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Abstract
The two-photon absorption and fluorescence of bulk cadmium sulfide were studied using 50-fs, 800-nm pulses from an unamplified Ti:sapphire laser. The fluorescence spectrum was measured to have a main peak at 522 nm, and the power of the fluorescence was shown to vary quadratically with the 800-nm beam power. This supports the theory that the fluorescence is excited by two-photon absorption and confirms previous work done with longer duration, higher energy excitation pulses. Pump-probe measurements provided additional confirmation of the two-photon absorption. Measured spectral broadening of the wings of the laser spectrum also was observed, which likely is due to self-phase modulation in the cadmium sulfide.
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1. Introduction
Cadmium sulfide (CdS) is a direct bandgap semiconductor with many interesting nonlinear electronic and optical properties. An understanding of the nonlinear optical behavior of CdS is necessary when using this material for applications involving optical switching and saturable absorption. Much work has been conducted concerning the multiphoton processes of CdS and its fluorescence [1–9]. Work investigating laser induced excitation of CdS was done using continuous wave systems [1], nanosecond and picosecond pulses [4], and femtosecond pulses [2,3,6–9]. Most of the femtosecond pulses used in previous work were generated using laser amplifiers [2,3,6,7,9] with pulse energies ranging from 0.5 µJ [7] to 1 mJ [2] and a minimum pulse duration of 100 fs [3]. Z-scan measurements were performed using an unamplified Ti:sapphire laser system with 75-fs pulses to measure the coefficients of two-photon absorption and self-phase modulation in CdS [8]. Our pump-probe system uses unamplified sub-nJ pulses with durations of approximately 50 fs, which is shorter than the pulses used in the previous work. In this paper, we show that these unamplified, shorter duration laser pulses cause two-photon absorption in bulk cadmium sulfide. We do this using the theory that two-photon absorption occurs when the fluorescent power depends on the square of the excitation beam power [1,6]. We also use a pump-probe technique to measure pump pulse induced changes in the transmission of probe pulses through the CdS sample. These pump-probe measurements are compared to a cross-correlation measurement of the pump and probe pulses using a second harmonic generation crystal. Since two-photon absorption and second harmonic generation are both two-photon processes, the signals should be comparable to each other. Also, the fluorescence spectrum of cadmium sulfide is measured and compared to the laser spectrum.
2. Experiment
Our sample of cadmium sulfide was purchased from the MTI Corporation of Richmond, California, USA. The sample is a 10 ${\times} $10 ${\times} $1 mm plate in the wurtzite structure with an orientation of (0001). The crystal is undoped and has optically polished surfaces. The CdS is placed such that its c-axis is parallel with the optical table, and the pump beam is incident at an angle of 12 degrees to the c-axis and has linear s-polarization. The CdS was placed in a mount that allowed for rotation about its c-axis; however, no significant change was observed in any of the data when the crystal was rotated.
The pulse source was a home-built, unamplified, Ti:sapphire laser pumped by a Lighthouse Photonics Sprout-D laser. The Ti:sapphire laser generated pulses centered at ∼800 nm with a repetition rate of 82 MHz. The single beam from the laser was split into pump and probe beams using an 80/20 beam splitter. Two prism-pair compressors were used to compensate for the material dispersion in the pump and probe paths, resulting in 50-fs pump pulses and 40-fs probe pulses delivered to the sample. The pulse durations were measured using a second-harmonic generation frequency-resolved optical gating (SHG FROG) system. The focused pump beam had a $1/{e^2}$ diameter of 47 ± 3 µm, while the probe beam had a diameter of 40 ± 4 µm. The average power of the probe beam was 0.62 mW corresponding to a pulse energy of 7.6 pJ and a peak intensity of 15 MW/cm2. The highest pump beam average power was 75 mW, corresponding to a pulse energy of 1.8 nJ and a peak intensity of 2.6 GW/cm2 accounting for the 50% modulation duty cycle of the acousto-optic modulator described below. The two-photon absorption saturation intensity of bulk CdS was reported to be 65 GW/cm2 [3], so our pump pulses were unable to significantly saturate the CdS.
We performed pump-probe measurements of both the transmitted and reflected probe beams, one at a time. Changes in the transmitted or reflected probe beams were measured with a silicon photodiode detector connected to a Stanford Research Systems Model SR560 Low-Noise Amplifier for initial filtering of the signal. From there the signal passed into a Stanford Research Systems SR510 lock-in amplifier. The pump beam was optically chopped with an IntraAction Corporation ATM-150 acousto-optic modulator driven by a function generator at 24 kHz. The pump and probe beams were cross-polarized to prevent the detection of pump beam light. The fluorescent spectrum of the CdS was measured by focusing the fluorescent light onto the entrance slit of an Ocean Optics Flame-S spectrometer. A diagram of the experimental system is shown in Fig. S1. No significant differences were found between the reflected and transmitted pump-probe scans; the reflected scans were simply much weaker than the transmitted ones. A plot of one reflection scan is shown in Fig. S2.
3. Results
3.1 Fluorescence
When the 800-nm pulses were focused onto the CdS it fluoresced with green light visible to the naked eye. A photo of this fluorescence taken with a cell phone camera is shown in Fig. S3. We measured the spectrum of the CdS fluorescence and overlayed it with the laser light spectrum in Fig. 1. when the average power of the pump laser beam was 75 mW.
Fig. 1. The normalized CdS fluorescence spectrum (solid green) and the Ti:sapphire laser spectrum (dotted red) are shown.
