List of Figures

1.1  Basic laser resonator. It is composed of an atomic, or molecular, gain medium and two mirrors aligned along the optical axis. The length of the cavity is L, and the diameter of the beam is 2w. The gain medium can be excited optically or electrically

1.2  Approximate emission ranges for three classes of laser dyes: the coumarins, the xanthenes, and the cyanines. The rhodamines belong to the xanthenes. The cyanines reach up to 1100 nm. The wavelength range shown is covered using several laser dyes

1.3  Molecular structure of C545T. This laser dye has a molecular weight of 430.56 m_u

1.4  Wavelength tuning range of a grating mirror laser cavity using C545T as gain medium

1.5  Simple two-level energy system including a ground level and an upper level

1.6  Energy-level diagram corresponding to a laser dye molecule, which includes three electronic levels (S₀, S₁, and S₂) and two triplet levels (T₁ and T₂). Each electronic level contains a large number of vibrational and rotational levels. Laser emission takes place due to S₁ → S₀ transitions

1.7  Approximate wavelength range covered by various types of semiconductors used in tunable lasers. This is only an approximate depiction and some of the ranges might not be continuous. Not shown are the InGaAs/InP semiconductors that emit between 1600 and 2100 nm or the quantum cascade lasers that emit deep into the infrared (see Chapter 9)

1.8  Conduction and valence bands according to E_K = ± (k²ħ²/2m)

1.9  Emission due to recombination transitions from the bottom of the conduction band to the top of the valence band

1.10  Potential well V(x) = 0 for 0 < x < L and V(x) = ∞ for x = 0 or x = L

1.11  Simplified illustration of a multiple-quantum well structure relevant to quantum cascade lasers. An electron is injected from the injector region into the active region at n₂ = 3. Thus, a photon is emitted via the 3 → 2 transition. The electron continues to the next region where the process is repeated. By configuring a series of such stages, one electron can generate the emission of numerous photons

1.12  (a) Transverse laser excitation. (b) Transverse double-laser excitation. (c) Longitudinal laser excitation

1.13  (a) Grating mirror resonator and (b) grating mirror resonator incorporating an intracavity etalon

1.14  Cross section of a TEM₀₀ laser beam from a high-power narrow-linewidth dispersive laser oscillator. The spatial intensity profile of this beam is near-Gaussian

1.15  Basic unstable resonator laser cavity

1.16  (a) Linear and (b) unidirectional eight-shaped ring dye laser cavities.

1.17  (a) Linear femtosecond laser cavity. (b) Ring femtosecond laser resonator. Both laser configurations include a saturable absorber and a multiple-prism pulse compressor

2.1  Propagation from s to x is expressed as 〈x|s〉

2.2  Propagation from s to x via an intermediate plane j is expressed as 〈x | j〉 〈j | s〉

2.3  Propagation from s to x via two intermediate planes j and k is expressed as 〈x | k〉 〈k | j〉 〈j | s

2.4  (a) Propagation from s to x via an array of N slits positioned at the intermediate plane j. (b) Propagation from s to x via an array of N slits positioned at the intermediate plane j and via an additional array of N slits positioned at k

2.5  Optical architecture of the N-slit laser interferometer. Light from a TEM₀₀ narrow-linewidth laser is transformed into an extremely elongated near- Gaussian source (s) to illuminate an array of N slits at j. Interaction of the coherent emission with the slit array produces interference at x. Thej-to-x intra-interferometric distance is D_{〈x | j〉}. This class of interferometric architecture was first introduced by Duarte (1991, 1993)

2.6  A two-dimensional representation of the 〈x | j〉 〈j | s〉 geometry

2.7  A detailed representation of the 〈x | j〉 〈j | s〉 geometry depicting the difference in path length and the angles of incidence and diffraction

2.8  (a) Measured interferogram resulting from the interaction of coherent laser emission at λ = 632.82 nm and two (N = 2) slits 50 μm wide, separated by 50 μm. The j-to-x distance is D_{〈x | j〉} 10 cm. (b) Corresponding theoretical interferogram from Equation 2.13. Note that the screen axial distance refers to the distance at the interferometric plane that defines the spatial width of the interferogram and that is perpendicular to the propagation axis

