1. Introduction

Laser calorimetry is a standard method of determining optical absorption. To separate bulk absorption and surface contribution when performing such measurements one usually uses a minimum of three samples of different thicknesses assuming that they are the same material and that the surfaces were polished and cleaned identically. Then a plot of the measured absorptance, the ratio of absorbed power to incident power versus thickness will yield the absorption coefficient as the slope of the resulting line and the surface loss as the ordinate intercept. Very often the three data points do not lie on a straight line and the intercept is an unphysical negative value. Incorrect results can be traced to the assumptions mentioned above not being met.

In the experiment reported in this paper we used a single sample of an isotropic material (a synthetic single crystal diamond) polished identically on all six surfaces eliminating the assumptions mentioned. Then we determined the absorption coefficient and the surface loss in the manner described above at four wavelengths between 1064 and 408 nm. As a consequence we could determine the dispersion of the surface loss term independently from the influence of the bulk absorption coefficient. This dispersion turns out to be exactly what the Rayleigh scattering law would predict. The strength of the surface loss varies as 1/(λ⁴). The only suggestion for absorption on the surface of the diamond we studied was at the shortest wavelength where bulk absorption was large. Absorption in single crystal diamond from its band edge at 225 nm (5.51 eV) in the mid-ultraviolet to longer wavelengths is a strong intrinsic absorber [1] that changes to an extrinsic absorber through the visible due to various nitrogen vacancy color centers [2–6]. As a consequence we recommend that studies of absorption in materials considered for high power laser systems be conducted in a manner similar to that described in this paper and at more than one wavelength if at all possible.

2. Experimental

2.1 Growth and polishing

Details of the growth of a single crystal diamond can be found elsewhere [7]. However, in brief, the sample used was prepared in a microwave plasma-assisted CVD reactor. It was produced from a homoepitaxial layer grown on a <100>-oriented diamond surface that had been prepared using high quality polishing techniques to minimize the roughness average (Ra) (< 20 nm) and therefore reduce the nucleation of dislocations in the epitaxial layer. For high purity products with low absorption, the key requirement is to minimize the impurities in the system [8]. Using techniques previously reported [9], the diamond utilized in this experiment has approximately 40 ppb of nitrogen impurities, which resulted in extremely low optical absorption across the visible and near-infrared spectrum [10]. The dimensions of the single crystal diamond sample were 5.5 × 3.6 × 1.9 mm. Polishing was performed in the usual manner, by the use of a scaife with a fine diamond powder. Additional information about the details of polishing diamonds have been reviewed by Wilks and Wilks [11]. Finally, the diamonds were cleaned in a nitric acid solution which was kept just under its boiling point. Upon microscopic inspection with a BX-41 Olympus Microscope utilizing objectives of 10X and 40X the samples showed no imperfection on the surfaces or voids or fractures inside the samples.

Atomic Force Microscopy (AFM) was performed using a Digital Instruments Dimension 3100 AFM in contact mode. Data was acquired on the top (shown in Fig. 1) and bottom two largest surfaces across a 5 x 5 µm scanning range. On both sides of this sample very few defects were found and the “top and bottom” surfaces yielded a Ra of 0.17 and 0.18 nm, respectively. Due to the lack of contaminants found by optical and AFM microscopies, the scattering phenomenon that is discussed in this work is not due to surface or bulk artifacts and is an intrinsic property of the diamonds studied.

 

Fig. 1 Atomic Force Microscope topography of a single crystal diamond sample displaying a contour plot covering a 5 × 5 µm scan range. Ra from the two largest surfaces was determined to be 0.17 and 0.18 nm.

