Experimental Optics Contact: Lisa Kaden (lisa.kaden@uni-jena.de) Malte Siems (malte-per.siems@uni-jena.de) Last edition: Ulrike Blumenröder, January 2017 Spectroscopy
Contents 1 Introduction 3 2 Theoretical Background 3 2.1 Spectrograph................................. 3 2.2 Beer-Lambert Law.............................. 5 2.3 Emission of electromagnetic radiation.................... 7 2.3.1 Discrete and Continous emission spectra.............. 7 2.3.2 Light emitting diodes (LED)..................... 8 3 Experiment 9 3.1 Experimental Setup.............................. 9 3.2 Spectrasuite Software............................. 10 3.3 Determination of spectra........................... 11 4 Measurement Tasks 12 4.1 Working with the spectrometer setup..................... 12 4.2 Identification of color filters by transmission and absorption measurements. 12 4.3 Studying the absorption of dyes....................... 13 4.4 Study of emission spectra........................... 13 A Preliminary Questions 14 B Final Questions 14
Keywords: electromagnetic spectrum, dispersion, monochromator, absorption, stimulated and spontaneous emission, Lambert-Beers-Law, black body radiator, LED. 1 Introduction This lab aims to investigate the fundamental principle of spectroscopy which is to investigate the properties of materials using light. Firstly a brief review of some of the properties of light. We characterise light based on its wavelength (λ), which is spread over a range of values across the electromagnetic spectrum. This also provides us with direct knowledge of the energy of the photons at a particular wavelength via: E = hν ν = c/λ E = hc/λ (1) We can use this information to look the behaviour of atoms and molecules and their interaction with light of a particular wavelength. The internal energy structure of a particular atom or molecule, in a quantum description, is composed of discrete levels with certain allowed and forbidden transitions between these levels. Light interaction of the correct energy (wavelength) can cause these levels to become excited. If the atom was interacting with photons of various wavelengths this would cause a very specific change in the photon energies after this interaction for that species of atom or molecule. This is the underlying principle of Spectroscopy. Here we will use this principle to investigate the spectral characteristics of different materials in various regimes (transmission, absorption & reflection). In the frame of the Labwork, the following objects will be investigated: glass color filters, food dyes, LEDs. With these objects, the following spectroscopic techniques will be applied: transmission, absorbance and emission measurements. 2 Theoretical Background 2.1 Spectrograph The main components of a spectrometer are shown in fig. 1 exemplary for a grating spectrometer. The incoming light of a point source is collimated (entrance slit S1 and lens or concave mirror SP1 as shown in fig. 1). The spatial separation of the different wavelengths is accomplished by a dispersive element ( G in fig. 1). Afterwards the light is focussed by a second lens (or mirror SP2 in case of fig. 1) in the plane of observation. Therefore the wavelength distance λ corresponds to a spatial separation x of [1]: dy p,g x = x(λ + λ) x(λ) = f 2 λ, (2) dλ 3
Figure 1: Schematic sketch of a grating spectrometer [1]. where f 2 corresponds to the focal length of the imaging lens and dy p,g describes the angle dλ dispersion of the prism (index p) or grating (index g). Prism spectrometers use the dispersion n(λ) of the refractive index that results in a wavelength dependent refraction angle (see fig. 2a)). The angle dispersion of a prism depends on the angle γ of the prism (see fig. 2 a)) and the dispersion dn of the prism material [1]: dλ dθ dλ = 2 sin(γ/2) dn 1 n 2 sin 2 dλ (γ/2) (3) Eq. 3 is derived under the assumption of a symmetric light path. Today commercially available systems mainly use diffraction gratings as dispersive element. Here the spatial separation is enabled through the wavelength dependent diffraction and interference (see fig. 2b)). The incoming parallel light hits the grating under an incidence angle α. The reflected rays interfere constructively under β if the grating equation is fulfilled. Therefore the angle dispersion of the grating arises from the grating equation [1]: z (sin α + sin β) = m λ dβ dλ = m z cos β (4) and is given by the grating constant z and the interference order m. The reflection angle is denoted as β (see fig. 2 b)). The most important characteristica for the performance of a spectrometer is the spectral 4
