...Gaussian Beams Enrique J. Galvez Department of Physics and Astronomy Colgate University Copyright 2009 ii Contents 1 Fundamental Gaussian Beams 1.1 Spherical Wavefront in the Paraxial region 1.2 Formal Solution of the Wave Equation . . 1.2.1 Beam Spot w(z) . . . . . . . . . . 1.2.2 Beam Amplitude . . . . . . . . . . 1.2.3 Wavefront . . . . . . . . . . . . . . 1.2.4 Gouy Phase . . . . . . . . . . . . . 1.3 Focusing a Gaussian Beam . . . . . . . . . 1.4 Problems . . . . . . . . . . . . . . . . . . . 1 1 3 6 8 8 9 10 12 15 15 17 20 21 25 25 26 26 27 29 30 31 31 33 35 35 36 39 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 High-Order Gaussian Beams 2.1 High-Order Gaussian Beams in Rectangular Coordinates 2.2 High-Order Gaussian Beams in Cylindrical Coordinates . 2.3 Irradiance and Power . . . . . . . . . . . . . . . . . . . . 2.4 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Wave-front interference 3.1 General Formalism . . . . . . . . . . . . . . . . 3.2 Interference of Zero-order...
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...Arcacia Godfrey 1/15/15 Unit 2 Assignment 2 New Technology in my field Electrical Engineers at Oregon state university have developed new technology to monitor medical vital signs, with sophisticated sensors so small and cheap they could fit onto a bandage, be manufactured in high volumes and cost less than a quarter. A patent is being processed for the monitoring system and it’s now ready for clinical trials, researchers say when commercialized, it could be used as a disposable electronic sensor with many potential applications due to its powerful performance, small size, and low cost. Heart monitoring is one obvious candidate, since the system could gather data on some components of an EKG, such as pulse rate and atrial fibrillation its ability. Its ability to measure EEG brain signals could find use in nursing care for patients with dementia. ‘’current technology allows you to measure these pulse rate and skin responses. Also the university of Utah engineers have developed a polarizing filter that allows in more light, leading the way for mobile device displays that last much longer on a single battery charge and cameras that can shoot in dim light. Polarizers are indispensable in digital photography and LCD displays, but they block enormous amounts of light wasting energy and making it more difficult to photography in low light. Thirdly Microsoft is releasing a $199 fitness band that also checks your email and even pays for coffee as the company software company seeks...
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...Optical Modulators. In solid state modulators 3 types are there. They are Bulk, Integrated Optical and All-Fiber Modulators. 1. Bulk In these modulators the signal propagates through a uniform block of material. They lack wave guiding. They require high electrical drive power and external optics to couple in of optical fibers. They require high electrical drive power and external optics to couple out of optical fibers. 2. Integrated Optical How IO materials are formed? : By fabricating waveguides directly into modular material. For this modulators Low external power is needed. No external optics needed. 3. All-fiber The optical signal never leaves the fiber. In All-Fiber Modulators low external power is necessary. There is no need of external optics or precision alignment. Modulation capabilities of the glass are very poor. Electro-optic Effect Electro optic effect is the base for most of the optical modulators. In linear electro- optic Effect, The refractive indices of crystals are linked to external electric field. In this Modulator the light propagating in an anisotropic medium can be decomposed into its normal modes, or Eigen waves. It can be determined by the index ellipsoid In certain crystals the application of an external electric field will redistribute the charges in the molecules. It results in a size change and orientation change of the index ellipsoid. This is the electro-optic effect. This effect relates the dimensions of the index...
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...Sarah has been an honest, humble person, which wants nothing but the best for herself and her friends. She is young and does not understand the impact that her choices effect numerous people. For example the fact that she did not leave to go home because of curfew indicates that she is thinking that it is alright for her to forego curfew and the wishes of her family. Instead she gave into the peer pressure that was administered by her new friends. There are additional factors that contribute to Sarah’s attitude and reasons why she did what she did. First it was apparent that Sarah suffered from a case of Normative social influence, which defined as a need to conform due to social pressures. Due to the fact that she was new to the school and the group that she was hanging out with did not want her to do, it made her make a choice of going to the party. Second is a combination of items, unanimous group of people, giving her response in front of everyone, and she had a high level of admiration for her new friends. The feeling of acceptance and knowing that you “fit in” with a group of people is one of the most important things for a fifteen year old female. She needs to have the reassurance that comes along with it. Finally, Sarah suffered for parts of the evening from cognitive dissonance, which is defined as is the excessive mental stress and discomfort experienced by an individual who holds two or more contradictory beliefs, ideas, or values at the same time. This is similar...
