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Detection of biological impurities in aerosol microparticles
Journal of Quantitative Spectroscopy & Radiative Transfer 88 (2004) 89 – 95 www.elsevier.com/locate/jqsrt
Detection of biological impurities in aerosol microparticles Halina P. Ledneva, Liudmila G. Astafyeva∗ Stepanov Institute of Physics, National Academy of Sciences of Belarus, Scorina prospect 68, Minsk, 220072, Belarus Received 19 November 2003; accepted 30 January 2004
Abstract We report the results of a study of the bimodal laser regime in aerosol microparticle for a mixture of an active substance and a saturable absorber as a microimpurity of fluorophores and chromatophores that occurs in bioparticles. It is concluded that the steady states of a microlaser are very sensitive to the presence of very small concentrations of a saturable absorber, which may be used for detection of biological impurities. 䉷 2004 Elsevier Ltd. All rights reserved. Keywords: Aerosol microparticle; Biological impurity; Microlaser; Saturable absorption
1. Introduction Nonlinear interactions and laser oscillations in dielectric aerosol microparticles with weak absorption attract attention due to an extremely high quality of quasi normal modes in such microcavities [1–5]. The high sensitivity of modal radiation to weak absorption allows one to develop a reliable method, such as the intracavity laser spectroscopy, for the detection of small quantities of impurities, including biological impurities in the environment. This technique can actually be called micro-intracavity laser spectroscopy. Our discussion is limited only to the case of very small concentrations of a saturable absorber as opposed to the case in which the concentration of saturable absorber is large and the illumination intensity is high; as a consequence, the imaginary part of the refractive index may develop large inhomogeneities [6]. Furthermore, additional saturable absorption due to a microscopic impurity can be an important [5] reason for enriching dynamics. It is known that in experiments with a glass ball doped with Nd ions or a dye droplet under the action of intensive laser light, pumping multimodal radiation is emitted [3–5]. A ∗ Corresponding author. Fax: +375-17-284-08-79.
E-mail address: [email protected] (L.G. Astafyeva). 0022-4073/$ - see front matter 䉷 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jqsrt.2004.01.004
90
H.P. Ledneva, L.G. Astafyeva / Journal of Quantitative Spectroscopy & Radiative Transfer 88 (2004) 89 – 95
separate mode appears in the structural resonance of the particle and can be described by the frequency and the quality factor as well as by its spatial structure both inside and outside the particle. It is known that the quality factor of a certain mode increases with increasing mode number [1]. The value of the intensity inside the spatial structure of the mode, as shown in [7], becomes maximal for a mode number depending on the refractive index, loss, and particle radius due to the existence of optimal conditions for focusing. In this paper, we consider the bimodal laser regime in a spherical aerosol microparticle assuming a mixture of an active substance and a saturable absorber as impurity on the first mode with a very small concentration. An understanding of the changes in the internal TE- and TM-polarization optical field distributions resulting from the saturable absorption of fluorophores and chromatophores that occurs in bioparticles is important for bioaerosol detection. Absorbing molecules in the particle are assumed to be randomly oriented with their absorption proportional to the absorption index ma . There are several ways to consider systems with a large number of modes [8–10]. Below we describe, by analogy with [9,10], another approach to describing the interaction of many modes in a spherical particle, which permits us to take into account the spatial overlap of the modes along with other traditional mechanisms of interaction. 2. Basic equations The vector Maxwell equations for the field in the spherical coordinate system (r, , ) are usually written in the scalar form [11] by introducing the linear differential operator L = r × ∇/i and expressing the electric field E in the scalar Debye potential . For the transverse electric mode (or TE mode), E = i∇ × (r ) where r is the radius vector and is the angular frequency of light. The components of the electric field are given by E =
*(r ) i , cr sin *
E =
i *(r ) , cr *
Er = 0.
