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Two-photon magnetoabsorption experiments are reported for the first time. From the splitting of the 2p excitons of ZnO in a magnetic field of 42 kG the hole masses and the g values for the upper valence bands r 9 and r 7 are deduced, Two-photon spectroscopy has gained growing importance as a spectroscopic method in studying electronic properties in solids. Because of the changed selection rules as compared with ordinary spectroscopy (one-photon absorption), two-photon data yield information on excited states which are commonly forbidden for onephoton transitions.* Two -photon measurements with polarized light allow symmetry assignments to be determined for the different excited states. Much more quantitative information on band parameters (e.g., effective masses, g-values) are expected from two-photon magnetoabsorption, since transitions with Ara= ±2, ±1, and 0 are two-photon allowed, as compared with Am = ±1 and 0 in one-photon absorption. In this Letter we report the first observation of two-photon magneto-optic absorption in ZnO. Because of its rather large band gap (3.5 eV) and its pronounced exciton structure, ZnO is well suited for this kind of experiment. One-photon data 2 ' 3 on ZnO show three well-resolved exciton series, which are interpreted as transitions to S excitons from the three valence bands [symmetry T 7 (A), T 9 (J5), and T 7 (C)] and a T 7 conduction band. The two-photon spectrum looks quite different: It shows very narrow exciton lines close to the corresponding 2s transitions. This is shown for the A and B excitons in Fig. 1. For polarization parallel to the c axis one gets in one-photon absorption the C series and in two-photon absorption again a single pronounced exciton line, 4 which is close to the 2s line in the one-photon spectrum. We interpret the two-photon lines as transitions to 2p excitons. The shift of about 2.5 meV to lower energies as compared with the 8 ( Q 2 i Q_ Q. o o <

The formalism for the polarization dependence of the two-photon absorption is extended to include circularly polarized light. Measurements with linearly and circularly polarized light on TlCl allow a unique decomposition of the spectrum into the different symmetry contributions. Die Formeln fiir die Polarisationsabhangigkeit der Zwei-Photonenabsorption werden auf zirkular polarisiertes Licht erweitert. Die Meesungen mit linear und zirkular polarisiertemLicht an TlCl ermoglichen eine eindeutige Zerlegung des Spektrums in die verschiedenen Symmetrieanteile.

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