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...Screenplay EXT. DESERT - DAY Ember, a 22 year old with burnt orange eyes and long brown hair held up in a pony tail, combs over the sand with a metal detector and shuffles around to the music playing from a radio off screen. The sand covered radio is sitting on the pulled down tailgate of a Grey Ford Ranger coated with even more sand. RADIO And that was Bustin Jiebers new hit song Condolences. Before we go to commercial break I would just like to give a friendly reminder to keep an eye on the sky this week for the annual meteor shower. If you missed last nights sky show, no need to wory because it will be going on all week.. Ember clicks off the radio and plops down onto the bed of the truck. She wipes the sweat from her forehead and take a swig of water from the cantine sitting behind the radio. Ember lays down in the truck and stares into the cloudless blue sky. She notices a small red dot int he sea of blue and squints to try and get a clearer look at what it is. The dot seems to be getting bigger ever so slightly and then her eyes begin to widen. The dot was actually something hurteling down from the sky. Ember jerks back up to her feet and starts sprinting with her metal detector away from the car as the object crashes down into her truck right were she was lying. EMBER My truck! Ember tries to walk closer but a small explosion fromt he crash erupts and nocks her to the ground as she covers her face from the heat of the fire and bright...
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...magnitude and direction of rotation of the plane of lineraly polarized light by a chiral compound is a specific physical property of the compound that can be used to characterize it. Most biomolecules are chiral and hence rotate polarized light. In this experiment you will study the optical rotation of a series of mixed monosaccharide solutions and determine the relative concentrations of them. The instrument used to study optical rotation in chiral molecules is called a polarimeter. A polarimeter takes light vibrating in all planes, isolates the light vibrating in a single plane, projects the light through a tube filled with a solution of chiral compound, and measures the amount of rotation. The observed angle of rotation of the plane of polarization by an optically active liquid, solution, or (more rarely) gas or solid is usually denoted by the symbol α. The angle may be either positive (+) or negative (-) depending on whether the rotation is clockwise, that is, to the right (dextro) or counterclockwise, that is, to the left (levo) as seen by an observer towards whom the beam of polarized light travels (this is opposite from the direction of rotation viewed along the light beam). Biot discovered that the observed rotation is proportional to the length l of the cell or tube containing the optically active liquid or solution and the concentration c (or density in the case of a pure liquid): α = [α] × l × c (Biot's law). The value of the proportionality constant [α] depends on the units...
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...I am the Human Resource Manager assigned to hire new sales associates in the fiber optic division. Upon interviewing each candidate only one candidate stands apart from the rest. I considered Jake, but quickly disqualified him due to instability. Making a change from a career as an accountant to sales shows he is not willing to work for a company for the long run. He is new to sales and does not have prior knowledge of fiber optics. Lynn has good people skills and is a leading expert in the fiber optics field, but lacks the experience as well as English-speaking skills necessary to meet the criteria. This job requires that the sales representative be articulate, sophisticated, and knowledgeable about fiber optics. Karen appears to be an ideal candidate for the job, she has been in sales for five years and has been awarded the Sales Representative of the Year at her previous company. She also has the knowledge base necessary to run the fiber optic division since she graduated at the top of her class in fiber optic engineering. I would like to interview Karen again and ask if traveling Monday-Friday and also working after hours would be an issue. According to Bell (2007) “women are often stereotyped as being uncommitted workers and as being likely to leave the workforce when (if) children arrive” (p. 394). As a woman I have seen discrimination and for this reason I will not be discriminating against Karen simply because she is getting married and might have children in...
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... of a transparent dielectric medium is defined as the ratio of the speed of an electromagnetic wave in empty space to its speed in the medium. . It is a measure of the slowing factor for light traveling in that medium The refractive index can be expressed as a function of the electric and magnetic properties of the medium . For most of the materials that are transparent to visible light and . Hence the magnetic properties have a small effect on the light propagation. When an electromagnetic wave is incident on a medium, it electrically polarizes the molecules. This changes the value of which in its turn, determines the index of refraction. The process is wavelength dependent: different wavelengths will induce different polarizations of the molecules and, as a result, and will be different. So, the index of refraction changes with wavelength: The phenomenon described above is known as the dispersion of light. Equation is the dispersion relation. For most of the materials, decreases with the wavelength (see figure1). This phenomenon is known as normal dispersion. The decreasing is more rapid at shorter wavelengths. This causes a Figure 1. Normal dispersion curved plot of versus. where, are empirical curve of flint glass constants whose values depend on the specific material. 2. The prism spectroscope( working principle, setup, application) A spectroscope is an instrument for visual observation. A prism’s spectroscope main...