Then intensity of the electric field can be written as B = |E |2 + |E |2 .
qn (t)dn n (kmr)Yn (, )eit . Here k = /c, Yn (, ) are For a bimodal system, we can write = n+1 n spherical harmonics of the degree n, and the coefficients dn for a resonant mode of the transverse electric field inside the particle are given by dn = i n
m 2n + 1 . n(n + 1) mn (ka)n (kma) − n (ka)n (kma)
Here, m is the refractive index of the active substance, a is the radius of the particle, n and n are spherical Ricatti–Bessel and Ricatti–Hankel functions, and the primes denote differentiation with respect to the argument in the parentheses. The basic system of equations for the amplitudes q1 and q2 and the corresponding phases 1 and 2 of two neighboring modes and the components of the matrix of the gain coefficients k11 , k22 , k12 is the following: dq1 vc1 + (1 + k1 )q1 − [q1 k11 + q2 k12 (cos + 1 sin )] = 0, dt 2
H.P. Ledneva, L.G. Astafyeva / Journal of Quantitative Spectroscopy & Radiative Transfer 88 (2004) 89 – 95
q1
91
d1 vc1 + [q1 k11 1 + q2 k12 (1 cos − sin )] = 0, dt 2
dq2 vc2 + 2 q2 − [q2 k22 + q1 k12 r21 (cos − 2 sin )] = 0, dt 2 q2
d2 vc2 + [q2 k22 2 + q1 k12 r21 (2 cos + sin )] = 0, dt 2
dk11 0 =D(k11 − k11 ) − 11 c1 B1 [q12 k11 + q1 q2 k12 (cos + 1 sin )] dt − 12 c2 B1 [q22 k22 + q1 q2 k12 r21 (cos − 2 sin )],
(1)
dk12 0 =D(k12 − k12 ) − 12 c1 B1 [k12 (q22 + r21 q12 ) + q1 q2 k11 (cos − 1 sin ) dt + q1 q2 k22 (cos + 2 sin )], dk22 0 =D(k22 − k22 ) − 12 c2 B2 [q12 k11 + q1 q2 k12 (cos − 1 sin )] dt − 22 c2 B2 [q22 k22 + q1 q2 k12 r21 (cos + 2 sin )], dk1 = D1 (k01 − k1 ) − B1 k1 |E1 |2 . dt Here r21 = c2 /c1 , and cj = 1/(1 + 2j ), (j = 1, 2); k01 = 4 ma / . Furthermore, v is the phase velocity of light, D and D1 are the decay rates of populations in the active medium and saturable absorber, = 2 − 1 , j = a − j is the tuning of the mode frequency 1 with respect to the resonant frequency a in units of the spectral gain line width, and k1 is the absorption coefficient of the saturable absorber. The elements of the gain coefficient matrix kij include the self-action due to standing waves k11 , k22 and the cross-action between the neighboring modes k12 . kij = k(r, t)i (kmr)j (kmr)Yi (, )Yj (, ) dv, dv = r 2 sin dr d d. (2) v
The integrals of self-saturation and cross-saturation in the modes are as follows (see also [12]): 11 = 41 (kma)[S12 () + Q21 ()]2 dv, v 22 = 42 (kma)[S22 () + Q22 ()]2 dv, v 12 = 21 (kma)22 (kma)[S1 ()S2 () + Q1 ()Q2 ()]2 dv. v
(3)
Here Qj () = Pj (cos )/ sin , Sj () = −Pj (cos ) sin , Pj (cos ) are Legendre polynomials, j = 1, 2 and the primes denote differentiation with respect to the argument in the parantheses. It has been shown in [7] that the quantities 11 , 22 and 12 , which describe the degree of coverage of the spatial modes, depend on the mode number n due to the focusing properties of spherical particles. Depending on n, 11 can be greater or smaller than 22 .
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H.P. Ledneva, L.G. Astafyeva / Journal of Quantitative Spectroscopy & Radiative Transfer 88 (2004) 89 – 95
Fig. 1. Internal intensity distribution in the equatorial plane of a microsphere for TE polarization resonance mode with n = 47: (a) s = 1, (b) s = 2. The arrow shows the direction of the incident laser beam.
