22 Lab Experiments Experiment-143 S DIFFRACTION GRATING Dr Jeethendra Kumar P K KamalJeeth Instrumentation & Service Unit, No-610, 5 th Main, 8 th Cross, JRD Tata Nagar, Bangalore-560 092. INDIA. Email: jeeth_kjisu@rediffmail.com Abstract Using 625nm laser light and three different gratings, diffraction pattern is observed. From the diffraction pattern the angle of diffraction is determined and the grating constant is calculated and compared with the standard values. Introduction The ability of a diffraction grating to physically separate the different wavelengths made it one of the most powerful optical tool for the study of matter. If the incoming light is multicolored or consists of more than one wavelength, then the angle of diffraction differs from color to color, resulting in multiple image of the slit opening with different colors. If the incoming light is single color then different orders of slit images are seen with varying intensities. The concept of grating came from the single slit. A single slit is a narrow opening (<1mm wide and 10-50mm wide). When intense beam of light passes through this narrow opening, the light rays falling on the edges of the opening get bent or get diffracted. The diffracted rays interfere constructively and destructively to form fringes. These fringes are dark and bright slit images. Instead of single slit opening one can have two or double slit opening [1, 2], three slit or n slit opening. The diffraction pattern observed for multiple slit opening is found to have sharper fringes than observed through a single slit. More the slit opening clearer is the slit image. Or a multiple slit opening have the power of producing more clear and distinct slit images or fringes [3]. Such a multiple slit opening is called diffraction grating. Figure-1 shows one of the diffraction grating used in this experiment. Figure-1, 500LPI Diffraction Grating used in this experiment
Lab Experiments 23 Diffraction Grating is present in nature [4]. The feathers of peacock, butterfly and some insects have fine structures when white light falls on them the rainbow color is observed which makes them attractive. In recent times the CDs and DVDs also produce rainbow colors which indicate the grating effects. Diffraction grating is a powerful tool which was responsible for the discovery of many elements and to the study of light emitted by stars and heated objects. The first diffraction grating was made by German Physicist Joseph Von Fraunhofer (1787-1820) in 1820. He tied thin wires over a metal frame to produce the first diffraction grating trough which he was able to see the D 1 and D 2 lines of sodium light. However, he was not satisfied with that grating and he developed a ruling engine (a machine to draw lines on glass and thin metal foil there by making slit opening). The engine composed of two important parts 1. A carriage which holds the grating material 2. A sharp cutting tool of diamond During the process of ruling, lines are drawn with diamond tool. The diamond tool is dragged across the glass plate one line after the other line. Fraunhofer first coated the glass plate with gold and then ruled it with his ruling machine. This provided multiple slit opening. At the position of ruling the gold coating was removed and light passed through it. The remaining gold coating blocked the light. With this grating Fraunhofer measured accurately the wavelengths of absorption lines in the solar spectrum now known as Fraunhofer lines [5]. Latter Albert A Michelson (1852-1931) made ruling engine and produced grating as big as 10cm wide. The real quality grating was produced by Henry Augustus Rowland (1848-1901) a physics professor of Hopkins University in the year 1883. Rowland s machine was the major contribution to the history of Physics which really made wonderful gratings. Figure-2 shows Rowland preparing a grating. Rowland s ruling engine containing a screw of nearly flawless pitch. He used spherically curved glass plates for diffraction gratings which resulted in very high resolution and accurate rulings. The Suns spectrum recorded with this grating was 10 time more superior than observed earlier. He started making and selling the gratings throughout the world. Figure-2, Henry Augustus Rowland preparing a grating using ruling engine Picture courtesy:www.chem.ch.huji.ac.il/~engenik/history/rowland.html Preparation of a Grating
