Cavity-Ringdown Spectroscopy an Ultratrace-Absorption Measurement Technique

American Chemical Society: ACS Symposium series 720 Edited by Busch and Busch

Cavity-Ringdown Spectroscopy – An Ultratrace-Absorption Measurement Technique

Trace absorption measurements (especially gas phase)

Small fractional absorptions down to sub-ppm levels per mass in the cavity

Monitors exponential decay of radiation in an optical cavity (time related to absorption coefficient)

Detection limit = statistical

Beer-Lambert Law

Long-Path Approach

Increase effective absorption pathlength by use of multipass absorption cells (transverse cell up to 48 times or more)

DOAS

DIAL

TDLAS

Open-path Fourier-transform Spectroscopy

Alternatives: Photoacoustic spectroscopy, thermal lensing spectroscopy, laser-induced fluorescences, laser-induced photofragmentation/photoionization, (2+2) resonance-enhanced multiphoton ionization (REMPI), intercavity laser absorption spectroscopy (ICLAS)

Cavity Ringdown spectroscopy

Optical cavity of two or more mirrors

Short pulse of light injected into the cavity (coherence length less than the length of the cavity)

A measure of the ratio of the energy stored in the cavity to that lost by the cavity is referred to as the Q (quality) of the cavity (high Q=longer to decay)

Exponential decay (resemble ringing pattern)

Species introducedàBeer’s lawàdecrease Q

Empty cavity composed of two mirrors with the same reflectivity R, intensity within cavity will decrease exponentially

[EQUATIONS]

Experimental Implementation

Tunable pulsed laser source (ex. Excimer pumped dye laser injected light) (15ns pulse duration)

Minimize diffraction losses à diameters of the mirrors would be chosen to be large with respect to the beam diameter at the mirrors

Photomultiplier tube àto wave form digitizer (ex. Digital oscilloscope, sampling rate of ions)àsignal to computeràpoints fitted to exponential decay curve

Cavity Mirrors

Multilayer (1/2 wavelength optical path) dielectric mirrors (resistant to chemical attack) have a higher reflectance over narrow wavelength than metallic mirrors

Layer coating deposited by evaporation on a transparent substrate

Backside coated with anti-reflection coating

Analog to Digital àcompromise between number of data points collected (sampling rate) and precision of the measure value (resolution)

Optical Cavities (ray optics in periodic focusing systems)

Resonance: when the frequency of a periodic driving force approaches the natural oscillation frequency of the system

Cavity resonator = an enclosure with a particular volume, which is capable of storing energy that oscillates between one form and another

=distributed resonators à different forms of energy distributed through out the volume of the cavity

(decrease the size of resonant cavity=increase frequency of electromagnetic waves that can oscillate in the cavity)

Optical Region

2 or more mirrors

stable geometrically if a paraxial ray bundle is refocused within the cavity after successive reflection so that optical energy is contained or trapped within the cavity VS unstable if ray bundles escapes cavity

Matrix Optics

Two Mirror Cavities

Confocal

Concentric

Long radius

Hemispherical

Semi-confocal

Fabry-Perot

Mode Formation in Optical Cavities

(Mode: 1.The characteristic of the propagation of light through a waveguide that can be designated by a radiation pattern in a plane transverse to the direction of travel. 2.The state of an oscillating system such as a laser that corresponds to a particular field pattern and one of the possible resonant frequencies of the system.) –standing waves-

Oscillating character of light within cavity

Resonant modes (longitudinal (or axial), transverse)

Standing waves developed within the cavity = cavity mode

Stability of cavity depends on g-parameters

“photon bullet” pulsed laser with very short pulse duration (~15ns)

less than the length of the optical cavity

returning wave can never overlap initial wave (wavelength too short)

therefore: mode formation unimportant

CRD spectroscopy: use continuous-wave lasers, therefore: wave formation

Longitudinal:

Determine the resonant oscillation of frequencies that satify the wavelength requirements of the cavity along a given optical path (ie. The electric vector is zero at the reflecting surface)

Resonantàphase delay of a wave corresponding to a round trip = 2*pi*p, p=longitudinal mode index

Transverse:

Travel over slightly different optical paths; determine the intensity pattern and divergence of the propagating beam

àeach mode (propagating along a unique direction) can have various allowed longitudinal modes associated with it (separated by deltav)

many eigenmodes à each represent a mode, characterized by a particular transverse amplitude distribution, TEM (transverse electromagnetic modes)

the frequency spacing between two successive transverse modes is usually much smaller than the spacing between two successive longitudinal modes and depends on the characteristics of the cavity (length, mirror radii)

Fabry-Perot Cavity: beam transmitted as long as separation (L) between reflecting surfaces of the mirror is one integral multiple of half the wavelength of the light

àcan be used to scan a certain spectral range by varying the value of L. If the spacing between the mirrors is fixed, the cavity is known as a Fabry-Perot etalon. (Etalon: Two flat glass plates separated by a parallel spacer, with the inner surfaces of the plates coated with a partially reflecting layer. When the etalon is placed in a beam of monochromatic light, multiple interference occurs, forming circular fringes in the manner of the Fabry-Perot interferometer.)