2.9  (a) Measured interferogram resulting from the interaction of coherent laser emission at λ = 632.82 nm and N = 100 slits 30 μm wide, separated by 30 μm. The j-to-x distance is D_{〈x | j〉} = 75 cm. (b) Corresponding theoretical interferogram from Equation 2.13

2.10  Theoretical interferometric/diffraction distribution using a ≤2% uncertainty in the dimensions of the 30-μm slits. In this calculation, N = 100 and the j-to-x distance is D_{〈x | j〉} = 75 cm. A slight deterioration in the spatial symmetry of the distribution is evident

2.11  Theoretical near-field diffraction distribution produced by a 4-mm aperture illuminated at λ = 632.82 nm. The j-to-x distance is D_{〈x | j〉} = 10 cm

2.12  Theoretical interferometric distribution illustrating a cascade calculation. It incorporates diffraction-edge effects in the illumination. In this calculation, the width of the slits in the array is 30 μm separated by 30 μm, N = 100, and the j-to-x distance is D_{〈x | j〉} = 75 cm. The aperture-to-grating distance is 10 cm

2.13  Emergence of secondary diffraction (±1) orders as the j-to-x distance is increased. (a) At a grating-to-screen distance of D_{〈x | j〉} = 5 cm, the interferometric distribution is mainly part of a single order. At the boundaries, there is an incipient indication of emerging orders. (b) As the distance is increased to D_{〈x | j〉} = 10 cm, the presence of the emerging (±1) orders is more visible. (c) At a distance of D_{〈x | j〉} = 25 cm, the emerging (±1) orders give rise to an overall distribution with clear shoulders. (d) At a distance of D_{〈x | j〉} = 75 cm, the −1, 0, and +1 diffraction orders are clearly established. Notice the increase in the width of the distribution as the intra-interferometric distance D_{〈x | j〉} = increases from 5 to 75 cm. The width of the slits is 30 μm separated by 30 μm, N = 100, and λ = 632.82 nm

2.14  Incidence below the normal (−) and diffraction above the normal (+)

2.15  Incidence above the normal (+) and diffraction above the normal (+) .

2.16  Incidence below the normal (−) followed by diffraction below the normal (−)

2.17  Incidence above the normal (+) followed by diffraction below the normal (−)

2.18  A reflection diffraction grating is formed by approaching a reflection surface at an infinitesimal distance to the array of N-slits

2.19  Single prism depicting refraction at minimum deviation

3.1  Boundary at a transmission grating depicting corresponding path differences. Further details on the geometry of the transmission grating are given in Chapter 2

3.2  Path differences in a diffraction grating of the reflective class in Littrow configuration. From the geometry, sin Θ = (Δx/l)

3.3  Beam divergence for two different apertures at wavelength λ. (a) An expanded laser beam is incident on a microhole of diameter 2w. (b) The same laser beam is incident on a microhole of diameter 4w

3.4  Beam divergence for (a) λ = 450 nm and (b) λ = 650 nm. In both cases, an expanded laser beam is incident on identical microholes of diameter 2w

3.5  Beam divergence determined from the generalized interference equation. (a) Beam profile following propagation through a distance of 0.5 m. (b) Beam profile following propagation through a distance of 5 m. Here, w₀ 100 = μm and λ = 632.82 nm. Using the difference in beam waist w over the propagation distance, the beam divergence is determined to be Δθ ≈ 1.9 mrad

3.6  Reflection telescopes used in astronomical observations: (a) Newtonian telescope; (b) Cassegranian telescope

3.7  Generic experimental configuration of a source emitting two indistinguishable quanta traveling in opposite directions with entangled polarizations. This experimental arrangement is a simplified rendition of the original configuration introduced by Pryce and Ward

3.8  Experimental configuration of a source emitting two pairs (n = 4) of indistinguishable quanta traveling in four different directions (N = 4) with entangled polarizations. In the theoretical development, it is assumed that all detectors are identical (d₁ = d₂ = d₃ = d₄ = d)