The 522-nm peak corresponds to a photon energy of 2.38 eV, which is comparable with previously reported fluorescence attributed to the recombination of electrons with trapped holes in the CdS [5,7]. The fluorescence spectrum has a broad tail of longer wavelength spectral components which is most likely due to impurities in the CdS [6]. The spectrum from the CdS also shows some broadening of the laser spectrum’s wings which likely is due to self-phase modulation [8,9]. Figure 2 shows the integrated fluorescence power in the 522-nm peak as a function of the 800-nm laser beam power, as well as a quadratic fit $({Y = A{X^2}} )$. The close agreement between these data and the quadratic fit helps confirm that the fluorescence is due to a two-photon process [1,6].
Fig. 2. The integrated fluorescent power in the 522-nm peak is shown here (points) as a function of the 800-nm laser beam power along with the quadratic fit (dashed curve).
3.2 Pump power dependence
A series of pump-probe measurements were performed to determine how the fractional probe transmission depends on the average pump power. We measured seven different scans for the different pump beam powers shown in Fig. 3. The fractional transmission of the probe pulse decreases when it arrives at the sample at the same time as the pump pulse. This is due to enhanced two-photon absorption in which photons from the probe pulse combine with photons from the pump pulse. We analyzed the power dependence for both the scan amplitude (Fig. 4) and background (Fig. 5). The background is the pump-probe signal at the beginning of the scan well before the arrival of the pump pulse. The signal amplitudes show a linear relationship with the pump power up to 20 mW. The signal backgrounds were fit to a quadratic function.
Fig. 3. Scans of the fractional change in the probe transmission are shown here for various pump beam powers.
Fig. 4. The amplitudes of the pump-probe scans for different pump powers are shown (dots) along with a linear fit (dashed line). The linear relationship for pump powers up to 20 mW is consistent with two-photon absorption.
Fig. 5. Shown here are the background signals of the pump-probe transmission scans versus pump power (dots) and a quadratic fit (dashed curve). The quadratic dependence suggests the background is due to the CdS fluorescence.
The linear relationship between the pump-probe signal amplitude and the pump power is consistent with a two-photon absorption process in which one photon from the pump pulse combines with one photon from the probe pulse. The deviation from this linear relationship for pump power greater than 20 mW may indicate some saturation of the two-photon absorption. The quadratic relationship between the background signal and the pump power suggests that the background signal is due to the CdS fluorescence. This is the same type of dependence we observed between the fluorescence spectral power and the pump power shown in Fig. 2. Previous work found the carrier recombination time to be on the order of nanoseconds [4], which means some fluorescence persists in the 12 ns time between subsequent pulses in our system.
3.3 Cross-correlation
Using a beta barium borate (BBO) second-harmonic generation crystal with a thickness of 30 µm, we measured the cross-correlation of the pump and probe pulses for comparison with a CdS pump-probe transmission scan. The cross-correlation measurement was done using the pump-probe system after replacing the CdS with the BBO and rotating the pump beam polarization to be parallel to the probe beam polarization. For the cross-correlation measurement, the 400-nm light generated between the pump and probe beams was measured, which is a positive signal in-phase with the modulated pump beam power. Conversely, the pump-probe transmission signal was a negative signal that decreased as the modulated pump beam power increased. To compare it to the cross-correlation the transmission signal values were multiplied by negative one and both data sets were normalized.
The full-width-at-half-maximum (FWHM) for the pump-probe transmission signal was 73 fs, and the FWHM for the cross-correlation was 56 fs. The similarity of these two measurements as shown in Fig. 6 suggests that the CdS underwent a nearly instantaneous, two-photon process. Although these measurements match quite closely, a small asymmetry in the background of the transmission scan can be seen; the pump-probe signal is slightly lower for positive time delays than for negative time delays. This asymmetry was found in both transmission and reflection pump-probe scans for various pump powers. The asymmetry likely is due to the change in the CdS fluorescence after the relatively large pump pulse excitation.
Fig. 6. The BBO cross-correlation (dotted) and CdS pump-probe transmission (solid) measurements are nearly identical as expected if the pump-probe signal is due to two-photon absorption.
4. Summary
We have shown that 50-fs, sub-nJ, 800-nm pulses focused onto a piece of CdS cause it to emit visible green fluorescence. Spectral measurements of this fluorescence light show that the fluorescence has a peak at 522 nm and there is some broadening of the laser spectrum that likely is due to self-phase modulation. Analysis of the power of the fluorescence shows that it depends quadratically on the power of the 800-nm pump beam. This supports the theory that the fluorescence is due to two-photon absorption of the pump beam. Further confirmation of this theory was done by performing pump-probe measurements with the CdS. Specifically, the fractional change in the transmission of probe pulses was measured as a function of the time delay between the pump and probe pulses. The amplitude of these pump-probe scans showed a linear dependence on the pump beam power. This is explained by a two-photon absorption process in which one photon from the probe beam combines with one photon from the pump beam. Another confirmation of the two-photon theory is the good comparison between the pump-probe scan and a second-harmonic cross-correlation measurement of the pump and probe pulses. Our work used shorter duration pulses than in previous work to confirm these nonlinear effects are observable even with unamplified Ti:sapphire laser pulses. This suggests the possibility of applications involving the two-photon absorption of cadmium sulfide with these shorter-duration, lower-energy pulses.
Funding
College of Saint Benedict; Saint John’s University Physics Department and the Office of Undergraduate Research and Scholars.
Acknowledgments
The authors express their appreciation to Dean Langley for use of equipment involved with this research. Funding was provided by the College of Saint Benedict and Saint John’s University Physics Department and the Office of Undergraduate Research and Scholars.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
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