3. Results and conclusions We have considered steady states for the bimodal laser regime and concluded that when a saturable absorber is absent, then the bimodal laser regime is reached if the values of the gain coefficients exceed the first threshold for both modes. As an example, the spatial distribution of the intensity in the mode with the azimuthal mode number n = 47, the radial mode numbers s = 1 and 2, absorption index m = 1.5 − i10−8 , and radius a = 3.5 m is shown in Fig. 1. In the presence a saturable absorber, the quality factor and the spatial structure of the mode change. Therefore, the dynamics of lasing changes as well. In this case, we obtain from (1) that the bimodal steady
H.P. Ledneva, L.G. Astafyeva / Journal of Quantitative Spectroscopy & Radiative Transfer 88 (2004) 89 – 95
93
Fig. 2. The ratio of the intensity coefficients of two modes as a function of the ratio of the gain coefficient to the loss coefficient 0 at K 0 = 0.9 for m = 1.5 − i10−8 and azimuthal mode number n: (1) 40–41; (2) 47–48; (4) 61–62; (3) 47–48; (m = 10−7 ). K11 a 22
state exists when the following condition is met: 0 0 )(2 − 22 k22 ) (1 + k1 − 11 k11 2 0 2 2 − 12 k12 (cos − 1 2 sin + (1 − 2 ) sin cos ) > 0.
(4)
In this case the overlap of the spatial modes and their nonlinear coupling leads to the existence of solutions below the first threshold for the bimodal steady state, as can be seen in Fig. 2. This figure illustrates the dependence of the ratio Q = q2 /q1 of the steady intensity coefficients q1 and q2 of the two modes on 0 = k 0 /( + k ). The area where this state exists becomes wider with the relative gain coefficient K11 1 1 11 increasing coefficient of the spatial overlap, the quality, and the beginning gain. For the modes with numbers 61 and 62, curve 4 is characterized by higher Q values than for the other modes. Their spatial coverage of the modes is more effective due to a much greater ratio of the intensities than that for the modes with numbers 40–41. Curves 2 and 3 demonstrate the result of changing the absorption coefficient of the saturable absorber. For curve 2, the coefficient of the spatial overlap of the modes is equal to 0.95 and the intensity of the first mode is a bit smaller than that of the second one. At the same time, for curve 3 a tenfold increase in the absorption enhances the local focal effect; as a result, the intensity of the second mode is twice that of the first one. Therefore, curve 3 corresponds to greater Q values and approaches curve 4 in Fig. 3. The steady intensity values q1 (curve 1) and q2 of the two modes 47–48 as functions of
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H.P. Ledneva, L.G. Astafyeva / Journal of Quantitative Spectroscopy & Radiative Transfer 88 (2004) 89 – 95
Fig. 3. Steady intensity values q1 (curve 1) and q2 of two modes 47–48 as a function of the ratio of the gain coefficient to the 0 in bistability area: 2–3 (m = 10−8 ); 4–5 (m = 10−7 ). loss coefficient K11 a a
0 in bistability area: 2–3 (m = 10−8 ); 4–5 (m = 10−7 ) correlation between the intensities the ratio K11 a a of the modes. There are two values of the steady intensities for one of the two modes in the area over the first laser threshold shown in Fig. 3. The frequencies of each of the two modes in this case are shifted to one side from the resonance frequency. The area of coexistence of several values of the steady intensities and frequencies can be changed due to the presence of an impurity acting as a saturable absorber. So, for the modes with numbers 47 and 48 under the action of pumping absorption for ma = 10−8 curves 2 and 3 correspond to the intensity of the higher-quality mode n = 48 equal to 0.9 times the intensity of the mode 0 = 1.49 at K 0 = 1.21. A tenfold with a smaller quality n = 47 and the upper boundary of bistability K11 22 increase of absorption (ma = 10−7 ) in curves 4 and 5 leads to a shift of the boundary to a smaller value 0 = 1.34 due to the increase in the ratio of the spatial structures up to the 1.8. K11 Thus, the steady state and microlaser dynamics are very sensitivity to the presence of the very small concentrations of a saturable absorber, which may be used for the detection of biological impurities.
Acknowledgements This study was partially supported by the Belarus Republican Foundation for Fundamental Research under Grant No. F03-043.
