0 Terahertz spectroscopy measurements For general medicine and pharmacy students author: József Orbán, PhD. teaching facility: Univerity of Pécs, Medical School Department of Biophysics research facility: MTA TKI High-Field Terahertz Research Group Pécs, 2013. november 25.
Terahertz spectroscopy measurements For general medicine and pharmacy students Spectroscopy background Similarly to the ultraviolet (UV), visible (VIS) and infrared (IR) spectroscopy the electromagnetic radiation in the terahertz (THz: 1012 Hz) frequency range can also be used for spectroscopy and can provide useful information about the energy state and vibrations of molecules. The terahertz frequency falls into the far infrared range and is on the short wavelength edge of the microwave range of the total electromagnetic spectrum (1. figure). As in case of UV/VIS/IR spectroscopy the most used and basic measurement method is based on the measurement of absorption of radiation transmitted through the studied sample, the terahertz radiation can be used this simple way as well. The relative decrease of radiation intensity requires in all cases a so called control measurement to which the sample transmitted intensity is compared. The measurement is performed in two steps control and sample measurement as for all single path spectroscopes. The absorption can be calculated by the following formula: 1. equation X-ray and gamma ultraviolet visible infrared microwaves radiowaves in which I and I0 are the transmitted intensities for the sample and for the control measurements calculated for each wavelength (λ) of the spectrum, correspondingly. 1. figure: Terahertz radiation falls into the far infrared (FIR) range of the total electromagnetic spectrum. The sample is placed between the source of the radiation (called emitter) and the detector. The control measurement is performed either without sample or in case of solutions the solvent is used without the molecule of our interest (solute). 1
amplitude amplitude The terahertz spectrometer 2 The source of the terahertz radiation is a short time pulsed laser (3. figure) providing ~100 femtosecond (fs: 10-15 s) time long pulses. These laser pulses generate similarly ~100 fs long terahertz pulses. These pulses contain energy on a wider range of frequency (0-5 THz) hence are not monochromatic. The energy packed in the pulses has a typical intensity-time distribution profile (see 2. figure). The absorbance spectrum can be calculated with high precision on a limited frequency range (0,2-3 THz) using the available instrument (Menlo Systems K8 THz spectrometer). The calculated absorbance values at the edges of the total frequency range (0-5 THz) have low reliability, are not acceptable for spectroscopy. A B time time 2. figure: The change of electric field in time of a typical THz impulse. The real signal shape (A) and the measured amplitudes at discrete time intervals (B) are shown. Varying the density of data points the achievable precision of information can be influenced. The beam of terahertz impulses originated from the emitter is focused onto the sample using appropriate lenses. Passing the substance, the diverging beam is gathered with a similar lens to the focusing lens and is finally directed to the detector (3. figure). Both the emitter and the detector are optically gated dipole antennas. The previous one emits THz frequency radiation when the incoming laser impulse creates varied electric field strength between the two poles of the antenna. The latter one converts THz pulses to electric signal that is proportional to the electric field strength of the incoming THz pulse. This signal is acquired and processed by an electronic device, called lock-in amplifier. The emitter is switched on and off by a high frequency electric (square-wave) signal, thus the lock-in amplifier can compare the signal produced by the detector in on and off state. The signal of the latter case is subtracted from the first and thus the signal is corrected for background noise, hence the signal-to-noise ratio is increased. This background subtraction is repeated several times by the lock-in amplifier and as a consequence with long time integrating the noise reduced signals, the instrument eliminates further random measurement errors. The laser impulses are split in 50-50% ratio by a beamsplitter to create two pathes for the measurement: the emitter and the detector beams (3. figure). The first goes to the emitter and is responsible for the formation of THz pulses, the latter switches the photoswitchable detecting antenna on and off. The pulses arriving to the detector