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...Chapter outline: * Sending bits with electricity and copper wires * (AC) (AC) Sending bits with light and fiber-optic cables * Frequency Amplitude Phase Frequency Amplitude Phase Sending bits with radio waves and no cable Electrical Current – the amount of electricity that flows past a single point Electrical Current – the amount of electricity that flows past a single point Sending voiceand data from mobile phones through wireless wan Data: amplitude and phase shift Sending voiceand data from mobile phones through wireless wan Data: amplitude and phase shift Direct Current (DC) – flows in one direction. Alternating Current (AC) – changes direction over time. Direct Current (DC) – flows in one direction. Alternating Current (AC) – changes direction over time. Creating Circuits using Network Cable Creating Circuits using Network Cable Sending Bits with Radio Waves and No Cables (Wireless) Sending Bits with Radio Waves and No Cables (Wireless) Sending Data over Electrical Circuits Sending Data over Electrical Circuits Flexible cord with an outer plastic cover ( jacket) that holds wires (conductor). Flexible cord with an outer plastic cover ( jacket) that holds wires (conductor). -Bit rate over 1 circuit -Encoding bit over 1 circuit -Sending bits over multiple circuits -Bit rate over 1 circuit -Encoding bit over 1 circuit -Sending bits over multiple circuits SENDING BITS (DATA) USING ELECTICITY, CABLES, RADIO WAVES...
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...Full-depth epidermis tomography using a Mirau-based full-field optical coherence tomography Chien-Chung Tsai,1 Chia-Kai Chang,1 Kuang-Yu Hsu,1 Tuan-Shu Ho,1 Ming-Yi Lin,2 Jeng-Wei Tjiu,2,4 and Sheng-Lung Huang1,3,* 2 1 Graduate Institute of Photonics and Optoelectronics, National Taiwan University, Taipei 10617, Taiwan Department of Dermatology, National Taiwan University Hospital and College of Medicine, National Taiwan University, Taipei, Taiwan 3 Department of Electrical Engineering, National Taiwan University, Taipei 10617, Taiwan 4 jengweitjiu@gmail.com * shuang@ntu.edu.tw Abstract: With a Gaussian-like broadband light source from high brightness Ce3+:YAG single-clad crystal fiber, a full-field optical coherence tomography using a home-designed Mirau objective realized high quality images of in vivo and excised skin tissues. With a 40 × silicone-oilimmersion Mirau objective, the achieved spatial resolutions in axial and lateral directions were 0.9 and 0.51 μm, respectively. Such a high spatial resolution enables the separation of lamellar structure of the full epidermis in both the cross-sectional and en face planes. The number of layers of stratum corneum and its thickness were quantitatively measured. This label free and non-invasive optical probe could be useful for evaluating the water barrier of skin tissue in clinics. As a preliminary in vivo experiment, the blood vessel in dermis was also observed, and the flowing of the red blood cells...
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...1.) A Netgear wireless access point is using a Marconi antenna, Figure 1. Let’s assume the antenna is working in ISM Band @ frequency, f=2.4 [GHz], and is having the impedance, Za=50 [Ω]. They ask to calculate: 1a.) lambda_0[m] = c_0/f[Hz] lambda_0[m] = (3*10^8)/(2.4[GHz]) lambda_0[m] = 0.125[m] 1b.) la[m] = k_1 * (lambda_0[m])/4 la[m] = 0.95 * (0.125[m])/4 la[m] = 0.0296875 1c.)Va[Vrms] = ((50)^(1/2))*10^((15-30)/20) Va[Vrms]= 1.25743343 =====================================================================2.) A LAN server is located on the first floor level of a bank building and is connected via RG-58 cables, to various client computers located on all of the floors of the skyscraper. Let’s assume that you are a field engineer working for a LAN service company and you have the task to find out a faulty cable serving the client. To locate the failure in that cable you are using a Fluke DSP-2000 Cable Analyzer, connected at the floor level, set on TDR test. The screen of the instrument is illustrated in Figure 2. Based on the screen reading, they ask to: 2a). Locate the distance to the failure point on that cable, d [m], with respect to the LAN server’s position, and back-and-fourth propagation time, t [nsec], of the test pulses generated by the instrument, if the velocity factor of the UTP cable, k=0.66 (Given: Speed of light in free space, c_0=3*108 [m/sec]). Reading of the DSP-2000 screen is providing the distance to the failure point, d[m]: d[m]=______30...