H.P. Ledneva, L.G. Astafyeva / Journal of Quantitative Spectroscopy & Radiative Transfer 88 (2004) 89 – 95
95
References [1] Chang RK, Campillo AJ, editors. Optical processes in microcavities. Singapore: World Scientific; 1996 [2] Sandoghdar V, Treussart F, Hare J, Lefevre-Seguin V, Raimond J-M, Haroche S. Very low threshold whispering-gallerymode microsphere laser. Phys Rev 1996;54:R1777–80. [3] Lu B, Wang Y, Li Y, Liu Y. High-order resonance structures in a Nd-doped glass microsphere. Opt Commun 1994;108: 13–6. [4] Lin H-B, Eversole JD, Campillo AJ. Spectral properties of lasing microdroplets. J Opt Soc Am B 1992;9:43–52. [5] Popp J, Fields MH, Chang RK. Q switching by saturable absorption in microdroplets: elastic scattering and laser emission. Opt Lett 1997;22:1296–8. [6] Hill SC, Videen G, Wenbo Sun, Qiang Fu Scattering and internal fields of a microsphere that contains a saturable absorber: finite-difference time-domain simulations. Appl Opt 2001;40:5487–94. [7] Ledneva HP, Kotomtseva LA, Pavlovsky GB. Proceedings of the Fourth Conference on Laser Physics and Spectroscopy, Grodno, 1999, p. 253–5 [in Russian]. [8] Pieroux D, Mandel P. On the rate equation approximation for free-running multimode lasers. Quant Semiclass Opt 1997;9:L17–22. [9] Oraevsky AN, Scalli M, Velichansky VL. Quantum dot laser. Quant Electron 1998;25:211–6. [10] Samson AM, Kotomtseva LA, Loiko NA. Selfpulsing in lasers. Minsk: Nauka i Tekhnika; 1990 [in Russian]. [11] Prasad S, Glauber RJ. Initiation of superfluorescence in a large sphere. Phys Rev A 1985;31:1583–97. [12] Ledneva HP, Korzhov AV, Kotomtseva LA, Astafyeva LG. The effect of spatial field distribution on two-mode lasing in a spherical microparticle. Opt Spectrosc 2003;94:476–80.
Detection of biological impurities in aerosol microparticles Halina P. Ledneva, Liudmila G. Astafyeva∗ Stepanov Institute of Physics, National Academy of Sciences of Belarus, Scorina prospect 68, Minsk, 220072, Belarus Received 19 November 2003; accepted 30 January 2004
Abstract We report the results of a study of the bimodal laser regime in aerosol microparticle for a mixture of an active substance and a saturable absorber as a microimpurity of fluorophores and chromatophores that occurs in bioparticles. It is concluded that the steady states of a microlaser are very sensitive to the presence of very small concentrations of a saturable absorber, which may be used for detection of biological impurities. 䉷 2004 Elsevier Ltd. All rights reserved. Keywords: Aerosol microparticle; Biological impurity; Microlaser; Saturable absorption
1. Introduction Nonlinear interactions and laser oscillations in dielectric aerosol microparticles with weak absorption attract attention due to an extremely high quality of quasi normal modes in such microcavities [1–5]. The high sensitivity of modal radiation to weak absorption allows one to develop a reliable method, such as the intracavity laser spectroscopy, for the detection of small quantities of impurities, including biological impurities in the environment. This technique can actually be called micro-intracavity laser spectroscopy. Our discussion is limited only to the case of very small concentrations of a saturable absorber as opposed to the case in which the concentration of saturable absorber is large and the illumination intensity is high; as a consequence, the imaginary part of the refractive index may develop large inhomogeneities [6]. Furthermore, additional saturable absorption due to a microscopic impurity can be an important [5] reason for enriching dynamics. It is known that in experiments with a glass ball doped with Nd ions or a dye droplet under the action of intensive laser light, pumping multimodal radiation is emitted [3–5]. A ∗ Corresponding author. Fax: +375-17-284-08-79.
