(a) A schematic showing the incident pump field , the reflected pump field , the forward-propagating pump field in the film , the backward-propagating pump field in the film , and the pump field transmitted into the sapphire substrate . The subscript is for the pumping configuration (pump polarization perpendicular to the incident plane) and for the pump configuration (pump polarization parallel to the incident plane). The heavy arrows indicate that the various pump fields result from resonant Fabry–Pérot buildup in the film. The pump angle of incidence is shown and the propagation angles and depend upon the pump orientation . (b) Extraordinary-polarized SHG produced by either the or pumping configurations. The SHG field produced in reflection is , the forward- and backward-propagating SHG fields in the film are and , respectively, the SHG field emerging into the sapphire substrate is , and the SHG field exiting the substrate is . The propagation angles and are also given and depend upon the pump orientation . Heavy arrows indicate that the SHG fields results from Fabry–Pérot reflections of both the pump and SHG in the film. The axes of the film and sapphire substrate are parallel to the coordinate axis. The relative thickness of the film and sapphire substrate is not to scale in either (a) or (b).
A schematic showing the apparatus used to generate and record rotational Maker fringes from the samples. is the output of the mode-locked -switched laser; is the attenuator used to set the power incident on the sample; is a polarizer that sets the polarization fidelity of the input pump beam (shown as a dashed line); FR is a glass Fresnel rhomb to set the state of polarization of the pump beam on the sample; is a telescope to expand and collimate the pump beam; is a lens to focus the pump on the sample; is a lens that collects and collimates the SHG (shown as a solid line) and residual pump beam (dashed); is an analyzer to select the state of polarization of the SHG; is a harmonic beam splitter to reject the residual pump beam; BD is a beam dump for the residual pump beam; is a bandpass filter; PMT is a photomultiplier tube for detecting the SHG; PA is a current-sensitive preamplifier; BC is a boxcar averager; is a computer that records the SHG data and controls the stage motion; SC is the control electronics for the rotation/translation stage system; is the pump angle of incidence; , , and are the lab axes fixed with respect to the pump beam; , , and are the crystal axes.
(a) Data and simulation of Maker fringes for the pumping case for the MOCVD grown GaN sample. Superimposed on the graph are the data and simulations for the corresponding quartz reference scan. The GaN and quartz SHG data are on the same scale. (b) Data and simulation of Maker fringes, and corresponding quartz SHG reference scan, for the pumping case are shown for the sample illustrated in (a). The GaN and quartz SHG data are on the same scale, but the scale is not the same as that used in (a). (c), (d) Similar to (a), (b) but results for the thick HVPE grown GaN sample are shown.
(a) Data and simulation of Maker fringes for the pumping case, and corresponding quartz SHG reference scan for the MOCVD grown sample with . The quartz and data are displayed on different scales because of the relatively weaker SHG output resulting from this pump orientation for this high value of . (b) Data and simulation of Maker fringes, and corresponding quartz SHG reference scan, for the pumping case for the sample illustrated in (a). The and quartz SHG data are displayed on the same scale in this case.
Graph illustrating and as a function of Al fraction . Also included are results for the bulk free-standing HVPE grown GaN plate, the theoretical results for GaN and AlN given by Ref. 11, and the experimental results for AlN given by Refs. 21 and 22. Note that the data of Ref. 21 are scaled by choosing .
Maker fringes and simulations for the bulk free standing HVPE grown GaN sample. For clarity, the graphical results are displaced vertically, the quartz reference scans are omitted, and only portions of the ranges are displayed: (a) data and simulation for the pumping case and (b) data and simulation for the pumping case.
Maker fringes and simulations for the thick HVPE GaN sample remaining on its sapphire substrate. For clarity, the reference data is omitted and only portions of the ranges are displayed: (a) data and simulation for the pumping case and (b) data and simulation of the pumping case. Although resolvable, the visibility of the high-frequency Maker fringes is much less than predicted by the simulation.
Maker fringes and simulations for the bulk free-standing high-pressure-grown GaN sample. For clarity, the graphical results are displaced vertically, the quartz reference scans are omitted, and only portions of the ranges are displayed: (a) data and simulation for the pumping case and (b) data and simulation of the pumping case.
A summary of the computed values of the nonlinear coefficients and is given for the GaN and samples. The reference level was set using . The listed values of the refractive indices , , , and were used to fit the simulations to the Maker fringe data in computations of the nonlinear coefficients. As indicated in our earlier paper (Ref. 10), samples with and 0.363 each supported only one extraordinary-polarized guided mode at , consequently a reliable value for could not be evaluated at this wavelength. The lack of precluded computation of for these two samples. The values of sample thickness computed from fitting the data are also given in the table. The “,” “,” and “,” designations in the first column refer, respectively, to crystal growth by high-pressure, HVPE, and MOCVD methods. The first two samples were free-standing while all of the other samples remain on their (0001) sapphire growth substrates. The estimated uncertainty in is and the estimated uncertainty in is . The consistency of the computation of via the and simulations is indicated in the second and third columns.
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