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...public (restaurants, pub, etc), polarized glasses has numerous merits. First of all, it is not an electronic device. It is easy to manage. Second of all, it is inexpensive compare to shutter glasses. Based on B2B market system, their requirements are slowly expanding. In this paper, we propose an ameliorated new i-PR (in cell black stripe Patterned Retarder) structure for a patterned retardertype 3D display. 2. Concept 2.1.Patterned Retarder type 3D LCD From the patterned retarder panel, left images’ data input odd line and right’s input even line. Odd and even line’s match to right and left handed circularly polarization status respectively as shown in Fig. 1. By using spatial sequential, the image will go to your left and right eye. Figure 2 shows the changes of its polarization status when we are watching the 3D images. Output of TFT LCD has linearly polarization status in the whole active area. Optically Patterned Retarder is expressed as a quarter wave plate. Its optical axis has alternatively +/- 45 degree...
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...------------------------------------------------- ------------------------------------------------- ------------------------------------------------- Faculty of Engineering ------------------------------------------------- ------------------------------------------------- Subject: Satellite Communication Systems ------------------------------------------------- ------------------------------------------------- Assignment Number: Project One/Part A Date Submitted: 26/10/2012 ------------------------------------------------- ------------------------------------------------- Assignment Title: Project One ------------------------------------------------- ------------------------------------------------- Student Name(s) and Number(s) Tutorial Group: ------------------------------------------------- Chao Wang 11275955 ------------------------------------------------- Declaration of Originality: ------------------------------------------------- The work contained in this assignment, other than that specifically attributed to another source, is that of the author(s). It is recognised that, should this declaration be found to be false, disciplinary action could be taken and the assignments of all students involved will be given zero marks. In the statement below, I have indicated the extent to which I have collaborated with other students, whom I have named. ------------------------------------------------- Signature ------------------------------------------------- ...
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...Very Cheap Ez-12 D.I.Y. Parabolic Reflector WiFi gain for Router, AP and USB WiFi dongle * 1. Open the template (Windsurfer.jpg) in MS Paint or something like that and resize if desired. Ensure that you keep the square on the diagram square. 2. Print image on business card stock or acetate (document protector). 3. Cut it out and open the six slots of the reflector with scissors or a hobby- or break-knife. If the used paper is too thin, make a ‘copy’ of it on thicker cardboard. 4. Glue tin foil to the back side of the reflector surface. When using also a copy on thicker cardboard, glue the tin foil on the copy of the reflector and than glue them together and glue also the copies of the holder together. Use a good kind of glue like Bisonkit transparant. 5. Cut the crosses in the holder with a hobby- or break-knife. 6. Assemble by placing the six tabs of the holder in the six slots of the reflector. Fold the tabs after placing and fix them with glue. 7. Place the assembly on the WiFi antenna and aim the reflector in the direction of the ‘target’ (to WiFi dongle, Router or AP) to get maximum performance. Tell a friend about this idea. Note: If printed at the download size you will see about 6-9 dBi of gain. If you double the size of the image before you print it you will see about 9-12 dBi of gain. If you place two reflectors on an AP or router with two antennas you will see an additional increase in performance. * Types without external antennas can’t be improved this way...
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...Optical Pumping Lab Report [Basic Principle] Before discussing the optical pumping, we have to mention the energy levels of the atom and their splitting due to the interaction between the spin of electron, orbital angular momentum of electron and spin of nuclei. We denote them with S, L, and I respectively. And the total angular momentum of electron is denoted by J, (Grand) total angular momentum is denoted by F. Therefore we will have to deal with the LS interaction, IJ interaction and later the interaction between the Grand total angular momentum and external magnetic field. A very schematic picture of the energy levels of 87Rb under a weak external field is shown in Fig. 1. After applying an weak external magnetic field on the atom, the formally degenerated energy level with same F will further split into 2F+1 sublevels, denoted by mF which is the projection of Grand total angular momentum to the direction of external field B0. Fig. 1 Until now we haven't mention any thing about the optical pumping. Now we have the atom well prepared, the only thing we have to do is to illuminate the vapor of Rubidium with some well tuned highly polarized light. Well tuned means the spectrum of the incident light is better to be narrow, this can be achieved by using a interference filter to screen out the unwanted light and let only the D1 line pass, namely when this light illuminated on the Rb vapor, only transitions between sublevels originated from 5S1/2 and sublevels originated...
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