E-mail address: [email protected] (L.G. Astafyeva). 0022-4073/$ - see front matter 䉷 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jqsrt.2004.01.004
90
H.P. Ledneva, L.G. Astafyeva / Journal of Quantitative Spectroscopy & Radiative Transfer 88 (2004) 89 – 95
separate mode appears in the structural resonance of the particle and can be described by the frequency and the quality factor as well as by its spatial structure both inside and outside the particle. It is known that the quality factor of a certain mode increases with increasing mode number [1]. The value of the intensity inside the spatial structure of the mode, as shown in [7], becomes maximal for a mode number depending on the refractive index, loss, and particle radius due to the existence of optimal conditions for focusing. In this paper, we consider the bimodal laser regime in a spherical aerosol microparticle assuming a mixture of an active substance and a saturable absorber as impurity on the first mode with a very small concentration. An understanding of the changes in the internal TE- and TM-polarization optical field distributions resulting from the saturable absorption of fluorophores and chromatophores that occurs in bioparticles is important for bioaerosol detection. Absorbing molecules in the particle are assumed to be randomly oriented with their absorption proportional to the absorption index ma . There are several ways to consider systems with a large number of modes [8–10]. Below we describe, by analogy with [9,10], another approach to describing the interaction of many modes in a spherical particle, which permits us to take into account the spatial overlap of the modes along with other traditional mechanisms of interaction. 2. Basic equations The vector Maxwell equations for the field in the spherical coordinate system (r, , ) are usually written in the scalar form [11] by introducing the linear differential operator L = r × ∇/i and expressing the electric field E in the scalar Debye potential . For the transverse electric mode (or TE mode), E = i∇ × (r ) where r is the radius vector and is the angular frequency of light. The components of the electric field are given by E =
*(r ) i , cr sin *
E =
i *(r ) , cr *
Er = 0.
Then intensity of the electric field can be written as B = |E |2 + |E |2 .
qn (t)dn n (kmr)Yn (, )eit . Here k = /c, Yn (, ) are For a bimodal system, we can write = n+1 n spherical harmonics of the degree n, and the coefficients dn for a resonant mode of the transverse electric field inside the particle are given by dn = i n
m 2n + 1 . n(n + 1) mn (ka)n (kma) − n (ka)n (kma)
Here, m is the refractive index of the active substance, a is the radius of the particle, n and n are spherical Ricatti–Bessel and Ricatti–Hankel functions, and the primes denote differentiation with respect to the argument in the parentheses. The basic system of equations for the amplitudes q1 and q2 and the corresponding phases 1 and 2 of two neighboring modes and the components of the matrix of the gain coefficients k11 , k22 , k12 is the following: dq1 vc1 + (1 + k1 )q1 − [q1 k11 + q2 k12 (cos + 1 sin )] = 0, dt 2
H.P. Ledneva, L.G. Astafyeva / Journal of Quantitative Spectroscopy & Radiative Transfer 88 (2004) 89 – 95
q1
91
d1 vc1 + [q1 k11 1 + q2 k12 (1 cos − sin )] = 0, dt 2
dq2 vc2 + 2 q2 − [q2 k22 + q1 k12 r21 (cos − 2 sin )] = 0, dt 2 q2