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2.2 Calorimetry

Laser calorimetry measurements were performed as described previously and details of the general technique can be found in our previous work [12, 13]. A brief description is provided here. The sample was mounted in a thermally insulated chamber where it was suspended from a monofilament. Thermocouples, with 5 mK sensitivity, were glued to the edges of the sample and the laser beam was directed into the sample so that it did not directly strike any of the thermocouples. Since one dimension of the sample was ~2 mm thick it was necessary to focus the laser beam into the central region of the sample. This was done by focusing down to a spot size of roughly 50 μm which results in Rayleigh range, the distance along the propagation direction of a beam from the waist to the place where the area of the cross section is doubled, of ~10 mm in air and ~25 mm in the diamond due to its refractive index of ~2.4 in the visible. The use of more than one thermocouple allowed for a consistency check and to be sure that no scattered laser light struck any of the thermocouples. For the calorimetry measurements, several cw laser wavelengths were used; a 1064 nm (Nd:YAG laser, assembled at CREOL); a frequency doubled Nd:YAG 532 nm laser, and two 445 and 405 nm diode lasers. The power of these lasers impinging on the samples ranged from 100 mW to 400 mW depending on the available power and how strongly the sample absorbed at each wavelength. The major source of error in these measurements comes from the power meters and is estimated to be approximately 15%.

3. Results and discussion

The single crystal, CVD grown diamond used in this study, was cut and polished with dimensions of 0.19, 0.36, and 0.55 cm. Calorimetry at several wavelengths was used to determine the absorptance, A(λ). The absorptances as functions of length for each wavelength are plotted and fit with a linear regression in Fig. 2 using Eq. (1):

 

Fig. 2 The absorptance versus path length in the single crystal diamond (408 nm; purple squares, 446 nm; blue circles, 532 nm; green triangles, and 1064 nm; black diamonds). The data has been fit with a linear regression using Eq. (1) and the results of this equation are tabulated in Table 1. The y-intercept is the surface loss and the slope is the absorption coefficient in cm⁻¹.

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Since this is done at several wavelengths the dispersion of these quantities can be obtained. Shown in Fig. 3(a) are the results of the surface loss versus wavelength that have been fit with a Rayleigh function and shown in (b) are the results plotted as a function of Rayleigh scattering (λ⁻⁴). The Rayleigh function fitting regression, which yielded a vertical offset of −9.8 × 10⁻⁶ (practically zero), and a multiplicative factor of 2.1 × 10⁷ cm⁴ in front of the λ⁻⁴ fit the data with a coefficient of determination, R², equal to 0.97. It is noted that the data point at 408 nm is slightly off the Rayleigh fit, however a fit with an R² equal to 0.97 shows strong agreement between our data and Rayleigh scattering.

 

Fig. 3 (a) Surface loss (α_surf) from Eq. (1) versus wavelength and fit with a Rayleigh function regression. (b) Surface loss versus wavelength plotted as a function of Rayleigh scattering (λ⁻⁴) and fit with a linear regression. Data points are plotted with the following scheme: 408 nm; purple squares, 446 nm; blue circles, 532 nm; green triangles, and 1064 nm; black diamonds.

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Note from Table 1 the absorption coefficient, α(λ), increases as the wavelength approaches the deep blue at 408 nm as expected from extrinsic absorption.

Table 1. Data which has been fit with a linear regression using Eq. (1). Graphical results for the dispersion of surface loss are plotted in Figs. 2 and 3.

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Further confirmation that surface loss for the diamond sample is due to Rayleigh scattering from surfaces having Ra of 0.17 – 0.18 nm comes from the fact that Ra << λ . Rayleigh scattering is applicable when the scatterers are much smaller than the wavelength of light being scattered. The parameter that determines if this criterion is met is X given in Eq. (2).

4. Conclusions

A single synthetic sample of single crystal diamond has been studied by laser calorimetry to determine its bulk absorption coefficient and, importantly, its surface losses at several wavelengths. This allowed the dispersion of the surface losses to be determined. The sample was cut into a parallelepiped having three different lengths and polished identically on all six sides so that the absorptance could be accurately determined. The dispersion measurements were accomplished by probing the sample using wavelengths at 1064, 532, 446, and 408 nm through its three polished pairs of sides. A Rayleigh function fitting regression (1/λ⁴) fit the surface loss remarkably well implying that no surface absorption was present on the sample’s surface, only surface scattering. Atomic Force Microscopy was used to quantify the surface roughness and found the two largest area surfaces to be extremely well-polished that further verifies that surface loss in this sample is determined by Rayleigh scattering. To our knowledge, this is the first time such an optical measurement described herein has been performed.