24 Lab Experiments Diffraction gratings are now made in three different methods 1. Ruling Engine 2. Interference Lithography (IL) 3. Scanning Beam Interference Lithography (SBIL) Ruling Engine In this method lines are drawn by diamond tool on plates at equidistant. The diamond tool is dragged across the glass plate and ruling of one groove is complete, the plate moves forward by one grating space by a mechanical arrangement and the second ruling takes place. This is continued until the entire glass plate is ruled. The major draw back of this method is its speed. It takes hours together to grate a one inch plate. Further the continuous operation of the machine for such a long time also resulted in wear and tear in the machine. Hence the accuracy of grating started de-iterating as the machine becomes old. This is a series process through which one line is drawn at a time, hence to replace this series process a parallel process in which all the lines are drawn simultaneously is thought of, which resulted in Interference lithography. Interference Lithography (IL) In this parallel process [6, 7] first dark and bright images are formed on a photo resist. And the images is exposed and developed to get a permanent pattern. The photo resist is then sandwiched between to glass plates to obtain grating. The dark and bright images are formed by using two intense beam of light, which interference and produce interference fringes of equal width on a photo resist as shown in Figure-3. Laser Ligtt source-1 Laser Ligtt source-2 Interference fringes Glass plate Photo resist Figure-3, Schematic of interference lithography system IL is faster and the exposure time is less than 1 minute which makes the process complete in few minutes. The only disadvantage of this method is large grating is difficult to make. The interference fringes formed are uniform when it is formed in a small area (about 25mm x 25mm). Non uniformity creeps in as fringes are formed on a larger area (This effect is also observed in air wedge experiment). Hence large gratings are difficult to make. This difficulty is over come by new method which combines both the above techniques.
Lab Experiments 25 Figure-4, Photo resist after exposure and development Picture courtesy; www.doitpoms.ac.uk/t1plib/dd1-6/diffraction1.php Scanning Beam Interference Lithography (SBIL) SBIL is developed by a team of Professors, scientists and students of MIT [8]. In this method after one exposure the photo resists and glass plate fixed to a movable stage which moves by an electro mechanical arrangements and the second unit of the photo resist is exposed. In this process the fringes remain the same for all the exposure. Hence the quality of the grating is uniform and extremely good. Further any length grating can be obtained by this method. The only precision requirement is the movement of the stage so that continuity is not lost. With the present day computer technology this is achieved accurately. The photo resist and substrate moves in the direction of fringe and strip of photo resist is exposed hence is called Scan. Because of the stage motion which is similar to ruling engine SBIL is also called as a nanoruler because it has nano meter accuracy. This machine also finds wide applications in semiconductor technology which may further reduce the size of ICs in the future. Figure-5 shows the process of SBIL. UV laser Reflector Reflector Photo resist Fringes Photo resist Stage Figure-5, Schematic of SBIL