d2 vc2 + [q2 k22 2 + q1 k12 r21 (2 cos + sin )] = 0, dt 2
dk11 0 =D(k11 − k11 ) − 11 c1 B1 [q12 k11 + q1 q2 k12 (cos + 1 sin )] dt − 12 c2 B1 [q22 k22 + q1 q2 k12 r21 (cos − 2 sin )],
(1)
dk12 0 =D(k12 − k12 ) − 12 c1 B1 [k12 (q22 + r21 q12 ) + q1 q2 k11 (cos − 1 sin ) dt + q1 q2 k22 (cos + 2 sin )], dk22 0 =D(k22 − k22 ) − 12 c2 B2 [q12 k11 + q1 q2 k12 (cos − 1 sin )] dt − 22 c2 B2 [q22 k22 + q1 q2 k12 r21 (cos + 2 sin )], dk1 = D1 (k01 − k1 ) − B1 k1 |E1 |2 . dt Here r21 = c2 /c1 , and cj = 1/(1 + 2j ), (j = 1, 2); k01 = 4 ma / . Furthermore, v is the phase velocity of light, D and D1 are the decay rates of populations in the active medium and saturable absorber, = 2 − 1 , j = a − j is the tuning of the mode frequency 1 with respect to the resonant frequency a in units of the spectral gain line width, and k1 is the absorption coefficient of the saturable absorber. The elements of the gain coefficient matrix kij include the self-action due to standing waves k11 , k22 and the cross-action between the neighboring modes k12 . kij = k(r, t)i (kmr)j (kmr)Yi (, )Yj (, ) dv, dv = r 2 sin dr d d. (2) v
The integrals of self-saturation and cross-saturation in the modes are as follows (see also [12]): 11 = 41 (kma)[S12 () + Q21 ()]2 dv, v 22 = 42 (kma)[S22 () + Q22 ()]2 dv, v 12 = 21 (kma)22 (kma)[S1 ()S2 () + Q1 ()Q2 ()]2 dv. v
(3)
Here Qj () = Pj (cos )/ sin , Sj () = −Pj (cos ) sin , Pj (cos ) are Legendre polynomials, j = 1, 2 and the primes denote differentiation with respect to the argument in the parantheses. It has been shown in [7] that the quantities 11 , 22 and 12 , which describe the degree of coverage of the spatial modes, depend on the mode number n due to the focusing properties of spherical particles. Depending on n, 11 can be greater or smaller than 22 .
92
H.P. Ledneva, L.G. Astafyeva / Journal of Quantitative Spectroscopy & Radiative Transfer 88 (2004) 89 – 95
Fig. 1. Internal intensity distribution in the equatorial plane of a microsphere for TE polarization resonance mode with n = 47: (a) s = 1, (b) s = 2. The arrow shows the direction of the incident laser beam.
3. Results and conclusions We have considered steady states for the bimodal laser regime and concluded that when a saturable absorber is absent, then the bimodal laser regime is reached if the values of the gain coefficients exceed the first threshold for both modes. As an example, the spatial distribution of the intensity in the mode with the azimuthal mode number n = 47, the radial mode numbers s = 1 and 2, absorption index m = 1.5 − i10−8 , and radius a = 3.5 m is shown in Fig. 1. In the presence a saturable absorber, the quality factor and the spatial structure of the mode change. Therefore, the dynamics of lasing changes as well. In this case, we obtain from (1) that the bimodal steady
H.P. Ledneva, L.G. Astafyeva / Journal of Quantitative Spectroscopy & Radiative Transfer 88 (2004) 89 – 95
93
Fig. 2. The ratio of the intensity coefficients of two modes as a function of the ratio of the gain coefficient to the loss coefficient 0 at K 0 = 0.9 for m = 1.5 − i10−8 and azimuthal mode number n: (1) 40–41; (2) 47–48; (4) 61–62; (3) 47–48; (m = 10−7 ). K11 a 22
state exists when the following condition is met: 0 0 )(2 − 22 k22 ) (1 + k1 − 11 k11 2 0 2 2 − 12 k12 (cos − 1 2 sin + (1 − 2 ) sin cos ) > 0.