Figure 2: Sketch of a) prism, b) reflection grating. The angles are denoted as in eq. 3 and 4 resolution R: R = λ λ. It describes how good two wavelengths with λ = λ 1 λ 2 can be imaged seperately in the observation plane. In case of a prism it can be described by [1]: (5) R = B 4 dn 1 n 2 /4 dλ, (6) where B describes the length of the prism as shown in fig. 2. Eq.6 is determined under the assumption that the diffraction entrance area is given by the length of the prism. and in case of a grating spectrometer [1]: R = m K, (7) where m describes the interference order and K the number of illuminated grating grooves. 2.2 Beer-Lambert Law The law describes the attenuation of the radiation intensity I 0 when it has passed through an absorbing medium of thickness b and concentration c. Let us consider an absorbing solution of concentration c with an extinction coefficient ɛ l and of differential thickness db. The differential decrease in the intensity di is proportional to the extinction coefficient ɛ l and the concentration c of the medium: di I = ɛ l c db. (8) 5
Integration of eq.8 yields: I(b) = I 0 e ɛ l c b, (9) where I 0 denotes the incoming intensity at b = 0. Usually the Beer-Lambert Law is written in the form: E = log ( I0 ) ( ) 1 = ɛ c b = log, (10) I T where I [W/m 2 ] is the intensity of light after passing an object of thickness b [m] and I 0 [W/m 2 ] is the intensity of the incoming light. Furthermore c [mol/l] describes the concentration of the solution and ɛ [l/(mol m)] is the wavelength dependent extinction coefficient (to the base 10) and can be derived from ɛ l by ɛ = log(e)ɛ l 0.434ɛ l. The validity of Lambers-Beers Law is only given for rather low concentrations where no saturation of the absorbance can be observed. The linear relation between absorbance (extinktion) and the concentration of a solution can be used to determine the extinction coefficient ɛ for an unknown solution by measuring the absorbance for different concentrations. This should result in a linear increase of the absorbance with increasing concentration as shown in fig. 3. Therefore the slope of the increase contains the product ɛb: ɛb = A 2 A 1 C 2 C 1. (11) Therefore ɛ can be determined from eq. 11, when the thickness b of the cuvette is known. Nevertheless the concentration plot as shown in fig. 3 can also be used as a calibration plot to determine the concentration of an unknown solution as is indicated by the red line in fig.3. Figure 3: Absorbance as a function of concentration, the curve slope is equal to ɛb. The red line indicates the determination of an unknown concentration by measuring its absorbance. 6
In Optics the law is rather known in the form of eq. 12 [1]: I(b) = I 0 e α b, (12) where b[m] describes the thickness of the material and α[1/cm] describes the absorption coefficient that can be obtained from the imaginary part of the complex refractive index N = n + iκ, via α = 4πκ λ 0, where λ 0 refers to the respective wavelength in vacuum. 2.3 Emission of electromagnetic radiation 2.3.1 Discrete and Continous emission spectra Let us consider a system with the energy level E i > E k as shown in fig. 4. The transition between the two energy levels is possible by emission or absorption of a photon with energy: hν = E = E i E k (13) Nevertheless experimentally the intensity of the emitted radiation with frequencies corresponding to eq. 13 are quite different and not all of the possible transitions can be observed. This demonstrates that the transitions have different probabilities. Figure 4: Absorption, stimulated and spontaneous emission in a two-level-system, after [2]. Those probabilities can be described by the Einstein coefficients of emission and absorption [2]. If we consider N i atoms at an energy E i and N k with an energy E k that are exposed to a radiation field with the spectral density w ν (ν). Within steady state the emission rate has to be equal to the absorption rate: A ik N i + B ik w ν (ν) N i = B ki w ν (ν) N k. (14) Therein A ik, B ik and B ki are the Einstein coefficients for the spontaneous emission, stimulated emission and absorption respectively. As can be seen from eq. 14 the probability per 7
time for stimulated emission and absortpion is proportional to the spectral density of the radiation field. The probability for spontaneous emission on the other hand just depends on the wavefunction of the involved states [2]. The Einstein coefficients depend on the square of the transition dipole moment [2]: M ik = e ψ i rψ k dr, (15) where ψ i,k describes the wave function of the respective states. Therefore only transitions with M ik 0 are possible. Transitions between discrete energy levels as described in eq. 13 result in a line spectrum. Nevertheless the emitted radiation is not fully monochromatic but rather exhibits a certain spectral distribution around the frequency ν 0 with maximum emission power P 0. The frequency range ν = ν 1 ν 2 with P(ν 1 ) = P(ν 2 ) = P 0 /2 determines the FWHM of the emission line. Besides the discrete emission spectra as observed for instance in case of a vapor discharge lamp the spectrum of a thermal emitter like a light bulb shows a continious emission spectra. The continious radaition emitted by a black body radiator can be described by Plancks Law: w ν (ν)dν = 8πhν3 c 3 dν e hν/kt 1, (16) where w ν (ν) describes the spectral energy density. 2.3.2 Light emitting diodes (LED) The principle structure of a LED is a pn-junction as shown in fig. 5 a). Nevertheless LEDs are based on direct semiconductors as III-V-compounds like GaAs, GaAsP or GaN. When the LED is biased in forward direction majority carriers (electrons from the n-doped side and holes from the p-doped side) are driven across the pn-junction where they recombine. The released energy is then emitted as electromagnetic radiation (fig. 5 a)). The electric symbol and configuration for a LED in operation is shown in fig. 5 b). 8
