Angular spectrum calculations for arbitrary focal length with a scaled convolution

Odate, Satoru; Koike, Chiaki; Toba, Hidemitsu; Sugaya, Ayako; Sugisaki, Katsumi; Uchikawa, Kiyoshi

doi:10.1364/oe.19.014268

Cited by 31 publications

(28 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Li et al [14] developed an AS with a band-limiting filter that adapts the resolution. Odate et al [15] proposed a scaled convolution AS, which is restricted to the cases of focused field calculations by the lens. Shimobaba and co-workers [16,17] developed scaled AS employing a nonuniform Fourier Transform, and Yu et al [18] proposed an approach based on the chirped z-transform.…”

mentioning

confidence: 99%

Angular spectrum-based wave-propagation method with compact space bandwidth for large propagation distances

Kozacki

Falaggis

2015

Opt. Lett.

View full text Add to dashboard Cite

Rigorous propagation methods enable diffraction calculations at high NA. However, for the case of large propagation distances and full NA calculations of a signal, common solutions require zero padding or upsampling. This Letter overcomes these problems by introducing a sampling scheme based on compact space bandwidth product representation, which adjusts the sampling frequency of input and propagated field according to the evolution of the generalized space bandwidth product. This sampling concept allows proposing a novel AS method enabling high efficiency, high accuracy, and high-NA diffraction computations at larger propagation distances without need of zero padding or upsampling. The method has several advantages: (1) high accuracy for larger propagation distances; (2) reduced sampling with minimal computation effort; (3) zooming capability; and (4) both focusing and defocusing propagations possible.

show abstract

mentioning

confidence: 99%

Angular spectrum-based wave-propagation method with compact space bandwidth for large propagation distances

Kozacki

Falaggis

2015

Opt. Lett.

View full text Add to dashboard Cite

show abstract

“…Which is twice as much as reported in [14] but is needed to satisfy Nyquist criterion. Where z is the overall optical path length.…”

Section: System Model Layoutmentioning

confidence: 86%

Optimal VIA Placement in Under Filled Embedded Multimode Waveguides

Riegel¹,

Howard²,

Middlebrook³

2013

OPJ

View full text Add to dashboard Cite

The self-imaging property of multimode waveguides creates a challenging problem when finding the optimal placement position of an out-of-plane coupler for embedded waveguides. This problem is compounded when the waveguides are coupled using a small input such as a vertical cavity surface emitting laser (VCSEL) or a single mode fiber where only some of the modes are generated. When the waveguide system is under filled, the coupling efficiency for the optical vertical interconnect assembly (VIA) can vary by as much as 6.2 dB depending on the length of the proceeding waveguide due to different output fields from the self-imaging property. This requires sweeping each individual VIA over the entire range of possible coupler positions to find the total maximum coupling efficiency. This process increases in complexity when a VIA supports several parallel channels all having a different optical path length. If a VIA can be placed in a calculated position from the end of a terminated embedded waveguide dependent upon the modal structure then blind pick and place methods may be used. The optimal coupler placement was determined based on smallest average VIA attenuation, smallest attenuation variance, and worse-case alignment scenario.

show abstract

“…Various authors have derived sampling criteria for the ASM and the RSC, highlighting suitable combinations of sampling intervals, field sizes, and propagation distances [14][15][16][17][18][19][20][21][22][23][24]. The Nyquist-Shannon sampling theorem is commonly used as a starting point for sampling considerations (e.g., [14][15][16]). If it is only applied to the chirp functions of the ASM and the RSC without taking the phase distribution of the input field into account, then the allowed propagation distances of the ASM and the RSC are restricted to specific regions that are independent of the input field.…”

Section: Introductionmentioning

confidence: 99%

“…If it is only applied to the chirp functions of the ASM and the RSC without taking the phase distribution of the input field into account, then the allowed propagation distances of the ASM and the RSC are restricted to specific regions that are independent of the input field. To extend the range of propagation distances allowed by the Nyquist-Shannon sampling theorem, modified versions of the ASM and the RSC were introduced [16][17][18]. Alternative sampling criteria are based on the Wigner distribution and the space-bandwidth product [19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of nonparaxial scalar diffraction integrals for focused fields

2014

View full text Add to dashboard Cite

In this paper, we present sampling conditions for fast-Fourier-transform-based field propagations. The input field and the propagation kernel are analyzed in a combined manner to derive sampling criteria that guarantee accurate calculation results in the output plane. These sampling criteria are also applicable to the propagation of general fields. For focal field calculations, geometrical optics is used to obtain a priori knowledge about the input and output fields. This a priori knowledge is used to determine an optimum balance between computational load and calculation accuracy. In a numerical example, correct results are obtained even though both the input field and the propagation kernel are sampled below the Nyquist rate. Finally, we show how chirp z-transform-based zoom-algorithms may be analyzed using the same techniques.

show abstract

Angular spectrum calculations for arbitrary focal length with a scaled convolution

Cited by 31 publications

References 6 publications

Angular spectrum-based wave-propagation method with compact space bandwidth for large propagation distances

Angular spectrum-based wave-propagation method with compact space bandwidth for large propagation distances

Optimal VIA Placement in Under Filled Embedded Multimode Waveguides

Numerical solution of nonparaxial scalar diffraction integrals for focused fields

Contact Info

Product

Resources

About