4.1  Generalized multiple-prism arrays: (a) Additive configuration; (b) compensating configuration. Depiction of these generalized prismatic configurations was introduced by Duarte and Piper

4.2  Multiple-prism beam expander geometry in additive configuration and its mirror image. A dispersive analysis through the multiple-prism array and its mirror image is equivalent to a double-pass, or return- pass, analysis. This type of description for multiple-prism grating assemblies was first introduced by Duarte and Piper

4.3  Additional perspective on the multiple-prism grating assembly used to perform the dispersive multiple-return pass analysis as explained by Duarte and Piper. The multiple-prism configuration can be either additive or compensating and can be composed of any number of prisms

4.4  (a) MPL grating semiconductor laser oscillators incorporating a (+, +, +, −) compensating multiple-prism configuration (a) and a (+, −, +, −) compensating multiple-prism configuration (b)

4.5  HMPGI grating solid-state organic laser oscillator incorporating a compensating (+, −) double-prism configuration

4.6  Optimized multiple-prism grating tunable organic laser oscillator incorporating a compensating (+, −) double-prism configuration. This oscillator demonstrated single-transverse-mode beam characteristics and single-longitudinal-mode emission at Δν ≈ 350 MHz and Δt ≈ 3 ns

4.7  Single dispersive prism, made of fused silica, with a negative dispersion of ∇_λϕ_2,1 ≈ −0.0386 for the D₂ line of sodium at λ = 588.9963 nm. The calculations indicate a severe beam deviation

4.8  Double-prism Amici configuration comprising a fused silica prism and a higher diffractive index Schott SF10 prism. Here, ∇_λϕ_2,2 ≈ -0.0330 at λ = 588.9963 nm and the exit beam is in the same direction, albeit still displaced, as the incident beam. (Drawing not to scale.)

4.9  Three-prism Amici, direct-vision, configuration. The first and third prisms are made of fused silica (n₁ = n₃ = 1.458413), whereas the second prism, positioned at the center of the configuration, is made of Schott SF10 (n₂ = 1.728093). As explained in the text, this compound prism is formed by unfolding the double-prism configuration shown in Figure 4.8. Here, the overall dispersion is ∇_λϕ_2,3 ≈ +0.0720 at λ = 588.9963 nm, and the exit beam is collinear with the incident beam as discussed in the text. (Drawing not to scale.)

4.10  Double-prism pulse compressor

4.11  Four-prism pulse compressor obtained by symmetrically unfolding the double-prism configuration

5.1  Reflection boundary defining the plane of incidence. Sometimes, the plane of incidence is also referred to as the plane of propagation

5.2  Reflection intensity as a function of angle of incidence. The angle at which the reflection vanishes is known as the Brewster angle

5.3  Various forms of polarization and their vector representation in Jones calculus

5.4  Generalized multiple-prism array in additive configuration (a) and compensating configuration (b). Depiction of multiple-prism arrays in this form was introduced by Duarte and Piper

5.5  Double-prism expander as described in the text

5.6  Generic Glan–Thompson polarizer. The beam polarized parallel to the plane of incidence is transmitted while the complementary component is deviated (drawing not to scale)

5.7  Solid-state MPL grating dye laser oscillator, yielding single-longitudinal-mode emission, incorporating a Glan–Thompson polarizer output coupler. The reflective coating is applied to the outer surface of the polarizer

5.8  Generic Wollaston prism. The lines and circle represent the direction of the crystalline optical axis of the prism components (drawing not to scale)

5.9  Attenuation of polarized laser beams using a Glan–Thompson polarizer: (a) polarizer set for ~100% transmission; (b) clockwise rotation of the polarizer, about the axis of propagation by π/2, yielding ~0% transmission. The amount of transmitted light can be varied continuously by rotating the polarizer in the 0 ≤ θ ≤ π/2 range

5.10  Side view of double Fresnel rhomb. Linearly polarized light is rotated by π/2 and exits with polarized orthogonally to the original polarization