26 Lab Experiments Laser light diffraction using grating A laser consists of single wavelength falling on a grating will produce diffraction pattern. The principal maximum intensity of the diffracted light is given by dsinθ = mλ 1 Where d is grating constant or the distance between two consecutive rulings θ is the angle of diffraction m = 1, 2, 3 m is called order of diffraction λ is the wavelength of the light used In the above equation all the terms are constant except θ. The angle θ can be measured by experiment either using spectrometer or by measuring accurately the distance between source and image and distance between the consecutive maximums. Different order of diffraction is the result of different incident angle θ. Hence to specify order θ has been rewritten as θ m, which indicate the diffraction angle for m th order. Figure-6 indicates process of diffraction, using laser light and grating. The m th order diffraction angle is given by θ m = tan -1 x m f 2 Where x m is the distance of m th order diffraction pattern from the centre 0 th order diffraction f is the distance between the screen and the grating 2x 2 2x 1 Image screen Order m 2 1 1 2 x m m Diffraction patteren Left Right xm= distance betwwen central maxim and m th order maxima f f = distance between grating and im age screen Tan m = x m f m Grating Laser Source Figure-6, Process of diffraction using grating
Lab Experiments 27 Distance f between the grating and the image screen is our choice which can be fixed as required and the distance x m can be measured accurately from the diffraction pattern. Hence angle of diffraction θ m can be determined. Substituting θ m in Eaquation-1, grating constant d can be determined mλ d = 3 Sinθ m In this experiment using laser light and three different gratings, grating constant is determined. Apparatus Used 625nm diode laser, Indian assembled 500LPI (lines per inch), Indian assembled 15000LPI and imported 15000 LPI gratings, image screen. The complete experimental setup is shown in Figure-7. Experimental procedure The experiment is divided in to two parts Part-A, Diffraction With 500LPI gratings Part-B, Diffraction With 15000LPI gratings Figure-7, Complete experimental setup Part-A, Diffraction with 500LPI grating 1. The laser is placed on a sturdy table and switched on. At about two meters away on the path of the laser a white laminated wooden screen is placed. The leveling screws of the laser are adjusted such that the laser beam exactly falls on the centre of the screen. The exact distance between the grating stand and image screen are noted f = 2.0m = 200cm 2. The 500LPI grating is now placed on the grating stand close to the laser source and the diffraction pattern is observed as shown in the Figure-8. Equally spaced diffracted laser
28 Lab Experiments light spots are observed. The total numbers of spots are counted. The central direct ray is very bright in the picture as the order increased the brightness deceased. Maximum order of diffraction observed = 8. Left Right Order-m 7 2 1 1 2 7 Figure-8, Diffraction pattern observed f=2m (color picture front cover) 3. The centre of the spots of the diffraction pattern are marked on the screen using a pencil and after marking all the diffraction pattern, the image screen is removed and the distances between consecutive order of diffraction is measured using a scale and tabulated in Table-1. The distance between the two first orders diffraction spots are measured. 2x 1 = 5.3 cm Similarly the distance between two second order diffraction spots are measured and recorded in Table-1. 2x 2 = 10.5cm This is continued up to 8 th order 2x 8 = 42.5cms 4. Using equation-2 diffraction angles are calculated for first order diffraction and noted in Table-1 θ m = tan -1 θ 1 = 0.759º x m x 1 2.65-1 f = tan = = 0. 01325 f 200 Similar calculations are made for different orders of the diffraction and the diffraction angle is calculated and presented in Table-1. 5. Grating constant is calculated for first order diffraction using equation-3. d = mλ Sinθ m 9 1x625x10 = Sin(0.759) 9 625x10 = 0.01324 = 47173x10 9 = 47173nm Similar calculations are done for different orders of the diffraction and the grating constant obtained is tabulated in Table-1. And the average value of grating constant is calculated.