Used as/for: (1)reflector, (2) studies of mode characteristics of laser, (3) obtaining single frequency operation of a laser, (4) mode selection, (5) line-width narrowing

Free Spatial Range (FSR): frequency separation between two successive transmission frequencies (or resonant modes) –indicates how nearly identical two wavelengths must be to produce adjacent, same-order fringes (fringe: interference band)-

Full Width at Half Maximum: width of transmission bands obtained with the Fabry-Perot cavity; ecomes progressively narrower as R approaches 1.

Finesse: (of an FP etalon) is a measure that characterizes the quality of the resolution obtained with the cavity and is given by the ratio of the free spectral range to full width at half max of a transmission –measure of the interferometer’s ability to resolve closely spaced spectral lines-

Surface defect must be less than l/60

All modes are characterized by 3 indices (1 for longitudinal, 2 for transverse)

TEM modes: rectangular cross sectionsàHermite-Gaussian Waves, cylindrical à Laguerre-Gaussian Waves

Mode formation & Cavity Ringdown Spectrometry

Relationship: pulse duration (tp), round-trip transit time (tr), relaxation time of the absorbing species (T2)

Case I: T2<<tpàquasi-continuous-wave light (tr>tp =>”photon bullet” tr<tp =>cavity modes present due to interference

Case II: T2>>tpàspecies interact with a series of light pulses during their lifetime -> absorption spectrum from Fourier-transform of the time-domain variation of field intensity inside cavity

**for both cases: linewidths of species must be greater than spacing between modes**

Cavity Stability: g-parameters

Simple CRDS: Pulsed Cavity Ring-down Spectroscopy

Chapter 6

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Acousto-optics

Study of interactions between sound waves and light in a solid medium. Sound waves can be made to modulate, deflect, and focus light waves, important factors in laser and holographic applications. (intensity and position of beam)

Acoustic wave and laser beam in medium

-acoustic waves behaves like an sinusoidal grating àdiffract laser beam into several orders (higher frequency of acoustic = larger diffracted angle)

angular relationshipàintensity of light diffracted (deflected) is proportional to the acoustic power (Pac), the material of merit (M2), geometric factors (L/H), and inversely proportional to the square of the wavelength

laser beam frequency shifted by an amount equal to the acoustic frequency

Birefringence: separation of a light beam as it penetrates a doubly refracting object into two diverging beams, commonly known as ordinary and extraordinary beams

AOTF (Acousto-optic tunable filter)

-electronically tunable spectral bandpass filter

-solid state, no moving parts, wavelength selector

-near infrared (vibrational) spectroscopy (700nm-2or3microm)

-crystal: acoustic (vibrational) waves, at radio frequencies (RF) are used to separate a single wavelength of light from a broadband or multicolour source

-transducer is bonded to one side of the TeO2 crystal à emits vibrations (acoustic waves) when RT is applied to it (frequency = frequency of applied RF)àacoustic waves pass through TeO2 and cause the crystal lattice to be alternatively compressed and relaxed

AOTF only diffracts one specific wavelength of light (determined by “phase matching”)=filter, not diffraction grating

Perturbation is required to be a superposition of propagating eigenmodes of the acoustic wave equation

-photoelastic medium (photoelastic: double refraction is produced when stress is applied to a transparent material. Plastics can be formed into models of structures that are subjected to stress. The resulting double refraction clearly indicates the stress distribution in the models when viewed in polarized light.)

-interaction between acoustic and optical waves in mediated by the 4th rank photoelastic tensor which describes the dielectric impermeability tensor perturbation caused by the propagating strain wave.

Acoustic eigenmodes

-time and space varying particle displacement vector field

-sinusoidal displacement wave of amplitude

-radian frequency

-wave vector

-acoustic wavelength

-propagating with a phase velocity

-direction

-unit polarization

Optical eignemodes

Maxwell’s equations (optical propagation through a homologus lossless anisotripic medium) (Anisotropic: substance that exhibits different properties along different axes of propagation or for different polarizations of a travelling wave)

Faraday’s law (induced electric field and a time varying magnetic field)

Ampere’s law (creation of magnetic field due to a dielectric flux, a conductivity current a source of current)

àassume no current, no free electric charges, no free magnetic monopoles

Hermitia second rank permittivity tensor

Scalar permeability

Heterodyne: interaction between two oscillations of unlike frequencies that forms other oscillations, specifically those with a frequency equal to the frequency difference of the former oscillations.