5.11  Basic prism operator for polarization rotation using two reflections. This can be composed of two 45° prisms adjoined π/2 to each other (note that it is also manufactured as one piece). (a) Side view of the rotator illustrating the basic rotation operation due to one reflection. The beam with the rotated polarization exists the prism into the plane of the figure. (b) The prism rotator is itself rotated anticlockwise by π/2 about the rotation axis (as indicated), thus providing an alternative perspective of the operation: the beam is now incident into the plane of the figure and it is reflected downward with its polarization rotated by π/2 relative to the original orientation

5.12  Broadband collinear prism polarization rotator

5.13  Transmission fidelity of the broadband collinear polarization rotator: (a) intensity profile of incident beam, prior to rotation, and (b) intensity profile of transmitted beam with rotated polarization

6.1  Geometry for propagation through distance l in free space. The displacement l is along the z-axis that is perpendicular to x

6.2  Thin convex lens

6.3  N optical elements in series

6.4  Geometry for propagation through distance l in region with refractive index n

6.5  Slab of material with refractive index n such as an optical plate

6.6  Concave lens

6.7  Galilean telescope

6.8  Astronomical telescope

6.9  Flat mirror

6.10  Curved mirror

6.11  Reflective telescope of the Cassegrainian class. These reflective configurations are widely applied to unstable resonators, which in the far field can yield a near-TEM₀₀ laser beam profile

6.12  Generalized flat reflection grating

6.13  Flat reflection grating in Littrow configuration

6.14  Single prism

6.15  Multiple-prism beam expander

6.16  Single prism preceded by a distance L₁ and followed by a distance L₂

6.17  Generalized multiple-prism array (a) Describes an additive configuration and (b) a compensating configuration

6.18  Series of telescopes separated by a distance L_m

6.19  MPL grating laser oscillator

6.20  Unfolded laser cavity for multiple-return-pass analysis. L₁ is the intracavity distance between the polarizer output coupler and the gain medium, L₂ is the intracavity distance between the gain medium and the multiple-prism expander, and L₃ is the intracavity distance between the multiple-prism expander and the diffraction grating

7.1  Mirror–mirror laser cavity. The physical dimensions of the intracavity aperture relative to the cavity length determine the number of transverse modes

7.2  Cross section of diffraction distribution corresponding to a large number of transverse modes. Here, w = 1.5 mm, L = 10 cm, λ = 632.82 nm, and the Fresnel number becomes N_F ≈ 35.56

7.3  Cross section of diffraction distribution corresponding to a near-TEM₀₀ corresponding to w = 250 μm, L = 40 cm, and λ = 632.82 nm, so that N_F ≈ 0.25

7.4  Mode beating resulting from DLM oscillation. (a) Measured temporal pulse. (b) Calculated temporal pulse assuming interference between the two longitudinal modes

7.5  Fabry–Pérot interferogram corresponding to SLM emission at Δν ≈ 350 MHz

7.6  Near-Gaussian temporal pulse corresponding to SLM emission. The temporal scale is 1 ns/div

7.7  Grating-mirror tunable laser cavity

7.8  Grating-mirror laser cavity incorporating intracavity etalons

7.9  Grazing-incidence grating cavities: (a) open cavity; (b) closed cavity

7.10  Grating efficiency curve as a function of angle of incidence at λ = 632.82 nm

7.11  Figure 7.11 Two-dimensional transmission telescope Littrow grating laser cavity. This class of telescopic cavity was first introduced by Hänsch.

7.12  Long pulse MPL grating solid-state organic dye laser oscillator incorporating a (+, +, +, −) compensating multiple-prism configuration. Laser linewidth is Δν ≈ 650 MHz at a pulse length of Δt ≈ 105 ns.

7.13  Optimized compact MPL grating solid-state organic dye laser oscillator. Laser linewidth is Δν ≈ 350 MHz at a pulse length of Δt ≈ 3 ns

7.14  Solid-state HMPGI grating organic dye laser oscillator. Laser linewidth is Δν ≈ 375 MHz at a pulse length of Δt ≈ 7 ns

7.15  (a) MPL and (b) HMPGI grating high-power pulsed CO₂ laser oscillators. The prisms are made of ZnSe and the output couplers are made of Ge

