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Pulse Train Modulation Techniques

Nonlinear processes involving light/matter interactions are not trivial to detect in many instances. In particular, absorptive processes such as two-photon absorption (TPA) and sum frequency absorption (SFA) may be detected by monitoring the transmission of light through a sample although the small signals are generated on a relatively large background and consequently make it extremely difficult to do. Alternative methods involve detecting the effects of excited state relaxation subsequent to two-photon excitation. Two-photon generated fluorescence is by far the most sensitive way to detect two-photon absorption, provided that radiative relaxation pathways are available. For nonfluorescent materials, Z-scan methods are commonly used to determine two-photon absorption coefficients although they usually require an amplified laser system and have low sensitivity. In our lab we have developed sensitive ways to measure TPA directly with high repetition rate, low energy ultrashort laser pulses. This is experimentally accomplished by modulating the intensity of a pulse train that impinges on a sample. The laser pulses with repetition rate f0 from a mode-locked laser are sinusoidally intensity modulated at frequency f. As shown in figure 1, the sinusoidal modulation of the laser pulse train is distorted after propagation through a medium that exhibits TPA. The “tall” (high intensity) pulses are absorbed more strongly than the “short” (low intensity) pulses because of the quadratic laser intensity dependence. The distortion also means that the

Figure 1. The principle of the loss modulation method used to measure TPA.

transmitted light experiences loss at new modulation frequencies. These frequencies occur at nf0 ± 2f and are not generated by linear processes. Calculations illustrate that for a focused Gaussian beam, the ratio of the amplitude of the signals measured at 1f and 2f (TPA signal) is,

where, δ, C and n are the TPA cross section, the concentration and the refractive index of the sample, respectively; τ and λ are the width and center wavelength of the pulse; and L and Z0 are the total path length of the sample and the Rayleigh range of the incident beam in air (Z0 = πr^2/λ, where r is the radius of the focal point). A Mach-Zehnder interferometer and two acousto-optic modulators (AOM's) are used to generate the sinusoidally modulated pulse train. The AOM's shift the frequency of the laser pulses in each arm of the interferometer by a different amount. The pulses are then recombined to interfere and give the intensity modulated pulse train. For example, if the two AOM's are driven at 200 MHz and 201 MHz respectively, the modulation frequency will be generated at 1 MHz (f), while TPA signal will be expected at 2 MHz (2f). In the experimental setup, the modulated beam is focused into a sample and the transmitted light is collected with a photodiode. A lock-in amplifier measures P1F and P2F according to the reference frequency. The reference frequency for the lock-in amplifier was obtained by splitting part of the modulated pulse train to be detected with a photodiode. A P2F/P1F ratio as small as 5x10-6 may be achieved routinely. We have used this method to measure TPA signals of rhodamine 6G (R6G) and some other biological chromophores (melanin, hemoglobin and cytochrome C).

Other nonlinear processes may also be detected in addition to TPA. Sum frequency absorption (SFA – instantaneous) or excited state absorption (ESA) may be detected by employing two pulses at different wavelengths. These experiments are akin to traditional pump-probe experiments. In our experimental setup, two synchronized mode-locked pulse trains at different colors are used where one of the pulse trains are intensity modulated (pump). The modulation transfers to the other pulse train (probe) when nonlinear absorption takes place in the medium. This process is depicted in figure 3. Since SFA is instantaneous and does not involve any intermediate states, the signal is only present when the pulses are temporally overlapped. When intermediate states are involved, different nonlinear processes (bleaching, stimulated emission or excited state absorption) can be studied by varying the time delay between the pump and probe pulses.

Figure 3. Principles of the two-color modulation transfer experiments.

The laser system used in the two-color experiments involves a mode-locked Ti: Sapphire laser (Spectra Physics, Tsunami, 80MHz, 100fs) and a synchronously pumped optical parametric oscillator (Spectra Physics, Opal, 80MHz, 120fs). Other wavelengths may also be generated by second harmonic generation in a nonlinear crystal. Each laser provides one of two wavelengths used in experiments. Either of them can be used as the pump beam or the probe beam depending on which one is modulated. The pump beam is intensity modulated, and the probe beam is not. A filter blocks the pump beam and the probe beam is detected with a photodiode. A lock-in amplifier is used to extract the signal in the probe beam at the modulation frequency. In our experiments we can measure up to 10-6 absorption changes caused by either two-photon absorption or excited state absorption with lock-in detection. Figure 4 displays a typical time-resolved transient absorption decay curve for a melanin sample. The multi-exponential decay illustrates that several relaxation pathways are present in the melanin sample.

Figure 4. Transient absorption decay curve for Sepia melanin (pump - 775nm; probe – 1300nm). The curve may be fitted with a double-exponential decay with time constants of 450±50fs and 3±0.5ps.