Figure 5: a) Schematic sketch of the working principle of LEDs, after [2] b) Electric circuit for a LED in operation. 3 Experiment Safety information: The laser system used within measurement task 4 is classified as a Class 2 Laser. A Class 2 laser is hazardous if the eye is exposed directly, but diffuse reflections such as from paper or other matte surfaces are not harmful. 3.1 Experimental Setup This is a quick and easy-to-use instrument for generating UV and visible region spectra from any light source. The spectrophotometer (mirrors, grating, slit, and detector) are housed in an optical bench small enough to fit into the palm of your hand. The basic configuration of the measurement setup is shown in fig.6. Figure 6: Sketch of the experimental setup As a light source a Halogen lamp is used. The sample is placed into the sample holder and illuminated via an optical fiber. The spectrometer accepts light energy transmitted through an optical fiber or free spaced and disperses it via the fixed grating across the linear CCD detector that is designed to provide output readings at 3648 evenly-spaced locations in the wavelength range of choice. The output from the detector is then fed into the computer via USB to software, processed, and displayed on the monitor as "counts" per millisecond. (One "count" is equivalent to one photon hitting the chip). Thus, the display you see is the result of more than 3500 different outputs being fed into the computer and processed. This 9
happens fast enough for you to be looking at the spectra generated by the instrument in "real time". The transmission measurements are done with the configuration shown in fig. 6. Therein we basically do not consider any losses due to scattering. For the measurement of the emission spectra the emitting object is used as a light source (LED, laser...). This is done be decoupling the second fiber from the sample holder as shown in fig. 7. The dark current spectrum (the signal without emission from the investigated object) has to be taken as a reference one. Figure 7: Emission measurement setup. 3.2 Spectrasuite Software The setup includes an analysis software from Ocean Optics whose basic features are explained below. 1. Open the program Ocean Optics - Spectra Suite. Fig. 8 below shows the toolbar that will appear at the top of the screen. 2. Turn on the light source and open the mechanical shutter to observe the spectrum from the light source. 3. Inspect the spectrum. The top should be near the top of the window, but not off scale. If it is too big or too small, it will be necessary to adjust the mechanical shutter or the integration time to produce the best possible spectrum. The integration time is the time, in milliseconds, that the instrument counts photon for display on the screen. Find the integration time control on the left side of the toolbar and adjust it until you are comfortable that the maximum signal is the right size. For emission spectra, it may be necessary to use a large integration time to identify very weak peaks. 4. When you are happy with the spectra click the Save icon ( ) in the SpectraSuite toolbar. Name and save the file. Then click the open as overlay icon from the SpectraSuite toolbar allowing you to view and analyze the captured spectra. 5. Click on the screen to activate the cursor. This will be used to identify wavelengths and signal strengths for each line or peak you are interested in. Click on the screen and the cursor will move to that location. Identify the wavelengths of all the lines that you can identify. Record both the wavelengths and signal intensities in your notebook. 10
6. For directly displaying the transmission spectra you need to internally store the dark and reference spectrum at first ( see section 3.3). This can be done by pushing the button with the grey bulb (dark spectrum) and the button with the yellow bulb (reference spectrum), as shown in fig. 8. Figure 8: SpectraSuite Software Toolbar 3.3 Determination of spectra For the measurement of transmission and absorbance spectra at first a " dark" and " reference" spectrum have to be taken: I d is a "dark spectrum", which takes account of any background radiation and thermal fluctuations. I 0 is the reference spectrum. It depends on the specific measurement task The transmission (T) of the sample can then be calculated with: T = I T I d I 0 I d (17) where I T is the transmitted spectrum. Once the instrument has reference spectra and a sample is inserted in the holder, the computer calculates the ratio of the counts hitting the detector to the stored reference counts for each of the 3648 elements, converts these to absorbance (transmission) values, and plots the result on the screen. Nevertheless for the determination of the absorbance spectra eq. 10 is used. Again, the computer operates at a speed that makes all this appears to happen instantaneously. 11