7.16  MPL (a) and HMPGI (b) grating semiconductor laser oscillators

7.17  (a) MPL transmission grating semiconductor laser oscillator designed to produce circular TEM₀₀ emission. The semiconductor is oriented to emit its elongated beam with the long axis perpendicular to the plane of propagation. Intracavity prismatic beam expansion (parallel to the plane of propagation) renders a nearly circular output beam. (b) MPL grating semiconductor laser oscillator configuration designed to produce circular TEM₀₀ emission. The same expansion strategy is used as in (a) while using a reflection grating in Littrow configuration and beam expansion at both ends of the cavity. The multiple-prism beam expansion illuminating the grating can be as large as necessary to yield very narrow linewidths

7.18  Generic DFB laser configuration

7.19  Multiple-prism tuning

7.20  Diffraction grating deployed in near-grazing-incidence configuration

7.21  Figure 7.21 Diffraction grating deployed in Littrow configuration. Here, the angle of incidence equals the angle of diffraction (Θ = Φ).

7.22  A synchronous wavelength tuning configuration

7.23  Solid etalon depicting incidence and refraction angles

7.24  Longitudinal tuning applicable to laser microcavities. The cavity length L is changed by a minute amount ΔL (see text)

7.25  Dispersive cavity linewidth at two slightly different frequencies. It is assumed that Δλ₁ ≈ Δλ₂, while the intracavity FSR changes.

7.26  Polarization preference as explained by Duarte (1990b): (a) An excitation beam polarized perpendicular to the plane of propagation yields emission also polarized perpendicular to the plane of propagation; (b) the same excitation emission polarized parallel to the plane of propagation yields emission, in the same molecular active medium, partially polarized in both directions (see text).

7.27  Multiple-stage single-pass laser amplification

7.28  Master oscillator Forced oscillator laser configuration

8.1  Optical configuration for frequency doubling generation

8.2  Optical configuration for sum-frequency generation

8.3  Optical configuration for difference-frequency generation

8.4  Basic OPO configuration

8.5  Dispersive OPO using a HMPGI grating configuration as described by Duarte

8.6  Simplified representation of self-focusing, due to n = n₀ + n₁I, in an optical medium due to propagation of a laser beam with a near-Gaussian intensity profile.

8.7  The concept of optical phase conjugation

8.8  Basic phase-conjugated laser cavity

8.9  Optical configuration for H₂ Raman shifter. The output window and the dispersing prism are made of CaF₂

8.10  Stokes and anti-Stokes emission in H₂ for λ_P nm = 500

8.11  Schematics for determining the frequency difference (2ν − ν) in the optical clockwork approach. This is a simplified version of the intensity versus frequency diagram considered by Diddams et al.

10.1  NSLI depicting the Galilean telescope, the focusing lens, the multiple-prism beam expander, the position of the N-slit array (j), or transmission surface of interest, and the interferometric plane (x). The intra-interferometric distance from j to x is D_{〈x | j〉} = . A depiction of approximate beam profiles, at various propagation stages, is included on top. This drawing is not to scale

10.2  Intensity profile of an extremely elongated, approximately 1:1000 (height:width), near-Gaussian laser beam

10.3  Measured interferogram (a) and calculated interferogram (b). Slits are 30 μm wide, separated by 30 μm, and N = 100. The intra-interferometric distance is D_{〈x | j〉} 75 cm and λ = 632.82 nm. This calculation assumes uniform illumination (see Chapter 2)

10.4  Computational time, in a universal computer, as a function of the number of slits. For these calculations, the slit width is 30 μm, the interslit width 30 μm, the j-to-x distance is D_{〈x | j〉} 75 cm, and λ = 632.28 nm

10.5  Very large NSLI configured without the focusing lens. In this class of interferometer, the intra-interferometric path is in the 7 ≤ D_{〈x | j〉} ≤ 527 m range, although larger configurations are possible. In these NSLIs, the TEM₀₀ beam from the He–Ne laser is transmitted via a spatial filter

10.6  Interferometric alphabet: (a) a (N = 2); (b) b (N = 3); (c) c (N = 4). (d) z (N = 26). For these calculations, the slits are 50 μm, separated by 50 μm, D_{〈x | j〉} = 50 cm, and λ = 632.82 nm

