Biophotonics. Light Matter Interactions & Lasers. NPTEL Biophotonics 1

Transcription

1 Biophotonics Light Matter Interactions & Lasers NPTEL Biophotonics 1

2 Overview In this lecture you will learn, Light matter interactions: absorption, emission, stimulated emission Lasers and some laser applications Keywords: stimulated emission, lasers, laser applications NPTEL Biophotonics 2

3 Induced Dipoles Light as we know is an EM wave and they way it interacts with matter is by polarizing the molecules making up matter. Polarization in this context means slight disturbance in the symmetry of the electron cloud to create a dipole moment. Some molecules, like water, have a permanent dipole moment. Other molecules, are induced due to the oscillating electric field of light. In linear optics the induced dipole moment vector p= αe, where α is called the polarizability of the medium. For isotropic materials αis a scalar but for anisotropic materials α will be a tensor and the direction of p and E may not coincide. NPTEL Biophotonics 3

4 Induced Dipoles The interaction of light with materials can be understood in terms of the scattering of light by the induced dipoles. There are two types of scattering processes, elastic and ineleastic. In elastic scattering there is no exchange of energies, i.e. photons with frequencies different from the incident photon are not produced, e.g. scattering of light by gas molecules in the atmosphere. In inelastic scattering photons of different frequencies are produced, e.g. Raman scattering. NPTEL Biophotonics 4

5 Light Absorption As we saw before, electrons are situated in various energy levels in a molecule. It is possible for a photon, which is a quantum of EM radiation, to interact with an electron by causing its state to change, i.e. causing it to occupy a different energy level. When an electron absorbs a photon to move to a higher energy state that is available, it is called absorption. This is shown in the diagram below. Einstein described the rate of this transition by W abs = B if N i ρ. Here B if is the probability of transition from the initial state, ito the final state f, N is the number of electrons in istate incident per second and ρis the density of photons. NPTEL Biophotonics 5

6 Light Absorption The diagram shows the schematic of the absorption process where the electron absorbs a photon of energy hνand moves to a higher energy state. The difference in energies of the final and initial state is equal to the photon energy. The closely spaced lines are the vibrationalenergy levels. hν NPTEL Biophotonics 6

7 Spontaneous Emission An electron in a higher energy state can come down to a lower energy state by emitting a photon with an energy equal to the difference between the two states. In this case, the rate of this process is given by W em = A if N i. Here A if is the transition probability from state ito state f and N i is the number of electrons in the initial state. This rate is independent of the photons density. The adjoining figure depicts the spontaneous emission process. Notice that it is exactly similar to the absorption process except that the directions are reversed. hν NPTEL Biophotonics 7

8 Stimulated Emission It is also possible to have a different emission mechanism called stimulated emission. In stimulated emission, an electron in a higher energy state is stimulated to move down to a lower energy state with energy difference hνby an incident photon of the same energy. The incident and emitted photons share all attributes such as direction, phase and polarization. In other words stimulated emission produces coherent photons. NPTEL Biophotonics 8

9 Stimulated Emission The adjoining picture depicts the process of stimulated emission by an incident photon. The rate of this process is given by W st.em = B if N i ρ. The coefficient B if is the same as the absorption transition probability, N i is the number of electrons in the excited state and ρis the density of incident photons hν hν NPTEL Biophotonics 9

10 Rate Balance and Population Inversion Using Einstein s relations for the rate of the absorption and emission processes, the rate balance for net emission can be written as, W net = N f (A if + B if ρ) B if N i ρ When stimulated emission is present, it dominates over spontaneous emission so the expression is simply B if ρ(n f N i ). The state f, being higher in energy compared to state i, has a lower probability of being occupied than state i. So N f will normally be much lesser than N i and emission rate will be negligible. NPTEL Biophotonics 10

11 Population Inversion If somehow it is possible to create and maintain a population inversion, i.e. N f >> N i, then using stimulated emission, we can amplify photons, i.e. an incident photon will created one stimulated photon which will create another stimulated photon and so on. In this manner we can create a light amplifier using stimulated emission. A device which does this is called a laser (Light Amplification by Stimulated Emission of Radiation) NPTEL Biophotonics 11

12 Creating Population Inversion Population inversion can be created by using multi-level systems as shown in the diagrams below. Consider a three level system as shown in the bottom left figure. If the decay from state 3 to 2 is fast but the decay from state 2 to 1 is slow, by pumping the electrons from 1 to 3, we end up in a situation where the population of state 2 is higher than 1, creating the required population inversion hν hν hν hν NPTEL Biophotonics 12

13 Creating Population Inversion A spontaneously emitted photon can then cause the stimulated emission of photons from electrons in the excited state. Similarly a 4 level system with the lifetime of 3 2 transition lifetime much slower than 4 3 and transition 2 1 transition. Electrons are pumped from state 1 to 4 and end up accumulating in level 3 creating an inverted population with respect to state hν hν hν hν NPTEL Biophotonics 13

14 Laser Resonator The schematic below describes the construction of a laser resonator. Two mirrors create a open resonating structure, where one of the mirrors is only partially polished to allow some light to leak through. The other mirror has very high reflectance. The medium where population inversion can be created, called the gain medium, is kept between the mirrors. Pumping High Reflector Gain Medium Schematic of a laser resonator Partial Reflector Laser Output NPTEL Biophotonics 14

15 Laser Resonator Some gain media exist in solid form, others can be gas mixtures and still others can be in the liquid form. Light in the cavity gets reflected multiple times each time amplifying the output. Electrons from the lower level are constantly pumped to the higher levels electrically or optically using flash lamps for instance. Laser output can be pulsed or continuous as described later. Pumping High Reflector Gain Medium Schematic of a laser resonator Partial Reflector Laser Output NPTEL Biophotonics 15