sample antenna makes it sensitive for a short time consistent with the period of the incoming laser pulses (~100 fs is the detection time window for each pulses). 3 fs timed, pulsed laser 50-50% delay line emitter detector electric pulse generator lock-in amplifier 3. figure: Schematic drawing of the function of a terahertz spectrometer. The electric units are labeled blue, the optical ones are shown in red. Dashed red lines correspond to the path of pulsed laser and THz beams. The 50-50% ratio beamsplitter divides the laser light into emitter and detector beams. The pulses travelling in the detector beam path can be delayed in time compared to the pulses propagating in the emitter path using the delay line unit (DLU). This optomechanic device is retroflecting a beam parallel to the incident beam and its position can be varied thus the flight time of pulses can be precisely altered. As a consequence the time resolution of the system is defined on optical/geometrical positioning bases. This laserlight pulse based optical control permits us to study the THz signal transmitted through the sample down to 100 fs time steps that is the time resolution of the system. At the same time it means that the transmitted THz pulse is not measured from only one single pulse but from chosen finite number of measurements at different time points of the total time range of the THz signal. With this step-by-step measurement we perform an approximation process to gain the real shape of the pulse in time (2. figure). This setup requires the delay line unit (DLU) that we can position by 1 micrometer precision. Keep in mind that the light in 10 fs travels 3 microns only (this can be calculated using the propagation speed of light in vacuum; c 3 10 8 m/s). Important fact is that the laser pulses directed to and reflected from the DLU by an increase of 15 microns in pathlength results in a double; 30 micron space delay that corresponds to 100 fs time delay. This way the pulses travelling in the detector path are delayed by 100 fs compared to the pulses propagating in the emitter beam. As a consequence, by steps of (at least) 15 micrometers in the detection path we can measure the sample transmitted THz signal by steps of 100 fs (at least).
Time domain frequency domain transformation 12 FFT amplitude (a.u.) The THz pulses formed by the emitter are energy quanta limited in space and time propagating in one direction from the emitter toward the detector in our case. The finite number intensity data measured at different time points define the intensitytime function which should be converted to intensity-frequency (or intensity-wavelength) function that is called spectrum. 4 10 8 6 4 2 0 0,0 0,5 1,0 1,5 frequency (THz) 2,0 This function defines the amount of energy 4. figure: the spectrum (amplitude-frequency plot) (or intensity) brought by the pulse at a given of a THz pulse that propagated in air containing vapour (dew) of water. The absorption peaks of frequency (4. figure). The Fast Fourier water can be seen as valleys on the curve. Transformation (FFT) is used to convert time domain data to frequency domain data (spectrum). According to the simplified mathematical background we can state that all types of (periodic) signal in time can be described as a sum of sinus signals with independent periodicity and amplitudes. A simple and single sinus signal s intensity at any moment of time (I(t)) is defined by the sinus function s frequency (ω) and amplitude (A): 2. equation Therefore a complex signal can be written in the following form: 3. equation where k is the number of the components. To rewrite it in a more elegant way let s use the sum function (i is integer number, varied from zero to k): 4. equation The signal decomposed to its components has number k pairs of characterizing data: the defined values of frequencies (ωi) and the related amplitudes (Ai). If we plot these amplitudes against the related frequencies then we get the spectrum. In the complicated (discrete) Fourier transformation the signal is decomposed in the space of complex numbers: 5. equation where ω0 is the base frequency, N is the number of elements in the data (pair) set, k is a constant proportional to a selected frequency and ejωt=cos(kω0t)+j sin(kω0t). For further explanation of FFT method please find appropriate mathematical books. Applying the Fast Fourier Transformation method (FFT) with some useful considerations and simplifications the computational time requirement and the complexiticity can be significantly decreased. Using computers and softwares of nowadays these FFT calculations can be easily performed even for large data sets.