	The Warren Research Group at Duke University Home Research LASERS NMR Publications Personnel Useful Links Contact Pulse Train Modulation Techniques Nonlinear processes involving light/matter interactions are not trivial to detect in many instances. In particular, absorptive processes such as two-photon absorption (TPA) and sum frequency absorption (SFA) may be detected by monitoring the transmission of light through a sample although the small signals are generated on a relatively large background and consequently make it extremely difficult to do. Alternative methods involve detecting the effects of excited state relaxation subsequent to two-photon excitation. Two-photon generated fluorescence is by far the most sensitive way to detect two-photon absorption, provided that radiative relaxation pathways are available. For nonfluorescent materials, Z-scan methods are commonly used to determine two-photon absorption coefficients although they usually require an amplified laser system and have low sensitivity. In our lab we have developed sensitive ways to measure TPA directly with high repetition rate, low energy ultrashort laser pulses. This is experimentally accomplished by modulating the intensity of a pulse train that impinges on a sample. The laser pulses with repetition rate f0 from a mode-locked laser are sinusoidally intensity modulated at frequency f. As shown in figure 1, the sinusoidal modulation of the laser pulse train is distorted after propagation through a medium that exhibits TPA. The “tall” (high intensity) pulses are absorbed more strongly than the “short” (low intensity) pulses because of the quadratic laser intensity dependence. The distortion also means that the Figure 1. The principle of the loss modulation method used to measure TPA. transmitted light experiences loss at new modulation frequencies. These frequencies occur at nf0 ± 2f and are not generated by linear processes. Calculations illustrate that for a focused Gaussian beam, the ratio of the amplitude of the signals measured at 1f and 2f (TPA signal) is, where, δ, C and n are the TPA cross section, the concentration and the refractive index of the sample, respectively; τ and λ are the width and center wavelength of the pulse; and L and Z0 are the total path length of the sample and the Rayleigh range of the incident beam in air (Z0 = πr^2/λ, where r is the radius of the focal point). A Mach-Zehnder interferometer and two acousto-optic modulators (AOM's) are used to generate the sinusoidally modulated pulse train. The AOM's shift the frequency of the laser pulses in each arm of the interferometer by a different amount. The pulses are then recombined to interfere and give the intensity modulated pulse train. For example, if the two AOM's are driven at 200 MHz and 201 MHz respectively, the modulation frequency will be generated at 1 MHz (f), while TPA signal will be expected at 2 MHz (2f). In the experimental setup, the modulated beam is focused into a sample and the transmitted light is collected with a photodiode. A lock-in amplifier measures P1F and P2F according to the reference frequency. The reference frequency for the lock-in amplifier was obtained by splitting part of the modulated pulse train to be detected with a photodiode. A P2F/P1F ratio as small as 5x10-6 may be achieved routinely. We have used this method to measure TPA signals of rhodamine 6G (R6G) and some other biological chromophores (melanin, hemoglobin and cytochrome C). Other nonlinear processes may also be detected in addition to TPA. Sum frequency absorption (SFA – instantaneous) or excited state absorption (ESA) may be detected by employing two pulses at different wavelengths. These experiments are akin to traditional pump-probe experiments. In our experimental setup, two synchronized mode-locked pulse trains at different colors are used where one of the pulse trains are intensity modulated (pump). The modulation transfers to the other pulse train (probe) when nonlinear absorption takes place in the medium. This process is depicted in figure 3. Since SFA is instantaneous and does not involve any intermediate states, the signal is only present when the pulses are temporally overlapped. When intermediate states are involved, different nonlinear processes (bleaching, stimulated emission or excited state absorption) can be studied by varying the time delay between the pump and probe pulses. Figure 3. Principles of the two-color modulation transfer experiments. The laser system used in the two-color experiments involves a mode-locked Ti: Sapphire laser (Spectra Physics, Tsunami, 80MHz, 100fs) and a synchronously pumped optical parametric oscillator (Spectra Physics, Opal, 80MHz, 120fs). Other wavelengths may also be generated by second harmonic generation in a nonlinear crystal. Each laser provides one of two wavelengths used in experiments. Either of them can be used as the pump beam or the probe beam depending on which one is modulated. The pump beam is intensity modulated, and the probe beam is not. A filter blocks the pump beam and the probe beam is detected with a photodiode. A lock-in amplifier is used to extract the signal in the probe beam at the modulation frequency. In our experiments we can measure up to 10-6 absorption changes caused by either two-photon absorption or excited state absorption with lock-in detection. Figure 4 displays a typical time-resolved transient absorption decay curve for a melanin sample. The multi-exponential decay illustrates that several relaxation pathways are present in the melanin sample. Figure 4. Transient absorption decay curve for Sepia melanin (pump - 775nm; probe – 1300nm). The curve may be fitted with a double-exponential decay with time constants of 450±50fs and 3±0.5ps. Website concerns - contact mike.conti@duke.edu