(4)
In this case the overlap of the spatial modes and their nonlinear coupling leads to the existence of solutions below the first threshold for the bimodal steady state, as can be seen in Fig. 2. This figure illustrates the dependence of the ratio Q = q2 /q1 of the steady intensity coefficients q1 and q2 of the two modes on 0 = k 0 /( + k ). The area where this state exists becomes wider with the relative gain coefficient K11 1 1 11 increasing coefficient of the spatial overlap, the quality, and the beginning gain. For the modes with numbers 61 and 62, curve 4 is characterized by higher Q values than for the other modes. Their spatial coverage of the modes is more effective due to a much greater ratio of the intensities than that for the modes with numbers 40–41. Curves 2 and 3 demonstrate the result of changing the absorption coefficient of the saturable absorber. For curve 2, the coefficient of the spatial overlap of the modes is equal to 0.95 and the intensity of the first mode is a bit smaller than that of the second one. At the same time, for curve 3 a tenfold increase in the absorption enhances the local focal effect; as a result, the intensity of the second mode is twice that of the first one. Therefore, curve 3 corresponds to greater Q values and approaches curve 4 in Fig. 3. The steady intensity values q1 (curve 1) and q2 of the two modes 47–48 as functions of
94
H.P. Ledneva, L.G. Astafyeva / Journal of Quantitative Spectroscopy & Radiative Transfer 88 (2004) 89 – 95
Fig. 3. Steady intensity values q1 (curve 1) and q2 of two modes 47–48 as a function of the ratio of the gain coefficient to the 0 in bistability area: 2–3 (m = 10−8 ); 4–5 (m = 10−7 ). loss coefficient K11 a a
0 in bistability area: 2–3 (m = 10−8 ); 4–5 (m = 10−7 ) correlation between the intensities the ratio K11 a a of the modes. There are two values of the steady intensities for one of the two modes in the area over the first laser threshold shown in Fig. 3. The frequencies of each of the two modes in this case are shifted to one side from the resonance frequency. The area of coexistence of several values of the steady intensities and frequencies can be changed due to the presence of an impurity acting as a saturable absorber. So, for the modes with numbers 47 and 48 under the action of pumping absorption for ma = 10−8 curves 2 and 3 correspond to the intensity of the higher-quality mode n = 48 equal to 0.9 times the intensity of the mode 0 = 1.49 at K 0 = 1.21. A tenfold with a smaller quality n = 47 and the upper boundary of bistability K11 22 increase of absorption (ma = 10−7 ) in curves 4 and 5 leads to a shift of the boundary to a smaller value 0 = 1.34 due to the increase in the ratio of the spatial structures up to the 1.8. K11 Thus, the steady state and microlaser dynamics are very sensitivity to the presence of the very small concentrations of a saturable absorber, which may be used for the detection of biological impurities.
Acknowledgements This study was partially supported by the Belarus Republican Foundation for Fundamental Research under Grant No. F03-043.
H.P. Ledneva, L.G. Astafyeva / Journal of Quantitative Spectroscopy & Radiative Transfer 88 (2004) 89 – 95
95
References [1] Chang RK, Campillo AJ, editors. Optical processes in microcavities. Singapore: World Scientific; 1996 [2] Sandoghdar V, Treussart F, Hare J, Lefevre-Seguin V, Raimond J-M, Haroche S. Very low threshold whispering-gallerymode microsphere laser. Phys Rev 1996;54:R1777–80. [3] Lu B, Wang Y, Li Y, Liu Y. High-order resonance structures in a Nd-doped glass microsphere. Opt Commun 1994;108: 13–6. [4] Lin H-B, Eversole JD, Campillo AJ. Spectral properties of lasing microdroplets. J Opt Soc Am B 1992;9:43–52. [5] Popp J, Fields MH, Chang RK. Q switching by saturable absorption in microdroplets: elastic scattering and laser emission. Opt Lett 1997;22:1296–8. [6] Hill SC, Videen G, Wenbo Sun, Qiang Fu Scattering and internal fields of a microsphere that contains a saturable absorber: finite-difference time-domain simulations. Appl Opt 2001;40:5487–94. [7] Ledneva HP, Kotomtseva LA, Pavlovsky GB. Proceedings of the Fourth Conference on Laser Physics and Spectroscopy, Grodno, 1999, p. 253–5 [in Russian]. [8] Pieroux D, Mandel P. On the rate equation approximation for free-running multimode lasers. Quant Semiclass Opt 1997;9:L17–22. [9] Oraevsky AN, Scalli M, Velichansky VL. Quantum dot laser. Quant Electron 1998;25:211–6. [10] Samson AM, Kotomtseva LA, Loiko NA. Selfpulsing in lasers. Minsk: Nauka i Tekhnika; 1990 [in Russian]. [11] Prasad S, Glauber RJ. Initiation of superfluorescence in a large sphere. Phys Rev A 1985;31:1583–97. [12] Ledneva HP, Korzhov AV, Kotomtseva LA, Astafyeva LG. The effect of spatial field distribution on two-mode lasing in a spherical microparticle. Opt Spectrosc 2003;94:476–80.