4 Measurement Tasks 4.1 Working with the spectrometer setup Learning Target: Getting to know the working principle of the spectrometer. Learn how to use the software. Tasks: 1. Observe the influence of the integration time on the spectrum of the halogen lamp, discuss the effect of the integration time on the spectra by measuring the spectrum of the halogen lamp with different integration times. 2. When chosen a suitable integration time start to take the dark spectrum, the spectrum of the halogen lamp and the spectrum after inserting a glass plate as reference. 3. Measure the spectrum after inserting a color filter given by the assistant. 4. Take the transmission and absorption spectrum of the color filter and compare those results with the calculated spectra from your reference and dark spectrum. 4.2 Identification of color filters by transmission and absorption measurements Learning Target: understanding transmission, absorption and the working principle of color filters understanding the differences between "Longpass" and "Bandpass" filters Tasks: 1. Measure the transmission and absorption of different color filters given by the assistant (use "Filter1" as reference) 2. Identify the filter labels by comparing your results with the data sheets given by the assistant. Which of them are Longpass and Bandpass filters? 3. Combine two different Longpass Filters. What will be the cutoff frequency? 4. Try to combine the given filters in a way to approximately create a bandpass for the wavelength region between 500-700 nm. 12
4.3 Studying the absorption of dyes Learning Target: understanding Lambert-Beers-Law using Beers Law to identify the concentration of an unknown solution Tasks: 1. Take the dark spectrum. Insert a cuvette with 1 ml water into the spectrometer setup and take the spectrum as reference. 2. Slowly add small amounts of dye and measure the absorption spectrum (when the spectrum appears to be constant). 3. Measure the absorption of an unknown solution given by the assistant and determine the concentration by using your calibration plot. 4. Repeat the task with a second dye given by the assistant. 5. Mix two different dyes and observe the resulting spectrum. Attention: Don t forget to note the volumes you added to the solution. Avoid bubbles in the syringe. To maintain reliable results you should use the same cuvette during one measurement series and make sure that it is oriented the same way for each measurement. 4.4 Study of emission spectra Learning Target: understanding different emission mechanisms Tasks: 1. Measure the emission spectra of the halogen lamp, measure the spectrum of the room light and if possible the daylight. 2. Measure the emission spectra of three different LEDs, determine the full width at half maximum 3. Measure the emission spectrum of two different lasers 4. Compare the different spectras with each other, what makes them different and why? Attention: Emission spectra of LED and Lasers should be taken in the dark. 13
A Preliminary Questions 1. Sort the following electromagnetic radaition from highest to lowest energy and additionally give the wavelength region of the respective radiation: VIS, X-Ray, microwaves, γ-rays, infrared, radio waves, UV-radiation 2. You want to measure two spectral lines seperated by dλ = 0.02 nm at a wavelength of 500 nm. You have the choice between a prism spectrometer (prism of base length B = 10 cm made out of glass with n = 1.81 and a dispersion dn/dλ = 4400/cm) and a grating spectrometer (width: 10 cm and 500 grooves/mm) that is illuminated over its full width and will be operated in the second interference order. Calculate the spectral resolution. Which of the spectrometers do you choose for your speific measurement task? What conclusion can you draw about possible disadvantages of the prism spectrometer? 3. How can you optically determine the bandgap of a direct semiconductor like GaAs E G = 1.42 ev? 4. Consider a thin slice of silicon (10 µm) that is illuminated with 826 nm and 500 nm. How much of the incoming intensity is transmitted? N 826nm = 3.67 + i 0.0052, N 500nm = 4.3 + i 0.0732 5. Explain the physical background of line broadening in emission spectra. 6. What kind of radiation field has to be prepared in order to built a laser? 7. What determines the emitted wavelength of a LED? 8. Why are indirect semiconductors not used for LEDs? B Final Questions What are the so called Fraunhofer Linien? How can you build a white light emitting LED? 14
References [1] W. Demtröder, "Experimentalphysik 2: Elektrizität und Optik", 3.Auflage, Springer (2004). [2] W. Demtröder, "Experimentalphysik 3: Atome, Moleküle und Festkörper", 3.Auflage, Springer (2004). [3] E. Hecht, "Optics", Addison-Wesley 2002. [4] Saleh Teich, "Fundamentals of photonics", Wiley 2007. 15