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Comparative Study of Transfer Matrix...

Carcamo, Mario .

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Comparative Study of Transfer Matrix Formalism vs Single-Mode Model for Semiconductor Microcavities.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Comparative Study of Transfer Matrix Formalism vs Single-Mode Model for Semiconductor Microcavities./
Author:	Carcamo, Mario .
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2020,
Description:	49 p.
Notes:	Source: Masters Abstracts International, Volume: 81-09.
Contained By:	Masters Abstracts International81-09.
Subject:	Optics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27737072
ISBN:	9781392403853

Comparative Study of Transfer Matrix Formalism vs Single-Mode Model for Semiconductor Microcavities.
Carcamo, Mario .

Comparative Study of Transfer Matrix Formalism vs Single-Mode Model for Semiconductor Microcavities. - Ann Arbor : ProQuest Dissertations & Theses, 2020 - 49 p.

Source: Masters Abstracts International, Volume: 81-09.

Thesis (M.S.)--The University of Arizona, 2020.

This item must not be sold to any third party vendors.

An optical semiconductor micrcavity consisting of two distributed bragg reﬂectors (DBRs) and a quantum well between, can be modeled using a transfer matrix approach, which solves the propagation through the DBR mirrors and the cavity segment in between the mirrors. Such an approach is easy to use if the interband polarization of the quantum well PQW is a given function of time or frequency, which includes the case of linear optical response, where PQW is given in terms of the linear susceptibility and the electric ﬁeld at the position of the quantum well, EQW. In many cases of practical interest, the quantum well response is a nonlinear function of EQW, in which case the transfer matrix approach becomes impractical. In such cases, a time diﬀerential equation for PQW, which is of the formi¯ h dPQW(t) dt= F[PQW(t),EQW(t)]where F is a nonlinear function of PQW, is solved via time-stepping from earlier to later times. To obtain the electric ﬁeld EQW needed as input to the PQW solution, a commonly used phenomenological approach utilizes the single-mode equationi¯ h dEQW(t) dt= hωcEQW(t)−ΩPQW(t) + S(t)with the source term S(t) being deﬁned byS(t) = ¯ htcE+ inp(t)and corresponding constants that are deﬁned in section 5 of this thesis. However, apart from containing phenomenological parameters, the simple source term entering the single-mode equation does not account for propagation, retardation, and pulse ﬁltering eﬀects of the incident light ﬁeld traversing the DBR mirror. In this thesis, an alternate approach is presented along with evidence of its validity using a bounded convolution integral instead. The integral is used to determine the electric ﬁeld as a function of time and therefore can be used to determine the time derivative of the polarization. The integral being EQW(t) =Z t −∞ [A(t−t0)E+ inp(t0) + B(t−t0)PQW(t0)]dt0. We show in the ﬁnal sections that it is adequate to use this bounded integral to resolve pulses in the time domain. Evidence of that is done using a gaussian pulse and linear response. This method could then be used in conjunction with a time stepping algorithm to resolve nonlinear responses.

ISBN: 9781392403853Subjects--Topical Terms:

517925
Optics.

Comparative Study of Transfer Matrix Formalism vs Single-Mode Model for Semiconductor Microcavities.
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100 1 $a Carcamo, Mario . $3 3558147
245 1 0 $a Comparative Study of Transfer Matrix Formalism vs Single-Mode Model for Semiconductor Microcavities.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2020
300 $a 49 p.
500 $a Source: Masters Abstracts International, Volume: 81-09.
500 $a Advisor: Binder, Rolf.
502 $a Thesis (M.S.)--The University of Arizona, 2020.
506 $a This item must not be sold to any third party vendors.
520 $a An optical semiconductor micrcavity consisting of two distributed bragg reﬂectors (DBRs) and a quantum well between, can be modeled using a transfer matrix approach, which solves the propagation through the DBR mirrors and the cavity segment in between the mirrors. Such an approach is easy to use if the interband polarization of the quantum well PQW is a given function of time or frequency, which includes the case of linear optical response, where PQW is given in terms of the linear susceptibility and the electric ﬁeld at the position of the quantum well, EQW. In many cases of practical interest, the quantum well response is a nonlinear function of EQW, in which case the transfer matrix approach becomes impractical. In such cases, a time diﬀerential equation for PQW, which is of the formi¯ h dPQW(t) dt= F[PQW(t),EQW(t)]where F is a nonlinear function of PQW, is solved via time-stepping from earlier to later times. To obtain the electric ﬁeld EQW needed as input to the PQW solution, a commonly used phenomenological approach utilizes the single-mode equationi¯ h dEQW(t) dt= hωcEQW(t)−ΩPQW(t) + S(t)with the source term S(t) being deﬁned byS(t) = ¯ htcE+ inp(t)and corresponding constants that are deﬁned in section 5 of this thesis. However, apart from containing phenomenological parameters, the simple source term entering the single-mode equation does not account for propagation, retardation, and pulse ﬁltering eﬀects of the incident light ﬁeld traversing the DBR mirror. In this thesis, an alternate approach is presented along with evidence of its validity using a bounded convolution integral instead. The integral is used to determine the electric ﬁeld as a function of time and therefore can be used to determine the time derivative of the polarization. The integral being EQW(t) =Z t −∞ [A(t−t0)E+ inp(t0) + B(t−t0)PQW(t0)]dt0. We show in the ﬁnal sections that it is adequate to use this bounded integral to resolve pulses in the time domain. Evidence of that is done using a gaussian pulse and linear response. This method could then be used in conjunction with a time stepping algorithm to resolve nonlinear responses.
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710 2 $a The University of Arizona. $b Optical Sciences. $3 1019548
773 0 $t Masters Abstracts International $g 81-09.
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793 $a English
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