Transducer is usually a piezoelectric crystal (piezoelectric effect: The interaction between electrical and mechanical stress-strain factors in a material. When piezoelectric crystal is compressed, an electrostatic voltage is generated across it, or when an electric field is applied, the crystal may expand or contract in particular directions.) metalized on both faces so that an electric field can be applied.

When a sound wave travels through a transparent material, it causes periodic variations of index of refraction (series of compressions and rerefactions moving through material)

Sound pressure high = high compression = increase index of refraction

- transit time of the acoustic-beam across the diameter of the light beam imposes a limitation on the rise time of the switching and therefore limits modulation bandwidth

- to increase bandwidth, one focuses the light beam to a small diameter at the position of interaction (minimize transit time)

Procedure from ADVANCED OPTICS LAB – ECEN 5606 Kelvin Wagner Experiment No. 13 (Sept 17, 2001)

5 Procedure

1. RF section. Hook up the HP 8111 pulse generator to the I port of the RF mixer, and the

HP RF 8601A oscillator to the L port, and observe the RF output on an oscilloscope and

RF spectrum analyzer as you vary the mixer levels and offsets. An RF mixer has three input ports, one for the local oscillator, one for the mixing waveform and one for the IF output, and it should be driven with signals of an appropriate amplitude, typically 10mW or less, have your TA show you how. Set the offset and amplitude on the pulse generator to obtain

a clean pulsed RF waveform, with as little modulation in the off time as possible. What is

the rise time of the pulse generator, and the modulated RF output? Apply this pulsed RF

waveform to the 1W RF amplifier. Make sure the output power is less than 1 Watt peak

in order to be sure of not blowing out the piezo-electric transducer . Apply this pulsed RF

signal to the acoustooptic modulator that is on a rotation stage.

2. Bragg alignment. Spatial filter and collimate the HeNe laser as a 1-2mm pencil beam and

align the beam onto the AO modulator aperture. Find the Bragg diffraction by rotating,

tilting and translating the AOM. Optimize the diffraction efficiency visually, by looking at a

card placed 10-30cm beyond the AOM as you vary the alignment and identify the diffracted

spot or spots. Often a good starting place for this alignment procedure is to come in at normal incidence with the HeNe, so that numerous diffraction orders are generated, both

plus and minus, then to rotate to maximize the +1 order and suppress all of the others.

Sketch your setup and the output plane, showing why this is the +1 order, and not the -1

order. Now rotate the AOM to produce primarily the -1 order and sketch your setup.

3. Acousto-optic modulation. Block the undiffracted beam and place the power meter in the

diffracted beam; measure the diffraction e±ciency as a function of applied RF power which

is controlled by varying the pulse amplitude. Plot your results, remember to correct for the

duty cycle of the RF pulses. Now place a high speed photodetector in the diffracted beam,

and observe the detected output on an oscilloscope. Re-optimize the diffraction and measure

the diffraction efficiency by detecting both the diffracted and undiffracted waveforms, looking

for depletion of the undiffracted beam. Make sure that you are not saturating your detector.

What is the rise time that you were able to obtain with this configuration. This is not the

proper way to operate an acoustooptic modulator for high speed modulation, but it will

work for low speed applications.

4. Access time-diffraction efficiency trade-off. Re-collimate the laser beam with a 5-

10mm diameter, place an iris in the beam, and place a lens beyond the aperture and one

focal length before the modulator so you are focusing to a tiny spot in the center of the

AOM. Realign angle and position to maximize the diffraction e±ciency, paying attention

to the vertical alignment of the spot with the acoustic column. Now observe a far-field

output plane as you open and close the aperture. Sketch and describe your observations. Is

the diffracted output spot well separated from the undiffracted spot? Is the diffracted spot

always circular, or does it change its shape for very wide apertures? The optimal setting for

the aperture, in the sense of efficiency-rise time trade-off, is the largest aperture at which the

full beam is diffracted, and phase matching selectivity has not become overly constraining.

Place a high speed photodetector in the diffracted beam, and open the aperture so that

the diffracted and undiffracted beams overlap. How can you verify that the diffracted beam

is Doppler shifted due to the acoustic motion, and what is that Doppler shift? Now with

the aperture smaller so the beams don’t overlap, measure the rise time and peak diffraction

efficiency (not diffracted power, but ratio of diffracted output to input) as a function focal

spot size, varied inversely ¢ = ¸F=A by opening and closing the aperture A (or perhaps by

z-shifting the AOD). Note the RF power levels. Do not confuse total power with diffraction

efficiency, since you are varying the total power as you open and close the aperture. Another

way to determine the diffraction efficiency is to look at the depth of the hole dug in the

undiffracted light as the acoustic pulse scrolls through the focal spot. Plot your results of

rise time and diffraction efficiency as a function of the spot size in the crystal. What is the

optimal spot size and aperture setting in the sense of maintaining high diffraction efficiency