10.7  Interception sequence for the interferometric character a (N = 2) the slits are 50 μm, separated by 50 μm, D_{〈x | j〉} = 10 cm, and λ = 632.82 nm. (a) Original interferometric character. (b–d) Show the distortion sequence of the interferometric character due to the insertion of a thin beam splitter into the optical path. (e) Interferometric character a showing slight distortion and displacement due to the stationary beam splitter

10.8  The interferometric character c (N = 4). Here, the slits are 570 μm, separated by 570 μm, D_{〈x | j〉} = 7 235 m, and λ = 632.82 nm

10.9  The interferometric character c (N = 4), as described in Figure 10.8, destroyed by optical interception. See text for further details

10.10  The interferometric character c (N = 4), as described in Figure 10.8, distorted due to turbulence generated by a thermal source. See text for further details

10.11  The interferometric character c (N = 4) showing a slight unevenness due to incipient atmospheric turbulence. Here, the slits are 1000 μm, separated by 1000 μm, D_{〈x | j〉} = 35 m, and λ = 632.82 nm

10.12  The interferometric character b (N = 3) used as a control. Here, the slits are 570 μm, separated by 570 μm, D_{〈x | j〉} = 7.235 m, and λ = 632.82 nm

10.13  The interferometric character b (N = 3) intercepted by a spider web silk fiber positioned at D_{〈x | j〉} = 7.235 − 0.150 m. The slits are 570 μm, separated by 570 μm; the interferogram is recorded at D_{〈x | j〉} = 7.235 m and λ = 632.82 nm. (Reproduced from Duarte, F.J., et al., J. Mod. Opt., 60, 136–140, 2013. With permission from Taylor & Francis.)

10.14  Theoretical interferometric character b (N = 3) assuming interception by a spider web silk fiber positioned at D_{〈x | j〉} = 7.235 − 0.150 m (see text). The slits are 570 μm, separated by 570 μm; the interferometric plane is positioned at D_{〈x | j〉} = 7.235 m and λ = 632.82 nm

10.15  Transmission signal showing no interference from an optical homogeneous imaging surface (a) and interferogram from an imaging surface including relatively fine particles (b)

10.16  NSLI configured in the reflection mode

10.17  Near-field modulation signal in a weak interferometric domain arising from the interaction of laser illumination, at λ = 632.82 nm, and a grating composed of N = 23 slits 100 μm wide separated by 100 μm. The intra-interferometric distance is D_{〈x | j〉} = 15. cm. Measured modulation signal (a) and calculated signal (b). Each pixel is 25 μm wide

10.18  Measured double-slit interferogram generated using a broadband visible light source. The slits are 50 μm wide separated by 50 μm and the intra-interferometric distance is D_{〈x | j〉} = 10 cm

10.19  Three-color industrial PMPML printer used to expose a scale of images at various laser intensities for sensitometric measurements. The telescope expands the beam in two dimensions, whereas the multiple-prism beam expander magnifies in only one dimension parallel to the plane of propagation

10.20  Diffraction profile of the illumination line at λ = 532 nm

11.1  Sagnac interferometer. All three mirrors M₁, M₂, and M₃ are assumed to be identical

11.2  Triangular Sagnac interferometer

11.3  Mach–Zehnder interferometer

11.4  Prismatic Mach–Zehnder interferometer

11.5  Michelson interferometer

11.6  N-slit interferometer. CMOS, complementary metal–oxide– semiconductor; TEM₀₀, single transverse mode

11.7  The Hanbury Brown and Twiss interferometer. The light, from an astronomical source, is collected at mirrors M₁ and M₂ and focused onto detectors D₁ and D₂. The current generated at these detectors, i₁ and i₂, interfere at the electronics to produce an interference signal characterized by an equation of the form of Equation 11.18 with N = 2

11.8  Fabry–Pérot interferometer (a) and Fabry–Pérot etalon (b). Dark lines represent coated surfaces. Focusing optics is often used with these interferometers when used in linewidth measurements

11.9  Multiple-beam interferometer: (a) Multiple internal reflection diagram; (b) detailed view depicting the angles of incidence and refraction