16 Wavelength, Polarization and Beam Profile Stimulated emission produces photons which are coherent. In order to choose output parameters such as polarization, extra elements are added to the laser resonator. For e.g. a polarizer in the resonator will determined the output polarization. The resonator, also called laser cavity, described above can support several modes which slightly different frequencies (wavelength). In order to have single wavelength operation it is necessary to add an element called an etalon which is a device that uses interference to create a narrow transmission band centered around a single cavity mode. This ensures single wavelength operation with high spectral purity. NPTEL Biophotonics 16

17 Operation Contd In addition to single mode operation, typically the beam profile of laser output is gaussianshaped as described in previous slides. Beam divergence is quite low and laser beams can be easily focused to diffraction limited spots for applications such as imaging. NPTEL Biophotonics 17

18 Pulsed and CW Operation As pointed out earlier, lasers can be operated in a pulsed mode, where the output consists of bursts of radiation at fixed intervals of time, or in continuous (wave) mode (CW), where output is continuous in time. CW operation is achieved by maintaining a constant population inversion rate that keeps the gain in the medium equal to the cavity losses attaining a steady power output. Pulsed operation can be achieved in several different ways. The simplest would be to pulse the pumping source which would create gain only for intermittent periods of time thus causing a pulsed output. NPTEL Biophotonics 18

19 Pulsed Operation Contd There are also other methods to create pulsed lasers which we will describe in later slides. In fact some of these methods can be used to create pulses that are as small as tens of femto-seconds (10-15 s). As we will see later lasers capable of producing such small pulses, called ultra-fast lasers have opened up new ways of probing matter. NPTEL Biophotonics 19

20 Q Switching As we mentioned before, the simplest way to produce a pulsed laser is to use a pulsed pump. Another way to create pulsed output is called Q switching, i.e. modulating the quality factor of the cavity actively or passively. In active Q-switching, an element such as an acousto-optic (AO) or electro-optic (EO) modulator, described in a later lecture. By switching the modulators on and off, the gain in the cavity is modulated producing pulsed output. NPTEL Biophotonics 20

21 Passive Q Switching Passive Q switching is done using materials that are called saturableabsorbers. These are materials where the absorption coefficient decreases with increasing intensity. When this happens, output can only be emitted from the laser cavity after a sufficiently large number of round trips (amplification factor) inside the cavity. Then the intensity is high enough for the gain to offset the losses and the output is dumped out. The intensity goes down again and losses dominate until intensity come up to a level where losses are dominated. Q switching can produce pulse widths around a nanosecond NPTEL Biophotonics 21

22 Mode locking: Ultra-fast Lasers In order to produce even shorter pulses, a technique called mode-locking can be used. As we mentioned during the discussion on diffraction gratings, the width of the mthdiffracted order is inversely proportional to number of slits or modulations in the grating. A similar effect happens here. As we mentioned earlier, the cavity supports a number of modes. If we are able to lock the phase of all the modes to a single value, the output is the resultant of modes with different frequencies and same phase. In time domain the resultant output is a compressed pulse with pulse width which is the ratio of round-trip time to the number of modes. NPTEL Biophotonics 22

23 Ultra-fast Lasers As the number of modes is proportional to the bandwidth (spectral region where laser gain is possible), one can produce small pulses by using gain media which have large bandwidths. For e.g. using Titanium doped Sapphire (Al 2 O 3 ), one can create pulses less than 10 fs. Ultra-fast lasers consists of femto-second (fs) pulses with repetition rates of the order of MHz.The average pulse power is defined as the pulse energy of each pulse times the repetition rate. The instantaneous power is defined as pulse energy per pulse divided by the pulse width. This value can be extremely large due to the small pulse width. NPTEL Biophotonics 23

24 Ultra-fast Lasers The extremely large instantaneous power implies an extremely large number of photons that are squeezed into a small time window. Such high photon densities enable many non-linear optical processes that are not possible with low powers. The other useful aspect of ultra-fast lasers is that even though the instantaneous power is very large, the average power level can be quite low. Therefore it is possible to use these light sources for various biological applications without causing damage to living tissue. NPTEL Biophotonics 24

25 Some Common Lasers Commercial lasers available today cover a wide range of operating wavelengths and output power levels. A few of the important ones are summarized below. Gas lasers such as, Helium-Neon (He-Ne), nm, various applications Argon-ion, 488/514 nm, useful for fluorescence excitation CO2 laser, 10.6 µm, laser cutting, cosmetic surgery Dye lasers covering range from 400 nm to 800 nm capable of producing nanosecpulses. Nd-YAG laser operating at 1064 nm, frequency doubled operation (described later) produces 532 nm output. Ti-Sapphire laser, tunable from 690 nm to 1000 nm. Wide bandwidth capable of producing ultra-short pulses. NPTEL Biophotonics 25

26 Diode Lasers Another important class of lasers is the diode lasers which are made with semiconducting materials. In a forward biased pnjunction, electron hole recombination produces photons. The production rate can be controlled by the injection current. Beyond a certain threshold, stimulated emission takes place and laser output is produced. Diode lasers are generally not very tunable, but they provide a compact and economic laser source and has enabled several technologies such as optical data storage, optical communication links and laser printing. NPTEL Biophotonics 26

27 Laser Applications Lasers find applications in a large number of areas, too numerous to list in a single slide. Some important applications are given below. Applications requiring long temporal or spatial coherence, diffraction limited focusing, non-linear optics using ultra-fast pulses etc. require the use of lasers Laser based imaging techniques Optical data storage Optical sensors Biomedical, surgical applications Optical communication links Study of non-linear optical phenomena NPTEL Biophotonics 27