Symmetry Assignments of Two‐Photon Transitions in TlCl

Fröhlich, D.; Staginnus, B.; Thurm, S

doi:10.1002/pssb.19700400130

Cited by 31 publications

(8 citation statements)

References 16 publications

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“…I n a first step we derive the three basis functions with spherical quantum numbers (u,,, u +~, u -~) for an arbitrary propagation direction b which is for Faraday configuration the direction of the applied magnetic field b = B/lBI. Starting with the Cartesian basis functions (uz, uy, u,) we get for the Zeeman term (equation (1) Adding up the polarization dependent parts for all three components one gets the total rate which is consistent with the result derived by Frohlich et al [8] (equation ( We then get a n extra factor % which is included in the dynamical factor in order to be consistent with the results for linearly polarized light by Inoue and Toyozawa [lo]. For details on this point we refer t o papers by Doni et al [ll] and Girlanda [12], who give a separation of.…”

Section: Formalismsupporting

confidence: 77%

Polarization Dependence of Two‐Photon Magnetoabsorption of the 1S Exciton in Cu₂O

Fröhlich¹,

Kenklies²

1982

Physica Status Solidi (b)

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The formalism for the two-photon polarization dependence of a I ? : state ( o h symmetry) in a magnetic field is developed. Experiments on the IS exciton (yellow series) in Cu,O yield an unambiguous assignment of magnetic quantum numbers, thus allowing to determine g-values.Es werden Formeln fur die Zwei-Photonenpolarisationsabhangigkeit fur einen I?:-Zustand (Oh-Symmetrie) in einem magnetischen Feld abgeleitet. Experimente am IS-Exziton der gelben Serie von Cu,O liefern eine eindeutige Zuordnung der Quantenzahlen. Damit lassen sich g-Werte bestimmen.

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Section: Formalismsupporting

confidence: 77%

Polarization Dependence of Two‐Photon Magnetoabsorption of the 1S Exciton in Cu₂O

Fröhlich¹,

Kenklies²

1982

Physica Status Solidi (b)

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“…The coefficients ac of equation (15) were thus determined. With our more stringent equation (14) we have ar: cc 1A+I2, ar: cc 9 1A+I2, ar: cc f lA-I2, ar: cc IA+I2, (18) with l,4+l2 = 10 lA-1, in the experimental situation of paper [5]. Qualitatively, our results (18) are in good agreement with experimental results (Fig.…”

Section: ___-___supporting

confidence: 94%

“…This can be easily proved either using the projection operators technique (see, for instance, the paper [18] for the treatment of a similar situation) or applying the even simpler procedure of [ 191. Furthermore, the reduced matrix elements involving s-like excitons, the momentum operator P and the final p-like excitons are the same regardless of the nature of the final state, as can be easily verified by carrying out the decomposition of the final states and using Table 1 Notice the detailed information contained in (14) with respect to the less stringent expression 4 4 cc a14e1, e2) + a,E(e1, e2) + %Tl(% e,) + a,T*(e,, e,) 9 [5] and experimentally in [ 5 ] , is clearly violated by Matsuoka's experiments.…”

Section: ___-___mentioning

confidence: 84%

A Note on the Polarization Dependence of Two‐Photon Absorption Coefficient in Crystals

Doni¹,

Girlanda²,

Parravicini³

1974

Physica Status Solidi (b)

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The expression of the two-photon absorption coefficient in crystals is discussed using explicitly the Wigner-Eckart theorem for finite symmetry groups. It is discussed how to separate the dynamical part, which contains appropriate reduced matrix elements of the momentum operator, from the geometrical part, which depends on the polarization vectors of both the radiation beams. For the geometrical part the standard results of the literature are recovered; detailed new information for the two-photon absorption rate is supplied by the dynamical part. To illustrate the procedure, the case of TlCl is considered as a specific example.Nous traitons le facteur d'absorption optique pour transitions B deux photons dans les cristaux en appliquant explicitbment le thBorbme de Wigner-Eckart au groupe fini des operateurs de symmBtrie ponctuelle. On Btudie comme on peut &parer la partie dynamique de la partie gbometrique, la premiere Atant determinee par les 616ments de matrice r6duits de l'operateur d'impulsion, la deuxibme contenant les vecteurs de polarization des deux faisceaux incidents. Pour le facteur gbometrique, nous retrouvons les r6sultats bien connus; le facteur dynamique fournit des detaillbes nouvelles conaissances A propos du facteur d'absorption B deux photons. L'application de notre procedure pour le cristal de TlCl est enfin donnBe comme un exemple.

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“…The interaction Hamiltonian, up to second order in the potential vector of the radiation field, takes the form [8] 1 c)2A. [r , (4) hj~t=…”

Section: -Selection Rules and Polarization Dependencementioning

confidence: 99%

Excitons: Linear and non-linear optical effects

Girlanda

1993

Il Nuovo Cimento D

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Summary. --Selection rules and polarization dependence properties of one-and two-photon optical spectroscopies to exciton states in semiconductors are briefly discussed. The non-local effects in the description of the exciton in semiconductors are also considered and their importance is shown by presenting a gauge-invariant calculation of the two-photon transition rates to 2p Wannier excitons states in a two-band model. One-and two-photon optical spectroscopies provide complementary information on the electronic properties of solids. In two-photon absorption the transitions are governed by different selection rules with respect to one-photon absorption [1]. The possibility of varying the relative polarization and the frequency of the absorbed photons increases the flexibility of these two techniques [2][3][4][5][6][7]. Excitons in semiconductors are described by an effective Hamiltonian containing a non-local potential [8], in this case the gauge invariance of the transition rates is not straightforward. The standard velocity form of the interaction A .pe/mc between the electronic system and the radiation field is no longer valid for Hamiltonians containing non-local potentials [8,9].In sect. 2 selection rules for one-and two-photon transitions to exciton states are presented. In sect. 3 the non-local effects in the optical transitions to excitons are discussed, giving also an example of the two-photon transition to 2p Wannier exciton states in a two-band model semiconductor.(*) In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.

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Symmetry Assignments of Two‐Photon Transitions in TlCl

Cited by 31 publications

References 16 publications

Polarization Dependence of Two‐Photon Magnetoabsorption of the 1S Exciton in Cu₂O

Polarization Dependence of Two‐Photon Magnetoabsorption of the 1S Exciton in Cu₂O

A Note on the Polarization Dependence of Two‐Photon Absorption Coefficient in Crystals

Excitons: Linear and non-linear optical effects

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Symmetry Assignments of Two‐Photon Transitions in TlCl

Cited by 31 publications

References 16 publications

Polarization Dependence of Two‐Photon Magnetoabsorption of the 1S Exciton in Cu2O

Polarization Dependence of Two‐Photon Magnetoabsorption of the 1S Exciton in Cu2O

A Note on the Polarization Dependence of Two‐Photon Absorption Coefficient in Crystals

Excitons: Linear and non-linear optical effects

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Polarization Dependence of Two‐Photon Magnetoabsorption of the 1S Exciton in Cu₂O

Polarization Dependence of Two‐Photon Magnetoabsorption of the 1S Exciton in Cu₂O