Lab Experiments 29 Table-1 500 LPI grating, f=200cm Distance Diffraction 2x m (cm) angle (θ m )º 1 5.3 0.759 47173 2 10.5 1.50 47635 3 16.0 2.29 46925 4 21.2 3.03 47296 5 26.5 3.79 47277 6 32.0 4.56 47168 7 37.1 5.30 47363 8 42.5 6.06 47362 Average d = 47232nm, N=537LPI Diffraction angle for different order f-200cm Diffraction Order = m Diffraction Order = m Grating Constant d ( nm) Table-2 500 LPI grating, f=150cm Distance Diffraction 2x m (cm) angle (θ m )º 1 4.0 0.759 47119 2 7.9 1.52 47123 3 11.9 2.27 47338 4 15.9 3.03 47295 5 19.9 3.79 47277 6 24.0 4.57 47065 7 27.9 5.31 47274 8 32.0 6.08 47206 9 36.0 6.84 47230 10 40.2 7.63 47071 Average d = 47200 nm, N=539LPI Diffraction angle for different order f-150cm Diffraction Order = m Grating Constant d ( nm) Table-3 500 LPI grating, f =100cm Distance Diffraction 2x m (cm) angle (θ m )º 1 2.65 0.76 47119 2 5.30 1.51 47435 3 7.90 2.27 47338 4 10.6 3.03 47295 5 13.3 3.80 47152 6 16.0 4.57 47065 7 18.6 5.32 47186 8 21.3 6.07 47284 9 24.1 6.87 47025 10 26.8 7.63 47071 11 29.5 8.39 47117 Average d = 47189 nm, N=538LPI Diffraction angle for different order f-100cm Grating Constant d ( nm)
30 Lab Experiments 6. Number of rulings per unit area N of the grating is calculated from the average value of grating constant as follows 1 1 N = 21172 9 d = 47232x10 = Lines per meter = 211.72 Lines per cm = 211.72x2.54 = 537.8 Lines per inch Which is close to manufactures data of 500LPI. 7. Trial is repeated for f =1.5m and f =1m. The readings obtained are tabulated in Table-2 and Table-3 respectively for 1.5m and 1m. Part-B, Diffraction with 15000LPI grating 8. Experiment is repeated with 15000 LPI Indian assembled and imported gratings. In these cases only first order diffraction is observed. Hence for the first order diffraction the readings are taken for different f values. Second order diffraction is noticed for f =20cms and 10cms. The readings obtained are tabulated in Table-4 and Table-5 respectively for Indian assembled and imported gratings. Table-4 f (cm) 2x 1 (cm) θ 1 º d (nm) N (LPI) 20 14.3 19.67 1856 13680 25 17.8 19.59 1864 13626 40 28.5 19.60 1863 13632 50 35.5 19.54 1868 13595 Average N = 13633 Lines per inch Diffraction angle for first order diffraction with 15000 LPI Indian assembled grating Table-5 f (cm) 2x 1 (cm) θ 1 º d (nm) N (LPI) 10 9.0 24.22 1523 16677 20 17.5 23.62 1559 16289 30 26.3 23.66 1556 16315 40 34.6 23.38 1574 16132 50 44.1 23.79 1549 16393 Average N = 16361 Lines per inch Diffraction angle for first order diffraction with 15000 LPI imported grating Note: because of the large LPI the distance f need to be small to observe higher order diffraction. However, keeping grating close to the screen makes the marking of the pattern difficult. Hence we have marked only the first order diffractions in this case. Results
Lab Experiments 31 The results obtained are tabulated intable-6. Table-6 Parameters 500 LPI Indian 15000 LPI Indian 15000 LPI Imported Grating constant d (nm) 47200 1552 1862 Maximum order of the spectrum (m max ) 11at f =100cms 2 at f = 20cms 2 at f =20cms observed Number of lines per unit length (LPI) 538 16361 13633 Experimental Results Discussion 1. Higher order (up 12 th Order) diffraction is observed with small LPI grating. Hence low LPI grating is preferred for this experiment. 2. The diffraction angle remained the same for given grating irrespective of the distance between grating and screen 3. The LPI calculated is in good agreement with the manufactures value within the limits of ± 9% the maximum. 4. With low LPI grating diffraction takes place at small angles hence higher order diffraction is observed. References [1] Sarmistha Sahu, Fraunhofer diffraction at single slit, LE Vol-2, No-3, Sept.-2002, Page-15. [2] Jeethendra Kumar P K, Fraunhofer diffraction at circular aperture, LE Vol-3, No-4, Dec-2004, Page-284. [3] Francis A Jenkins and Harvey E White, Fundamentals of Optics, 4 th Edn. Page-356. [4] Diffraction grating, Wikipedia the free encyclopedia [5] J V Fraunhofer, Kurtzer Bericht von den Resultaten neuerer Versuche uber die Gesetze des Lichtes, und die Theorie derselben, Ann. D. Physik, 74: 337-378, 1823. [6] Antoine Labeyrie and Jean Flamand, Spectrographic performance of holographically made diffraction grating, Opt. Comm. 1(1), 5-8, 1969. [7] D Rutherford and G Schmahl, High precision gratings produced with laser light and photo resist layers, Optik 30, 475-487, 1970. [8] Carl G Chen and Mark Schattenburg, A brief history of grating and the making of the MIT nanoruler. WWW