LIST OF SYMBOLS xxi M=phasor amplitude of sinusoidal magnetic dipole moment M optical ray matrix or ABCD matrix n refractive index;also,photon number n(t)(number of photons per cav- ity mode) n2 optical Kerr coefficient n2e or n2r N=atomic number or level population;usually interpreted as atoms per unit volume,sometimes as total number of atoms AN=population difference,or population difference density,on an atomic transition(△N≡N-N) N=Fresnel number a2/LA for an optical beam or resonator Ne collimated Fresnel number for an unstable optical resonator Neg=equivalent Fresnel number for an unstable optical resonator M=population,or population density,in atomic energy level E p=perimeter,period or round-trip path length,for cavities or periodic lensguides;also,electric polarization (electric dipole moment per unit volume)as real function of time,and laser mode density or mode num- ber p=electric polarization (electric dipole moment per unit volume)as real vector function of space and time Pm path length (round-trip)through an atomic or laser gain medium P=power,in watts;also,pressure,in torr P(t)=polarization driving term for n-th order cavity mode in coupled-mode expansion P=phasor amplitude of sinusoidal electric polarization g=axial mode index g=complex gaussian beam parameter or complex radius of curvature reduced gaussian beam parameter,d/n r=amplitude reflectivity of mirror or beamsplitter;also,dimensionless or normalized pumping rate;displacement off axis of optical ray r=reduced slope n dr/dz for optical ray r=shorthand for spatial coordinates z,y,z ij complex scattering matrix element,or mirror or beamsplitter reflection coefficient Tp=dimensionless pumping rate or inversion ratio,relative to threshold pumping rate or threshold inversion density dr volume element,dV or dz dy dz R=power reflectivity of mirror or beamsplitter (=r2);also,electrical resistance;radius of curvature for mirror,dielectric interface,or optical wave R=reduced radius of curvature R/n Rp=pumping rate in atoms per second and,usually,per unit volume s spatial frequency (cycles/unit length) s shorthand for transverse spatial coordinates x,y ds transverse area element dA or dr dy S=multiport scattering matrix (matrix elements Sij)
xxii LIST OF SYMBOLS t time;also,amplitude transmission through mirror,beamsplitter,or light modulator t=complex amplitude transmission coefficient through mirror,beamsplit- ter or light modulator j=complex scattering matrix element,or mirror/beamsplitter transmis- sion coefficient T=power transmission of mirror or beamsplitter (=t);also,cavity round-trip transit time,or temperature(K) T=dimensionless susceptibility tensor T=laser oscillation build-up time Thr temperature of "nonradiative"surroundings Trad temperature of radiative surroundings Ti energy decay time,population recovery time,longitudinal relaxation time T2 dephasing time,collision time,transverse relaxation time T?=effective T2 or dephasing time for inhomogeneous (gaussian)transition i=complex (and usually normalized)optical wave amplitude U=energy or,more commonly,energy density (energy per unit volume) Ua=energy density in a collection of atoms or atomic energy level popula- tions Ubr=energy density of blackbody radiation v velocity of an atom,an electron,or a wave =complex spot size for Hermite-gaussian modes vg group velocity v=phase velocity V,Ve volume (of a cavity mode-er field pattern) w=gaussian spot size parameter (1/e amplitude point) wi;total relaxation transition probability (per atom,per second)from level E to level Ej Wi;stimulated transition probability (per atom,per second)from level E to level E Wp=pumping transition probability (per atom,per second) x(t)=displacement of electronic charge in classical electron oscillator model zD dispersion length for dispersive pulse broadening ER Rayleigh range for a gaussian or collimated optical beam Z=atomic number 2"=dimensionless population saturation factor,with values between 2=1 (lower level empties out rapidly)and 2"=2 (lower level bottlenecked) 3"=dimensionless polarization overlap factor for atomic interactions,with numerical value between 0 and 3
LASERS
1 AN INTRODUCTION TO LASERS Lasers are devices that generate or amplify coherent radiation at frequencies in the infrared,visible,or ultraviolet regions of the electromagnetic spectrum. Lasers operate by using a general principle that was originally invented at micro- wave frequencies,where it was called microwave amplification by stimulated emission of radiation,or maser action.When extended to optical frequencies this naturally becomes light amplification by stimulated emission of radiation, or laser action. This basic laser or maser principle is now used in an enormous variety of devices operating in many parts of the electromagnetic spectrum,from audio to ultraviolet.Practical laser devices in particular employ an extraordinary va- riety of materials,pumping methods,and design approaches,and find a great variety of applications.The study of laser and maser devices and their scientific applications is often referred to as the field of quantum electronics. From an electronics-engineering viewpoint,the developments that followed the operation of the first ruby laser in 1960 suddenly pushed the upper limit of coherent electronics from the millimeter-wave range,using microwave tubes and transistors,out to include the submillimeter,infrared,visible,and ultraviolet spectral regions (and soft X-ray lasers are now on the horizon).All the familiar functions of coherent signal generation,amplification,modulation,information transmission,and detection are now possible at frequencies up to a million times higher,or wavelengths down to a million times shorter,than previously.But it has also become possible for engineers and scientists,in fields of technology ranging from microbiology to auto manufacture,to perform an almost unlimited variety of new and unexpected functions made possible by the short wavelengths, high powers,ultrashort pulsewidths,and other unique characteristics of these laser devices. In the twenty-odd years since the first appearance of coherent light,lasers have become widespread and almost commonplace devices.The importance and the excitement of the laser and its applications,however,still can hardly be overestimated.The objective of this book is to explain in detail how lasers work, what the performance characteristics of typical lasers are,and how lasers are employed in a wide variety of applications.Our goal in this opening chapter is
2 CHAPTER 1:AN INTRODUCTION TO LASERS feedback and mirror oscillation mirror atoms (laser medium) aser output beam 月=100% ft↑t↑ =80% pumping process FIGURE 1.1 Elements of a typical laser oscillator. to give an abbreviated overview of these same points,as a synopsis of what will be presented in much more detail in the remainder of the book. 1.1 WHAT IS A LASER? Lasers,broadly speaking,are devices that generate or amplify light,just as tran- sistors and vacuum tubes generate and amplify electronic signals at audio,radio or microwave frequencies.Here "light"must be understood broadly,since differ- ent kinds of lasers can amplify radiation at wavelengths ranging from the very long infrared region,merging with millimeter waves or microwaves,up through the visible region and extending now to the vacuum ultraviolet and even X- ray regions.Lasers come in a great variety of forms,using many different laser materials,many different atomic systems,and many different kinds of pump- ing or excitation techniques.The beams of radiation that lasers emit or amplify have remarkable properties of directionality,spectral purity,and intensity.These properties have already led to an enormous variety of applications,and others undoubtedly have yet to be discovered and developed. Essential Elements of a Laser The essential elements of a laser device,as shown in Figure 1.1,are thus:(i) a laser medium consisting of an appropriate collection of atoms,molecules,ions, or in some instances a semiconducting crystal;(ii)a pumping process to excite these atoms (molecules,etc.)into higher quantum-mechanical energy levels;and (iii)suitable optical feedback elements that allow a beam of radiation to either pass once through the laser medium (as in a laser amplifier)or bounce back and forth repeatedly through the laser medium (as in a laser oscillator). These elements come in a great variety of forms and fashions,as we will see when we begin to examine each of them in more detail. Laser Atoms and Laser Pumping For simplicity we will from now on use "atoms"as a general term for whatever kind of atoms or molecules or ions or semiconductor electrons may be used as the laser medium.A pumping process is then required to excite