Application of Terahertz spectroscopy 5 The terahertz frequency range can be used to study weak chemical bonds (i.e. hydrogen, van der Waals bonds), or the low frequency intra- and intermolecular vibrations. The molecular transitions in the microsecond-picosecond range probed by THz radiation supplement our knowledge of different energy and time scaled vibrations. The IR spectroscopy is appropriate to probe the fs-ps (10-15 10-12 s) and the electron paramagnetic resonance (EPR) spectroscopy the μs-ms (10-6 10-3 s) time scaled molecular changes and vibrations. Due to the recent development of THz radiation emitting sources it is possible to study biological molecules (peptides and proteins) and their hydration shell, as well. The water molecules forming the hydration shell have role in the function of proteins and also in the intestinal absorption of drugs and nutrition. The water highly absorbs the infrared radiation, including THz waves. When we perform a measurement the relative humidity in the air must be precisely controlled and kept constant. This is an important precondition of comparable control and sample measurements. The best solution is if we can decrease the relative humidity below 5% some way. At well-defined frequencies characteristic water absorption lines show up (see: 4. figure). These specific lines are related to hydrogen bonds and vibrations of water molecules. Water based solutions can be measured in infrared and in THz spectroscopy if the sample width is less than 10-200 μm, otherwise the water absorption hides the studied molecule s (solute) own absorption. Finally, it is important to note that similarly to UV spectroscopy THz requires special materials having low absorption in the THz regime, with other words THz-transparent materials if it is possible it can also be transparent in visible range. Principally thin walled plastic (teflon, high density polyethylene, etc.) containers or cuvettes are used for this purpose. Measurement method Using the available time-domain terahertz spectroscope (Menlo Systems K8 TDTS) we can study molecules having well defined absorption lines in the THz range. Chemically not bound, separate amino acids, nucleic acids have characteristic absorption spectra in the 0-3 THz range (limits of the indicated instrument). The water-free powder form of the molecules should be placed to the appropriate plastic sample holder. Sample preparation is easy; none of the dry powders require further precautions. After starting the spectroscope and optimizing the amplitude of the THz pulses the first step is to set the delay line unit to a position that corresponds to equal path lengths in the emitter and detector paths. This is the starting point for further settings and the zero time point of the signal is defined this way at the same time. Good quality measurement can be achieved by appropriate time steps (0,1 ps = 100 fs). The THz signal is only ~100 fs long, but passing the sample it widens thus the best is to gather data from a 60 picosecond (6 10 11 s) time range. To receive a good quality FFT transformation result we should precisely define the zero signal level that can be done by collecting data 5-10 ps
before the THz signal. As a consequence the total time window to measure turns to be around 70 ps. This results in ~700 data points applying the above defined time resolution. With these settings we may detect the shape of the THz signal with high enough precision. Please use appropriate names ( talkative names ) for the measurement files to facilitate the latter file searches. The name should include the name of the molecule, the name of the user, any further information that helps to recognize the file. 6 At the end compare the transmitted spectra of the THz signals of the sample and control measurements using the software based on FFT method. Compare the calculated absorption spectra in the 0-3 THz range corresponding to the different studied molecules. Make conclusions from the received spectra: the characteristics absorption frequencies, maximum amplitudes and the half width of the peaks. 1) Start the instrument (thermostating unit, laser power supply, lock-in amplifier, computer) 2) Start the spectroscope controller software. After the initialization step set the delay line unit s position to equal pathlengths in the detector and emitter beams. 3) The laser reaches the modus synchronized state helping to switch from continuous to pulse mode automatically. This step requires setting the temperature of the laser to 35ºC. In the next step find the optimal THz intensity leaving the emitter and reaching the detector by fine adjustment of the micrometer screws that moves the detector and emitter antennas. 4) Set the appropriate starting and ending DLU positions in the software. The measurement should start 5-10 ps earlier (important for determining the zero signal level) and 60 ps long time window for the signal and post signal period. Set the time steps to have at least 5-600 data points leading to an approximate 0,1 ps (100 fs) time resolution. 5) Perform the control measurement. This may be the transmitted signal in air or through an empty sample holder (or filled with the buffer, but without the molecule of our interest). The sample holder should be placed right in the middle between the lenses of the emitter and detector. Save the reference measurement data with an appropriate name that helps to choose later this data as reference for sample measurements. 6) Replace the control substance or position the sample between the lenses and determine the transmitted THz signal for each sample separately. Save the results of the different molecules with corresponding names. 7) Calculate the transmission spectra for the control and for the sample(s) then determine the characteristic absorbance spectra for the different samples. Use either the ( ) 1. equation, or the FFT based software. 8) Make conclusions from spectroscopy viewpoint about the properties and characteristics of the absorption spectra. Can the different molecules be differentiated based on their spectra?
7 The present teaching material made by József Orbán (PhD), was supported by the European Union and the State of Hungary, co-financed by the European Social Fund in the framework of TÁMOP-4.2.4.A/ 2-11/1-2012-0001 National Excellence Program (2013-14). This material was made for the University of Pécs, Medical School, Department of Biophysics as a research associate at the MTA TKI High-Field Terahertz Research Group.