11.10  Fabry–Pérot interferogram depicting single-longitudinal-mode oscillation, at Δν ≈ 700 MHz, from a tunable multiple-prism grating solid-state oscillator

11.11  Measured double-slit (N = 2) interferogram generated with a broadband light source. The slits are 50 μm wide separated by 50 μm and D_{〈x | j〉} = 10 cm. Comparison with other two-slit interferograms generated with coherent sources (see Figures 11.12 and 11.13) reveals lack of spatial definition and low visibility as defined by Equation 11.50

11.12  Double-slit interferogram from an electrically excited organic semiconductor interferometric emitter at λ ≈ 540 nm. The visibility of this interferogram is less than V ≈ 0.90. Here, N = 2, the slits are 50 μm wide separated by 50 μm, and D_{〈x | j〉} = 5cm

11.13  Double-slit interferogram from an electrically excited organic semiconductor interferometric emitter at λ ≈ 540 nm. The visibility of this interferogram is less than V ≈ 0.90. Here, N = 2, the slits are 50 μm wide separated by 50 μm, and D_{〈x | j〉} = 5cm

11.14  Interferograms at λ₁ = 580 nm (a), λ₂ = 585 nm (b), λ₃ = 590 nm (c), and nm (d). These calculations are for slits 100 μm wide, separated by 100 μm, and N = 50. The j-to-x distance is D_{〈x | j〉} = 100 cm.

11.15  Multiple-etalon wavelength meter

11.16  (a) Fizeau wavelength meter. (b) Geometrical details of a Fizeau interferometer

12.1  Simple optical configuration for absorption measurements using a spectrometer

12.2  Simplified optical configuration for fluorescence and emission measurements, in an optically pumped laser system, using spectrophotometers. A narrow-linewidth tunable laser excites longitudinally a molecular medium, such as I₂, and the emission is detected by spectrometer 1 via a filter F used to stop residual emission from the pump tunable laser. In addition, the emission can also be detected via the reflection of the Brewster window of the optical cell in spectrometer 2. The fluorescence and emission are detected orthogonally to the optical axis in spectrometer 3 as described by Duarte

12.3  Fluorescence spectrum of the I₂ molecule generated using pulsed narrow-linewidth tunable laser excitation in the vicinity of λ = 589.586 nm. The tuning range is 30 GHz or ~1 cm⁻1 as described by Duarte

12.4  Long-optical path double-prism spectrometer

12.5  Dispersive assembly of multiple-prism spectrometer. The angle of incidence I_1,m and the angle of emergence I_2,m are identical for all prisms. In addition to the cumulative dispersion, resolution is determined by the path length toward the exit slit and the dimensions of the slit

12.6  (a) Basic grating spectrometer. The resolution is mainly determined by the dispersion of the grating, deployed in a non-Littrow configuration, and by the optical path length toward the exit slit (S₂). (b) A variation on the basic grating spectrometer consists in deploying a high-dispersion diffraction grating in conjunction with a high spatial resolution digital detector (CCD or CMOS) to register the diffracted light

12.7  Czerny–Turner spectrometer. Mirrors M₁ and M₂ provide the necessary curvature to focus the diffracted beam at the exit slit

12.8  Double-grating Czerny–Turner spectrometer. Mirrors M₁ and M₂ provide the necessary curvature to focus the diffracted beam at the exit slit

12.9  Architecture of the prism grating wavelength meter. A reference wavelength (λ_R) beam and the measurement wavelength (λ_M) beam are combined at the entrance beam splitter (BS). The reference beam is used to provide the initial reference wavelength (λ_R) and for alignment purposes (λ_M > λ_R). A second BS sends light from (λ_M) beam to a Fabry–Pérot (F–P). The (λ_M) and (λ_R) beams are separated at the prism. The (λ_M) beam undergoes deflection at the prism grating assembly, whereas the (λ_R) beam returns back on its original path. The measurement beam (λ_M) undergoes augmented angular deflection at the prism grating system and its position is registered by a photodiode array or CCD. Resolution is a function of the overall prism grating dispersion, the distance between the prism and the photodiode array detector, and the spatial resolution (pixel dimensions) of the digital detector