the limiting case of short pulses, absorption can be expressed through the fluence

(9)~~ ~~ F=\int_{0}^t I(t) \mathrm{d}t

where time t should be small compared to the relaxation time the medium; it is assumed that the intensity is zero at t < 0. Then, the saturable absoprtion can be written as follows:

(10)~~ ~~ A=\frac{\alpha}{1+F/F_0}

where saturation fluence F0 is constant.

In the intermediate case (neither cw, nor short pulse operation), the rate equations for excitation and relaxation in the optical medium must be considered together.

Saturation fluence is one of the factors that determine threshold in the gain media and limits the storage of energy in a pulsed disk laser.[16]

Competing mechanisms

Absorption saturation, which results in decreased absorption at high incident light intensity, competes with other mechanisms (for example, increase in temperature, formation of color centers, etc.), which result in increased absorption.[17][18][19] In particular, saturable absorption is only one of several mechanisms that produce self-pulsation in lasers, especially in semiconductor lasers.[20]

See also

References

  1. ^ H. Zhang et al, “Induced solitons formed by cross polarization coupling in a birefringent cavity fiber laser”, Opt. Lett., 33, 2317–2319.(2008).
  2. ^ D.Y. Tang et al, “Observation of high-order polarization-locked vector solitons in a fiber laser”, Physical Review Letters, 101, 153904 (2008).
  3. ^ http://www.batop.com/index.html
  4. ^ H. Zhang et al, “Coherent energy exchange between components of a vector soliton in fiber lasers”, Optics Express, 16,12618–12623 (2008).
  5. ^ H. Zhang et al, “Multi-wavelength dissipative soliton operation of an erbium-doped fiber laser”, Optics Express, Vol. 17, Issue 2, pp.12692-12697
  6. ^ L.M. Zhao et al, “Polarization rotation locking of vector solitons in a fiber ring laser”, Optics Express, 16,10053–10058 (2008).
  7. ^ Bao, Qiaoliang; Zhang, Han; Wang, Yu; Ni, Zhenhua; Yan, Yongli; Shen, Ze Xiang; Loh, Kian Ping; Tang, Ding Yuan (2009). "Atomic layer graphene as saturable absorber for ultrafast pulsed lasers". Advanced Functional Materials 19. http://www3.ntu.edu.sg/home2006/zhan0174/AFM.pdf. Retrieved August 27, 2009. 
  8. ^ http://www.natureasia.com/asia-materials/highlight.php?id=594
  9. ^ http://www.nanowerk.com/spotlight/spotid=14231.php
  10. ^ Kuzmenko, A. B.; van Heumen, E.; Carbone, F.; van der Marel, D. (2008). "Universal infrared conductance of graphite". Phys Rev Lett 100 (11): 117401. doi:10.1103/PhysRevLett.100.117401. PMID 18517825. 
  11. ^ Zhang, H. et al.,. "Graphene mode locked, wavelength-tunable, dissipative soliton fiber laser". Applied Physics Letters 96: 111112. http://www.sciencenet.cn/upload/blog/file/2010/3/20103191224576536.pdf. 
  12. ^ S. Colin; E. Contesse, P. Le Boudec, G. Stephan, and F. Sanchez (1996). "Evidence of a saturable-absorption effect in heavily erbium-doped fibers". Optics Letters 21: 1987–1989. doi:10.1364/OL.21.001987. 
  13. ^ D.Kouznetsov; J.-F.Bisson, K.Takaichi, K.Ueda (2005). "Single-mode solid-state laser with short wide unstable cavity". JOSAB 22 (8): 1605–1619. doi:10.1364/JOSAB.22.001605. http://josab.osa.org/abstract.cfm?id=84730. 
  14. ^ Zhang, H.; Tang, D. Y.; Zhao, L. M.; Bao, Q. L.; Loh, K. P. (2009). "Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene". Optics Express 17 (20): 17630. http://www3.ntu.edu.sg/home2006/zhan0174/OE_graphene.pdf. 
  15. ^ Han Zhang,Qiaoliang Bao,Dingyuan Tang,Luming Zhao,and Kianping Loh. "Large energy soliton erbium-doped fiber laser with a graphene-polymer composite mode locker". Applied Physics Letters 95: P141103. http://www3.ntu.edu.sg/home2006/zhan0174/apl.pdf. 
  16. ^ Korelitz, BI; Sommers, SC (2008). "Storage of energy in disk-shaped laser materials". Research Letters in Physics 2008 (5): Article ID 717414. doi:10.1155/2008/717414. PMID 2008. http://www.hindawi.com/journals/rlp/aip.717414.html. 
  17. ^ J.-F.Bisson; D.Kouznetsov, K.Ueda, T.Fredrich-Thornton, K.Petermann, G.Huber (2007). "Switching of emissivity and photoconductivity in highly doped Yb3+:Y2O3 and Lu2O3 ceramics". Applied Physics Letters 90: 201901. doi:10.1063/1.2739318. http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=APPLAB000090000020201901000001&idtype=cvips&gifs=yes. 
  18. ^ Chan, HL; Tse, AM; Chim, AM; Wong, VW; Choi, PC; Yu, J; Zhang, M; Sung, JJ; M.Söderlund, H.J.Hoffman, D.Kliner, J.Koplow,J.L.Archambault, L.Reekie, P.St.J.Russell, and D.N.Payne (2007). "Photodarkening measurements in large mode area fibers" (). Proceedings of SPIE 6553 (5): 64531E. doi:10.1117/12.712545. PMID 17645476. http://bookstore.spie.org/index.cfm?fuseaction=detailpaper&cachedsearch=1&productid=712545&producttype=pdf&CFID=6551164&CFTOKEN=3433140. 
  19. ^ L. Dong; J. L. Archambault, L. Reekie, P. St. J. Russell, and D. N. Payne (1995). "Photoinduced absorption change in germanosilicate preforms: evidence for the color-center model of photosensitivity". Applied Optics 34: 3436. doi:10.1364/AO.34.003436. http://www.opticsinfobase.org/abstract.cfm?URI=ao-34-18-3436. 
  20. ^ Thomas L. Paoli (1979). "Saturable absorption effects in the self-pulsing (AlGa)As junction laser". Appl.Phys.Lett. 34: 652. doi:10.1063/1.90625. http://link.aip.org/link/?APPLAB/34/652/1. 

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